UNIVERSITY of CALIFORNIA Noise of AlGaN/GaN HEMTs and...

UNIVERSITY of CALIFORNIASanta Barbara

Noise of AlGaN/GaN HEMTs and Oscillators

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

in

Electrical and Computer Engineering

by

Christopher Sanabria

Committee in charge:

Professor Robert A. York, ChairProfessor Umesh K. MishraProfessor Mark J. RodwellDr. Yifeng Wu

June 2006

The dissertation of Christopher Sanabria is approved:

Chair

June 2006


Copyright c© 2006

by


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Curriculum Vitæ


EDUCATION

Bachelor of Science in Electrical Engineering, Magna Cum Laude, University ofNotre Dame, May 2001.

Master of Science in Electrical and Computer Engineering, University of California,Santa Barbara, December 2002.

Doctor of Philosophy in Electrical Engineering, University of California, Santa Bar-bara, June 2006.

PROFESSIONAL EMPLOYMENT

May 1998 - August 1998, Intern, Delphi-Delco Electronics, Kokomo, IN.

May 1999 - August 1999, Intern, Delphi-Delco Electronics, Kokomo, IN.

May 2000 - August 2000, Intern, Texas Instruments, Houston, TX.

September 2001 - March 2002, Teaching Assistant, Department of Electrical andComputer Engineering, University of California, Santa Barbara.

June 2003 - September 2003, Intern, Agilent Labs, Agilent Technologies, Palo Alto,CA.

March 2002 - May 2006, Research assistant, Department of Electrical and ComputerEngineering, University of California, Santa Barbara.

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PUBLICATIONS

S. Gao,C. Sanabria, H. Xu, S. Heikman, U. K. Mishra and R. A. York,MMIC Class-F Power Amplifiers using Field-Plated GaN HEMTs, accepted IEEE Proceedings onMicrowave, Antennas and Propagation, 2006.

C. Sanabria, A. Chakraborty, H. Xu, M. J. Rodwell, U. K. Mishra, and R. A. York,The Effect of Gate Leakage on the Noise Figure of AlGaN/GaN HEMTs, IEEE Elec-tron Device Letters, January 2006, pp. 19-21.

C. Sanabria, H. Xu, A. Chakraborty, M. J. Rodwell, U. K. Mishra, and R. A. York,Noise Figure Measurements and Modeling of Field-Plated AlGaN/GaN HEMTs, In-ternational Conference on Nitride Semiconductors, Bremen, Germany, August 2005.

C. Sanabria, H. Xu, S. Heikman, U. K. Mishra, R. A. York,A GaN Differential Os-cillator with Improved Harmonic Performance, IEEE Microwave and Wireless Com-ponents Letters, July 2005, pp. 463-465.

H. Xu, C. Sanabria, S. Heikman, S. Keller, U. K. Mishra, and R. A. York,HighPower GaN Oscillators using Field-Plated HEMT Structure, IEEE Microwave The-ory and Technique International Microwave Symposium, June 2005.

C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.York, Influence of Epitaxial Structure in the Noise Figure of AlGaN/GaN HEMTs,IEEE Microwave Theory and Technique Transactions, Vol. 53, February 2005, pp.762-769.

H. Xu, C. Sanabria, Y. Wei, S. Heikman, S. Keller, U. K. Mishra, and R. A. York,Characterization of two field-plated GaN HEMT structures, IEEE Topical Workshopon Power Amplifiers for Wireless Communications, September 2004.

H. Xu, C. Sanabria, A. Chini, Y. Wei, S. Heikman, S. Keller, U. K. Mishra and R. A.York, A new field-plated GaN HEMT structure with improved power and noise per-formance, IEEE Lester Eastman Conference on High Performance Devices, August2004.

H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York,A C-bandhigh-dynamic range GaN HEMT low-noise amplifier, IEEE Microwave and WirelessComponents Letters, Vol. 14, June 2004, pp. 262 264.

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C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.York, Influence of the Heterostructure Design on Noise Figure of AlGaN/GaN HEMTs,Device Research Conference, June 2004.

H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York,Robust C-band MMIC Low Noise Amplifier using AlGaN/GaN HEMT Power Devices, 8th Wide-Bandgap III-Nitride Workshop, September 2003.

vi

Abstract


by


GaN HEMTs will likely become the solid-state device of choice for power in mi-

crowave and millimeter-wave circuits. These products, such as base stations and other

communication systems, tend to be space-constrained. Hence solutions continuously

move from a hybrid (circuit board plus components) approach to a microwave mono-

lithic integrated circuit (MMIC). To be successful in a MMIC design, GaN will have

to perform well in other areas besides power. One of the most crucial metrics of a

system is its noise. The noise of GaN devices and circuits has only been critically

examined in the last five years.

This work will investigate several aspects of the noise performance of GaN HEMTs.

Measurements of noise figure (NF) and low-frequency noise (LFN) are used to char-

acterize devices. Modeling useful for calculations and circuit simulation are applied,

with some introduced. Several studies of NF and LFN are presented. Some confirm

or challenge previous publications while others are new observations. Two differen-

tial oscillators were built to characterize the phase noise. As it is believed that GaN

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HEMTs will replace GaAs HEMTs in various applications, the NF, LFN, and phase

noise of the two are compared.

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Contents

List of Figures xii

List of Tables xvi

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review of Noise in GaN HEMTs . . . . . . . . . . . . . . 51.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Noise Figure Modeling of AlGaN/GaN HEMTs 122.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.2 Shot Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Other Sources of Noise . . . . . . . . . . . . . . . . . . . . . 16

2.3 Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Noise Figure and Noise Parameters . . . . . . . . . . . . . . . . . . . 212.5 HEMT Noise Figure Models . . . . . . . . . . . . . . . . . . . . . . 25

2.5.1 van der Ziel and Pucel Models . . . . . . . . . . . . . . . . . 252.5.2 Fukui Model . . . . . . . . . . . . . . . . . . . . . . . . . . 282.5.3 Pospieszalski Model . . . . . . . . . . . . . . . . . . . . . . 292.5.4 Pospieszalski and Correlated Noise Models Applied to Al-

GaN/GaN HEMTs . . . . . . . . . . . . . . . . . . . . . . . 312.6 A Proposed Noise Figure Model . . . . . . . . . . . . . . . . . . . . 35

2.6.1 Setup Details . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6.2 Derivation of Noise Parameters . . . . . . . . . . . . . . . . 392.6.3 Derivation of Drain Noise Source . . . . . . . . . . . . . . . 442.6.4 Noise Parameter Scaling . . . . . . . . . . . . . . . . . . . . 492.6.5 Discussion of the Model . . . . . . . . . . . . . . . . . . . . 53

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3 Noise Figure Measurements and Studies 603.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2 Device Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.3 Noise Figure Measurement Setup and Method . . . . . . . . . . . . . 623.4 Bias Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5 GaN HEMT Noise Figure Studies . . . . . . . . . . . . . . . . . . . 75

3.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.5.2 Al Composition in the Barrier . . . . . . . . . . . . . . . . . 763.5.3 AlN Interlayer . . . . . . . . . . . . . . . . . . . . . . . . . 783.5.4 Gate Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . 813.5.5 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 843.5.6 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 91

3.6 Comparison of High-Performance GaN HEMTs to Other Material Sys-tems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4 Low-Frequency Noise of GaN HEMTs 1014.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.2 Review of Low-Frequency Noise . . . . . . . . . . . . . . . . . . . . 1024.3 Low-Frequency Noise Setup . . . . . . . . . . . . . . . . . . . . . . 1074.4 GaN HEMT Low-Frequency Noise Modeling . . . . . . . . . . . . . 1134.5 GaN HEMT Low-Frequency Noise Studies . . . . . . . . . . . . . . 119

4.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.5.2 Passivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.5.3 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 1214.5.4 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 122

4.6 Comparison to GaAs HEMTs . . . . . . . . . . . . . . . . . . . . . . 1234.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5 GaN HEMT Based Oscillators 1285.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.2 Concerning Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . 1295.3 MMIC Process Description . . . . . . . . . . . . . . . . . . . . . . . 1345.4 Differential Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.4.1 High Linearity Oscillator . . . . . . . . . . . . . . . . . . . . 1355.4.2 Low-Phase Noise Oscillator . . . . . . . . . . . . . . . . . . 140

5.5 Comparison to Other Oscillators . . . . . . . . . . . . . . . . . . . . 143

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5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

6 Summary, Conclusions, and Future Directions 1496.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1496.2 Future Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

A ADS Files 154A.1 Small-Signal Extraction . . . . . . . . . . . . . . . . . . . . . . . . . 155A.2 Noise Figure Simulation . . . . . . . . . . . . . . . . . . . . . . . . 158A.3 Correlated Noise Model Extraction . . . . . . . . . . . . . . . . . . . 160

B Matlab Code for Noise Parameter Modeling 163

C Matlab Code for Pospieszalski Noise Parameter Modeling 166

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List of Figures

1.1 Cartoon of a very simple transmitter. . . . . . . . . . . . . . . . . . . 21.2 Cartoon of a CDMA-like spectrum with four channels. . . . . . . . . 3

2.1 Cartoon showing the device small-signal model on a cross section ofa HEMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Equivalent model of a transistor driven by a noisy source of impedanceZsource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Noise and gain circles on a Smith Chart. . . . . . . . . . . . . . . . . 242.4 Pucel noise model in a small-signal circuit. . . . . . . . . . . . . . . 272.5 Pospieszalski noise model in a small-signal circuit. . . . . . . . . . . 292.6 Comparison of Correlated Noise and Pospieszalski models to mea-

sured noise parameters versus frequency. . . . . . . . . . . . . . . . . 342.7 A simplified HEMT circuit model including noise sources. . . . . . . 362.8 Cartoon showing the effect of source degeneration. . . . . . . . . . . 382.9 Circuit model used for deriving noise figure. . . . . . . . . . . . . . . 392.10 Cartoon used for deriving the channel noise. . . . . . . . . . . . . . . 472.11 Variation inΓ for different drain and gate voltages. . . . . . . . . . . 492.12 Noise parameters versus total gate width. . . . . . . . . . . . . . . . 512.13 Noise parameters versus number of gate fingers for a constant total

gate width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.14 Noise parameters predicted with the proposed model and compared to

measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.15 Relative contributions of different noise sources to the overall noise

figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Typical epitaxial structures for the devices in this work. . . . . . . . . 613.2 Schematic of the source-pull noise figure setup. . . . . . . . . . . . . 633.3 Coplanar waveguide attenuator. . . . . . . . . . . . . . . . . . . . . . 653.4 Noisefactor, fτ andfmax for devices from different samples versus

current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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3.5 Variation in expected minimum noise figure with changes in threesmall-signal parameters. . . . . . . . . . . . . . . . . . . . . . . . . 68

3.6 Change in noise parameters with drain-source voltage. . . . . . . . . 693.7 Typical plots of the noise parameters versus drain source current with

Correlated Noise and Pospieszalski models. . . . . . . . . . . . . . . 713.8 Noise variables for the Pospieszalski and a CN noise model versus

drain-source current. . . . . . . . . . . . . . . . . . . . . . . . . . . 733.9 Minimum noise figure, small signal associated and maximum gain for

devices on sapphire and SiC substrates. . . . . . . . . . . . . . . . . 753.10 Noise parameters versus frequency for devices of different aluminum

composition in the barrier. . . . . . . . . . . . . . . . . . . . . . . . 773.11 Minimum noise figure of samples with different aluminum composi-

tion in the barrier at varying drain-source current. . . . . . . . . . . . 783.12 Minimum noise figure, fτ , andfmax versus drain-source current for a

sample with and without an AlN interlayer. . . . . . . . . . . . . . . 793.13 (a) Associated and maximum gain and (b) source resistance for de-

vices with and without an AlN interlayer at different applied currents. 803.14 (a) Minimum noise figure, (b) device associated gain, and maximum

gain versus frequency for devices with different gate leakage currents 823.15 Simulated (line) and measured (crosses) noise parameters for devices

with different gate leakage currents. . . . . . . . . . . . . . . . . . . 833.16 fτ and fmax of devices with different field-plate lengths. . . . . . . . . 843.17 Noise parameters versus frequency for devices with field plates of dif-

ferent length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.18 Typical change in gate leakage for devices of increasing field-plate

length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.19 Electric field profile for a device with and without a field plate. . . . . 873.20 Small-signal parameters that change with a field plate. . . . . . . . . 893.21 Minimum noise figure versus gate width for devices with and without

a long field plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.22 Minimum noise figure of the field-plated devices at different measure-

ment frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.23 Noise parameters versus drain-source current of a thick cap device

(triangles) and a standard HEMT (squares). . . . . . . . . . . . . . . 923.24 Minimum noise figure of two 0.15µm gate length transistors provided

by Tomas Palacios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.1 Sketch of the key features of low-frequency noise. . . . . . . . . . . . 1034.2 Variation ofα with (a) drain-source voltage bias and (b) frequency of

extraction for two devices on the same sample. . . . . . . . . . . . . 106

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4.3 Measured noise floor of the HP 3561A DSA only and with the SRSSR560 LNA (short-circuited input). . . . . . . . . . . . . . . . . . . 109

4.4 Schematic of the setup used for device drain-side low-frequency noisemeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.5 A typical low-frequency plot. . . . . . . . . . . . . . . . . . . . . . . 1124.6 Plots of the measured drain low-frequency noise with (a) change in

drain-source current and (b) voltage. . . . . . . . . . . . . . . . . . . 1144.7 Measured gate low-frequency noise versus gate-source voltage (and

current). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.8 Change in low-frequency noise with gate width at various decade fre-

quencies for three devices. . . . . . . . . . . . . . . . . . . . . . . . 1164.9 Change in low-frequency noise with gate length. . . . . . . . . . . . . 1164.10 Proposed low-frequency noise modeling of the HEMT with a gate and

drain noise source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.11 Measurement of devices on a sapphire and SiC substrate at a bias of

Vds 5 V, Ids 30 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204.12 (a) Low-frequency noise of a device before and after passivation. (b)

Low-frequency noise at 10 Hz and 1 kHz of a device before and afterpassivation at differentVgs . . . . . . . . . . . . . . . . . . . . . . . . 120

4.13 Comparison of standard passivated HEMTs to an unpassivated thickcap HEMTs. Bias isVds = 5 V andIds = 30 mA. . . . . . . . . . . . . 122

4.14 Low-frequency noise of field-plated devices. . . . . . . . . . . . . . . 1234.15 Low-frequency noise comparison of GaN and GaAs HEMTs. . . . . . 124

5.1 Examples of typical phase noise plots. . . . . . . . . . . . . . . . . . 1315.2 Circuit schematic of the oscillator (biasing not shown). . . . . . . . . 1365.3 Photograph of the high linearity oscillator. . . . . . . . . . . . . . . . 1365.4 Measurements of the oscillator: (a) power spectrum (b) frequency

pulling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.5 Output power, second harmonic power, and efficiency of the high-

linearity oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.6 Circuit schematic of the low-phase noise oscillator (biasing not shown). 1405.7 Photograph of the low-phase noise oscillator. . . . . . . . . . . . . . 1415.8 Measured phase noise of the oscillator. . . . . . . . . . . . . . . . . . 1425.9 Phase noise at 100 kHz and 1 MHz offsets versus drain-source bias

for a few oscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1425.10 Relative comparison of GaN oscillator to a typical oscillator with low

phase noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

A.1 First page oftemplatesmall signal parameterextraction.dds. . . . . 156

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A.2 Schematic used for simulating S-parameters of the small-signal circuitand for optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 158

A.3 Schematic used for simulating noise parameters. . . . . . . . . . . . . 159A.4 Schematic used for extracting correlated noise model noise variables. 162A.5 Data display used for extracting correlated noise model noise variables. 162

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List of Tables

2.1 Extracted small-signal parameters for various samples. Devices havea gate geometry of 0.7× 150µm. . . . . . . . . . . . . . . . . . . . 21

2.2 Comparison of Pospieszalski and Correlated Noise models to mea-sured data. Devices have a gate geometry of 0.7× 150 µm . . . . . . 33

2.3 Comparison of the various noise models’ input and output noise currents. 56

3.1 Minimum noise figure for devices in many technologies. . . . . . . . 94

5.1 Comparison of GaN oscillators from this and other works to oscilla-tors in other materials (FET, MMICs, only). . . . . . . . . . . . . . . 144

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Acknowledgements

BEHIND the candy Santa Barbara exterior of sun, perfect weather, surfing, andtourists is a university that is a powerhouse of research that I didn’t have the

foggiest idea existed until I decided to come to graduate school. I’ve been impressedwith the faculty, facilities, labs, peers, and the graduate sciences and engineering pro-grams at UCSB. It has made for a great research experience and I want to thank andacknowledge all those who have helped me along the way toward getting my Ph.D.

I would first like to thank my advisor Professor Robert York. Not only did hetake me in, he has provided (along with my co-advisor) five years of constant, un-interrupted, financial support. Watching peers struggle with funding shortfalls andchanging projects has made me realize what a blessing funding is. I would also liketo thank him for giving me a great deal of freedom. This was frightening for me atfirst as I thought I would become lost, but later I realized what research I wanted to doand was able to do it without restraint. Professor York has always steered me in theright direction on important matters of publications, research, and things in general.We had many good, frank, talks that I enjoyed.

I thank my co-advisor Professor Umesh Mishra for many things. The first is theamusement of watching someone juggle the work of five men like some god with 10arms. Yet, when I needed to discuss work, we always got a few minutes in and I neverfelt pushed away. I also salute the GaN program he has put together at UCSB. Umeshis one of the smartest, and slyest, individuals I have met and it was fun to be aroundfor the show. I also really appreciate the happy hours he would host.

My other committee members, Professor Mark Rodwell and Dr. Yifeng Wu, havebeen a great help to me not only in preparing the thesis but in important researchdiscussions over the years. Professor Rodwell’s class notes on noise and exchangeshave steered me through to the basic truths about noise figure. With Dr. Wu I’ve hadmany conversations: load-pull, noise, circuits, and even high-end audio equipment. Ihave enjoyed it all. I also thank Professor Long for the conversations that we havehad.

My peers in the trenches have been of tremendous help toward this work. HongtaoXu taught me his fabrication techniques for MMICs and offered very useful sugges-tions for my microwave circuits. We worked collectively on several projects and be-came friends. Tom´as Palacios, the wonder Spaniard, has been of tremendous help. Hisenormous curiosity, knowledge, and keen eye helped me out several times by pointingme in the right direction or giving me inspiration that lead to useful research. Mygroup mates (past and present), Nadia, Val, Raj, Jaehoon, Jiwei, Justin, Paolo (e-lo?),Vicki, Conradin, Jim, and Pengcheng have helped me out many a time (or helped pro-vide a refreshing work break). The small army known as Professor Mishra’s grouphave also helped a great deal: Rob, Siddarth, Likun (Mona), Mike, Dario, Arpan, Ale,Naiqian, Sten, Lee M., Ilan, Yuvaraj, Felix, Pei Yi, Eric, Chang, Chris, Jeff, Karl, and

xvii

Man Hoi. I would especially like to thank those who grew my material for devices andcircuits, Arpan, Sten, Stacia, and Nick, without whom I would have had no project.

I also had useful discussions with students in the groups of both Professors Rodwelland Long. I had many conversations, interactions, and chats with Vikas and Joe,whose projects focused heavily on phase noise. Vikas also provided the GaAs devicesthat were measured in this work and both of them helped with equipment and setups.Navin, Zack, and Paidi all gave me some useful information at one point or another.Also, I had discussions with Adam about low-frequency noise and Professor ElliotBrown let me borrow some equipment from his personal collection for a measurement.

I thank Agilent and Maury for their technical support on various pieces of equip-ment (I calleda lot). I am greatful to the cleanroom staff (Jack, Bob, Neil, Tom,Brian T., Bill, Don, Mike, Luis and Ning) who kept our excellent facilities going 24x7and for being available for the occasional evening crisis. The assistants over the year(Masika, Pam, Emeka, Lee B., and Laura) have been a big help with red tape. I thankVal de Veyra and the other assistants in the ECE graduate student office, with whom Ihad a good laugh because of a non-unique nickname in my email address book.

I very much thank Dr. Harry Dietrich and the Office of Naval Research (ONR) whofunded and oversaw the Center for Advance Nitride Electronics (CANE) program thatI was on.

I would also like to thank Dr. Joy Vann-Hamilton. Joy, who was director of theMinority Engineering Program (MEP) while I was an undergraduate at the Universityof Notre Dame, listened to all my unhappy college complaints, pointed me towardresources that got me through undergraduate, and is solely responsible for my goingto graduate school. Grad school wasn’t even on my radar and I didn’t think I had thetalent. I can’t thank her enough.

As if I hadn’t thanked enough people and entities, I would also like to thank all myfriends who made my time here enjoyable (even if it was jokes at my expense, Perkand Dave). Also, I don’t know what my parents did that I turned out the way I did,but I want to give them applause for all that they have done. Don’t worry, I won’t doanything to embarrass you like I did at high school graduation.

Finally, no stay in Santa Barbara is complete without picking up a wife. Sarah, whowould have guessed we would meet here instead of at Notre Dame? I thank you forhandling all my rants with grace, giving me hope when I had none, distracting me so Iwould realize there are a whole lot of interesting things to do in the world, and beingsome one worth living for.

“Thanks y’all”...

xviii

For those who never quit.

xix

1Introduction

1.1 Motivation

GALLIUM nitride (GaN) and its related compound materials, indium nitride

(InN) and aluminum nitride (AlN), have already been commercialized for

several applications. This is an impressive feat for an immature technology where each

year research continues to bring improvements. The reason for this rush to market is

the needs the nitrides are addressing. For optical applications, GaN-based solutions

include LEDs, lasers, and detectors in the UV and blue wavelengths. For electronic

applications, GaN high electron mobility transistors (HEMTs) provide some of the

highest microwave power performance to be found from solid state devices.

GaN-based electronics have two major setbacks. The first is the cost. This re-

sults largely from the expensive substrates needed, with the better substrates currently

costing nearly an order of magnitude more than lower-performance options. The other

hurdle is growth immaturity, which causes reliability to be mediocre. Because of these

disadvantages, if another material system (Si, GaAs, InP, etc.) can meet the needs of an

1

CHAPTER 1. INTRODUCTION

application, industry will choose it over GaN. This means GaN HEMTs are being con-

sidered mainly for power amplifiers in microwave products such as base stations [1,2].

Industry has a great need for these products to be compact. Designers continuously

move from hybrid (a circuit board with discrete components) to integrated (a single,

small chip) solutions. Instead of a chip with just a power amplifier, it is preferred to

have the amplifier, and complete transmit and receive paths, in a single chip called a

front-end module (FEM). Figure 1.1 shows an example of a simple transmitter, and the

preferred integration boundary of power amplifier plus other components. It may be

possible that GaN monolithic microwave integrated circuits (MMICs) provide better

performance in terms of power, radiation hardness, and operation temperature, leading

to future products.

ModulatorFrom

DSP

Oscillator

Mixer Filter Power

Amp.

Antenna

Ideally implemented as a single transmitter MMIC

Figure 1.1: Cartoon of a very simple transmitter.

2


Frequency

Power

Channel

Width

Channel

SpaceNoise

Side

Band

Noise

Floor

Figure 1.2: Cartoon of a CDMA-like spectrum with four channels.

Basic GaN MMIC building blocks are now appearing in the literature [3–7], and

it is only a matter of time before GaN transmit and receive MMICs are made. An

important metric of such circuits will be their noise performance. In particular, phase

noise and noise figure (NF) are common figures of merit for characterizing noise. A

main focus of this work is examining these aspects of GaN HEMTs and oscillators.

Communication channel spacing is set based on specifications of the maximum

noise a channel will produce out-of-band. This is shown in figure 1.2. Setting the

space between channels as small as possible isextremelyimportant due to regulated

bandwidth restrictions.1 Typically the component that sets the minimum on this noise

1In fact, whenever the Federal Communications Commission (FCC) auctions bandwidth the sellingprice is in the hundreds of millions [8].

3


performance is an oscillator in the circuit, as in figure 1.1. An oscillator provides

a signal source at a (usually variable) reference frequency. In addition, oscillators

produce a large amount of noise at frequencies close to the reference frequency. This

is called phase noise.

It is understood that various device noise sources contribute to the phase noise.

These include thermal, shot, and low-frequency (also called flicker, or 1/f) sources.

The quantitative analysis of how these sources contribute to the phase noise is difficult

even for the simplest of cases. A qualitative description that embodies many important

points was presented by Leeson [9], and is described as

L (∆ω) = 10 log

2FkT

Psig

1 +

(ω0

2Q∆ω

)2

(1 +

∆ω1/f3

|∆ω|

) (1.1.1)

where the script L is the phase noise in a 1 Hz bandwidth at an offset angular fre-

quency,∆w, from the carrier angular frequency,ω0, Q is the quality of the resonator,

Psig the signal power, and F the effective noise figure.2 Shot and thermal noise sources

contribute to F, a measure of the background noise of the device and circuit. The low-

frequency noise (LFN) contributes through∆ω1/f3, a corner frequency for the phase

noise that presumably relates to the corner frequency of the LFN. From equation 1.1.1,

we can discern that knowledge of the noise sources in the device and circuit will help

in understanding the phase noise, and if we can reduce them the phase noise will be

2The parameter F here is not the device noise figure or factor but an “Effective noise figure” whichsome see as just a fitting parameter. F in this chapter should not be confused with noise factor in theother chapters.

4


improved. Leeson’s equation also tells us that ifPsig can be increased, we should

see an improvement in phase noise. Because GaN devices are capable of providing

an order of magnitude more power than gallium arsenide (GaAs) devices, the next

best commercial material, it is of great interest to know if the phase noise of GaN

circuits can be better than GaAs circuits. One of the goals of this work is to answer

this question.

This dissertation will look at several aspects of the noise performance of GaN

HEMTs. NF and LFN measurements are used to evaluate the noise performance of

the GaN HEMTs. Comparisons are made to measurements of GaAs HEMTs, the most

similar commercial device, which GaN is trying to displace. Models for NF and LFN

noise, some old and some new, are presented. To study the phase noise, differen-

tial oscillators were constructed and measured. Their performance is explained in the

context of LFN.

A quick review of previous noise measurements and studies of GaN HEMTs and

oscillators is now presented, followed by a sketch of this work.

1.2 Literature Review of Noise in GaN HEMTs

This section gives a short background of the GaN HEMT literature for NF, LFN,

and phase noise prior to this work (late 2002). Most publications after this point in

time are already referenced throughout the work. More background information on

5


each noise subject can also be found at the beginning of its respective chapter.

Of the three types of noise measurements performed on GaN HEMTs, LFN has

the longest history. Reports of measurements first started to appear in 1998 [10, 11].

Because LFN measurements can be used as a way of monitoring crystal quality, some

reports came from materials scientists [12]. Physicists have measured GaN LFN and

are using some of the following arguments to explain it: tail states near the band gap

edge [11], mobility fluctuations [13], and tunneling of electrons from the channel to

traps in surrounding layers [12]. No theory is yet accepted as the best explanation.

Various other LFN papers have appeared [12,14–16]. Most measurements are at very

low biasings such that the device is in the linear region. The only publication that stud-

ies gate and drain LFN for the full biasing range of a GaN HEMT is Hsu et al. [17].

This paper will be returned to in chapter 4. Due to the use of the Hooge parame-

ter, the devices not being optimized HEMTs (some are doped channel HFETs), and

measurements only in the linear region, many of the above results are not of use to a

circuit designer or device engineer who is trying to characterize and optimize LFN.

Accurate measurements of LFN can also be difficult. Therefore, this work presents

measurements and modeling of LFN that will be of use to the engineering community.

The first published NF report for a GaN HEMT was performed by Ping in 2000 [18].

For a 0.25 x 100µm gate device, a minimum noise figure (NFmin) of 1.06 dB and a

gain of 12 dB at a frequency of 10 GHz was demonstrated. This was followed shortly

6


by Nguyen [19], presenting a NFmin of 0.6 dB at 10 GHz and 13.5 dB gain with a

0.15 x 100 µm gate. Other results [20, 21], with improved performance, followed

the next year. After optimizing the device geometry, Moon showed in 2002 that a

GaN HEMT could present similar NF at a similar biasing to a GaAs HEMT [22]. The

next notable result in the field was when Lu showed that GaN HEMTs on a sapphire

substrate can have similar NFmin performance to HEMTs on a SiC substrate [23]. All

previously published results had been on SiC substrates. This work seeks to extend

on the noise figure literature and to confirm or deny some of the previously published

results, in addition to adding new studies. Table 3.1 lists many GaN (as well as GaAs,

SiGe, and InP) HEMT NF results.

Prior to this work, GaN oscillator references were scarce. The first GaN oscillator

was reported by Shealy in 2001 [24]. The phase noise was respectable: -92 dBc at

100 kHz for a 6 GHz carrier frequency. While Shealy’s work was a hybrid design, the

first MMIC oscillator was presented by Kaper in 2002 [25]. He estimated (but did not

show measurements) the phase noise to be -87 dBc at 100 kHz. These works left room

for further investigation. A summary of all published GaN oscillators appears in table

5.1.

The existing literature was thin at the beginning of this project. The noise research

of GaN has since approximately doubled to tripled. Because noise is difficult to mea-

sure, second and third opinions are valuable. This work will do this, in addition to its

7


own unique studies and modeling.

1.3 Thesis Outline

Chapter 2 builds up to a NF model. This model is an extension of previous mod-

els and fills the need of understanding how various noise sources and small-signal

parameters influence NF and other noise parameters without the need for prior NF

measurements. The chapter starts with reviews of noise sources, the equivalent circuit

model, NF and parameters, and previous models. The proposed model is then derived

and discussed in detail.

With the modeling in place, several NF studies are presented in chapter 3. Effects

of bias and gate leakage are studied. Different epitaxial structures are compared, as

is the addition of a field plate. High-frequency GaN HEMT devices were borrowed,

measured, and compared to HEMTs in other technologies (in particular, GaAs).

A LFN setup was constructed and measurements performed to help understand the

phase noise performance. Chapter 4 covers these results. It first shows through mea-

surements why the Hooge parameter should not be used for comparing devices (only

materials). LFN versus bias shows the need for an improved model for the drain noise,

which was then added. LFN studies are then presented and comparisons to measured

GaAs HEMTs are made.

Differential oscillators are constructed in chapter 5 and phase noise is measured

8


and evaluated. The first version had excellent linearity but poor phase noise. A second

version had good phase noise. The oscillators are compared to other published GaN

oscillators and to differential oscillators in Si and GaAs technologies.

References

[1] T. Kikkawa, T. Maniwa, H. Hayashi, M. Kanamura, S. Yokokama, M. Nishi,N. Adachi, M. Yokoyama, Y. Tateno, and K. Joshin, “An Over 200-W OutputPower GaN HEMT Push-Pull Amplifier with High Reliability,”IEEE MicrowaveTheory and Tech. Symp., pp. 1347–1350, 2004.

[2] Y. Okamoto, Y. Ando, T. Nakayama, K. Hataya, H. Miyamoto, T. Inoue, M. Senda,K. Hirata, M. Kosaki, N. Shibata, and M. Kuzuhara, “High-Power Recessed-GateAlGaNGaN HFET With a Field-Modulating Plate,”IEEE Trans. Electron Devices,vol. 51, no. 12, pp. 2217–2222, Dec. 2004.

[3] H. Ishida, Y. Hirose, T. Murata, Y. Ikeda, T. Matsuno, K. Inoue, Y. Uemoto,T. Tanaka, T. Egawa, and D. Ueda, “A High-Power RF Switch IC Using Al-GaN/GaN HFETs with Single-Stage Configuration,”Electron Devices, IEEETransactions on, vol. 52, no. 8, pp. 1893–1899, 2005.

[4] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. A. York, “Low Phase-Noise 5 GHz AlGaN/GaN HEMT Oscillator Integrated with BaxSr1−xTiO3 ThinFilms,” IEEE Microwave Theory and Tech. Symp., pp. 1509–1512, 2004.

[5] V. Kaper, R. Thompson, T. Prunty, and J. Shealy, “Signal Generation, Control,and Frequency Conversion AlGaN/GaN HEMT MMICs,”Microwave Theory andTechniques, IEEE Transactions on, vol. 53, no. 1, pp. 55–65, 2005.

[6] G. Ellis, J.-S. Moon, D. Wong, M. Micovic, A. Kurdoghlian, P. Hashimoto, andM. Hu, “Wideband AlGaN/GaN HEMT MMIC Low Noise Amplifier,” inMi-crowave Symposium Digest, 2004 IEEE MTT-S International, vol. 1, 2004, pp.153–156 Vol.1.

[7] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. York, “A C-Band High-Dynamic Range GaN HEMT Low-Noise Amplifier,”IEEE Microwave Compo-nents Lett., vol. 14, no. 6, pp. 262–264, Jun. 2004.

[8] R. Rast, “The Dawn of Digital TV,”Spectrum, IEEE, vol. 42, no. 10, pp. 26–31,2005.

[9] D. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,”Proc. IEEE,vol. 54, no. 2, pp. 329–330, 1966.

9


[10] D. V. Kuksenkov, H. Temkin, R. Gaska, and J. W. Yang, “Low-Frequency Noisein AlGaN/GaN Heterostructure Field Effect Transistors,”IEEE Electron DevicesLett., vol. 19, no. 7, pp. 222–224, July 1998.

[11] M. E. Levinshtein, F. Pascal, S. Contreras, W. Knap, S. L. Rumyantsev, R. Gaska,J. W. Yang, and M. S. Shur, “Low-Frequency Noise in GaN/GaAlN Heterojunc-tions.” Applied Physics Letters, vol. 72, no. 23, pp. 3053–5, June 1998.

[12] A. Balandin, Ed.,Noise and Fluctuations Control in Electronic Devices. Steven-son Ranch, CA: American Scientific Publishers, 2002.

[13] J. A. Garrido, B. E. Foutz, J. A. Smart, J. R. Shealy, M. J. Murphy, W. J. Schaff,L. F. Eastman, and E. Munoz, “Low-Frequency Noise and Mobility Fluctuationsin AlGaN/GaN Heterostructure Field-Effect Transistors.”Applied Physics Letters,vol. 76, no. 23, pp. 3442–4, June 2000.

[14] M. Levinshtein, S. Rumyantsev, M. Shur, R. Gaska, and M. Khan, “Low Frequencyand 1/f Noise in Wide-Gap Semiconductors: Silicon Carbide and Gallium Nitride,”Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G-Circuits, Devices and Systems], vol. 149, no. 1, pp. 32–39, 2002.

[15] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, andC. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-EffectTransistors for Microwave Communications,”Microwave Theory and Techniques,IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.

[16] S. Rumyantsev, N. Pala, M. Shur, M. Levinshtein, R. Gaska, X. Hu, J. Yang,G. Simin, and M. Khan, “Low Frequency Noise in GaN-Based Transistors,” inHigh Performance Devices, 2000. Proceedings. 2000 IEEE/Cornell Conferenceon, 2000, pp. 257–264.

[17] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hus-sain, “Characterization and Analysis of Gate and Drain Low-Frequency Noise inAlGaN/GaN HEMTs,” inHigh Performance Devices, 2002. Proceedings. IEEELester Eastman Conference on, 2002, pp. 453–460.

[18] A. Ping, E. Piner, J. Redwing, M. Khan, and I. Adesida, “Microwave Noise Perfor-mance of AlGaN/GaN HEMTs,”Electron. Lett., vol. 36, no. 2, pp. 175–176, Jan.2000.

[19] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, andC. Nguyen, “Robust Low Microwave Noise GaN MODFETs with 0.6 dB NoiseFigure at 10 GHz,”IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.

[20] S. Hsu and D. Pavlidis, “Low Noise AlGaN/GaN MODFETs with High Break-down and Power Characteristics,”Gallium Arsenide Integrated Circuit (GaAs IC)Symposium, 2001. 23rd Annual Technical Digest, pp. 229–232, Oct. 2001.

10


[21] W. Lu, J. Yang, M. Khan, and I. Adesida, “AlGaN/GaN HEMTs on SiC with over100 GHzfT and Low Microwave Noise,”IEEE Trans. Electron Devices, vol. 48,no. 3, pp. 581–585, Mar. 2001.

[22] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-Cray, and C. Nguyen, “Microwave Noise Performance of AlGaNGaN HEMTsWith Small DC Power Dissipation,”IEEE Electron Devices Lett., vol. 23, no. 11,pp. 637–639, Nov. 2002.

[23] W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, “DC, RF, and MicrowaveNoise Performance of AlGaN/GaN HEMTs on Sapphire Substrates,”IEEE Trans.Microwave Theory Tech., vol. 50, pp. 2499–2503, Nov. 2002.

[24] J. B. Shealy, J. A. Smart, and J. R. Shealy, “Low-Phase Noise AlGaN/GaN FET-Based Voltage Controlled Oscillators (VCOs),”IEEE Microwave ComponentsLett., vol. 11, no. 6, pp. 244–245, Jun. 2001.

[25] V. Kaper, V. Tilak, H. Kim, R. Thompson, T. Prunty, J. Smart, L. F. Eastman, andJ. Shealy, “High Power Monolithic AlGaN/GaN HEMT Oscillator,”IEEE GaAsDigest, pp. 251–254, 2002.

11

2Noise Figure Modeling of AlGaN/GaN

HEMTs

2.1 Introduction

TO characterize, compare, and improve the noise performance of devices, a

theoretical framework is needed that identifies the noise sources, how these

sources contribute to the overall noise, and how the noise changes with other param-

eters, such as bias and matching conditions. A common approach is to add discrete

noise sources to a small-signal model [1–3]. Depending on the model, the sources may

be correlated, adding complexity to the derivation and interpretation of the particular

model.

This chapter first fills in background for the model. Noise sources of interest to

noise figure (NF) are reviewed, as is a full small-signal model. NF is then defined

in § 2.4, along with the noise parameters NFmin , Γopt andrn. Those familiar with

noise sources, NF, and small-signal modeling could skip these sections and continue

on to § 2.5. The more widely-used models are presented along with their strengths

12

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS

and weaknesses in§ 2.5. Noise modeling derived from these previous models is then

introduced. Its strengths and weaknesses are also discussed. Finally, the NF model

is used for simulation of device noise figure performance of AlGaN/GaN HEMTs,

compared to other models, and discussed in depth.

2.2 Noise Sources

The two most common types of noise are shot and thermal noise. Both are referred

to as “flat” or “white,” meaning the noise power versus frequency is constant. Each

will be reviewed in this section. The relevance of other noise sources to NF is also

discussed.

2.2.1 Thermal Noise

Thermal noise was first studied in detail by Johnson in 1927 [4], and explained

mathematically by Nyquist [5]. Its physical origin is the agitation of electrons in a

conductor. The random scattering of electrons by atoms followed by their relaxation

back to a ground state leads to fluctuations that can be measured as a voltage or current.

The use of statistical analysis and thermal physics [6] leads to the following expression

that represents the available noise power from a resistance into a matched load

PThermal =

hf

2+

hf

exp(hfkT

)− 1

∆f (2.2.1)

13


whereh is Planck’s constant,k is Boltzmann’s constant, T is temperature, andf is the

frequency.

The term∆f is the bandwidth in which the noise is being measured. To determine

the total noise coming from, for example, an amplifier, this expression would be inte-

grated over the bandwidth of the amplifier. A noise measurement might be performed

over a small bandwidth, less than one Hertz for some low-frequency noise measure-

ments, showing the need to keep this fact in mind. When values are quoted and a

bandwidth is not specified, it is assumed to be a 1 Hz bandwidth. This convention is

followed in this work.

Equation 2.2.1 is a general expression, and is needed if operating at cryogenic tem-

peratures or extreme frequencies (such as the THz range). For most engineering pur-

poses, the simpler expression

PThermal ≈ kT∆f (2.2.2)

can be used. A handy value from this expression is that the available noise at room

temperature in a 1 Hz bandwidth is -174 dBm (4× 10−21 W).

When the load is not matched, or the noise needs to be expressed as a voltage or

current (described by a variance), the following forms are useful:

⟨v2n

⟩= 4kTR∆f (2.2.3)

⟨i2n⟩

=4kT

R∆f (2.2.4)

14


R is the resistance of the noise generating material or medium. A 1kΩ resistor gener-

ates 4 nV/√

Hz of noise. Not every resistor represented in a circuit schematic generates

noise. For example,rπ in a bipolar transistor is a manifestation of the transistor’s I-V

characteristics, and is not a real resistance.

Ideal reactive components do not generate noise. However, because real inductors

and capacitors are lossy, the circuit-modeled parasitic resistances of these components

will generate thermal noise. Also, these components shape the bandwidth of the noise

in ways similar to shaping a signal.

Finally, the above equations only apply at thermal equilibrium. A biased transistor

is notat thermal equilibrium. However, a small-signal model of a HEMT, which does

not include bias, can have its parasitic resistances considered at thermal equilibrium.

Later, in§ 2.6.3, the channel noise, which is a form of non-equilibrium thermal noise,

are derived. Further information on thermal noise can be found in [6–9].

2.2.2 Shot Noise

Shot noise was reported and explained by W. Schottky in 1918. The analogy of this

noise to buck shot being dropped into a bucket is the basis for its name [8]. Shot noise

exists when two conditions are met: (1) a DC current is flowing and (2) the charge

carriers composing the DC current cross a potential barrier. This second condition

is why resistors and the channel of a HEMT do not generate shot noise. The noise

15


exists because charge is discrete and will cross the potential barrier atrandomtimes.

If the charge crossed at the same time or equal time intervals, the spectrum of the shot

noise would not be white and could be better dealt with in circuit design (possibly by

filtering).

As with thermal noise, shot noise is not constant at all frequencies. The noise de-

creases at frequencies above which the transit time across the barrier is short compared

to the inverse of this frequency [7]. Because devices are operated at frequencies well

below this, the noise can be considered flat [7].

Using math from random processes [9], shot noise is describe by the following

equation for current fluctuations:

⟨i2n⟩

= 2qIDC∆f (2.2.5)

with q being electronic charge (1.6 × 10−19 C), IDC the DC current (Amps), and∆f

again the bandwidth of interest.

2.2.3 Other Sources of Noise

Shot and thermal are the important noise sources for NF modeling. Others exist, and

at frequencies lower than RF should be considered. They will be briefly mentioned

here. Flicker and generation-recombination noise (covered in detail in chapter 4) are

important for oscillator phase noise, but are not of concern for NF measurements in

the RF frequency range. Burst noise is interpreted as a type of low-frequency noise

16


with a 1/f2 spectrum. It also would not affect NF measurements in the GHz range, nor

has it been reported in GaN-based HEMTs. Avalanche noise is a form of shot noise,

and usually applies to a semiconductor junction. With a high enough field across a

junction, avalanche multiplication can occur [10]. This increase in carriers leads to

an increase in the shot noise proportional to the cube of the multiplication factor [9].

While the fields can be very high, no evidence has been shown that this type of noise

appears in GaN-based HEMTs. As will be seen in modeling later, shot and thermal

types of noise are sufficient to predict the noise figure of GaN HEMTs.

2.3 Equivalent Circuit Model

A small-signal model will be used in determining the device noise figure. Device

small-signal modeling has been covered extensively in the literature [11–17]. Here

a short summary will be given. The model used in this work is superimposed on

the cross section of a HEMT in figure 2.1. The parameters are bias-dependent but

frequency independent. In this chapter and chapter 3, the parameters are extracted at

the bias of best device minimum noise figure performance.

At the heart of the model is the gate-source capacitance,Cgs, and the transconduc-

tance,gm. The phase associated withgm, ωτ , is a necessary delay that accounts for

channel charge to redistribute after a change in gate voltage. The drain-source resis-

tance,Rds, is a measure of how effectively a signal can be extracted from the device.

17


Rg

Ri

Rds

DrainSource Gate

gmejwτvc

Cgs

Vc+

-Rs

Rgd

Cgd

Cpgd

Rd

Ld

Cpds

Lg

Cds

Cpgs

Ls

Figure 2.1: Cartoon showing the device small-signal model on a cross section of aHEMT.

This is because it will reduce the effective load of the device. There are two primary

causes for its degradation: conduction in the buffer due to poor growth (traps) and

spread of electrons from the 2DEG when the device is under extreme biasing (very

high electric fields).

The channel and gate-drain resistances,Ri andRgd, have vague physical interpre-

tations.Ri is regarded as either a physical channel resistance or charging resistance

for Cgs. Because it is hard to extract separately from the gate resistance,Rg, the two

are sometimes lumped together. The gate-drain capacitance,Cgd, is setup by the space

charge region between the gate and drain, similar toCgs, but typically an order of mag-

nitude smaller. It introduces a bothersome feedback which reduces the high-frequency

18


performance of the device. The gate-drain resistance,Rgd, is also argued as a charging

resistance forCgd. Any capacitance between the drain and source, which will be very

small, is accounted for withCds.

The parametersCgs, gm, τ ,Ri,Rds,Rgd,Cgd, andCds taken together are referred to

as theintrinsic device. The other elements of the model are unfortunate side-effects of

having to provide physical connections to the device and the parasitic and distributed

effects that occur when operating at frequencies in the GHz range. These parasitic

elements are called theextrinsicelements of the device.

The drain and source resistances,Rd andRs, come from two physical processes.

The first is the finite resistance of the 2DEG, and so the access regions between gate

source and gate drain contribute to these parasitics. The second source is the non-

ideal ohmic contact behavior between the metal pads and the semiconductor. These

resistances scale directly with the device width as used in§ 2.6.5. Because the gate

length is short (0.7µm here), the resistances of the gate metals contribute toRg.

From an AC viewpoint, the signal decays as it propagates along the length of the gate

resistance. A distributed model argument shows this resistance to be approximately

1/3 of its DC value [14]. All of these resistances generate thermal noise.Rs and

Rg will be important for modeling of noise figure as seen later. BecauseRd is at

the output, and its magnitude of noise is far smaller than the channel noise, it can be

ignored.

19


The drain, gate, and source inductances,Ld Lg, andLs, respectively, account for

signal delay along the various contact pads.Lg is usually largest, and will affect

any input match (noise or power) to the device. Finally there are the various pad

capacitances between their respective device terminals:Cpgs, Cpgd, andCpds. Cpgs

andCpgd are small, whileCpds for devices used in this work is of the same order as

Cgd.

S-parameter measurements of devices along with open and shorted test structures

were used to find the small-signal parameters. In addition, DC measurements of TLM

structures and some basic hand calculations [14] were used to determineRg, Rs, and

Rd. For a better fit, optimization was performed using Advanced Design System

(ADS). It is important to have accurate small-signal parameters; any discrepancies

directly translate into incorrect noise figure parameter prediction. Some ADS files

useful for extracting and optimizing the small-signal parameters can be found in ap-

pendix A.

Extracted small-signal parameters of devices from various samples are displayed in

table 2.1. The top half of the table is the intrinsic parameters, while the bottom half is

the extrinsic parameters. Many of the extrinsic parasitics come from the geometry of

the device or the pad parasitics and will be the same for the different samples. These

parameters will be used in this chapter and in chapter 3.

20


Sample: 15% 25% 25% 27% 35% 35%on SiC w/AlN

Intrinsic Ri (Ω) 6.2 8.24 8.86 9.23 8.23 4.07Parameters Rds (Ω) 577 588 622 562 833 627

Rgd (Ω) 75.7 287 238 96 96.2 33.4Cgd (fF) 19 19.1 13.5 20.6 18.7 29.9Cds (fF) 2.97 2.33 1.34 2.34 1.66 1.13Cgs (pF) 0.23 0.265 0.22 0.191 0.191 0.215gm (mS) 34.1 37 33.2 33 30.5 34.9τ (ps) 1.2 2.25 2.6 2 2.25 2.03

Extrinsic Rs (Ω) 10.2 6.18 5.19 4.04 4.31 5.30Parameters Rd (Ω) 17.9 10.24 8.99 7.41 7.20 7.54

Rg (Ω) ←− 3.03−→Ls (pH) ←− 12−→Ld (pH) ←− 22.3−→Lg (pH) ←− 45.6−→Cpgs (fF) ←− 1.38−→Cpds (fF) ←− 29.6−→Cpgd (fF) ←− 5.4−→

Table 2.1: Extracted small-signal parameters for various samples. Devices have a gategeometry of 0.7× 150µm.

2.4 Noise Figure and Noise Parameters

An amplifier provides gain to both the input signal and the noise. The amplifier will

also add noise from its intrinsic noise sources. This makes the signal to noise ratio at

the output worse than at the input. Expressing a ratio of these two ratios at a reference

temperature leads to the definition of noise figure.

F ≡ (S/N)in(S/N)out

∣∣∣∣∣T=Treference=290K

(2.4.1)

It can be applied to any two port [3] (by extension even to mixers [7]). Here, it will

21


be applied to a single HEMT. Sometimes NF is called noise factor, F. Traditionally,

the names were interchangeable, but now it is common that noise figure is the noise

factor expressed in decibels (NF = 10 log10(F)). This is the convention followed in

this work. Sometimes it is expressed as a temperature (Tnoise = (F − 1)Treference).

Noise figure by itself gives no details of the noise sources of the device or amplifier.

However, noise sources can be added as in Figure 2.2.Inoise is the equivalent short-

circuited noise current source andEnoise the equivalent open-circuited noise voltage

source. Together, they account for all noise sources of the device which can now be

modeled as a noiseless two port. These two sources will likely be correlated because

of the various physical noise sources of the device that contribute to them [8]. Models

that describe these sources of noise are discussed in the next section. An input is

connected to the device, represented as a source impedance in figure 2.2. This input

will generate its own noise, represented asEsource. This could be thermal noise from

Zsource

Noiseless

2-port

network

+-

Enoise

+-

InoiseEsource

Figure 2.2: Equivalent model of a transistor driven by a noisy source of impedanceZsource.

22


a passive network and/or active device noise. From this, F (and hence, NF) can be

written as [8]

F = 1 +

⟨|Enoise + InoiseZsource|2

⟩

〈Esource〉2(2.4.2)

As can be seen, the value of the source impedance actually affects the noise figure.

OnceEnoise andInoise have been determined through whichever model is applied, the

noise figure can be predicted for changing source impedance. F can also be expressed

as [18,19]:

F = Fmin +4Rn

Zo

|Γsource − Γopt|2

(1 − |Γsource|2) |1 + Γopt|2(2.4.3)

Γsource is the reflection coefficient of the source impedance. Equation 2.4.3 contains

four parameters that taken together are called thenoise parameters. They are:

Fmin The best achievable noise figure. It occurs only when the source impedance isset toZopt (converselyΓopt).

|Γopt| The magnitude of the source reflection coefficient that provides the minimumnoise figure,Fmin.

6 Γopt The angle of the source reflection coefficient that providesFmin.

Rn An effective “slope.” The larger its value, the quicker the noise figure increasesasΓsource is changed from its optimum value.1

These parameters are usually measured as described in§ 3.3. As can be reasoned

from equation 2.4.3, there are circles of constant noise on an impedance or Smith

1Rn has units of ohms. It can also be normalized to the reference impedance,Zo. Then the variableis usually written asrn instead.

23


NFmin

NFmin+1dB

NFmin+2dB

NFmin+3dB

Gmax

Gmax-1dB

Gmax-2dB

Figure 2.3: Smith Chart showing minimum noise figure and circles of constant noisefigure (solid circles) along with maximum gain and circles of constant gain (dashedcircles).

Chart plane. This is shown in Figure 2.3. It should not be surprising to find the small-

signal gain circles and noise circles do not overlap becauseΓopt is an intentional gain

mismatch to minimize noise [20].

That the noise performance changes with the source match is extremely important

for LNA design. In the next section, noise models for HEMTs that are more in depth

than in figure 2.2 will be reviewed. Once these noise sources are determined, they can

be used elsewhere, such as assisting in oscillator phase noise prediction.

24


2.5 HEMT Noise Figure Models

The major noise figure models used for HEMTs are now presented. The work by

van der Ziel, Pucel, Fukui, and Pospieszalski is the basis for most other investigations

and modeling of noise figure. The key ideas, equations, strengths and weaknesses of

each will be reviewed. Shortcomings found in each will show the need for further

work and provide motivation for the next section.

2.5.1 van der Ziel and Pucel Models

The theoretical work for noise sources in FETs at microwave frequencies was in-

troduced by van der Ziel in the early 1960s [3, 21, 22]. He derived noise sources for

the channel and “induced gate noise.” This gate noise is explained as fluctuating noise

in the channel capacitively coupling to the gate throughCgs andCgd, causing an ef-

fective, and correlated, noise source at the gate. The gate noise, channel (drain) noise,

correlation (C), and cross-term〈igi∗d〉 can be written as [3]

⟨i2g⟩

= 4kTaδω2C2

gs

5gd0∆f (2.5.1)

⟨i2d⟩

= 4kTaΓgd0∆f (2.5.2)

C =〈igi∗d〉√⟨i2g⟩〈i2d〉

(2.5.3)

〈igi∗d〉 =2

3jωCgskTa∆f (2.5.4)

25


ω is the angular frequency,Ta is the ambient temperature,gd0 is the drain-source con-

ductance whenVds is zero,δ is a parameter van der Ziel gives as 4/3, andΓ will be

derived in§ 2.6.2 (for now, it can be considered a constant of 2/3). Van der Ziel orig-

inally found a correlation of 0.395j for JFETs [3]. For aggressively-scaled HEMTs,

the correlation is experimentally found to be∼0.7j [23,24]. Van der Ziel does give ex-

pressions for noise figure, but they are often in terms of more complicated parameters,

under specific conditions, or for different devices, making them of limited use [3].

While the gate and drain noise expressions above allow for noise prediction, for accu-

rate results the correlation must be measured. This is because small changes in cor-

relation can have a large effect in predicted noise parameters. Also, the noise sources

are bias-and frequency-dependent.

In 1975, Pucel and his co-workers took what was learned from van der Ziel and

extended it in a very detailed publication [2]. Their work was explicitly for a GaAs

MESFET (and thus more applicable to a HEMT), whereas van der Ziel’s work was

mainly for JFETs. The Pucel modeling takes into account velocity saturation and how

the noise changes with bias based on changes in the small-signal parameters and their

noise variables P, R, and C. The model also uses a gate and drain noise source that

are correlated, shown in a small-signal model in figure 2.4. In this figure, the gate

and drain noise sources account for all noise generated by the intrinsic device (inside

the dashed “Noiseless” box). The parasitic resistances,Rg, Rs, andRd, still generate

26


Rg

Ri

Cgs

Rds

Drain

Source

Gate

gmejwτvc

Vc

+

-

Ls

Rs

Rgd Cgd

Cpgd

Rd Ld

CpdsCpgs

Lg Noiseless

Ig IdCds

Figure 2.4: Pucel noise model in a small-signal circuit.

thermal noise. The gate and drain noise sources are related to the noise variables by

P =〈i2d〉

4kTa |Y21|2 ∆f=

〈i2d〉4kTagm∆f

(2.5.5)

R =|Y21|2

4kTa |Y11|2 ∆f

⟨i2g⟩

=gm

4kTaω2C2gs∆f

⟨i2g⟩

(2.5.6)

and the same correlation as in equation 2.5.3. Although Pucel determined very de-

tailed expressions for these noise variables, for accurate results the modeling had to

be fitted to data. Today, if this model is used, the parameters are determined empiri-

cally [7], fitting to noise figure measurements. An excellent paper using this model on

GaN HEMTs that shows directly how to extract these parameters from measurements

is found in [25]. This method also treats both parts of the correlation, magnitude and

phase, as variables to be determined instead of restricting the phase to 90 (strictly

imaginary). This formulation is used in this work. Information about an ADS project

27


that helps in determining these parameters, contains a small-signal circuit with this

type of noise modeling, and calculates noise figure can be found in appendix A. Be-

cause it uses the same correlation as van der Ziel’s modeling, the Pucel model suffers

the same drawbacks. As mentioned, the parameters usually must be determined from

measurements, limiting its predictive power. Because the noise sources are similar for

both models, they will be referred to ascorrelated noise (CN) models in this work.

2.5.2 Fukui Model

Fukui garnered much attention in the late 1970s with the introduction of his empir-

ical model [26]. Although it involved empirical parameters, it was far simpler than

the previously reported noise models, was expressed directly in terms of the noise

parameters, and made clear how key small-signal parameters contributed to the noise

performance. The model is also convenient because the noise at different frequencies

and device scaling can be easily determined. His expressions for the noise parameters

are:

Fmin = 1 + k1fCgs

√Rg +Rs

gm(2.5.7)

Ropt = k3

[1

4gm+Rg +Rs

](2.5.8)

Xopt =k4

fCgs(2.5.9)

Rn =k2

g2m

(2.5.10)

28


The variablesk1−4, are the fitting parameters, and will change with the device tech-

nology and bias. While this model can be useful for hand calculations, the Pucel and

Pospieszalski models are more complete and directly usable in a simulator such as

ADS.

2.5.3 Pospieszalski Model

In the late 1980’s, Pospieszalski introduced a new noise figure model that took a

different approach than the previous methods by removing correlation between the

noise sources [1]. There are only two noise sources for the entire transistor: thermal

noise ofRi andRds. Instead of these resistors being at ambient temperature,Ta, they

are at higher effective temperaturesTg andTd, shown in figure 2.5.Tg is usually

(but not always) close to room temperature, whileTd can be several thousand degrees

Kelvin. These elevated temperatures are not linked to a physical temperature. There

Rg

Ri

Cgs

Rds

Drain

Source

Gate

gmejwτvc

Vc

+

-

Ls

Rs

Rgd Cgd

Cpgd

Rd Ld

CpdsCpgs

Lg

T = Tg

T = Td

Cds

4kTg/Ri∆f

4kTd/Rds∆f

Figure 2.5: Pospieszalski noise model in a small-signal circuit. Resistances (and theirthermal noise sources)Ri andRds are at elevated temperaturesTg andTd respectively.

29


have been attempts to link these noise temperatures to the device physics, but none

were viewed as successful. The noise can be described by the noise temperaturesTg

andTd as:

Fmin = 1 + 2

(f

fT

)2RiTdRdsTa

+2f

fTTa

√√√√RiTgTdRds

+

(f

fT

)2R2i T

2d

R2ds

(2.5.11)

Ropt =

√√√√(fTf

)2TgRiRds

Td+R2

i (2.5.12)

Xopt =1

ωCgs(2.5.13)

Rn =TgRi

Ta+

TdTaRdsg2

m

(1 + ω2C2gsR

2i ) (2.5.14)

After measuring S-parameters and noise parameters, the noise temperatures can be

extracted by solving the above equations. A Matlab script using equations 2.5.11

and 2.5.12 to perform this calculation can be found in appendix C. A criteria that

Pospieszalski mentions for the model to work is

1 ≤ 4Ropt

Rn(F − 1)< 2 (2.5.15)

The lower limit is fundamental and is because the noise of a 2-port modeled by a pair

of noise sources must be Hermitian and non-negative definite as shown by Pospieszal-

ski [27]. The upper limit comes from the model itself [1]. As with the other models, it

can be used to determine the match for noise and expected noise at other frequencies.

The model is criticized for its dependence onRi as a thermal noise source, which is

30


hard to determine precisely, and for the noise temperatures not having a physical basis.

As with the other models, the noise parameters must be measured prior to modeling.

Thus the model does not “predict” noise. In addition, the noise temperatures change

with device bias [28]. How they change with bias is reported in the literature, but not

modeled or predicted. Information for an ADS project that contains a small-signal

circuit with this type of noise modeling and that calculates noise figure can be found

in appendix A.

2.5.4 Pospieszalski and Correlated Noise Models Applied to Al-GaN/GaN HEMTs

Based on the above discussion, the Pospieszalski and CN models are useful for:

1. Modeling device noise figure in a circuit simulator versus frequency and inputmatch

2. Devices that are stable and well-characterized, such that the noise variables ofthe model (Tg, Td, R, P, C) do not change

3. Predicting noise at frequencies outside the range of available measurement equip-ment.

4. When the bias in a design will not be much different from what gives the bestNF performance

Thus, they are useful for basic LNA designs as shown in [17, 29]. The application of

these models to GaN-based HEMTs is relatively new, with very few publications [25,

28,30].

In table 2.2, the Pospieszalski and CN model have been applied to devices from six

samples. The fτ and fmax of the different devices at the biasing for best NFmin are

31


listed along with the bias at the top of the table. The next section contains the mea-

sured noise parameters, obtained as described in§ 3.3, along with the gain that could

be expected from the device having an input match ofΓopt and an output match for

small-signal gain. These noise measurements, along with the small-signal parameters

from table 2.1, were used to calculate the noise variables for both the Pospieszalski

and a CN model. These models’ variables are listed in table 2.2 with the predicted

noise parameters using each model at 5 GHz. The fit is generally very good. Both

models predict NFmin and|Γopt| well. The Pospieszalski model does not predict6 Γopt

as well as the other parameters, and the CN model has trouble with predictingrn.

From equation 2.5.13, it is seen that the Pospieszalski model’s prediction ofXopt only

depends onCgs. A better prediction agreement would be expected. An explanation for

this discrepancy will be offered in§ 3.5.4. Both these models fit the noise parameters

versus frequency, shown in figure 2.6 for one of the sets of measurements in table 2.2.

Variations in the predictedTg of Pospieszalski’s model is large, a factor of 4. This

is likely because of the differences inRi in the measurements of table 2.1, but they

change by only a factor of 2. This high sensitivity toRi might make the model difficult

to use in predicting noise. However, it should be stressed that the model works well

without the need for correlation.

32


Sample: 15% 25% 25% 27% 35% 35%on SiC w/AlN

Ids @ NFmin 20 13 10 19 11 10Vds @ NFmin 4 4 7 4 5 4fτ @ NFmin 19.7 19.4 21.4 23.3 22.3 21.3fmax @ NFmin 30.2 33.6 39 42.9 43.7 40.4

Measure Noise Parameters and Associated GainNFmin (dB) 1.14 1.13 1.1 1.16 1.15 1.18rn 0.772 0.707 0.648 0.83 0.796 0.723Γopt 0.727 0.716 0.746 0.774 0.76 0.7336 Γopt 20.5 21.3 23.2 19.8 19.5 23.9Gainassoc. (dB) 14 13.7 14.6 14.3 14 12.7

Using Pospieszalski ModelNFmin (dB) 1.18 1.1 1.1 1.04 1.07 1.03rn 0.749 0.597 0.729 0.81 0.839 0.721Γopt 0.702 0.666 0.715 0.744 0.744 0.726 Γopt 25.7 27.3 26.3 22.7 22.3 26.9Tg (K) 607 292 250 358 462 988Td (K) 3445 3018 3893 3469 4454 3966

Using a Correlated Noise ModelNFmin (dB) 1.23 1.3 1.21 1.28 1.25 1.33rn 1.21 0.989 0.831 1.04 0.977 0.95Γopt 0.806 0.758 0.778 0.797 0.783 0.7666 Γopt 19.2 21 22.5 19.6 19.2 23.6⟨i2g⟩ (

10−24 A2

Hz

)7.05 12.00 3.55 7.09 7.23 6.74

〈i2d〉(10−22 A2

Hz

)4.56 5.60 4.14 5.93 4.79 5.36

|C| 0.802 0.799 0.821 0.803 0.759 0.7396 C (degrees) 103 101 129 114 114 118

Table 2.2: Comparison of Pospieszalski and Correlated Noise models to measureddata. Devices have a gate geometry of 0.7× 150 µm .

33


4 6 8 10 12

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

4 6 8 10 12

0.0

0.3

0.6

0.9

1.2

1.5

1.8

Measured Pospieszalski Model CN Model

NF

min

(dB

)

Frequency (GHz)

r n

4 6 8 10 12

0.0

0.2

0.4

0.6

0.8

1.0

|Γo

pt|

0

30

60

90

120

150

180

Measured Pospieszalski CN Model

An

gle

Γo

pt

(de

g.)

Figure 2.6: Comparison of Correlated Noise and Pospieszalski models to measurednoise parameters versus frequency.

34


Lee’s study of the CN models to AlGaN/GaN HEMTs experimentally finds that the

correlation tends to a constant of 0.7 [25]. The average value for|C| found in table

2.2 is 0.718, in agreement with Lee. The average phase was found to be 110, which

is higher than the expected 90. However, when Lee de-embeds contributions from

extrinsic shot and thermal noise sources he finds the phase to be very close to 90 [25].

The average gate noise from table 2.2 is 7.3 pA2/Hz and the average drain noise is 506

pA2/Hz.

Average values for the Pospieszalski noise variables areTg of 493 K andTd of

3708 K. These numbers are only approximately close to those found in [28]; however,

in that reference the devices which had a gate length of 0.35µm (compared to 0.7µm

here) had anfτ of only 30 GHz, and thus were excessively noisy. Despite the accu-

racy in the Pospieszalski model, the condition in equation 2.5.15 was not met for the

modeling in table 2.2. The upper limit was broken; values of 8 were common.

2.6 A Proposed Noise Figure Model

A model that was developed for some of the noise studies in chapter 3 is now pre-

sented. It uses some of the formulation of the CN models, but without correlation and

replacement of the induced gate noise with a shot noise source. In addition, this model

can give accurate noise parameter results without prior noise parameter measurements.

35


Rg+Ri+Rs

Er

C'gs

Rds

Drain

Source

Gate

g'mvc

Vc

+

-

IsIc

Figure 2.7: A simplified HEMT circuit model including noise sources.

2.6.1 Setup Details

A circuit schematic of the model is represented in figure 2.7 with six small-signal

parameters and three noise sources. A full small-signal model is still used for small-

signal parameter extraction from a HEMT, but onlyRg, Rs, Ri, Cgs, gm, andRds are

used. The noise sources areEr, Is, andIc. Er is thermal noise from the two parasitic

resistances and channel resistance. Its voltage spectral density is written as

⟨E2r

⟩= 4kT (Rs +Rg +Ri) ∆f (2.6.1)

Is is a shot noise source. The DC current used for it is from a three-terminal measure-

ment at the bias of S-parameter extraction. This source can be represented between

gate-and-source or gate-and-drain with the resulting derivations being the same. The

current spectral density of this shot noise term is

⟨I2s

⟩= 2qIgs∆f (2.6.2)

36


Igs is the measured gate leakage current.

The final noise source isIc. It represents distributed thermal noise in the channel,

and is the same as found by van der Ziel [3]

⟨I2c

⟩= 4kTΓgm∆f (2.6.3)

Γ is a bias dependent quantity. For a saturated GaN HEMT and most other FETs, it

is a constant value of2/3. It will be derived in detail in§ 2.6.3. All three mentioned

noise sources will be assumed to beuncorrelated, greatly simplifying the math.

The derivation of the noise parameters is also simplified if the source resistance

can be transformed up from the source node toRi. This is often done in device

small-signal circuit calculations through the use of source degeneration,2 illustrated

in figure 2.8. Source degeneration modifies the values ofCgs andgm as follows [31]

C ′gs =

Cgs1 + gmRs

(2.6.4)

g′m =gm

1 + gmRs(2.6.5)

with Rs, Cgs, andgm being values extracted from the device andC ′gs and g′m the

degenerate values that appear in figure 2.7 and the math that follows. These equations

hold forωC ′gsRs 1. The thermal noise ofRs, ERs, can be moved to the input with

the same condition thatωC ′gsRs 1. As is seen, the effect of this degeneration is a

reduction in the effectiveCgs, andgm. Because the gate-drain capacitance,Cgd, is not

2The technique is also called emitter degeneration, depending on if the device in question is a FETor BJT type of device.

37


Ri

Cgs

Drain

Source

Gate

gmvc

Vc

+

-

Rs

Ri+Rs

C'gs

Drain

Source

Gate

g'mvc

Vc

+

-

ERs

ERs

Figure 2.8: Cartoon showing the effect of source degeneration.

used in this model,Ri, Rg, andRs can be lumped together as one resistance, further

simplifying the derivation.

Several assumptions have been made. The most worrisome is neglecting the in-

trinsic feedback capacitance,Cgd. Pospieszalski has shown [1] at typical noise mea-

surement frequencies removingCgd from the modeling introduces only a small error

(less than the typical precision of a noise measurement setup). So long as the mea-

surements are made far enough from the devicefτ , it should not cause alarm. As an

example, a device with anfτ of 50 GHz will probably not be used for LNA applica-

tions greater than half the device unity current gain frequency. A derivation including

Cgd was carried out but the expressions were too complicated for insight to be gained

from them.

Another important assumption is that the noise sources are uncorrelated. It is not

38


being implied that physically all the noise processes are not influencing one another.

However, to have a simple enough and insightful model, it is a necessary assumption.

As mentioned earlier, it has already been shown that not using correlation can give

accurate results [1,32].

Finally, neglecting many of the extrinsic parasitics is a minor assumption. The

inductances (Lg, Ls, Ld) and capacitances (Cpgs, Cpgd, Cpds) do not affect the noise

parameters as much as the intrinsic parameters. This will be seen in§ 2.6.5. Also, the

thermal noise ofRd pales in comparison to the noise generated by the channel.

2.6.2 Derivation of Noise Parameters

A load,RL, signal generator (not a noise source),Vgen, and generator impedance,

Zgen = Rgen +Xgen, are added to the model, redrawn in figure 2.9. Also, for conve-

nience, the collected resistances are renamed to

Rin

Er

C'gs

Rdsg'mvc

Vc

+

-

IsIc

Rgen

Vout

+

-

RL

Xgen Egen

Vgen

Zin

Figure 2.9: Circuit model used for deriving noise figure.

39


Rin = Rg +Ri +Rs (2.6.6)

Assume for the moment that the input and output are matched for power:RL = Rds

andZgen = Z∗in. equation 2.4.1 can then be rewritten

F =(S/N)in(S/N)out

=

|Vgen|24Zgen

/〈vin,noisev∗in,noise〉

4Zgen

|AvVgen|24Rds

/〈vout,noisev

∗out,noise〉

4Rds

=1

|Av|2

⟨vout,noisev

∗out,noise

⟩

⟨vin,noisev

∗in,noise

⟩ (2.6.7)

with Av defined as the voltage gain,vsignal,out = Avvgen. An interesting point is

that because noise figure is a ratio of powers, the output and input match cancel in

equation 2.6.7. This does not mean that the source impedance has no effect on noise

figure nor that a matched load has no effect on the output power. It means that the ratio

of signal-to-noise at the input only or the output only is not affected by the matching

conditions.

We need to define the input noise voltage. This may be from an active device, or

it may be unknown, but the derivation depends only on signal-to-noise ratio and the

source impedance. Here thermal noise ofZgen, represented asEgen in figure 2.9, is

used. The input noise can be written as

⟨v2in

⟩= 4kTRgen (2.6.8)

The bandwidth (∆ f , assumed to be 1 Hz) will no longer be included. The noise figure

is now

F =1

|Av|2

⟨vout,noisev

∗out,noise

⟩

4kTRgen(2.6.9)

40


The output noise,vout,noise, will depend on the contributions from the individual in-

ternal noise sources in the device and the input noise. Because the HEMT is modeled

by a small-signal circuit with noise sources, the output noise can be calculated with

standard small-signal methods.

The easiest contribution to the output noise to calculate is the channel noise. It is

merely Ohm’s law,Ic(Rds||RL). Thevenin and Norton representations can be used

such that the voltage gains fromVgen, Egen, andEr to the output will be the same.

This is the gain of a common source configuration as found in circuit textbooks [31]:

Av =vout

Egen, Vgen, Er= −ωτ

ω

jRL||Rds

(Rgen +Rin) + j(Xgen − 1/(ωC ′gs))

(2.6.10)

with ω being the angular frequency (2π×frequency) and defining

ωτ = g′m/C′gs (2.6.11)

The other gain needed is the shot noise contribution. Using Norton and Th´evenin

equivalent circuits again, it is easily found.

As =voutIs

= −ωτω

jRL||Rds(Rgen + jXgen)

(Rgen +Rin) + j(Xgen − 1/(ωC ′gs))

(2.6.12)

As expected, it is similar toAv. The total output noise is then expressed as

vout,noise = Av(Egen + Er)− (Rds||RL)Ic +AsIs (2.6.13)

but what is needed is the spectral density, and thus, noise power. Taking the complex

conjugate, followed by a statistical average, gives

⟨vout,noisev

∗out,noise

⟩= |Av|2

(⟨E2gen

⟩+ 〈E2

r 〉)

+ | (Rds||RL) |2 〈I2c 〉

41


+|As|2 〈I2s 〉 + |Av|2

⟨ErE

∗gen

⟩+A∗

vRL||Rds

⟨IcE

∗gen

⟩

+ ... 10 other cross terms (2.6.14)

It is not possible to calculate the various correlations. Most cross-terms will be zero

(shot and thermal noise will not be correlated). For simplicity, all sources are assumed

to be uncorrelated. Equation 2.6.14 is then reduced to

⟨vout,noisev

∗out,noise

⟩= |Av|2

(⟨E2gen

⟩+⟨E2r

⟩)+ | (Rds||RL) |2

⟨I2c

⟩+ |As|2

⟨I2s

⟩

(2.6.15)

Finally, combining equations 2.6.8, 2.6.9, 2.6.10, 2.6.12, 2.6.13, and equation 2.6.15

we obtain an expression for noise figure:

F = 1 +Rin

Rgen+ b

R2gen +X2

gen

Rgen+

a

Rgen

∣∣∣∣∣Rin +Rgen + j

(Xgen −

1

ωC ′gs

)∣∣∣∣∣

2

(2.6.16)with

a = g′mΓ(ω

ωτ

)2

(2.6.17)

b =qIgs

2kTreference(2.6.18)

The factor of 1 is the input noise contribution to the noise figure. If the device does

not generate noise, noise figure would be 1. There would then be no degradation in

the signal to noise ratio going into and coming out of the device. Equation 2.6.16

describes the noise figure in terms of the match provided to the device, the device

small-signal parameters, and the measured gate-leakage. There are no fitting param-

42


eters. This is not the minimum noise figure. To determine it, we find the source

impedance that minimizes equation 2.6.16. This is found by taking partial derivatives

and solving equal to zero.

F = Fmin∣∣∣

∂F∂Rgen

=0, ∂F∂Xgen

=0(2.6.19)

This leads to the following expressions for the optimal source impedance that provides

the minimum noise figure:

Xopt =1

ωCgs

a

a+ b(2.6.20)

Ropt =

√√√√1 + aRin

a+ bRin +

ab

(a+ b)2

1

(ωCgs)2(2.6.21)

The last parameter, the noise resistance, can be obtained by using equation 2.4.3

and the equation for noise figure, 2.6.16, at two different source impedances. The

most convenient to choose are the minimum noise figure and when the source is at

its reference impedance,Γgen = 0. We shall call the laterFZ0. Entering this into

equation 2.4.3 and rearranging,

Rn =Z0

4(FZ0 − Fmin)

∣∣∣∣∣1 +1

Γopt

∣∣∣∣∣

2

(2.6.22)

An explicit expression is complicated. A Matlab script that implements all four of

the noise parameters can be found in appendix B. These equations will be discussed

43


more in§ 2.6.5, and used in chapter 3. For the moment, let us turn our attention to the

factorΓ, and the derivation of the channel noise source.

2.6.3 Derivation of Drain Noise Source

We will quickly go through the derivation ofΓ (and, therefore, the channel noise

source) to show that it is not a fitting parameter. Van der Ziel has shown the formula-

tion for a MOSFET [3]. Here, it will be explicitly done for a HEMT. The formulation

involves the DC drain current,Id, so it is needed as well. Assume for the moment that

the device is biased in the linear region (no velocity saturation). Following arguments

as found in [11,33], the drain current can be written in general as

Id = g(Vx)dVxdx

= qµWns(x)dVxdx

(2.6.23)

W is the device width (cm), ns(x) is the sheet charge of the 2DEG (cm−2), andµ

is the mobility(cm2

V s

). Vx is the potential difference at a distancex from the source,

relative to the source.g(Vx) is the channel conductivity per unit length at some point

along the channel, which depends onVx.

An expression is needed forns(x) in terms ofVx. First, an effective capacitance can

be defined [11,33]

C =Q

V=

εBd + ∆d

(2.6.24)

with εB andd being the dielectric permittivity and thickness of the AlGaN layer re-

spectively and∆d the centroid of the electron wave functions in the quantum well

44


(that is, the 2DEG). The charge of this capacitance isqns(x), with a voltage along the

channel ofVg − Vt − Vx. Vt is the threshold voltage. Combining all this together and

rearranging

ns(x) =εB

q(d+ ∆d)(Vg − Vt − Vx) (2.6.25)

and substituting into equation 2.6.23

Id =µεBW

d+ ∆d(Vg − Vt − Vx)

dVxdx

(2.6.26)

We can now define

g(Vx) =µεBW

d + ∆d(Vg − Vt − Vx) (2.6.27)

Its usefulness will soon be apparent.Id can now be found. Because of continuity, the

DC current entering and leaving the device must be the same. Integrating over the

length of the device,L,

∫ L

0Iddx = IdL =

∫ Vd

0g(Vx)dVx (2.6.28)

which gives

Id =µεBW

L(d + ∆d)

[(Vg − Vt)Vd −

V 2d

2

](2.6.29)

From this, the transconductance (gm)

gm =∂Id∂Vg

=µεBW

L(d + ∆d)Vd (2.6.30)

45


and the saturation current,Id,sat, can be found. The saturation current is found by

differentiating equation 2.6.29 with respect toVd and setting it equal to zero. This

returns the voltage ofVd that maximizesId, which we will callVd,sat. However, if the

device has a short channel, the velocity may saturate before the above condition. Then

the voltage that the current saturates is the lesser of the following two quantities:

Vd,sat = Vg − Vt (2.6.31)

or

Vd,sat = EcritLg (2.6.32)

Ecrit is the critical field strength andLg is the device gate length. Putting equa-

tion 2.6.31 back into equation 2.6.29, we find the saturation current resulting from

channel pinch off.

Id,sat =1

2

µεBW

L(d+ ∆d)(Vg − Vt)2 (2.6.33)

equation 2.6.29 only works for a device in the linear region until the device saturates,

Id = Id,sat. Beyond this, the current can be approximated to be the same asId,sat (if

short-channel effects are ignored).

We will follow the work of van der Ziel to derive the channel noise [3]. Assume

that a thermal voltage noise source,vn, creates a drain noise current fluctuation,∆Id,

along the distributed channel. This is shown in figure 2.10. The thermal noise source

can be written as

〈vnv∗n〉 =4kT

g(V )(2.6.34)

46


Similar to equation 2.6.23, we can write an expression for the drain current fluctua-

tions:

∆Id = g(V )dV

dx+ vng(V ) (2.6.35)

with V = Vx + ∆V (x, t). Separating the derivative and integrating gives

∫ L

0∆Iddx =

∫ L

0g(V )dV +

∫ L

0vng(V )dx (2.6.36)

An expression for the noise only is desired. If we consider the drain AC shorted, the

first term on the right of the equality in equation 2.6.36 will be zero. Continuing we

have

∆IdL =∫ L

0vng(V )dx (2.6.37)

Taking the spectral density we have

〈∆Id∆I∗d〉 =1

L2

∫ L

0〈vnv∗n〉 g2(V )dx =

4kT

L2

∫ L

0g(V )dx (2.6.38)

with the use of equation 2.6.35. The variable being integrated over,x, can be changed

to V through the use of equation 2.6.23. It is rearranged here as

dx =g(V )

IddV (2.6.39)

g(V)

Vx(x) + ∆Vx(x,t)

+_

Vx(x+∆x) + ∆Vx(x+∆x,t)

Id + ∆Id(t)Vn

+_ +_... ...

Figure 2.10: Cartoon used for deriving the channel noise.

47


Substituting and changing the limits of integration we arrive at the following key equa-

tion:

〈∆Id∆I∗d〉 =⟨i2d⟩

=4kT

L2Id

∫ Vd

0g2(Vx)dVx (2.6.40)

It is now clear the usefulness of knowingId andg(Vx) explicitly. Combining equa-

tions 2.6.27, 2.6.29, and 2.6.40 leads to an expression for the noise

⟨i2d⟩

= 4kTgmΓ (2.6.41)

with

Γ =1 − Vd

Vg−Vt+

V 2d

3(Vg−Vt)2

1− 12

Vd

Vg−Vt

(2.6.42)

When the device saturates, the value ofVd that saturates the current is used in

equation 2.6.42 instead of the value past saturation. Equation 2.6.42 then becomes

Γ = 2/3. A plot of Γ for different gate and drain biasings is in figure 2.11. A thresh-

old voltage of -6 V has been assumed. It can be inferred from this graph that a device

operating in the linear region has a largerΓ.

One final note: while there was no evidence of hot electron effects in devices pre-

sented in this chapter, van der Ziel mentions that they will change the expected noise.

Instead of equation 2.6.40, the following equation would have to be used [3]

⟨i2d⟩

=4kT

L2Id

∫ Vd

0Te(x)g(Vx)

2dVx (2.6.43)

Te is the effective electron temperature. He gives an empirical relationship for it in

48


0 1 2 3 4 5 6 7 80.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Vds (V)

Γ Decreasing Vg

Vg=0

Vg=-6

Figure 2.11: Variation inΓ for different drain and gate voltages. The gate voltage isvaried from -6 to 0 V by steps of 1 V. The threshold voltage is -6 V.

terms of the electric field relative to the critical field value:

Te(x) =(1 +

E

Ecrit

)n(2.6.44)

n is either 0, 1, or 2. If it is zero, then we have equation 2.6.40. This leads to values of

Γ a few times 1 (as opposed to less than 1 when n = 0).

2.6.4 Noise Parameter Scaling

To the above model, scaling can be added for varying gate width and number of gate

fingers. Simple linear scaling based on a starting device width of 150µm and 1 gate

finger was performed. This allows prediction for a comfortable range of usable gate

49


fingers and widths, but will not be accurate for large devices (1 mm or greater). Based

on [34], the following equations can be used to scale the small-signal parameters:

Rs,new = Rs,old/s1 Ri,new = Ri,old/s1 Rg,new = Rg,olds2

Cgs,new = Cgs,olds1 Igs,new = Igs,olds1 gm,new = gm,olds1

(2.6.45)

with

s1 =Wg,new

Wg,old(2.6.46)

s2 =Wg,new/n

2new

Wg,old/n2old

(2.6.47)

The parameters labeled asnew, are the values to be determined based on the un-

scaled extracted values, theold parameters.n is the number of gate fingers. The

simulated noise parameters versus gate width for a single fingered device are in fig-

ure 2.12. With increasing unity-gate width, the noise increases. However, the mag-

nitude of the optimal match decreases, which may make matching simpler. Also, the

noise resistance drops, making a design more robust in terms of the expected noise.

These predicted results agree with measurements in [17]. At small gate widths,Rs

andRi will be large and keep a lower bound on NFmin (not shown in figure 2.12).

The noise increases with a wider gate finger because of increasing gate resistance and

gate leakage current (Fα Igs, R2g in equation 2.6.16). So as the width increases, NFmin

goes from being limited byRs andRi to Rg andIgs. The noise parameters are also

simulated against number of gate fingers in figure 2.13. Due to layout constraints and

considerations for symmetric designs (particularly CPW implementations), the gate

50


0 200 400 6000.8

1

1.2

1.4

1.6

Gate Width (µm)

NF

min

(dB

)

0 200 400 6000.4

0.6

0.8

1

Gate Width (µm)

|Γo

pt|

0 200 400 6000

10

20

30

40

Gate Width (µm)

Ph

as

eΓ o

pt

[deg

.]

0 200 400 6000

2

4

6

Gate Width (µm)

r n

(a) (b)

(c) (d)

Figure 2.12: (a) Minimum noise figure, (b) magnitude and (d) phase of optimumsource reflection, and noise resistance (c) all versus total gate width. Simulation fre-quency is 5 GHz.

finger number was kept to even values or a single gate. The total gate width is kept

constant at 150µm. A change in this parameter for small devices does little to affect

the match or the noise resistance. In going from one to two gate fingers, there is a

slight improvement in noise figure. This can be explained solely by an improvement

in gate resistance. Beyond two fingers, there is little additional benefit. These scaling

51


results will be used in§ 3.5.4 and§ 3.5.5.

Therefore, the best geometry is a smaller total gate width, to keepRg andIgs from

becoming to large, and two or four gate fingers. Too small a device, andRs andRi

will be too large. Many papers published for best NFmin performance typically have

device widths of∼100µm .

0 2 4 6 8 100.85

0.9

0.95

1

Gate Fingers

NF

min

(dB

)

0 2 4 6 8 100.76

0.77

0.78

0.79

0.8

Gate Fingers

|Γo

pt|

0 2 4 6 8 1014

15

16

17

18

Gate Fingers

Ph

as

eΓ o

pt

(de

gre

es)

0 2 4 6 8 100.7

0.72

0.74

0.76

0.78

0.8

Gate Fingers

r n

(a) (b)

(c) (d)

Figure 2.13: (a) Minimum noise figure, (b) magnitude and (d) phase of optimumsource reflection, and noise resistance (c) all versus number of gate fingers for a con-stant total gate width.

52


2.6.5 Discussion of the Model

The model is now checked against measurements, compared to the other noise mod-

els, and its limitations are discussed. Figure 2.14 shows noise parameter data for the

35% device of table 2.1 and prediction using the model in Matlab and a circuit simula-

tion. The fit forall four parametersis very good for both the small-signal simulation

and the equations entered into Matlab. The small-signal simulation using ADS is for a

4 6 8 10 120.5

1

1.5

2

2.5

Frequency (GHz)

NF

min

(d

B)

4 6 8 10 120.55

0.6

0.65

0.7

0.75

0.8

Frequency (GHz)

|Γo

pt|

4 6 8 10 1210

20

30

40

50

60

Frequency (GHz)

An

gle

Γo

pt (

Deg

ress

)

4 6 8 10 120.5

0.6

0.7

0.8

0.9

1

Frequency (GHz)

r n

Figure 2.14: Noise parameters predicted using the model (solid line) and in a fullsmall-signal circuit simulation (dotted line) compared to measurements (crosses). Thesmall-signal parameters are from table 2.1.

53


full small-signal model (includingCgd) and noise sources as in figure 2.7. The phase

match ofΓopt with the Matlab script could be further improved by including the gate

inductance. Only the small-signal parameters and gate leakage were needed for the

Matlab script. The measured noise parameters were not needed beforehand as with

the Pospieszalski and CN models. This predictive power can help in better designs of

noise performance for devices, accurate estimations of the noise and the match to the

device, and understanding differences in noise performance for devices as performed

in chapter 3.

Of interest is how much different noise sources contribute to the overall noise figure.

This is presented in figure 2.15 using the model at an optimal bias for noise perfor-

mance. The channel thermal noise accounts for half the contribution to noise figure.

The resistances contribute roughly in proportion to their values relative to one another

as one might expect; they are all lumped together at the input. However,Rs effectively

degrades thegm andCgs through source degeneration and should be minimized. The

gate leakage contributes about 10% for a device with a reasonably low amount of gate

leakage. This can be a much larger contributer, and will be discussed in§ 3.5.4.

Some insightful parallels can be drawn between this modeling (equations 2.6.16,

2.6.20, 2.6.21 and 2.6.22), and Pospieszalski’s model (equations 2.5.11, 2.5.12, 2.5.13,

and 2.5.14). The simplest to see is thatXopt is the same for both models if the gate

leakage tends to zero. If the gate leakage is negligible, then the reactance of the match

54


53%

11%

Ri 18%

Rg 7%

Rs 11%

DrainNoise

GateShotNoise

Figure 2.15: Relative contributions of different noise sources to the overall noisefigure.

reduces to that predicted by both Pospieszalski and Fukui. Not as easy to see is that

Ropt is of similar form for both models ifb→ 0. The other two parameters cannot be

compared so easily. However, the modeledRn for both show that it increases slightly

with increasing frequency and both predict thatFmin depends on the square of the

frequency (which will be linear in plots of NFmin vs. frequency).

All the noise models discussed so far have a noise source at the gate and drain.

Table 2.3 shows typical input and output noise currents for the models. All the models

predict relatively the same magnitude of output noise. The models with correlation

show an input noise similar to one another, but two orders of magnitude smaller than

what Pospieszalski or this work predicts. This means that the cross-correlation terms

55


(see, for example, equation 2.6.14) generate more noise than the gate noise. That

the model introduced here generates noise similar to that of Pospieszalski helps to

reinforce its validity.

Model: van der Ziel Pucel Pospieszalski This Work

〈iinput〉2(10−24 A2

Hz

)5.0 7.2 3100 1370

〈ioutput〉2(10−24 A2

Hz

)490 480 300 490

Table 2.3: Comparison of the various noise models’ input and output noise currents.

The model can help in predicting NF, but it has its limitations. The most important

is the modeling fails when the gain drops because it does not take into accountCgd

or self-heating effects. This means it fails at frequencies close tofτ (f > fτ/2) and

at high DC biasings (Ids > 40 mA). A derivation withCgd was undertaken, but no

closed form solutions could be found for the noise parameters and the equations were

too complicated to yield insight. It is possible that the gain could be corrected using

the Miller effect [31].

Also, the small-signal parameters must be accurately known. The parasitics re-

sistances need to be correctly modeled and the measured S-parameters must be as

accurate as possible. For example, the modeling was found to be poor when superior

network analyzer was substituted with a less accurate network analyzer.

56


2.7 Summary

This chapter lead up to the presentation of a noise figure model that does not need

prior noise parameter measurements for accurate prediction. It will be used in other

parts of this work. All necessary background leading up to it was introduced, its

derivation presented in full, the model’s strengths and weakness explained, and how it

compares to the other popular noise models discussed.

References

[1] M. W. Pospieszalski, “Modeling of Noise Parameters of MESFET’s and MOD-FET’s and Their Frequency and Temperature Dependence,”IEEE Trans. Mi-crowave Theory Tech., vol. 37, no. 9, pp. 1340–1350, Sept. 1989.

[2] R. A. Pucel, H. A. Haus, and H. Statz, “Signal and Noise Properties of Gallium Ar-senide Microwave Field-Effect Transistors,” inAdvances in Electronics and Elec-tron Physics. New York: Academic Press, 1975, vol. 38, pp. 195–265.

[3] A. van der Ziel,Noise in Solid State Devices and Circuits. New York: Wiley-Interscience, 1986.

[4] J. B. Johnson, “Thermal Agitation of Electricity in Conductors,”Nature, vol. 119,pp. 50–51, 1927.

[5] H. Nyquist, “Thermal Agitation of Electric Charge in Conductors,”Phys. Rev.,vol. 32, pp. 110–113, 1928.

[6] C. Kittel and H. Kroemer,Thermal Physics, 2nd ed. New York: W. H. Freemanand Company, 2000.

[7] S. A. Maas,Noise in Linear and Nonlinear Circuits. Boston: Artech House, 2005.

[8] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.New York: Cambridge University Pess, 2004.

[9] M. J. Buckingham,Noise in Electronic Devices and Systems. New York: JohnWiley & Sons, 1983.

[10] B. G. Streetman and S. Banerjee,Solid State Electronic Devices, 5th ed., ser. SolidState Physical Electronics. Upper Saddle River, NJ: Prentice Hall, 2000.

57


[11] W. Liu, Fundamentals of III-V Devices: HBTs, MESFETs, and HFETs/HEMTs.New York: Wiley-Interscience, 1999.

[12] B. Hughes and P. J. Tasker, “Bias Dependence of the MODFET Intrinsic Model El-ements Values at Microwave Frequenices,”IEEE Trans. Electron Devices, vol. 36,no. 10, pp. 2267–2273, Oct. 1989.

[13] G. Dambrine, A. Cappy, F. Heliodore, and E. Playez, “A New Method for Deter-mining the FET Small-Signal Equivalent Circuit,”IEEE Trans. Microwave TheoryTech., vol. 36, pp. 1151–1159, Jul. 1988.

[14] P. H. Ladbrooke,MMIC Design: GaAs FETs and HEMTs. Boston: Artech House,Inc., 1989.

[15] M. Berroth and R. Bosch, “Broad-Band Determination of the FET Small-SignalEquivalent Circuit,”IEEE Trans. Microwave Theory Tech., vol. 38, pp. 891–895,Jul. 1990.

[16] R. Anholt, Electrical and Thermal Characterization of MESFETs, HEMTs, andHBTs. Norwood, MA: Artech House Publishers, 1994.

[17] H. Xu, “MMICs using GaN HEMTs and Thin-Film BST Capacitors,” Ph.D. dis-sertation, University of California, Santa Barbara, 2005.

[18] H. Rothe and W. Dahlke, “Theory of Noisy Fourpoles,”Proceedings of the IRE,vol. 44, pp. 811–818, Jun. 1956.

[19] G. Gonzalez,Microwave Transistor Amplifiers: Analysis and Design, 2nd ed. Up-per Saddle River, NJ: Prentice-Hall, Inc., 1997.

[20] M. J. Rodwell, “ECE 594F Class Notes, Noise in Electronics and Optoelectronics,”2000.

[21] A. van der Ziel, “Gate Noise in Field Effect Transistors at Moderately High Fre-quencies,”Proc. IEEE, vol. 51, pp. 461–467, Mar. 1963.

[22] ——, “Thermal Noise in Field-Effect Transistors,”Proc. IRE, vol. 50, pp. 1808–1812, Aug. 1962.

[23] S. Lee, “Intrinsic Noise Characteriestics of Gallium Nitride High Electron MobilityTransistors,” Ph.D. dissertation, Purdue University, Aug. 2004.


[25] S. Lee, K. J. Webb, V. Tilak, and L. Eastman, “Intrinsic Noise Equivalent-Circuit Paramters for AlGaN/GaN HEMTs,”IEEE Trans. Microwave TheoryTech., vol. 51, pp. 1567–1577, May 2003.

58


[26] H. Fukui, “Design of Microwave GaAs MESFET’s for Broad-Band Low-NoiseAmplifiers,” IEEE Trans. Microwave Theory Tech., vol. 27, no. 7, pp. 643–650,Jul. 1979.

[27] M. W. Pospieszalski and W. Wiatr, “Comments on ”Design of Microwave GaAsMESFET’s for Broad-Band, Low-Noise Amplifiers,”IEEE Trans. Microwave The-ory Tech., vol. MTT-34, no. 1, p. 194, Jan. 1986.

[28] S. Nuttinck, E. Gebara, J. Laskar, and M. Harris, “High-Frequency Noise in Al-GaN/GaN HFETs,”IEEE Microwave Components Lett., vol. 13, no. 4, pp. 149–151, Apr. 2003.

[29] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. York, “A C-Band High-Dynamic Range GaN HEMT Low-Noise Amplifier,”IEEE Microwave Compo-nents Lett., vol. 14, no. 6, pp. 262–264, Jun. 2004.

[30] C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. Mishra, andR. York, “Influence of Epitaxial Structure in the Noise Figure of AlGaN/GaNHEMTs,” IEEE Trans. Microwave Theory Tech., vol. 53, pp. 762–769, Feb. 2005.

[31] P. R. Gray, P. J. Hurst, S. H. Lewis, and R. G. Meyer,Analysis and Design ofAnalog Integrated Circuits, 4th ed. New York: Wiley, 2001.

[32] F. Danneville, H. Happy, G. Dambrine, J.-M. Belquin, and A. Cappy, “Microscop-ice Noise Modeling and Macroscopic Noise Models: How Good a Connection?”IEEE Trans. Electron Devices, vol. 41, no. 5, pp. 779–786, May 1994.

[33] M. Shur,Physics of Semiconductor Devices. Prentice Hall, 1990.

[34] J. M. Golio, Ed.,Microwave MESFETs and HEMTs. Norwood, MA: ArtechHouse, Inc., 1991.

59

3Noise Figure Measurements and Studies

3.1 Introduction

WITH the frame work for noise figure laid in the previous section, we now

concentrate on noise figure measurements of AlGaN/GaN HEMTs. The

technology used to fabricated the devices is presented first. The setup used for the

measurements will be discussed, and the methodology used for comparisons explained.

The bulk of this chapter is devoted to several noise figure studies of AlGaN HEMTs.

These studies look at how different epitaxial material and device structures affect the

noise figure performance. The effect of a field plate (FP) and gate leakage on noise

figure are profound, and will be covered in§ 3.5.4 and§ 3.5.5. The modeling devel-

oped in the previous chapter is used to understand how a FP and gate leakage affect

the noise performance. Another interesting type of GaN HEMT, known as a thick cap

HEMT, was measured and will be briefly covered. It is of great interest to know about

the state-of-the-art of GaN HEMT noise performance and how it compares to HEMTs

in GaAs and Si material systems. This is done in§ 3.6

60

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES

3.2 Device Details

Devices from several samples with different epitaxial structures will be discussed,

but they are similar from growth and processing points of view. The devices were

all grown by metal-organic chemical vapor deposition (MOCVD) on both c-plane

sapphire and c-plane 4H-SiC substrates. The epitaxial structures that will most com-

monly appear in this work are in figure 3.1, which will be referenced throughout the

chapter. The key differences in the samples are choice of substrate (sapphire or SiC)

and inclusion of an AlN interlayer between the AlGaN barrier and the GaN channel.

29 nm 27% AlGaN: Si

1700 nm UID GaN

65 nm AlN

750 nm GaN: Fe

Sapphire Substrate

(a)

29 nm 35% AlGaN: Si

0.6 nm AlN

1700 nm UID GaN

65 nm AlN

750 nm GaN: Fe

Sapphire Substrate

(b)

29 nm 27% AlGaN: Si

1300 nm UID GaN

300 nm GaN: Fe

160 nm AlN

SiC Substrate

(c)

Figure 3.1: Typical epitaxial structure for the devices in this work: (a) standard HEMTon a sapphire substrate (b) HEMT with AlN interlayer (c) standard HEMT on silicon-carbide substrate

After choice of substrate, growth consists of a nucleation layer. This layer may in-

clude iron (Fe, an accepter) in it, as in figure 3.1 (a), to reduce the buffer conductive

(caused by unintentional doping). The decrease in conductivity improves the break-

down of the device for power applications. An unintentionally doped GaN layer grown

61


next will be the channel, and a 29 nm AlGaN Si-doped layer finishes the structure. The

Al composition varies with the sample, but is 27 % if not stated explicity.

Device processing began with Ti/Al/Ni/Au electron beam evaporated source and

drain contacts. These were annealed at 870C for 30 s in a rapid thermal annealer

(RTA). Device isolation was achieved by reactive ion etching (RIE) in Cl2. Stepper

photolithography Ni/Au/Ni gates were electron beam evaporated with a gate length of

0.7µm. SiN passivation was achieved with plasma-enhanced chemical vapor deposi-

tion (PECVD). If a field plate is used, it would now be added as a repeated and slightly

shifted gate metal layer. All devices in this chapter have a gate width of 1x150µm,

a gate-source spacing of 0.7µm, and a gate-drain spacing of 2µm. The pads are a

coplanar waveguide (CPW) layout.

Typical measurements of fτ and fmax are 23 and 47 GHz respectively. Contact

resistance is from 0.3 to 0.6Ω–mm. Charge and mobility vary with the Al composition

of the barrier. For compositions ranging from 15 % to 35 %, the mobility was found

to be 1100-1565 cm2/Vs and the charge 0.4-1.3x1013 cm−2 by Hall measurements.

More details about the device details and processing can be found in [1–4].

3.3 Noise Figure Measurement Setup and Method

Noise figure measurements were performed with a PC–controlled source–pull noise

figure setup. A schematic is in figure 3.2. At the heart of the system is the noise figure

62


NoiseSource

SourceTuner

LoadTuner

RF ProbeStation

Computer

TunerController

BiasController

NetworkAnalyzer

NoiseFigureMeter

BNCCable

Bias-TBias-T

RFSwitch

RFSwitch

GPIBCable

Figure 3.2: Schematic of the source-pull noise figure setup.

meter, noise source, and source tuner. The HP 8970S noise-figure meter system con-

sists of the HP 8970B noise figure meter, HP 8970C test set, and a signal generator

that acts as a local oscillator for the 8970C. Typical error is±0.15 dB. To find the de-

vice minimum noise figure, a variable source impedance is generated by a Maury Mi-

crowave MT982A02 mechanical motorized tuner. The load tuner was set to 50Ω. The

device gain during measurement could have been improved by moving the load tuner

63


to a small-signal match, but due to a combination of hardware and software problems

better measurements were obtained with it at the reference impedance. However, the

software automatically calculates the gain for a noise input match and power output

match.

The device S-parameters at each bias are needed. A Maury Microwave MT998C

RF switch box and an HP 8722D vector network analyzer (VNA) made it possible to

seamlessly switch between noise and S-parameter measurements of devices. All mea-

surements were performed on-wafer with Cascade-Microtech ACP40 ground-signal-

ground CPW probes. The bias was set automatically by an HP 6625A DC–power

supply system. All components were controlled over a general-purpose interface bus

(GPIB) by a Maury Microwave proprietary software program which calculates the

noise parameters.

The accuracy of the system was checked in two ways. The first was by measur-

ing devices that were characterized elsewhere. The second was fabrication of CPW

on-wafer 10 dB attenuators alongside devices and circuits. The schematic and a pho-

tograph of the attenuator are in figure 3.3. Figure 3.3 (c) shows the measured loss and

minimum noise figure (NFmin). A passive device’s loss and NFmin will be the same in

decimals. As can be seen, the agreement is good.

To make NF comparisons, several factors need to be taken into consideration. First,

devices across a GaN wafer are not uniform due to the quality of research-grade mate-

64


In

Out

GroundGround

R1

R1

2R22R2

4 5 6 7 8 9 10 11 12 13 14 159

9.2

9.4

9.6

9.8

10

10.2

10.4

10.6

10.8

11

dB

Frequency (GHz)

NFmin

Loss

R1R1

R2

In Out

(a)

(b) (c)

Figure 3.3: Coplanar waveguide attenuator (a) schematic, (b) photograph, and (c)measured loss and minimum noise figure against frequency.

0 20 40 60 80 100 120 140

1.3

1.4

1.5

1.6

1.7

1.8

1.9

F

(un

itle

ss)

Current (mA)

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

(1/G

Hz)

F

1/fτ1/fmax

0 20 40 60 80 100 120 140

1.2

1.4

1.6

1.8

2.0

2.2

F

(un

itle

ss)

Current (mA)

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

(1/G

Hz)

F

1/fτ1/fmax

Figure 3.4: Noisefactor, fτ and fmax for devices from different samples versuscurrent.

65


rial and growth reactors. These variations across a sample cause changes in the device

small-signal parameters and therefore in the fτ and fmax . Noise has a relationship to

fτ and fmax such that improvements in one of the quantities usually means an improve-

ment in the others. Figure 3.4 helps this argument. Here the inverse of fτ , inverse of

fmax, and noise factor, F (NF = 10 log10(F)), are plotted for devices from two samples

as the drain-source current is changed. As the current increases, all three parameters

increase. There appears to be a close relationship between F and 1/fmax. This relation-

ship can be seen from the modeling in the previous chapter. fτ and fmax are usually

defined as

fτ =gm

Cgs + Cgd(3.3.1)

fmax = fτ

√Rds

4(Ri +Rg)(3.3.2)

Examining the last term in equation 2.6.16, we see a factor 1/ω2tau that is very similar

to equation 3.3.1. An exact instance of fmax is not seen in equation 2.6.16 (there is no

Rds), but there is some similarity. The use of source degeneration, as demonstrated in

§ 2.6.1, modifiesCgs andgm. This would affect fτ , fmax, and thus NFmin. That NFmin

would depend on fmax instead of fτ also makes sense from a power argument: noise

figure and fmax are based on power quantities while fτ is a current gain quantity. The

conclusion of this aside is that devices with similar fτ and fmax should have similar

noise.

Device geometry is also important when making comparisons. As seen in§ 2.6.4,

66


a wider device has a larger NFmin. Also, a device of smaller gate length usually has

better fτ and fmax. For a fair comparison then, only devices of the same geometry

should be compared.

Finally, there is the matter of device bias. As the DC bias to the transistor is changed

the noise parameters also change. The optimum bias for NFmin may change with

devices from different samples. In all measurements in this work, the bias is swept

twice, firstVds thenIds, to find the best NFmin performance possible for the device.

It is better to sweepIds thanVgs as the threshold voltage changes across a sample.

The transistor’s noise parameters were then measured versus frequency at this bias. It

should be noted that the best bias for noise may not be the same as that of fmax, but it

is a good starting value.

To show the importance of having similar devices to NF, Rs, Ri, and Cgs variations

were simulated over the range of extracted values and entered into the model of chap-

ter 2. The results of this are in figure 3.5. Each parameter spans a change of NFmin of

0.2 to 0.3 dB. All measurements in this work are at a bias and source-impedance for the

best NFmin attainable from the device. For measurements versus bias, a frequency was

used that gave the most stable and repeatable measurement (usually 5 GHz, sometimes

10 GHz). As the bias was changed, S-parameters were re-measured and the optimum

source-impedance re-evaluated. When comparing devices from different samples, fτ

and fmax measurements were first performed to find devices with similar performance.

67


3 4 5 6 7 8 9 10 11 12

1.7

1.8

1.9

2.0

2.1

2.2

NF

min

(dB

)

Ri

Rs

Resistance (Ω)

0.20 0.21 0.22 0.23 0.24 0.25

Capacitance (pF)

Cgs

Figure 3.5: Variation in expected minimum noise figure with changes in three small-signal parameters.

3.4 Bias Dependence

Transistors in Low Noise Amplifiers (LNA) are biased at low currents and voltages

for maximum NF performance and to reduce power consumption. A GaN HEMT

biased at a “low” bias is likely beyond the breakdown of other material technologies.

Therefore, it is of interest to know how the noise parameters change with device bias,

which leads to some interesting results in this work. Also, knowing how the noise

changes with bias is necessary for noise sources extracted from NF measurements

that are included in device circuit simulations for oscillator phase noise.

Figure 3.6 displays all four noise parameters, the associated gain, and maximum

gain at a frequency of 10 GHz for drain-source voltages,Vds, 2 to 20 V. The drain-

68


Figure 3.6: Change in noise parameters with drain-source voltage at 10 GHz: (a)Minimum noise figure (b) magnitude and phase of optimum reflection coefficient (c)noise resistance (d) device associated and maximum gains.

69


source current,Ids, is kept constant at the best bias for NFmin. The small-signal asso-

ciated power gain is that available when the input is matched for noise and the output

for power. The maximum gain is of a small-signal input and output conjugate match.

NFmin flattens out aboveVds ∼3 V. The other noise parameters are nearly flat, except

for the phase which decreases slightly. This is probably from a slight change inCgd

with Vgd. From these measurements, it can be concluded that once the device saturates

the noise parameters can be considered constant.

What is more interesting is how the noise parameters change with the drain-source

current. The measured noise parameters of this are the solid circles in figure 3.7

for a sample with a sapphire substrate and 35 % Al in the barrier at a measurement

frequency of 5 GHz. Now we find that NFmin andrn increase with current. NFmin does

not increase because of a large increase in device noise. The reason is that the gain

drops with the increasing current. The gain is lower because the channel is opened

(loss of transconductance) and self-heating (from the high currents involved). That

the gain affects the noise figure directly is seen in equation 2.6.9. The magnitude

of the optimum source reflection coefficient,Γopt, decreases with increasing current

while its phase decreases. This is a result of the match changing with loss of gain and

increasingCgs.

To further investigate the usefulness of the Pospieszalski and CN models, they

were applied to these noise measurements. Measurements of fτ and fmax (needed

70


(a) (b)

(c) (d)

Figure 3.7: Typical plots of the noise parameters versus drain source current as mea-sured (circles) and using the Pospieszalski (dash-dot line) and CN (solid line) models:(a) Minimum noise figure (b) magnitude of optimum reflection coefficient (c) noiseresistance (d) and phase of optimum reflection coefficient. Measurement frequency is5 GHz.

71


for Pospieszalski’s formulation) and extracted small-signal parameters were collected

at each bias the noise parameters were measured at in figure 3.7. Then, using meth-

ods in§ 2.5, a small-signal model with noise sources from either Pospieszalski’s or

the CN formulation were created in ADS. ADS was then used to simulate the noise

parameters. The results were added to figure 3.7. The solid lines are simulations us-

ing the CN model and the dash-dot lines using the Pospieszalski model. Both models

predict the noise parameters for the GaN HEMT versus bias well and can be used for

bias-dependent noise parameter modeling of GaN HEMTs.

The modeling in§ 2.6 does not work to predict the noise parameters versus bias.

It only works at low biasings (Ids < ∼40 mA in this work) because it does not take

into account reduction in gain from self-heating. Because the Pospieszalski and CN

models are fitting to the data at these high biases, they predict the noise parameters

correctly. However, the model can still be used to explain trends seen in the noise

parameters versus bias. Equation 2.6.22 shows that as NFmin increases and|Γopt|

decreases with increasing current, thenRn should increase as well.

Figure 3.8 shows how the noise variables used for the simulations in figure 3.7

change with bias. These variables are the quantitative values of noise sources entered

in a circuit simulator, such as ADS. For example: shot noise changes with DC cur-

rent, thermal noise changes with resistance, and a Pospieszalski thermal noise source

changes with the noise temperature. We see in figure 3.8 (a) that the correlation coef-

72


(a)

(c)

(b)

Figure 3.8: Noise variables for the Pospieszalski and a CN noise model versus drainsource current: (a) magnitude and phase of the correlation coefficient and (b) gate anddrain noise for a CN model. The devicegm, multiplied by a factor of 10 to better fitthe scale, is also in (b). (c) Drain and gate noise temperatures of the Pospieszalskimodel for varying current.

ficient magnitude and phase are relatively flat versus current. This supports the work

of S. Lee on GaN HEMTs [5,6]. After detailed analysis using the CN model, Lee con-

cluded that the correlation coefficient could be considered constant with a magnitude

73


of 0.7 and phase of 90 after de-embedding extrinsic thermal and shot noise. Here,

we see the same magnitude but a slightly higher phase. The increase in phase is likely

from the shot noise of the gate leakage. While Lee’s results were only versus fre-

quency, we see here that it holds versus bias as well. To the author’s knowledge, there

is no reference in the GaN literature that has the noise variables using the CN model

versus bias. We might expect the input and output noise currents in figure 3.8 (b) to

behave as van der Ziel predicts in equations 2.5.1 and 2.5.2. Then the drain noise,

〈i2d〉, should follow changes ingm versus bias. Ten times the value ofgm (for the con-

venience of plotting) is also in figure 3.8 (b).〈i2d〉 appears to follow the same trend.

The gate noise,⟨i2g⟩, also seems to follow what van der Ziel would predict (aC2

gs/gm

dependence).

Turning to the Pospieszalski model in figure 3.8 (c), the two noise temperatures are

plotted againstIds. The gate noise temperature is relatively flat. This agrees with the

one GaN reference in the literature [7], and what is seen in GaAs HEMTs. Here, the

drain noise temperature drops. This is the opposite of what would be expected but is

easily explained. The sapphire sample the device was on did not have a good buffer,

makingRds low (less than 1 kΩ instead of∼1.5 kΩ). As the current increased,Rds

dropped off dramatically (900Ω to 100Ω). The termTd/Rds is prevalent through

Pospieszalski’s equations. In fitting to the data,Td decreased along withRds to keep

the correct proportion. In other samples with a good buffer (only a slight drop inRds),

74


Td will increase.

3.5 GaN HEMT Noise Figure Studies

3.5.1 Substrate

The effect of substrate on the noise parameters was carried out on samples with

SiC and sapphire substrates having 25% Al in the barrier and structures similar to

figure 3.1 (a) and (c). Versus frequency, devices from both samples had very similar

Figure 3.9: Minimum noise figure, small signal associated and maximum gain fordevices on sapphire and SiC substrates.

75


noise parameters. As the current was varied, a difference in performance of NFmin

emerged. Figure 3.9 shows that the sapphire sample had worse noise figure perfor-

mance at higher biasings. At 100 mA, the difference is more than 0.5 dB. Also plotted

are the associated and max gains for both devices shown. The sapphire sample gains

fall much quicker as the bias increases. As stated earlier, if the gain drops then the

noise figure will too. Devices on sapphire have degraded power performance at high

biasings because of self-heating. Here, we see it affects noise figure performance as

well. A previous study confirms the noise degradation is caused by self-heating with

temperature dependent measurements [8].

3.5.2 Al Composition in the Barrier

To investigate if changing the Al composition in the AlGaN barrier had an effect

on noise, four samples were grown with 15%, 25%, 27%, and 35% Al on a sapphire

substrate. The rest of the structure for all four samples was the same as in figure 3.1 (a).

Lu previously published this study for GaN HEMTs [9]. He found that devices of high

Al composition (35 %) had better noise performance than low Al composition (15 %).

However, the reported fτ and fmax for the samples were not similar. fτ increased with

higher Al composition from 25 GHz to 50 GHz and fmax increased from 55 GHz to

101 GHz. The four samples in this study had reasonably similar fτ and fmax. Noise

parameters of the four samples for changing frequency are plotted in figure 3.10. Also,

76


3 4 5 6 7 8 9 10 11 12 13

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

3 4 5 6 7 8 9 10 11 12 130.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

3 4 5 6 7 8 9 10 11 12 136

8

10

12

14

16

(b)(a)

35% 27% 25% 15%

NF

min

Frequency (GHz)

(d)

r n

Frequency (GHz)

4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

Frequency (GHz)

|Γ|

0

20

40

60

80

100

120

140

160

180

35% 27% 25% 15%

Ph

as

e

Γ

(De

gre

es)

(c)

Ga

in

(dB

)

Frequency (GHz)

Figure 3.10: Noise parameters versus frequency for devices of different aluminumcomposition in the barrier: (a) Minimum noise figure (b) magnitude and phase ofoptimum reflection coefficient (c) noise resistance (d) device associated gain.

77


0 20 40 60 80 100 120 140

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

NF

min

(dB

)

Current (mA)

35% 27% 25% 15%

Figure 3.11: Minimum noise figure of samples with different aluminum compositionin the barrier at varying drain-source current.

NFmin for the samples versusIds are in figure 3.11. The data are astonishingly similar

for noise measurements, and challenge the previous report. The application of the CN

and Pospieszalski models to these devices, presented earlier in table 2.2, also agrees

that the noise parameters should be very similar. It is interesting that the drain-source

current bias for best NFmin was similar for the different samples (15±5mA). For the

15 % Al sample this was nearly halfIds,sat while only 8 % Ids,sat for the 35 % Al

sample.

3.5.3 AlN Interlayer

The addition of an extremely thin (one or two monolayers) AlN layer between the

GaN channel and the AlGaN barrier has been found to increase the conduction-band

78


0 20 40 60 80 100 120 140

1.0

1.5

2.0

2.5

3.0

3.5

4.0

NF

min

(d

B)

Current (mA)

NFmin

AlN NF

min no AlN

fτ AlN

fτ no AlN

fmax

AlN f

max no AlN

0

5

10

15

20

25

30

35

40

45

F

req

ue

nc

y

(GH

z)

Figure 3.12: Minimum noise figure, fτ , andfmax versus drain-source current for asample with (squares) and without (circles) an AlN interlayer.

offset, better confining the 2-DEG and improving mobility [10]. This should improve

the device fτ and fmax. It is therefore worth determining if it improves the noise

performance as well. Samples with structures as in figure 3.1 (a) and (b) with 35%

Al in the barrier on sapphire substrates were measured for noise. Overall, devices on

the sample with the AlN-interlayer had fτ and fmax values marginally higher than the

sample without. However, for the noise measurements devices with as similar of fτ

and fmax as could be found were used.

There were no differences in the noise parameters versus frequency, but as the drain

current increased a large difference in NFmin was apparent. This is in figure 3.12 as

the solid symbols. At a current of 100 mA, there is a 0.4 dB difference and at the

79


0 10 20 30 40 50 60 70 80 90

6

8

10

12

14

16

18

20

22

24

26

with AlN interlayer without AlN

Rs

(Ω)

Current (mA)0 20 40 60 80 100 120 140

2

4

6

8

10

12

14

16

Gain AlN layer Gain no AlN Gmax AlN layer Gmax no AlN

(dB

)

Current (mA)

(a) (b)

Figure 3.13: (a) Associated and maximum gain and (b) source resistance for deviceswith and without an AlN interlayer at different applied currents.

max current a 0.8 dB difference. While the gain (figure 3.13 (a)), fτ , and fmax (also

in figure 3.12) do drop off slightly faster for the sample without the AlN, it is not as

dramatic as the sapphire/SiC substrate comparison and not enough to explain such a

large NFmin difference.

Rs appears to be the cause of the difference. Palacios has shown thatRs increases

drastically with drain-source current [11]. Figure 3.13 (b) shows the measured source

resistance (using the method in [11]) for devices from both samples. The devices with

the AlN-interlayer see anRs increase of about two times, while the devices without

the interlayer see an increase of three times. TheseRs measurements are only out to

80 mA (equipment limitations), instead of 135 mA as in figure 3.12. The difference

in Rs would be even larger at higher biases. As seen with the modeling using source-

degeneration in chapter 2,Rs can be thought of as directly adding noise at the input,

80


which increases the noise.

As mentioned, devices on the sample with the AlN-interlayer overall tend to have

higher fτ and fmax. These devices will have a slightly better NFmin. However, the

improvement is at best 0.1 dB in the X-band.

3.5.4 Gate Leakage

While trying to do a comparative study, devices from a sample (27% Al content

barrier with SiC substrate) that had similar fτ and fmax did not have similar NFmin.

In fact, NFmin differed by almost 1 dB despite the gains being identical as seen in

figure 3.14. It was realized that the gate leakage was very different for the three devices

in figure 3.14. The three terminal gate leakage, Igs, at a bias of Ids = 10 mA, Vds = 5 V

for the devices was found to be: 22µA (or 140 µA/mm); 73 µA (or 486 µA/mm);

141µA (or 940µA/mm). The devices are labeled as such in figure 3.14. We see that

as the gate leakage increases, so does the noise figure. To explore how gate leakage

affects the noise parameters, the modeling in§ 2.6 was used. Small-signal parameters

that approximately matched all three devices in figure 3.14 were entered into Matlab

using the script in appendix B. The gate leakage was swept from10−8 to 10−2 A and

the calculated noise parameters plotted (as lines) in figure 3.15 with data (crosses) for

the devices in figure 3.14. The circles are data from another sample that exhibits an

expected amount of gate leakage. The agreement of simulation and data for NFmin

81


Figure 3.14: (a) Minimum noise figure, (b) device associated gain, and maximum gainversus frequency for devices with different gate leakage currents. The gate leakagequoted is at the same bias as the noise measurements (Ids = 10 mA, Vds = 5 V).

is excellent. The other parameters do not agree perfectly, but it should be reiterated

that the small-signal parameters used were typical for all three devices (they were not

identical). No change inrn was predicted or measured.

Gate leakage has a large effect on the noise parameters. It must be monitored, along

with fτ andfmax, when measuring noise figure of GaN devices. While gate leakage

and NFmin have been studied previously [6, 12–14], these studies are all lacking in

at least one of the following ways: use of fitting, inadequate data, only predicting

NFmin, or not applied to GaN. The combination of analytical modeling (without fitting

parameters), data presented, and agreement of modeling and data here is unique and

82


10-8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

1

2

3

4

5

Igs

(A)

NF

min

(d

B)

10 -8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

0

0.2

0.4

0.6

0.8

1

Igs

(A)

|Γo

pt|

10 -8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

20

40

60

80

100

120

140

Igs

(A)

Ph

as

e Γ

op

t (d

eg

res

s)

10 -8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Igs

(A)

r n

(a) (b)

(c) (d)

Figure 3.15: Simulated (line) and measured (crosses) noise parameters for deviceswith different gate leakage currents: (a) Minimum noise figure (b) magnitude of op-timum reflection coefficient (c) noise resistance (d) phase of optimum reflection co-efficient. Frequency is 10 GHz. The circles are data from another sample with thetypically expected amount of gate leakage.

clear.

A final note: GaN HEMTs on MBE were measured by the author. Their power and

small-signal performance are comparable to MOCVD-based HEMTs, but the devices

had higher gate leakage and thus∼0.15 dB more noise.

83


3.5.5 Field-Plated Devices

The addition of a FP has led to GaN HEMTs having impressive power handling

capability at microwave frequencies [15, 16]. There is a penalty, which is shown in

figure 3.16.1 A FP increasesCgd, and that reduces fτ and fmax. In fact, the longer

the FP, the higher the breakdown and lower the fτ , fmax , and gain of the device. The

author decided to investigate the noise performance. Based on the studies presented

thus far, one would predict that a FP device would have worse NF performance.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

15

20

25

30

35

40

45

50

55

60

fτ fmax

Fre

qu

en

cy

(G

Hz)

Field-Plate Length (µm)

Figure 3.16: fτ and fmax of devices with different field-plate lengths.

This turned out not to be the case. Figure 3.17 (a) demonstrates that as the FP

length increases the NFmin improves despite decreasing gain (Figure 3.17 (d)). The

1For all measurements in this section, the devices with different FP lengths are on the same die of asample.

84


4 6 8 100.8

1.0

1.2

1.4

1.6

1.8

4 6 8 10

0.4

0.6

0.8

1.0

1.2

4 6 8 10

4

6

8

10

12

14

1.1 µm 0.9 µm 0.7 µm 0.5 µm None

1.1 µm 0.9 µm 0.7 µm 0.5 µm None

NF

min

(d

B)

Frequency (GHz)4 6 8 10

0.0

0.2

0.4

0.6

0.8

(a)

(c)

Frequency (GHz)

20

40

60

80

100

120

140

160

180

Ph

as

e

Γ

(de

gre

e)

(d)

(b)

r n

Frequency (GHz)

Ga

in

(dB

)

Frequency (GHz)

|Γ|

Figure 3.17: Noise parameters versus frequency for devices with field plates of differ-ent length: (a) Minimum noise figure (b) magnitude and phase of optimum reflectioncoefficient (c) noise resistance (d) device gain when matched at the input for best noiseperformance and the output for power performance.

85


improvement is almost 0.2 dB. There is little additional improvement for a FP longer

than 0.9µm. The match changes monotonically with the FP in Figure 3.17 (b). The

improvement in NF with a FP was first reported by the author in [17] and was later

confirmed in [18].

Several explanations to understand this result were explored. The first was to look

at the gate leakage. It was thought that maybe the FP was reducing the electric field

and possibly the gate-drain contribution to gate leakage. The three and two-terminal

gate leakage of 100µm wide devices with different FP lengths was measured. Some

of the three-terminal measurements are in figure 3.18. The bias was set toVds 5 V

(similar to noise measurements) andVds 20 V (a low bias for power) andVgs a volt

past the threshold voltage. It does not appear that the FP lowers gate leakage. In fact,

it appears to increase slightly with the FP.

Another thought was that perhaps there was a difference in electric field causing a

change elsewhere than gate leakage. The analysis ofΓ in § 2.6.3 was examined to see

if it might change because of a FP. This proved to not be true. A change inΓ would

mean a change in the DC I–V characteristics of a FP from a non-FP device. The only

real change is that the knee voltage is better defined for a FP device [19]. That would

only causeΓ to go to its final value of 2/3 quicker. More proof that it was not the

electric field-profile was found by two other means. One was to look at NFmin versus

drain source voltage. No difference was apparent. Another was to run an ATLAS

86


0.0 0.2 0.4 0.6 0.8 1.0 1.2

0

100

200

300

400

500

600

700

, Vds

20 V, V

ds 5 V

Gate

L

eakag

e

(µA

)


Figure 3.18: Typical change in gate leakage for devices of increasing field-platelength. Biasings areVds 5 V, Ids 10 mA andVds 20 V,Vgs one volt past threshold.

0.0 0.5 1.0 1.5 2.0 2.5

0.0

2.0M

4.0M

6.0M

Ele

ctr

ic

Fie

ld

(V/c

m)

Distance (µm)

no FP, Vds 5 V no FP, Vds 20 V FP, Vds 5 V FP, Vds 20 V

Figure 3.19: Electric field profile for a device with and without a FP at a bias ofVds 5and 20 V with the gate biased close toVt. The gray bars are the “physical lengths” ofthe gate and field plate. Atlas simulation provided by Yuvaraj Dora.

87


simulation and look at the difference in the electric field profile. This was done, and

the results are in figure 3.19.2 The simulations atVds 5 and 20 V show the total electric

field versus distance. The gate is biased close to the threshold voltage, as is the case

for best NFmin results. The bars sitting atop the x-axis represent the gate length (short)

and FP (long) lengths. While the peak electric field at the drain edge of the gate will

be significantly reduced when a HEMT is biased to 80 V or more, here for 5 and 20 V,

there is no difference. In fact, atVds 5 V, there is practically no change in the field.

The small-signal parameters were also examined. Those that were found to change

with a FP are in figure 3.20.Cgd increases because of the extra capacitance the FP

provides. ThatRgd decreases hints that it is either easier to chargeCgd or that the

leakage has increased the conductance between gate and drain.Rd decreases because

the effective distance between gate and drain is reduced by the length of the FP.Ri

does not appear to change. Any change in it is probably due to error in the small-signal

extraction having difficulty differentiatingRg andRi. As the gate now has another set

of fingers in parallel, its resistance, and thusRg, decreases. The FP and gate fingers

can be connected at their ends, further reducing gate resistance and the noise [20].

When trying to explain FP device NF performance, it was first thought thatRg was

the cause. However, the modeling at the time argued that the improvement inRg was

not enough to cause the difference, particularly for the results in [18]. It was later

realized the devices and the modeling were not the same. Devices of different widths,

2ATLAS simulation graciously provided by Yuvaraj Dora to the author’s specifications

88


0.0 0.2 0.4 0.6 0.8 1.0

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

R

gd

(Ω)

Cg

d

(fF

)

Field-Plate Length (µm)0.0 0.2 0.4 0.6 0.8 1.0

1

2

3

4

5

6

7

8

15

16

17

18

19

Rd Ri Rg

Re

sis

tan

ce

(Ω)


Figure 3.20: Small-signal parameters that change with a field plate.

and with/without the FP plus gate ends shorted, were being compared. The scaling

and modeling of chapter 2 were used yet again. How NFmin changes with gate width

for devices with and without a FP were simulated in Matlab and compared to the

author’s and Wu’s [18] measurements. Figure 3.21 makes this clear. The agreement

is very good, and it can now be concluded that the FP lowering the gate resistance

is what improves NFmin. That NFmin decreases despite the lower gain is because the

FP is acting as an external feedback capacitance between gate and drain (in parallel

with Cgd). Lossless feedback does not harm the noise figure, but it does lower the

gain [21]).

The reduction in NF does not justify the use of a FP as it reduces the gain consider-

ably (several decibels). Gain is in short supply at microwave frequencies and reducing

it so much may not justify NFmin improvement of just a few tenths of a decimal. In

89


0 50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

Gate Width (µm)

NF

min

(d

B)

No FP

Long FP

Difference

Figure 3.21: Minimum noise figure versus gate width for devices with and without along field plate at a simulation frequency of 10 GHz. The difference between them, indecimals, is plotted as the dotted line. The “x’s” are from this work (150µm ) and Y.Wu (243µm ) [18].

0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

NF

min


4 GHz 7 GHz 10 GHz

Figure 3.22: Minimum noise figure of the field-plated devices at different measure-ment frequencies of 4, 7, and 10 GHz. As the frequency increases, the improvementfrom a field plate decreases.

90


addition, the benefit is reduced the higher the operating frequency because of the skin

effect on the gate resistance. This is demonstrated in figure 3.22. At 4 GHz, the im-

provement can be as much as 0.3 dB, but at 10 GHz the improvement is 0.1 dB. This

agrees with the results in [18].

3.5.6 Thick-Epitaxial Cap Devices

Shen has proposed a HEMT with a thick GaN cap on top of the AlGaN [22]. The

advantage of this structure is that a SiN passivation is not needed. As passivation

leads to problems of reliability for standard HEMTs, this new HEMT holds great

promise. It has the record for power performance without passivation. Its small-signal

characteristics are similar to standard HEMTs. Dr. Shen allowed the devices to be

measured for noise. The performance was similar versus frequency (in particular,

the gains), although the drain-source current needed to be higher for optimum noise

performance. The reason for this is clear after viewing the noise parameters versus

bias in figure 3.23. The cap devices have a NFmin optimum bias at 45 mA instead of

10 mA as seen with normal HEMTs.Rn and NFmin follow remarkably similar trends,

further reinforcing arguments made earlier in the chapter. NFmin for the thick cap is

much lower at higher biasings than a standard HEMT, but is higher at low biasings.

The reason for this is likely the large gate leakage the device has at a low bias (68µA

atIds 10 mA for a 150µm wide device). If the leakage can be controlled, these devices

91


0 20 40 60 80 1002.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 20 40 60 80 1004

6

8

10

12

14

16

18

Standard HEMT

Thick Cap

NF

min

(d

B)

Current (mA)0 20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

(a)

(c)

Current (mA)

|Γ

|

0

20

40

60

80

100

120

140

160

180

Ph

as

e

Γ

(deg

ree

s)

(d)

(b)

r n

Current (mA)

Ga

in

(dB

)

Current (mA)

Figure 3.23: Noise parameters versus drain-source current of a thick cap device anda standard HEMT: (a) Minimum noise figure (b) magnitude and phase of optimumreflection coefficient (c) noise resistance (d) and associated gain. Measurement fre-quency is 10 GHz.

92


show great promise for noise performance.

3.6 Comparison of High-Performance GaN HEMTs toOther Material Systems

By now, the reader might have asked the question, “How does GaN HEMT noise

figure performance compare to other material systems?” This will now be addressed.

Most all the devices in this work have a gate length of 0.7µm due to equipment lim-

itations. It is hard to find published noise results in the literature at such a relatively

“long” gate length. In addition, many published noise figure results have large varia-

tions in the accuracy of their measurements.

Bearing this disclaimer in mind, 0.15µm gate-length devices optimized for high-

frequency performance were obtained from Tom´as Palacios. These devices are sim-

ilar to those in a recent publication that had an fτ of 150 GHz and fmax of over

200 GHz [23]. The measured NFmin against frequency is in figure 3.24 for two de-

vices. Repeated measurements at 10 GHz gave a consistent NFmin of 0.4 dB.

Keeping in mind this very good value, let us turn our attention to table 3.1. Here

we have an abundance of data on HEMTs from different material systems: GaN,

SiGe, InAlGaAs systems on GaAs and on InP. The gate lengths, gate widths, NFmin,

measurement frequency for NFmin, relevant information, and the reference number

found at the end of the chapter are all listed. Most obvious is that SiGe has some work

to do before its noise performance can be competitive with the other materials. InP

93


Lg (µm) Wg ( µm ) NFmin (dB) Freq. (GHz) Note Ref.

GaN HEMTs0.12 100 0.72 12 SiC substrate [24]0.15 150 0.4 10 T. Palacios, UCSB —0.15 200 0.6 10 SiC substrate [25]0.15 100 0.75 10 SiC substrate [26]0.17 100 1.1 10 Si substrate [27]0.18 100 0.7 12 Sapphire substrate [8]0.25 100 0.8 10 SiC sub., from graph [28]0.25 100 1.05 18 Sap., from graph [9]0.25 100 1.04 10 Sapphire substrate [29]0.25 200 1.9 10 SiC substrate [30]

Si/SiGe HEMTs0.1 100 1.6 10 from graph, pads de-emb. [31]0.1 90 1.7 10 [32]0.1 — 2.1 10 pads de-embedded [33]0.1 100 3.2 10 [34]

(In,Al)GaAs/(In,Ga,Al)As on GaAs HEMTs0.1 200 0.3 10 from graph [35]0.1 — 0.51 18 [36]0.1 100 0.64 26 mHEMT [37]0.1 100 1.1 40 mHEMT [37]0.13 140 0.31 12 pHEMT [38]0.13 140 0.45 18 pHEMT [38]0.25 — 0.7 18 [36]

(In,Al)GaAs/(In,Ga,Al)As on InP HEMTs0.1 50 0.8 60 [39]0.1 80 0.45 10 from graph [40]0.1 80 0.61 20 from graph [40]0.15 – 0.4 10 [41]0.2 – 0.48 10 [42]0.2 – 0.8 26 [42]

Table 3.1: Minimum noise figure for HEMT devices in many technologies. Also listedare the gate length and width, measurement frequency, some necessary information,and the reference.

94


6 8 10 12 14 16

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

NF

min

(dB

)

Frequency (GHz)

Figure 3.24: Minimum noise figure of two 0.15µm gate length transistors providedby Tomas Palacios.

provides the best performance, but GaAs and GaN are close competition in the X-

band. GaAs might have slightly better performance than GaN, but a 0.1 dB advantage

can be lost once the device is put in a circuit.

3.7 Summary

This chapter looked at a plethora of noise figure measurements of GaN HEMTs.

The methodology for procedures was explained and its importance made clear. Fac-

tors that changed NFmin (such as an AlN-interlayer and choice of substrate) were in-

vestigated. The importance of monitoring gate leakage was found and analyzed with

the modeling in§ 2.6. The unexpected result of a FP improving NFmin was discovered

95


and fully investigated, also with the use of the modeling from§ 2.6.

Together with modeling from the previous chapter, this chapter helps point out ways

of obtaining the best NFmin possible. Most important is reducing the gate leakage and

parasitic resistances at the input.Rg andRs also need to be minimized. The small-

signal power gain needs to be kept as high as possible. Self-heating causes an increase

in NFmin because of loss of device gain.

References[1] V. K. Paidi, “MMIC Power Amplifiers in GaN HEMT and InP HBT Technologies,”

Ph.D. dissertation, University of California, Santa Barbara, Sept. 2004.

[2] J. Xu, “AlGaN/GaN High-Electron-Mobility Transistors Based Flip-Chip Inte-grated Broadband Power Amplifiers,” Ph.D. dissertation, University of California,Santa Barbara, Dec. 2000.

[3] R. Vetury, “Polarization Induced 2DEG in AlGaN/GaN HEMTs: On the Origin,DC and Transient Characterization,” Ph.D. dissertation, University of California,Santa Barbara, Dec. 2000.

[4] K. Krishnamurthy, “Ultra-Broadband, Efficient, Microwave Power Amplifiers inGallium Nitride HEMT Technology,” Ph.D. dissertation, University of California,Santa Barbara, May 2000.

[5] S. Lee, K. J. Webb, V. Tilak, and L. Eastman, “Intrinsic Noise Equivalent-Circuit Paramters for AlGaN/GaN HEMTs,”IEEE Trans. Microwave TheoryTech., vol. 51, pp. 1567–1577, May 2003.


[7] S. Nuttinck, E. Gebara, J. Laskar, and M. Harris, “High-Frequency Noise in Al-GaN/GaN HFETs,”IEEE Microwave Components Lett., vol. 13, no. 4, pp. 149–151, Apr. 2003.

[8] W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, “DC, RF, and MicrowaveNoise Performance of AlGaN/GaN HEMTs on Sapphire Substrates,”IEEE Trans.Microwave Theory Tech., vol. 50, pp. 2499–2503, Nov. 2002.

96


[9] ——, “DC, RF, and Microwave Noise Performance of AlGaN-GaN Field EffectTransistors Dependence of Aluminum Concentration,”IEEE Trans. Electron De-vices, vol. 50, pp. 1069–1074, Apr. 2003.

[10] L. Shen, S. Heikman, B. Moran, R. Coffie, N.-Q. Zhang, D. Buttair,P. Smorchkova, S. Keller, S. DenBaars, and U. Mishra, “AlGaN/AlN/GaN High-Power Microwave HEMT,”IEEE Electron Devices Lett., vol. 22, no. 10, pp. 457–459, Oct. 2001.

[11] T. Palacios, S. Rajan, A. Chakraborty, S. Heikman, S. Keller, S. DenBaars, andU. Mishra, “Influence of the Dynamic Access Resistance in thegm andfτ Linearityof AlGaN/GaN HEMTs,”IEEE Trans. Electron Devices, vol. 52, no. 10, pp. 2117–2123, Oct. 2005.

[12] C. H. Oxley, “A Simple Approach Including Gate Leakage for Calculating theMinimum Noise Figure of GaN HEMTs,”Microwave and Optical Technology Let-ters, vol. 33, no. 2, pp. 113–115, Apr. 2002.

[13] F. Danneville, G. Dambrine, H. Happy, and A. Cappy, “Influence of the Gate Leak-age Current on the Noise Performance of MESFETs and MODFETs,”IEEE Mi-crowave Theory and Tech. Symp., pp. 373–376, 1993.

[14] D.-S. Shin, J. B. Lee, S. Min, J.-E. Oh, Y. J. Park, W. Jung, and D. S. Ma, “Ana-lytical Noise Model with the Influence of Shot Noise Induced by the Gate Leak-age Current for Submicrometer Gate-Length High-Electron-Mobility Transistors,”IEEE Trans. Electron Devices, vol. 44, no. 11, pp. 1883 – 1887, Nov. 1997.

[15] Y.-F. Wu, A. Saxler, M. Moore, R. P. Smith, S. Sheppard, P. Chavarkar, T. Wisleder,U. Mishra, and P. Parikh, “30-W/mm GaN HEMTs by Field Plate Optimization,”IEEE Electron Devices Lett., vol. 25, no. 3, pp. 117–119, Mar. 2004.

[16] T. Palacios, “Optimization of the High Frequency Performance of Nitride-BasedTransistors,” Ph.D. dissertation, University of California, Santa Barbara, Mar.2006.

[17] C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. Mishra, andR. York, “ Influence of the Heterostructure Design on Noise Figure of AlGaN/GaNHEMTs,” in Device Research Conference, vol. 1, Jun. 2004, pp. 43–44.

[18] Y.-F. Wu, M. Moore, T. Wisleder, P. Chavarkar, and P. Parikh, “Noise Characteris-tics of Field-Plated GaN HEMTs,”International Journal of High Speed Electronicsand Systems, vol. 14, pp. 192–194, 2004.

[19] A. Chini, D. Buttari, R. Coffie, S. Heikman, S. Keller, and U. Mishra, “12 W/mmPower Density AlGaN/GaN HEMTs on Sapphire Substrate,”IEEE Electron. Lett.,vol. 40, no. 1, pp. 73–74, Jan. 2004.

97


[20] H. Xu, C. Sanabria, A. Chini, Y. Wei, S. Heikman, S. Keller, U. Mishra, andR. York, “A New Field-Plated GaN HEMT Structure with Improved Power andNoise Performance,” inLester Eastman Conference on High Performance Devices,Aug. 2004.


[22] L. Shen, R. Coffie, D. Buttari, S. Heikman, A. Chakraborty, A. Chini,S. Keller, S. DenBaars, and U. Mishra, “High-Power Polarization-EngineeredGaN/AlGaN/GaN HEMTs Without Surface Passivation,”IEEE Electron DevicesLett., vol. 25, no. 1, pp. 7–9, Jan. 2004.

[23] T. Palacios, A. Chakraborty, S. Heikman, S. Keller, S. DenBaars, and U. Mishra,“Algan/gan high electron mobility transistors with ingan back-barriers,”IEEEElectron Devices Lett., vol. 27, no. 1, pp. 13–15, Jan. 2006.

[24] W. Lu, J. Yang, M. Khan, and I. Adesida, “AlGaN/GaN HEMTs on SiC with over100 GHzfT and Low Microwave Noise,”IEEE Trans. Electron Devices, vol. 48,no. 3, pp. 581–585, Mar. 2001.

[25] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, andC. Nguyen, “Robust Low Microwave Noise GaN MODFETs with 0.6 dB NoiseFigure at 10 GHz,”IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.

[26] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-Cray, and C. Nguyen, “Microwave Noise Performance of AlGaNGaN HEMTsWith Small DC Power Dissipation,”IEEE Electron Devices Lett., vol. 23, no. 11,pp. 637–639, Nov. 2002.

[27] A. Minko, V. Hol, S. Lepilliet, G. Dambrine, J. C. De Jaeger, Y. Cordier, F. Se-mond, F. Natali, and J. Massies, “High Microwave and Noise Performance of 0.17-µm AlGaNGaN HEMTs on High-Resistivity Silicon Substrates,”IEEE ElectronDevices Lett., vol. 25, no. 4, pp. 167–169, Apr. 2004.

[28] J.-W. Lee, V. Kumar, R. Schwindt, A. Kuliev, R. Birkhahn, D. Gotthold, andS. Guo, “Microwave Noise Performances of AlGaN/GaN HEMTs on Semi-Insulating 6H-SiC Substrates,”Electron. Lett., vol. 40, no. 1, pp. 80–81, Jan. 2004.

[29] A. Ping, E. Piner, J. Redwing, M. Khan, and I. Adesida, “Microwave Noise Perfor-mance of AlGaN/GaN HEMTs,”Electron. Lett., vol. 36, no. 2, pp. 175–176, Jan.2000.

[30] S. Hsu and D. Pavlidis, “Low Noise AlGaN/GaN MODFETs with High Break-down and Power Characteristics,”Gallium Arsenide Integrated Circuit (GaAs IC)Symposium, 2001. 23rd Annual Technical Digest, pp. 229–232, Oct. 2001.

98


[31] F. Aniel, M. Enciso-Aguilar, L. Giguerre, P. Crozat, R. Adde, T. Mack, U. Seiler,T. Hackbarth, H. Herzog, U. Konig, and B. Raynor, “High Performance 100 nm T-gate Strained Si/Si0.6Ge0.4 n-MODFET,” in International Semiconductor DeviceResearch Symposium, vol. 47, Dec. 2001, pp. 482–485.

[32] S. J. Koester, J. O. Chu, and C. S. Webster, “High-Frequency Noise Performanceof SiGe p-Channel MODFETs,”IEEE Electron. Lett., vol. 36, no. 7, pp. 674–765,Mar. 2000.

[33] M. Enciso, F. Aniel, P. Crozat, R. Adde, M. Zeuner, A. Fox, and T. Hackbarth, “0.3dB Minimum Noise Figure at 2.5 GHz of 0.13µm Si/Si0.58Ge0.42 n-MODFETs,”Electron. Lett., vol. 37, no. 17, pp. 1089–1090, Aug. 2001.

[34] W. Lu, A. Kuliev, S. Koester, X.-W. Wang, J. Chu, T.-P. Ma, and I. Adesida,“High Performance 0.1µm Gate-Length p-type SiGe MODFET’s and MOS-MODFET’s,” IEEE Trans. Electron Devices, vol. 47, no. 8, pp. 1645–1652, Aug.2000.

[35] H. Kawasaki, T. Shino, M. Kawano, and K. Kamei, “Super Low Noise Al-GaAs/GaAs HEMT with One Tenth Micron gate,”Microwave Symposium Digest,1989., IEEE MTT-S International, pp. 423–426, 13-15 June 1989.

[36] J. Mateos, D. Pardo, T. Gonzlez, P. Tadyszak, F. Danneville, and A. Cappy, “In-fluence of Al Mole Fraction on the Noise Performance of GaAs/AlxGa1−xAsHEMT’s,” IEEE Trans. Electron Devices, vol. 45, pp. 2081–2083, Sept. 1998.

[37] H. S. Yoon, J. H. Lee, J. Y. Shim, J. Y. Hong, D. M. Kang, and K. H. Lee, “Ex-tremely Low Noise Characteristics of 0.1µm Gamma-Gate Power MetamorphicHEMTs on GaAs Substrate,” inInternational Conference on Indium Phosphideand Related Materials, 2005, pp. 133–136.

[38] J.-H. Lee, H.-S. Yoon, C.-S. Park, and P. Hyung-Moo, “Ultra Low Noise Char-acteristics of AlGaAs/InGaAs/GaAs Pseudomorphic HEMT’s with Wide Head T-Shaped Gate,”IEEE Electron Devices Lett., vol. 16, pp. 271–273, June 1995.

[39] M.-Y. Kao, K. Duh, P. Ho, and P.-C. Chao, “An Extremely Low-Noise InP-BasedHEMT with Silicon Nitride Passivation,”Electron Devices Meeting Technical Di-gest., International, pp. 907–910, Dec. 1994.

[40] M. Murti, J. Laskar, S. Nuttinck, S. Yoo, A. Raghavan, J. Bergman, J. Bautista,R. Lai, R. Grundbacher, M. Barsky, P. Chin, and P. Liu, “Temperature-DependentSmall-Signal and Noise Parameter Measurements and Modeling on InP HEMTs,”IEEE Trans. Microwave Theory Tech., vol. 48, no. 12, pp. 2579–2587, Dec. 2000.

[41] Y. Ando, A. Cappy, K. Marubashi, K. Onda, H. Miyamoto, and M. Kuzuhara,“Noise Parameter Modeling for InP-Based Pseudomorphic HEMTs,”IEEE Trans.Electron Devices, vol. 44, no. 9, pp. 1367–1374, Sept. 1997.

99


[42] H. C. Duran, B.-U. H. Klepser, and W. Bachtold, “Low-Noise Properties of DryGate Recess Etched InP HEMT’s,”IEEE Electron Devices Lett., vol. 17, pp. 482–484, Oct. 1996.

100

4Low-Frequency Noise of GaN HEMTs

4.1 Introduction

IT is surprising that a subject that has been studied for almost 80 years would not be

well-understood. But such is the case of low-frequency noise (LFN), the largest

contributor to phase noise of oscillators [1]. The main motivation of this chapter is to

create a model for circuit simulation. Most of the LFN literature for GaN consists of

theoretical explorations of devices (in some studies, just films), or measurements at

very low device biasing not suitable for practical device modeling. GaN HEMT LFN

studies at biasings typical for circuits are presented in this chapter. A new empirical

model is also presented. It is difficult to make LFN comparisons, particularly to most

published works due to the many ways the data are presented, but measurements by

the author for both GaAs and GaN HEMTs will be examined. In addition to the above

topics, the LFN setup will be described in detail, as most LFN setups are either poorly

described in papers or cannot bias as high as is necessary for GaN HEMTs.

101

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS

4.2 Review of Low-Frequency Noise

The terms LFN, flicker, 1/f, and generation-recombination (G-R) noise need clari-

fication. Flicker (also called 1/f) noise refers to phenomena that generate noise with a

slope inversely proportional to the frequency, hence “one on f.” A sample spectrum,

showing flicker noise and other contributions, is shown in figure 4.1. Resistors and

bulk material tend to be strictly 1/f, but devices, including HEMTs, deviate as 1/fγ

whereγ is usually in the range of 0.7 to 1.3. For GaN HEMTs, experiments showγ

to be between 1 and 1.3 [2–4]. Generation-recombination noise refers to trap-related

capture and emission of carriers creating a spectrum of the form

SX(f) =⟨4∆X2

⟩ τ

1 + ω2τ 2(4.2.1)

that is measured as noise at low frequencies. Here,τ is the trap life time,ω the angular

frequency, andX a quantity that fluctuates (usually charge or mobility). Sometimes

the G-R spectrum, which will have a Lorentzian power spectral density, manifests

itself as a “bulge” on a 1/f spectrum, shown in figure 4.1. There is also a theory, most

often credited to McWhorter [5],1 that a continuum of traps, with spectra of the form

in equation 4.2.1, of different life times is the source of the 1/f noise spectrum. This

model appears to work for CMOS [2], but it is not accepted for all device technologies.

Therefore, when referring to the noise at these low frequencies (less than∼10 MHz),

be it from g-r, 1/f, or other unknown sources, the expression LFN will be used.

1In truth, he did not create the concept but extended the theory.

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1/f Reference Line

Frequency

Noise

Spectral

Density

(I2 or V2)G-R "Bulge"

1/fγ noise

Noise Floor

Corner Frequency

Noise spurs

(outside source/interference)

Figure 4.1: Sketch of the key features of low-frequency noise.

It has already been hinted that traps with energies in the material band-gap are

one source of LFN. There are other possible sources: surface effects (such as surface

states), the bulk material itself, dislocations, tunneling, non-uniform channel resis-

tance, quantum effects, and others. Evidence for trying to explain LFN from any one

of these possible sources can be found in the literature. It is likely due to a combination

of several sources and that there will never be a unifying 1/f model for all devices.

HEMTs show orders of magnitudes more LFN noise than bipolar junction-transistor

(BJT) types of devices. This suggests a surface area or high-field dependence. Early

GaN HEMTs and material showed much worse LFN noise than results reported later.

The excess in the LFN was attributed to traps and dislocations [3]. Leinshtein re-

103


ported [3] that GaN HEMTs had less LFN than observed in measurements of GaN

thin films, and suggested there was some suppression of LFN caused by the device.

Some types of LFN vary with the square of bias current, such as that of diodes. A

relationship that describes this, and that is used in circuit simulators is:

⟨i2g,1/f

⟩= Kf

IAf

DC

fFfe(4.2.2)

Kf , Af , andFfe are all fitting parameters,IDC is the DC current, andf is fre-

quency. For making theoretical comparisons of voltage, current, and resistance LFN

spectrums (SV (f), SI(f), andSR(f) respectively), the spectrum is often normalized

(SV (f)/V 2DC , SI(f)/I2

DC , andSR(f)/R2 respectively). These spectrums are related

through Ohm’s law, and lead to the question, “What’s really fluctuating and causing

1/f noise?” If it is the resistance (which for HEMTs, means the channel resistance),

it has been reasoned that it is because of changes in mobility or charge. Because the

resistance varies with the inverse of mobility and charge, fluctuations in one of these

two quantities generates 1/f noise (in theory at least). This has lead to the two ma-

jor principles on which most 1/f theories are based: carrier density fluctuation and

mobility fluctuation modeling. The former is used in the G-R model (equation 4.2.1)

discussed earlier. In fact, equation 4.2.1 can be used to describe both models. It is

debated whether charge or mobility fluctuations are the source of noise; data supports

both. These models have been applied to describe GaN HEMT LFN [2–4].

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An interesting empirical relationship was proposed in 1969 by Hooge:

SI(f)

I2DC

=αHNf

(4.2.3)

where N is the number of carriers in the device andαH is a dimensionless quantity

known as the Hooge parameter. It has since been used to characterize many materials

and devices. It has also been used as a figure of merit and at times as a constant, such

as for characterizing 1/f noise of materials. However, according to Hooge himself, it

was not meant to be considered a constant [6].αH was extracted for measurements

that appear in this chapter. As seen in figure 4.2 (a) and (b),αH changes considerably,

even with frequency of extraction (not surprising as the noise is not strictly 1/f). That

αH is not constant can be seen from other published results as well [3]. Therefore,

the author believes it should not be used for device comparisons and only for material

comparisons.

It is the aim of this chapter to create a LFN model that can be used in the computer-

aided design (CAD) software program Advanced Design System (ADS) and to make

comparisons of LFN in HEMTs. The theory discussed so far is not applicable to

circuit modeling. There is not yet agreement in the theory, and data are generally

at low biasings or not even for HEMTs. At high biasings where the electric fields

are high, traps may no longer be the dominant source of LFN. There is little published

literature of LFN models of HEMTs for use in circuit simulators. Therefore, work was

started from scratch. A setup that could handle the biasings typical of GaN HEMTs

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(a) (b)

Figure 4.2: Variation ofα with (a) drain-source voltage bias and (b) frequency ofextraction for two devices on the same sample.

was built. Measurements of bias-dependence and geometry were performed. Other

studies of LFN performance were performed as time permitted.

A final consideration is how to present the data. There is little consistency in units

and an astonishing number of different choices:A2/Hz, V 2/Hz, A/√Hz, V/

√Hz,

A2, V 2, nV/√Hz, input-referred versions of these and representations in dB or linear

formats. Sufficient information is not always presented in published articles to be

able to convert from one type of units to another. How the data is presented can also

give different results. For example, normalizingSI(f) by I2 gives a different trend

of noise versus gate width than not normalizing. The author decided that presenting

noise asA2/Hz would be most familiar and convenient for a circuit designer and for

comparison purposes.

More information about LFN can be found in [3, 7–9]. A very good and easy-to-

106


follow review can be found in [10]. The book edited by Balandin, [3], is a collection of

articles about noise in GaN including two that treat LFN of GaN HEMTs extensively.

4.3 Low-Frequency Noise Setup

It is hard to find a complete description for a LFN setup. Much time was spent

creating a satisfactory setup for GaN. Therefore, this section will explain what an ex-

perimentalist needs to know to create a setup. There are four main equipment concerns

for a LFN setup. The first is instrumentation to measure the power spectrum versus

frequency. The measurement range of interest is usually 10 Hz to 1 MHz (possibly

wider). Provided that a given spectrum analyzer can even measure such frequencies,

the LFN of the analyzer itself is usually larger than the device’s noise. Increased aver-

aging and reduction of the resolution bandwidth can help these problems; however, the

time for a single measurement becomes prohibitively long. Other instruments that can

be used include computer-controlled oscilloscopes (a long time sample is measured

and a FFT is then performed on a computer) and, the preferred tool, a dedicated FFT

instrument. An HP 3561A dynamic signal analyzer (DSA) is a dedicated instrument

for these types of measurements and was used in this work. It is part of the HP 3048

phase-noise system. The DSA noise floor was superior to other options available and

the HP 3048 software could automatically control it. However, the DSA could only

measure a maximum frequency of 100 kHz. Most measurements in this chapter were

107


preformed from 10 Hz to 100 kHz with∼300 points per decade.

Even with the DSA, the noise floor was not adequate for some measurements.

Therefore, the second equipment concern is the noise floor for which a low-noise

amplifier (LNA) is needed. A Stanford Research Systems SR560 LNA was used to

improve the noise floor. Its voltage gain was typically set to 40 dB (100 V/V, the

minimum to meet the instrument’s specified noise floor) and sometimes as high as

60 dB (for gate noise measurements). The HP3048 software could be adjusted for

the gain. The LNA was run off of internal lead-acid batteries while measuring. The

measured noise floor for the 3561A when its input was shorted is shown together with

the measured noise floor of the LNA (also shorted input) plus 3561A in figure 4.3. An

improvement of more than four orders of magnitude is seen. The measured noise floor

of the LNA in figure 4.3 is identical to its specifications.

The third equipment concern is biasing the device without interfering with the mea-

surement. Almost all DC power supplies, including older analog models, have active

circuitry to maintain the bias set point. This, combined with noise from the AC lines,

makes them impractical to use for LFN measurements. Hence, batteries are used.

9 V batteries are usually preferred as they are recognized to be low-noise. For GaN

HEMTs, even small devices can require high current (easily 100 mA or more). An

attempt to use several 9 V batteries for the drain lead to unexpected measurement

results once the device bias increased above the knee voltage. A rechargeable 12 V

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HP3561A alone

with SR560

Figure 4.3: Measured noise floor of the HP 3561A DSA only and with the SRS SR560LNA (short-circuited input).

lead-acid battery, that could output 90 mA without disturbing the measurement, was

used for the drain bias. A 9 V battery was used for the gate biasing (two in series for

large threshold devices). These were used with a bias box (discussed more below).

Biases ofVds from 0.1 to 12 V,Ids from 5 to 90 mA, andVgs from -0.05 to -9 V could

be obtained. This is far superior to most other setups, which are limited to biasing

conditions in the linear region of a GaN HEMT.

The final equipment concern is to protect the setup from outside electrical and me-

chanical interference. The setup was located on a vibration-isolation table, which

helped with mechanical interference (although it could still be determined when con-

struction work took place in the building or when a peer would walk by the setup).

109


A metal box, that could be grounded to the rest of the setup, was made to fit over

the sample and probes of the RF probe station to shield against electrical interference.

This was required to get a good measurement and helped to reduce spurs by∼30 dB.

Figure 4.4 shows the full schematic of the setup. The multimeters were Fluke

8012As and various hand-held battery-operated units. Multimeters for voltage and

current could be connected while measuring LFN, but ohm-meters had to be discon-

nected. A covered bias box was built. 10 turn, 3 W, 2 kΩ potentiometers were used

to vary the bias. The value of 2 kΩ was carefully selected to allow the maximum

range of measurable biasings. Ground loops destroy a measurement, so care must be

+-

3W

2kΩPot.

3W

2kΩPot.

12V

220Ω9V

10Ω

Bias Box

Capacitors

50pF to1000µF

Shielded

DeviceRds

+-

Voltmeter

Voltmeter

Ammeter

RL 100MΩ

50Ω

25pF

SR560 LNA

Gain = 1000 V/V

(60 dB)

BW: 0.01 to 1MHz

1MΩ

HP3561A

FFT Box

Figure 4.4: Schematic of the setup used for device drain-side low-frequency noisemeasurements.

110


taken with the grounding. The bias-box chassis and device shield were grounded to

the negative terminal of the battery. While other setups may use a load resistance,RL,

to keep the source resistance seen by the LNA a constant (making it easy to convert

the measured voltage spectrum to a current spectrum), the author found this additional

parallel resistance to limit the measurable range of biases and the dynamic range of

the DSA. Instead, the effectiveRL is determined for each LFN measurement. This

resistance is the parallel combination of that seen on the drain side of the bias box and

Rds of the transistor. A bank of capacitors were connected at the gate to provide an

AC short while measuring the drain LFN.

Most aspects of the measurement must be done manually, as automation would only

add noise and ruin the data. The steps for a measurement are:

1. Determine the DCRds of the device near the bias of interest (∆Vds/∆Ids).

2. Unplug power to drain and gate, and ground both ends of the drain pot (usingswitches on bias-box).

3. Disconnect the device and LNA.

4. Measure the resistance of the bias box,Rbox. This is the parallel combination ofboth halves of the potentiometer and associated circuitry.

5. Disconnect the multimeter used to measureRbox (this would add a voltage thatdisturbs the measurement).

6. Reconnect the device, LNA, and bias. Wait 1 minute for the LNA to settle (a voltchange at its input, such as turning on the device or changing the bias, causes itto saturate).

7. Measure. Adjust the measured voltage spectrum by the parallel combination ofresistances (SI = SV /(Rbox||Rds)

2).

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Figure 4.5: A typical low-frequency plot.

The setup was checked by measuring the noise spectrum of resistors. This is flat

with a voltage spectrum equal to its thermal noise.2 A typical HEMT’s LFN is shown

in figure 4.5. The dotted line is a 1/f reference line, showing the data is very nearly 1/f

in slope. There are several spurs, including one at 60 Hz (from lights and various AC

sources) and another large one at∼70 kHz (believed to be a radio signal). The spurs

were found to always be present, and are removed from all other measurements in this

chapter.

2Only when DC current flows through a resistor does it generate low-frequency noise.

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4.4 GaN HEMT Low-Frequency Noise Modeling

For modeling, the drain and gate LFN bias-dependence need to be determined. The

setup in§ 4.3 was used to measure drain noise while an AC short was applied to the

gate. LFN was measured with the drain voltage held constant atVds 5 V and the gate

voltage swept (changingIds). Then noise for a constantIds of 30 mA and varyingVds

was measured. Both of these results are plotted in figure 4.6. In this figure only three

of the decade values are plotted from each full LFN measurement for convenience

of displaying the data. Once the device saturates, the LFN does not change further

with Ids (and henceVgs). However, LFN increases withVds. This change, shown in

figure 4.6 (b), is more than an order of magnitude for the twelve volt bias range.

The magnitude of these LFN measurements at low biasings is consistent with the

literature. The only other published work of LFN noise of GaN HEMTs at high bias-

ings is by Hsu [4]. The measurements presented here for a saturated device agree with

that work, including the key result that the noise changes withVds. In fact, Hsu claims

more bulging at higher biases (Vds > 12 V), and that the bulging broadens. This in-

crease of LFN withVds was also observed in the GaAs devices to be discussed in§ 4.6.

The slope,γ, was extracted and found to typically be about 1.15, varying from less

than 1.1 to nearly 1.3. Bias dependence was not clear, but usuallyγ would decrease

with increasingVds and very slightly decrease with increasingIds. The changing of

γ with bias is not well understood. It has been shown to vary with temperature as

113


(a) (b)

Figure 4.6: Plots of the measured drain low-frequency noise with (a) change in drain-source current and (b) voltage.

well. Previous research points to trap effects, tunneling, and hot-carriers as directions

to explore [2,4].

Despite the measurements being of noise, devices biased the same had very similar

measurements. This means that devices at the same bias can be compared. This is

used as a basis for device comparison studies later in the chapter.

The gate LFN was measured with the drain AC shorted.Vds was set to 5 V and the

gate voltage was varied. As seen in figure 4.7, even at its noisiest the gate LFN is more

than three orders of magnitude smaller than the drain noise. Measurements above a

few kHz hit the noise floor of the setup. Hsu finds similar results [4], as does Riddle

for GaAs MESFETs [11]. It was discovered that devices that had a large change in

gate leakage with applied gate bias also had a large change in LFN. Conversely, if the

device gate leakage was relatively constant with gate bias, the LFN did not change

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Vgs, Igs

30 µAV,

15 µAV,

8.5 µAV,

4.5 µAV,

2.9 µAV,

Figure 4.7: Measured gate low-frequency noise versus gate-source voltage (andcurrent).

much. The device in figure 4.7 did have a large change in leakage as evident from the

x-axis labeling.γ was also very close to unity. These observations mean the gate LFN

can be modeled by the standard diode equation, 4.2.2. This helps reinforce the noise

figure modeling in chapter 2 using a shot noise source at the gate of the transistor.

It is desirable to add scaling to circuit modeling of noise, so the effect of device

geometry on LFN was also measured. Figure 4.8 shows that as the gate is made wider

the drain LFN noise increases. This trend agrees with the low-bias GaN HEMT LFN

measurements of Kuksenkov [12] and the HEMT modeling of Angelov [13]. This

trend is opposite to what is exhibited by MOSFETs [14]. Given this result, it makes

the gate length dependence all the more interesting. Figure 4.9 (a) and (b) show that a

shorter gate length increases the drain LFN. This means that the LFN does not display

115


Figure 4.8: Change in low-frequency noise with gate width at various decade frequen-cies for three devices.

(a) (b)

Figure 4.9: (a) Change in low-frequency noise as the gate length, Lg is changed. (b)The 1 kHz data from (a) with a best fit line.

116


a direct area dependence. It can be speculated that the gate length dependence LFN is

related to theVds dependence.

TheVds LFN dependence will harm the phase noise performance of GaN HEMT-

based oscillators. Also, it is not typical of previous LFN modeling, which has a current

dependence instead. Based on the measurements presented thus far, the gate and drain

have different LFN processes and should not be modeled in the same manner. It

needs to be determined whether the gate and drain LFN are mathematically correlated.

Measurements were performed with the gate AC shorted and not AC shorted, showing

no change in the drain LFN. The same was done for gate LFN measurements and the

drain did not appear to have an effect. Hsu found similar results [4]. Lee shows

that the gate and drain LFN are uncorrelated [15]. Therefore, a two-current noise

source model with no correlation as illustrated in figure 4.10 can be used. Based on

the measurements in this work, the following model of the drain LFN for a circuit

simulator is proposed:

<ig1/f2><ig1/f2>

<id1/f2><id1/f2>

Figure 4.10: Proposed low-frequency noise modeling of the HEMT with a gate anddrain noise source.

117


⟨i2d,1/f

⟩=Ki

(Wg,new

Wg,old

) (Lg,old

Lg,new

)c(msVds + 1)

fγ(4.4.1)

whereKi,ms, andc are fitting parameters representing the magnitude of the noise,

the slope change withVds , and an exponent of the change with gate length respec-

tively. Wg andLg are defined the same as in§ 2.6.4. Values found to work for devices

presented areKi = 4e-14,γ = 1.1,c = 1.5, andm = 2.6. As already mentioned, the

gate noise can be modeled with equation 4.2.2. Due to the limitations of hitting the

noise floor, the gate LFN geometry dependence could not be measured. However, as

it depends on the Schottky contact reverse-bias gate leakage, it might be assumed that

the gate LFN scales with the gate leakage as in equation 2.6.45. Parameters found to

work for the gate LFN areAf = 1.15,Ffe = 1, andKf = 2e-11.

The model was used to estimate the drain LFN corner frequency of the devices,

as equipment limitations prevented the measurement of this important quantity. The

noise figure modeling work in chapter 2 was used to estimate the noise floor, and

its intersection with the LFN was calculated. This value varies with bias because of

changes in LFN and gain, but was estimated to be close be 1-10 MHz. This is a

typical value for GaAs HEMTs. It was also attempted to use this model in phase noise

circuit simulations in ADS. However, limitations in the device model and the lack

of a native voltage bias-dependent low-frequency noise source component in ADS

prevented accurate prediction of phase noise.

118


4.5 GaN HEMT Low-Frequency Noise Studies

4.5.1 Substrate

There has already been some work comparing the noise of GaN HEMTs on different

substrates [3]. The findings were that SiC was less noisy than sapphire, having Hooge

parameters one to two orders of magnitude smaller. But the measurements were at

a low bias and it has already been explained why the Hooge parameter should not

be used for device comparisons. There is no data published comparing devices that

are in the saturation region. This was undertaken, and is presented in figure 4.11.

The devices are both biased atVds 5 V andIds 10 mA. Across the spectrum, there

is no apparent difference. While there appears to be a slight amount of bulging, it is

not stronger for either device. This suggests that at typical device biasings the LFN

is suppressed or another noise mechanism is stronger. Also, identical GaN HEMT-

based oscillators on both substrates constructed by the author (§ 5.4.1) did not show a

difference in LFN.

4.5.2 Passivation

There are two previous publications on the effect passivation has on LFN in GaN.

The first [16] measured HEMTs at a very low bias and normalized the noise to the

drain current. They showed that the passivation does improve the LFN performance,

119


Figure 4.11: Measurement of devices on a sapphire and SiC substrate at a bias ofVds5 V, Ids 30 mA

(a) (b)

Figure 4.12: (a) Low-frequency noise of a device before and after passivation. (b)Low-frequency noise at 10 Hz and 1 kHz of a device before and after passivation atdifferentVgs .

120


but based on their measurements the improvement varied with gate bias from as large

as an order of magnitude to almost no improvement. The other study also found

an improvement with passivation but only measured TLM structures [17]. LFN was

measured for a sample before and after passivation. In figure 4.12 (a), the LFN is

plotted for a device with and without passivation atVds 5 V andIds 10 mA. Passivation

improves the LFN by an order of magnitude across the spectrum. Passivation causes

a slight change in threshold voltage, so measurements were taken at different gate

biasings withVds still at 5 V. The measured data at 10 Hz and 1 kHz is plotted in

figure 4.12 (b). The improvement stays relatively constant with gate voltage. It is

believed that suppression of surface state traps, along with the increase of channel

charge, cause the improvement.

4.5.3 Thick-Epitaxial Cap Devices

After considering the result of passivation on LFN, it is interesting to look now at a

device that does not require passivation. Devices of similar design to those in§ 3.5.6

(AlGaN was used to cap the device instead of GaN) were measured. Figure 4.13 shows

LFN measurements of a few thick-cap devices (that have no passivation) and standard

passivated HEMTs. The performance of the thick-cap devices is as good as, if not

slightly better than, a passivated standard HEMT device. It can be concluded that a

LFN mechanism on the channel surface can be suppressed with either passivation or

121


Figure 4.13: Comparison of standard passivated HEMTs to an unpassivated thick capHEMTs. Bias isVds = 5 V andIds = 30 mA.

with another epitaxial layer.

4.5.4 Field-Plated Devices

A field plate (FP) was shown to lower NF in this work (§ 3.5.5). It has also been

shown that a FP improves oscillator phase noise in [18]. In fact, the longer the FP, the

less the phase noise. As the 30 dB/decade slope of this data suggests that a 1/f type of

noise is dominating the phase noise, it might be reasoned that the LFN of FP and non-

FP devices is different. If there is a difference, it is not apparent in the measurements

shown in figure 4.14. In part (a) of the figure, all FP and non-FP transistors display

the same LFN at different frequencies when biased under the same conditions. The

second plot, (b), shows that asVds increases, all devices’ LFN increase at nearly equal

122


(a) (b)

Figure 4.14: (a) Decade low-frequency noise data for devices with different FP lengthsat a bias ofVds 5 V andIds 30 mA. (b) 100 Hz low-frequency noise for different FPlengths atVds 3, 5, and 8 V.

rates. The answer to the origin of the phase noise improvement with a FP will need to

be answered elsewhere.

4.6 Comparison to GaAs HEMTs

In the previous chapter the NF of GaN was shown to be similar to GaAs. Let us now

examine the LFN of these two materials. A few GaN LFN reports have claimed that

the noise is comparable (such as [2]). These previous results are usually done with a

measured GaN device and information for a GaAs device from a data sheet or another

paper. In addition, the Hooge parameter is used as the figure of merit.

The author obtained GaAs HEMTs and measured the LFN of these devices. They

are from the TriQuint TQP13 pHEMT process, with anfτ of ∼95 GHz. The device

123


gate geometry is 0.13 x 93µm. This is not the same as the 0.7 x 100µm GaN HEMT

devices to which they are compared to. However, based on the model presented in this

chapter, approximating the magnitude of the GaAs devices to be 3 times smaller than

what is actually measured should make for a fair comparison. The question arises

of how to bias the different devices. The following bias was chosen: 1.5 times the

knee voltage of the fully open channel and 3/4 the total gate bias (positive turn-on to

negative cut-off).

Figure 4.15 shows the measurements of (a) the full spectrum of one GaN and one

GaAs device and (b) selected frequency points for a few GaN and GaAs devices.

The GaAs has not been corrected for its difference in geometry. Considering this

difference, the LFN from a few kHz to 1 MHz is similar for both types of devices.

The slope (γ) of the GaAs devices was found to typically be 0.8 (it is common in the

(a) (b)

Figure 4.15: Low-frequency noise comparison of (a) a GaN and GaAs HEMT (fullspectrum) and (b) multiple GaN and GaAs HEMTs (decade measurements). Bias forall devices isVgs = 3/4Vtotal, Vds = 1.5Vknee.

124


GaAs FET literature forγ to be between 0.7 and 1), which is much less than the 1.2 for

GaN. Therefore, at lower frequencies GaAs has less noise. In§ 5.5, it will be shown

that the close-to-carrier phase noise of GaN oscillators is worse than for GaAs-based

oscillators because of these different slopes.

4.7 Summary

This chapter has provided a useful collection of quality high-bias low-frequency

noise data. It was shown that the noise depends heavily onVds while remaining nearly

constant to a changing gate voltage. The geometry dependence has also been shown to

be different than what is seen in other devices. A scalable, bias-dependent, empirical

model was proposed that can be used in circuit simulators. It was demonstrated that

neither the choice of substrate nor the addition of a FP change the LFN. Suppression

of LFN from surface effects was demonstrated through measurements of unpassivated

and thick-cap devices. References to the literature were added to support all measure-

ments where previous work exists. The full details of a LFN setup were explained. A

final note is that bulging (g-r noise presumably from traps) would occasionally show

up. The bulge would be very broad with a spectrum from around 100 Hz to 1 kHz. It

was not always present, even across the same sample. With improvement of material

it can be expected that the LFN will improve.

125


References[1] A. Hajimiri and T. Lee,The Design of Low Noise Oscillators. Boston: Kluwer

Academic Publishers, 1999.

[2] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, andC. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-EffectTransistors for Microwave Communications,”Microwave Theory and Techniques,IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.


[4] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hus-sain, “Characterization and Analysis of Gate and Drain Low-Frequency Noise inAlGaN/GaN HEMTs,” inHigh Performance Devices, 2002. Proceedings. IEEELester Eastman Conference on, 2002, pp. 453–460.

[5] A. L. McWhorter, “Semiconductor Surface Physics,” R. H. Kinston, Ed. Philadel-phia: Univ. of Pennsylvania Press, 1956, pp. 207–228.

[6] F. N. Hooge, “1/f Noise Sources,”IEEE Trans. Electron Devices, vol. 41, no. 11,pp. 1926–35, Nov. 1994.

[7] A. van der Ziel, “Unified Presentation of 1/f Noise in Electron Devices: Funda-mental 1/f Noise Sources,”Proc. IEEE, vol. 76, no. 3, pp. 233–258, 1988.

[8] ——, Noise in Solid State Devices and Circuits. New York: Wiley-Interscience,1986.


[10] D. A. Bell, “A survey of 1/f noise in electrical conductors.”Journal of Physics C:Solid State Physics, vol. 13, no. 24, pp. 4425–37, Aug. 1980.

[11] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,North Carolina State University, 1986.

[12] D. V. Kuksenkov, H. Temkin, R. Gaska, and J. W. Yang, “Low-Frequency Noisein AlGaN/GaN Heterostructure Field Effect Transistors,”IEEE Electron DevicesLett., vol. 19, no. 7, pp. 222–224, July 1998.

[13] I. Angelov, R. Kozhuharov, and H. Zirath, “A Simple Bias Dependant LF FETNoise Model for CAD,” inMicrowave Symposium Digest, 2001 IEEE MTT-S In-ternational, vol. 1, 2001, pp. 407–410 vol.1.

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[16] A. V. Vertiatchikh and L. Eastman, “Effect of the Surface and Barrier Defectson the AlGaN/GaN HEMT Low-Frequency Noise Performance,”IEEE ElectronDevices Lett., vol. 24, no. 9, pp. 535–537, Sept. 2003.

[17] S. A. Vitusevich, M. V. Petrychuk, S. V. Danylyuk, A. M. Kurakin, N. Klein, andA. E. Belyaev, “Influence of Surface Passivation on Low-Frequency Noise Proper-ties of AlGaN/GaN High Electron Mobility Transistor Structures,”phys. stat. sol.(a), no. 5, pp. 816–819, Mar. 2005.

[18] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, and R. York, “High PowerGaN Oscillators Using Field-Plated HEMT Structure,” inMicrowave SymposiumDigest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.

127

5GaN HEMT Based Oscillators

5.1 Introduction

OSCILLATORS are a key component of many communication systems. They

set fundamental limits of channel spacing because of their phase noise. This

work has demonstrated that NF and LFN of GaN HEMTs are only slightly worse

than the far more technologically mature GaAs HEMTs. Here the phase noise will

be compared to similar integrated circuit designs in Si and GaAs. Some guidelines

for low-phase noise design are discussed. A recently-developed MMIC process at

UCSB [1] was ideal for making the designs, and it will be reviewed briefly. The focus

of the chapter is the design and measurement of two LC differential oscillators. The

first did not have impressive phase noise performance but its linearity was excellent.

It is also the first GaN differential oscillator to appear in the literature [2]. A second

similar oscillator was fabricated that had fairly good phase noise performance. These

oscillators are compared to other published results of differential oscillators in Si and

GaAs, as well as GaN HEMT oscillators of all designs.

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CHAPTER 5. GAN HEMT BASED OSCILLATORS

5.2 Concerning Phase Noise

The study of phase noise is a difficult undertaking. Entire books and dissertations

are devoted to its study [3–5]. Even today there is still not a consensus of how best to

approach the problem [6]. The reason for the difficulty of understanding phase noise

stems from three challenges. The first is that an oscillator is a non-linear problem, and

simple analytical analysis cannot capture all key aspects. The rigorous work is usually

too complicated for clear insight or practical design. LFN is the largest contributor to

phase noise, and the lack of its full understanding undermines any complete study of

phase noise. It is not unheard of for a designer to simulate phase noise without LFN

modeling in the circuit because of this shortcoming. Finally, the circuit design impacts

the phase noise, possibly in profound ways [5].

Defining phase noise is much simpler than designing for it. Any signal source is

bound to have fluctuations in phase and amplitude. We can write these fluctuations as

v(t) = v0(1− a(t)) cos(ω0t+ ψ(t)) (5.2.1)

v0 andω0 are the amplitude and angular frequency of resonance of the oscillator.

The amplitude fluctuations, a(t), and phase fluctuations,ψ(t), are both stochastic pro-

cesses. The power spectral density close to the carrier frequency is found to be [7]

Sv(ω) =v2024π(1− 〈φψ(0)〉)δ(ω − ω0) + Sa(ω − ω0)

+Sψ(ω − ω0) + 2Im [Sψa(ω − ω0)] (5.2.2)

129


Here we see the signal amplitude (v20/2) at the resonant frequency, along with an

autocorrelation term,φψ, from the phase fluctuations that reduces it.Sa is noise added

to the spectrum from the amplitude fluctuations, and is commonly known as amplitude

modulation (AM) noise. The phase fluctuations contribute to the spectrum throughSψ,

and is known as phase modulation (PM) or phase noise. A correlation term between

the amplitude and phase fluctuations can also contribute to the spectrum through the

cross spectral density,Sψa, called AM-PM noise. AM-PM noise is an odd function

(the others are even), and can lead to asymmetry of the noise spectrum around the

carrier. Proper circuit design reduces AM-PM noise. The nonlinearities of the gain-

producing element in an oscillator (usually, but not always, a transistor) provides a

restoring force that not only keeps the amplitude stable but also greatly reduces AM

noise. This means the noise near an oscillator’s resonance frequency is dominated by

phase noise.

Bearing in mind that there is AM, PM, and AM-PM noise, but PM (phase noise)

dominates, the phase noise can be observed with a spectrum analyzer. In fact, an Ag-

ilent E4440 spectrum analyzer with a phase noise personality was used for measure-

ments that appear in this chapter. Phase noise appears as a broadening of the frequency

of oscillation, shown in figure 5.1 (a). Its fine detail of shape varies, and is typically

one of three cases as seen in figure 5.1 (b-d). The resonator acts as a filter. Above or

below the resonant frequency a voltage signal would drop proportionally to 1/f, but

130


Frequency

Power

Noise Floor

ω0

Frequency

Power

1/f3

Noise Floor

Frequency

Power

1/f3

1/f2

Noise Floor

Frequency

Power

1/f3

1/f

Noise Floor

(a)

(c)

(b)

(d)

Figure 5.1: (a) A typical spectrum of an oscillator. (b-d) are zoomed in plots of thecircled portion in (a). The power in the various plots arenot scaled to one another.

the power would drop 1/f2 (20 dB/decade). This is exactly what happens to both flat

(such as thermal) noise sources and up-converted LFN leading to 20 dB/decade and

30 dB/decade slopes respectively. An oscillator with a very high Q, and the best noise

performance (the plots in figure 5.1 are not to scale to each other), would have a shape

such as that in figure 5.1 (b). The 1/f3 region is the resonator filtering up-converted

LFN, while the 1/f regions are up-converted LFN that is outside the resonator band-

width. If there were no LFN (a blissful ideality), the slope of the entire range would be

131


just 20 dB/decade. Figure 5.1 (c) is the most typical spectrum observed. Here again

is filtering of LFN, but now we see thermal noise being filtered as well. The last case,

figure 5.1 (d), is for an oscillator with an enormous amount of LFN. We will return

to this qualitative analysis later. Phase noise is specified in decibels below the carrier

(dBc) in a 1 Hz bandwidth at a offset-frequency from the carrier. For example, a phase

noise of -132 dBc/Hz at 100 kHz means the noise at a frequency 100 kHz in addition

to the oscillation frequency is 132 dB below the power the oscillator has at its resonant

frequency (ω0).

A concise background of phase noise would require more than a chapter. Despite

the complexity of phase noise, there are some guidelines that tend to show up repeat-

edly [3,5–9]:

• Increase the tank Q: This is the most important factor for improving phasenoise. Higher Q means more suppression of off-carrier frequency components.

• Minimize the LFN: Probably the next most important parameter after Q. Choiceof device (bipolars in general have much less LFN than FETs) and device ge-ometry can help, as well as improvement in material quality. But usually littlecan be done to quell LFN.

• Increase the Signal Amplitude: If all other influences could be consideredconstant, a larger signal amplitude increases signal to noise ratio and reducesthe phase noise.

• Minimize Other Noise Sources: Flat noise sources determine the phase noisein the 20 dB/decade range.

• Properly Design the Loop Gain: Designing the phase shift of the loop to havea maximum derivative at the center of the resonance of the loop gain maximizesthe resonator’s ability to attenuate phase noise.

132


• Linearize Cgs: The non-linearity ofCgs with Vgs makes the oscillator less sym-metric and increases noise. Additional capacitance can smoothCgs and improvephase noise. [3,10]

• Optimize the Circuit: Some oscillator topologies, particularly the Colpitts,provide better phase noise than others. Design of the circuit influences thephase noise performance. Use of techniques, such as automatic gain controland tapped resonators, can help as well.

The last point is the largest topic to expound upon. However, the other points go

far toward the goal of improving phase noise. Because of the very large powers GaN

HEMTs can produce, the improvement of phase noise with signal amplitude is of great

interest to GaN circuits and provides the motivation for building the oscillators in this

chapter.

To simulate phase noise, very accurate device small-signal, large-signal, and noise

modeling must be available. In addition, simulators vary in their accuracy in predicting

phase noise. Modeling from the previous chapters was used to attempt simulations

of phase noise. However, the device model had some shortcomings (discussed in

§ 6.2) that prevented even accurate modeling of the 20 dB/decade phase noise from

filtered thermal noise. Some interesting results could be determined: the gate-leakage

shot noise was found to be negligible compared to contributions of the gate resistance

thermal noise, the channel noise, and the LFN. It was also noted that a field plate (FP)

did help the simulated phase noise results. A surprising simulated improvement of

10 dB of a very long FP HEMT oscillator over a non-FP oscillator agrees with the

work of Dr. Xu [11]. The practices outlined above were followed as well as possible.

133


5.3 MMIC Process Description

The MMIC process developed by Hongtao Xu was used for circuit fabrication [1].

It integrates capacitors, inductors, resistors, and transmission lines. This follows the

HEMT process described in§ 3.2, but with additional steps. There are now two addi-

tional metal layers (metal 1, 1µm of gold, and metal 2, 3µm of gold), a resistor layer

(NiCr), and a dielectric spacer layer (3µm of PMGI). Inductors are made with metal

1 as an under-pass metal, then the dielectric spacer, and metal 2 to finish the over-pass

and most of the metalization of the square inductors. Capacitors are made with the

gate metal as a bottom electrode and the same film used for passivation as the capac-

itor dielectric. Metal 1 becomes the top electrode, and metal 2 connects the capacitor

bottom and top to the rest of the circuit (metal 2 is used over the PMGI to contact the

top electrode without shorting the capacitor). Resistor composition is Ti/SiO2/NiCr

and is protected by the same SiN film used for the capacitors and passivation. Trans-

mission lines are made exclusively with the thick metal 2. The same material structure

in § 3.2 is used here. Full details of the process, along with a process flow chart, can

be found in Hongtao Xu’s dissertation [1].

134


5.4 Differential Oscillators

5.4.1 High Linearity Oscillator

Some familiarity with oscillators will be assumed in this and the next subsection.

A background can be found in textbooks such as [8]. The oscillators were designed

primarily as test vehicles, making the circuit design more flexible and less conven-

tional than typical commercial configurations. Design goals were to minimize phase

noise and maximize power and linearity without regard to other constraints such as

device size or ease of implementation. Design started with a basic cross-coupled pair

of 2× 100µm-wide HEMTs, seen in figure 5.2. Typically the drain bias would be set

with a current mirror at the HEMT sources (marked with an S) but it was desired to

have the freedom to change the bias. This also eliminates the LFN from devices in the

current mirror.

The tank, represented by the capacitorCt and inductorsLt, primarily set the reso-

nance frequency. A fixed capacitor was used instead of a varactor to improve the Q of

the resonator and allow better insight of the phase noise performance of the HEMTs.

The passive components used for the tank were based on measurements of fabricated

capacitors and inductors at 5 GHz, with the best Q components picked for the desired

oscillation frequency. Typical unloaded Q values at 5 GHz are 25 and 65 for the square

spiral inductors and the SiN capacitors respectively.

135


C2C2

Ct

L1L1

C1C1

Lt Lt

L3C3

L3Load

L2L2

C3

Load

SS

Figure 5.2: Circuit schematic of the oscillator (biasing not shown).

C2

Ct

L1

C1Lt

L2

C3

L1

Lt

L2

C3

C1

C2

Figure 5.3: Photograph of the high linearity oscillator. Darker areas are the twoHEMTs. Passive components are labeled as in figure 5.2.

136


The output is taken on either side of the tank. To keep from loading the tank, and

to match to a 50Ω output, an L-match (L1 andC2) is used. Bias is provided at the

gate and through the L-matches with the output. This required the use of off-chip

bias-Ts for the RF/DC ports, but not for the gate bias port. The gate uses large square

inductors (L2) as RF chokes.C1 is a DC block that prevents the drain of the HEMTs

from shorting, andC3 isolates the DC of the gate and drain. The lengths of line used

to cross-connect the HEMTs are modeled by the inductorsL3. The photograph of the

oscillator in figure 5.3 labels most of the circuit elements found in figure 5.2. Circuit

size is 2 x 1.65 mm2.

The circuit was simulated using ADS. Transient and harmonic simulations were

performed. Monitoring these, along with the dynamic load-line at the drain port of the

HEMTs, the circuit was optimized to give as linear an output as possible.

Measurements were performed on-wafer with air-coplanar (Cascade Microtech ACP-

40 GSG) probes. Off-chip bias-Ts were used for both the drains and gates. One side

of the oscillator was terminated in a dummy 50Ω load. All measurements that follow

(power, linearity, phase noise) were performed using an Agilent E4440 spectrum ana-

lyzer with phase noise personality. Figure 5.4 (a) shows the measured spectrum from

one side providing 22.9 dBm of power at a 4.166 GHz oscillation frequency. The cir-

cuit is biased atVds 20 V, Ids 233 mA, andVgs -1 V. The analyzer had a 10 MHz span

and 33 kHz resolution bandwidth for the measurement. How the power and efficiency

137


(a) (b)

Figure 5.4: Measurements of the oscillator: (a) power spectrum (b) frequency pulling.

(a) (b)

Figure 5.5: Output power (single-sided), second harmonic power, and efficiency (fullcircuit) of the high-linearity oscillator for changes in device (a) drain-source voltageand (b) gate-source voltage.

138


compare to other oscillators will be discussed in§ 5.5.

Of interest is the oscillator pulling, which is the change in oscillation frequency

with DC bias. This was measured for both the gate and drain voltages and plotted in

figure 5.4 (b). It is typical to express the pulling as a ratio of change in frequency to

change in bias. Approximating the data as linear in figure 5.4 (b) gives a pulling of

4.3 MHz/V for the gate and 0.6 MHz/V for the drain. These changes are less than

0.4% of the frequency of oscillation.

The power, 2nd harmonic, and efficiency for changes in bias appear in figure 5.5 (a)

and (b). The third harmonic was so small as to be buried in the noise floor of the spec-

trum analyzer, making it∼70 dB below the carrier. The 2nd harmonic was typically

better than 30 dBc for all biasings measured. If the output were taken differentially,

even harmonics would cancel and the oscillator would make for an extremely linear

source.

This oscillator was the first GaN differential oscillator to be reported in the litera-

ture, and also the best reported linearity for a GaN oscillator [2]. However, the phase

noise was not impressive, being only -86.3 dBc and -115.7 dBc at best. A second,

similar, oscillator was constructed and is now presented.

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5.4.2 Low-Phase Noise Oscillator

The previous design was modified to improve phase noise performance. The Q

of the various inductors was reasoned to be a limiting factor, and were replaced. Mi-

crostrip lines,Lt in figure 5.6, were used in place of the tank inductors. The L-matches

were changed to tapped capacitors to help preserve the loaded tank Q. This meant the

drain biasing needed to be applied through the tank microstrip inductors. To provide

an AC ground acrossLt, the large blocking capacitor 2C3 was added. The circuit,

shown in figure 5.7, was slightly smaller than the previous at 2 x 1.4 mm2.

C2C2

CtC1

2C3Lt Lt

L1C4

L1Load

C1

L2L2

C4

Load

SS

Figure 5.6: Circuit schematic of the low-phase noise oscillator (biasing not shown).

140


C2 Ct

C3

Lt

C1

L2

C4

L2

C4

C2

Lt

C1

C3

Figure 5.7: Photograph of the low-phase noise oscillator. Passive components arelabeled as in figure 5.6.

Figure 5.8 is a typical measured phase noise spectrum. Above 10 kHz the oscillator

drift obstructs the measurement. From 10 kHz to 1 MHz the spectrum decreases with

a 30 dB per decade slope, similar to figure 5.1 (d). This means the low-frequency

noise (LFN) of the oscillator dominates and hides the 20 dB per decade thermal noise

region. So far, no published GaN-oscillator phase-noise measurements have shown

a strict 20 dB per decade slope below a 1 MHz offset [2, 11–15]. A phase noise

measurement above a 1 MHz offset usually approaches a spectrum analyzer’s noise

floor, hence the lack of phase noise measurements in the literature at larger offsets.

Now to answer the key question: does an increase of oscillator power improve the

phase noise? After the optimal bias forVgs was determined and set,Vds was varied.

141


Figure 5.8: Measured phase noise of the oscillator.

Figure 5.9: Phase noise at 100 kHz and 1 MHz offsets versus drain-source bias for afew oscillators.

142


The power of the oscillators increases from 15 dBm to 18 dBm asVds increased from

6 V to 35 V. BelowVds 5 V the power drops quickly (it was typically 7 dBm atVds

4 V). Phase noise for devices with differentVds is plotted in figure 5.9. The phase

noise does not improve with an increase in signal power, but actually increases. This

agrees with measurements in [12]. Of interest is that the general shape of figure 5.9 is

similar to the measured LFN bias dependence in figure 4.6. While proper design can

help to lower the offset frequency where the 30 dB/decade and 20 dB/decade slopes

meet, only Hajimiri’s model [5] addresses how this can be accomplished and its ability

to do this is still debated. With these results in mind, we now compare GaN oscillators

to other material systems for phase noise and for other oscillator measurements.

5.5 Comparison to Other Oscillators

A summary of measurements of several oscillators is found in table 5.1. Listed are

the measured frequency of oscillation (or range if the oscillator is tunable), the total

device (or devices) width, the oscillator power at its resonance frequency in addition

to second and third harmonics, the best efficiency of which the oscillator was capable,

phase noise measurements at 100 kHz and 1 MHz offsets, and the reference for each

work.

The table is separated into four parts depending on oscillator type. All oscillators in

the table are either HEMT or MESFET-based (no BJTs or HBTs) and integrated (no

143


Desc. Carrier Device Fund. 2nd 3rd Best Phase Noise Ref.Freq. Width Power Harm. Harm. Eff. 100 kHz,1 MHzGHz mm dBm dBm dBm % dBc/Hz

GaN HEMT OscillatorsColpitts 5.3 0.2 20.5 -11.5 – 14.1 -105 -123 [12]Hartley 9.56 1.5 32.3 – – 16 -87 -115 [16]VCO 9± 0.5 1.5 31.8 10.8 4.8 21 -77 – [14]Colpitts,1.1µm FP

5.02 0.5 30 ∼8 – 24 -104 -132 [11]

GaAs MESFET OscillatorGaAsVCO

11.5±0.3 – 9 >20 – – -91 -119 [17]

Differential Oscillators (Fixed Frequency), This Work§ 5.4.1 4.16 0.4 22.9 -19.2 <-55 9.4 -86.3 -115.7§ 5.4.2 3.7 0.4 17.5 -6.4 -12.1 13.7 -103 -132

Differential Oscillators (VCOs), GaAs and Si FETsSi, CMOS 4.7 0.286 -9 – – ∼2 -90 -110 [18]Si, CMOS 4.2 – -12 – – ∼1 -86 -106 [19]GaAs,MESFET

6.44 – 4.67 – – – -93 -112 [20]

Table 5.1: Comparison of GaN oscillators from this and other works to oscillators inother materials (FET, MMICs, only).

hybrid circuits with high Q tanks). In order from top to bottom, they are the current

published literature of GaN oscillators besides those in this work, a GaAs oscillator

that is not of a differential architecture, the differential oscillators presented in this

work, and finally differential tunable oscillators in Si and GaAs.

Comparing the phase noise with other GaN oscillators first, the low-noise oscillator

of this work compares well with the best phase noise values reported for GaN oscilla-

tors. The Colpitts oscillator of [12] used high-Q BST thin films as blocking capacitors

144


in its circuit and [11] used a FP on the devices in the oscillator, providing astonish-

ing improvements in phase noise (∼10 dB over the same circuit using devices with

no FP). The oscillators in Si and GaAs technologies all used varactors for frequency

tuning. This will degrade the tank Q and lead to poorer phase noise performance. As

a safe assumption, assume that the phase noise would be -10 dBc/Hz lower (better)

than what is stated in the table. With this adjustment, we see that GaN has better or

comparable phase noise at a 1 MHz offset, but by offsets≤ 100 kHz the phase noise

is worse. Work by Rice [15] agrees with these measurements. The reason for this

difference is because GaN oscillators are dominated by their LFN and never show the

20 dB/decade slope from thermal noise. This is better-explained by figure 5.10. Here

the phase noise is displayed comparatively for a GaN oscillator and a typical low-noise

oscillator in GaAs or Si. Note that the magnitudes of the phase noise are not the same,

as phase noise is expressed relative to the carrier. The measured absolute power of the

phase noise sidebands for the GaN oscillator will be much larger than in GaAs or Si.

GaN oscillators provide at least an order of magnitude more power than the other

technologies. For the total device width of the HEMTs, the oscillators in this work

provide an average amount of power compared to the other GaN oscillators. The

standout is the FP HEMT oscillator, with 2 W/mm. The linearity of the first oscillator

in this work is second to none. The efficiencies of the GaN oscillators appears to be

much higher than GaAs and Si.

145


Figure 5.10: Relative comparison of GaN oscillator to a typical oscillator with lowphase noise (figure courtesy of Dr. Robert York).

5.6 Summary

Two GaN HEMT-based differential oscillators were presented. The first displayed

very good harmonic suppression but poor phase noise. This oscillator was also the first

GaN differential oscillator to appear in the literature [2]. The second oscillator showed

excellent phase noise performance at a 1 MHz offset of -132 dBc/Hz. However, be-

cause GaN oscillator phase noise appears to be dominated by very large amounts of

LFN, the noise performance is worse at offsets closer to the carrier. The hoped-for

benefit of better phase noise with more oscillator power is shattered by measurements

that show that more power actually increases the phase noise. This could be expected

because of the HEMT drain LFN bias dependence withVds. Because of these two

146


problems, GaN does not appear to have an advantage over GaAs or Si oscillators for

phase noise.

References[1] H. Xu, “MMICs using GaN HEMTs and Thin-Film BST Capacitors,” Ph.D. dis-

sertation, University of California, Santa Barbara, 2005.

[2] C. Sanabria, H. Xu, S. Heikman, U. Mishra, and R. York, “A GaN DifferentialOscillator With Improved Harmonic Performance,”IEEE Microwave ComponentsLett., vol. 15, pp. 463–465, Jul. 2005.

[3] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,North Carolina State University, 1986.

[4] W. P. Robins,Phase Noise in Signal Sources. London, UK.: Peter PeregrinusLtd., 1982.

[5] A. Hajimiri and T. Lee,The Design of Low Noise Oscillators. Boston: KluwerAcademic Publishers, 1999.

[6] S. A. Maas,Noise in Linear and Nonlinear Circuits. Boston: Artech House, 2005.



[9] D. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,”Proc. IEEE,vol. 54, no. 2, pp. 329–330, 1966.

[10] V. Manan and S. Long, “A Low Power and Low Noise p-HEMT Ku Band VCO,”Microwave and Wireless Components Letters, IEEE [see also IEEE Microwaveand Guided Wave Letters], vol. 16, no. 3, pp. 131–133, 2006.

[11] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, and R. York, “High PowerGaN Oscillators Using Field-Plated HEMT Structure,” inMicrowave SymposiumDigest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.

[12] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. A. York, “Low Phase-Noise 5 GHz AlGaN/GaN HEMT Oscillator Integrated with BaxSr1−xTiO3 ThinFilms,” IEEE Microwave Theory and Tech. Symp., pp. 1509–1512, 2004.

147


[13] J. B. Shealy, J. A. Smart, and J. R. Shealy, “Low-Phase Noise AlGaN/GaN FET-Based Voltage Controlled Oscillators (VCOs),”IEEE Microwave ComponentsLett., vol. 11, no. 6, pp. 244–245, Jun. 2001.

[14] V. Kaper, R. Thompson, T. Prunty, and J. R. Shealy, “Signal Generation, Controland Frequency Conversion AlGaN/GaN HEMT MMICs,”IEEE Microwave The-ory and Tech. Symp., pp. 1145–1148, 2004.

[15] P. Rice, R. Sloan, M. Moore, A. R. Barnes, M. J. Uren, N. Malbert, and N. La-bat, “A 10 GHz Dielectric Resonator Oscillator Using GaN Technology,”IEEEMicrowave Theory and Tech. Symp., pp. 1497–1500, 2004.

[16] V. S. Kaper, V. Tilak, H. Kim, A. V. Vertiatchikh, R. M. Thompson, T. R. Prunty,L. Eastman, and J. R. Shealy, “High-Power Monolithic AlGaN/GaN HEMT Oscil-lator,” IEEE J. Solid-State Circuits, vol. 38, no. 9, pp. 1457–1461, Sept. 2003.

[17] C.-H. Lee, S. Han, B. Matinpour, and J. Laskar, “A Low Phase Noise X-bandMMIC GaAs MESFET VCO,”Microwave and Guided Wave Letters, IEEE [seealso IEEE Microwave and Wireless Components Letters], vol. 10, no. 8, pp. 325–327, 2000.

[18] P. Kinget, “A Fully Integrated 2.7 V 0.35 m CMOS VCO for 5 GHz WirelessApplications,”ISSCC Dig. Tech. Papers, p. 226227, 1998.

[19] M. Soyuer, K. Jenkins, J. Burghartz, and M. Hulvey, “A 3-V 4-GHz nMOSVoltage-Controlled Oscillator with Integrated Resonator,”Solid-State Circuits,IEEE Journal of, vol. 31, no. 12, pp. 2042–2045, 1996.

[20] S.-W. Yoon, E.-C. Park, C.-H. Lee, S. Sim, S.-G. Lee, E. Yoon, J. Laskar, andS. Hong, “5 6 GHz-Band GaAs MESFET-Based Cross-Coupled Differential Oscil-lator MMICs With Low Phase-Noise Performance,”IEEE Microwave ComponentsLett., vol. 11, no. 12, pp. 495–497, Dec. 2001.

148

6Summary, Conclusions, and Future

Directions For Noise Studies

6.1 Summary and Conclusions

THIS dissertation has looked at several aspects of the noise performance of

GaN HEMTs: noise figure, low-frequency noise, and phase noise. The noise

figure of GaN HEMTs is comparable to GaAs HEMTs. However, the gate leakage

needs to be well-controlled. Source resistance might also be too large a contributor for

small devices. At high biasings, self-heating causes the gain to drop, and an increase

in source resistance quickly degrades the noise figure performance.

A simple model, that included device scaling, was put together that not only pre-

dicts the minimum noise figure well, but also the other noise parameters:|Γopt|,6 Γopt,

andrn. It is useful for hand and Matlab calculations to predict and understand noise

without the need for noise parameter measurements beforehand. It was successfully

used to understand how gate leakage and a field plate influence noise figure. The

model does not work when the gain of the transistor drops, such as at high biasings

149

CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS

or frequencies close tofτ . It was shown that the Pospieszalski and correlated noise

models can be successfully applied to GaN HEMTs, even for noise versus bias.

Summarizing the other noise figure studies, devices on either SiC or sapphire sub-

strates can have the same minimum noise figure as long as the bias is low. Thick-cap

devices show low noise at high biasings. However, their noise at lower biasings is

sub-par because of a very large amount of gate leakage.

A low-frequency noise setup that works at biasings typically needed for GaN HEMTs

was constructed and thoroughly explained. Unlike many other setups, this allowed

bias dependent studies well into the device saturation region. From this, a strongVds

dependence for the drain was discovered and a scalable, bias dependent, model that

could be entered in a circuit simulator was introduced. The gate was found to follow

the low-frequency noise modeling for a diode, as could be expected for a Schottky

contact.

Low-frequency noise studies were performed. Passivation was found to improve the

low-frequency noise by an order of magnitude. An unpassivated thick-cap device has

the same low-frequency noise performance as a passivated standard HEMT. A field-

plate does not appear to help LFN, unlike noise figure. GaN HEMT low-frequency

noise is worse than that of GaAs HEMTs because the slope of the noise is much larger.

The phase noise of two GaN HEMT-based differential oscillators were explored.

The first had poor phase noise, but very good harmonic suppression, and was the

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first GaN HEMT differential oscillator in the literature. The second oscillator showed

excellent phase noise performance at large offsets, but poor performance at closer

offsets because of the phase noise being dominated by the low-frequency noise. The

GaN power advantage that was hoped would improve the oscillator signal-to-noise,

and thus phase noise, was more than offset by the increase of low-frequency noise

with power. Because of these problems with low-frequency noise, GaN oscillators do

not perform better - they do not even meet the performance typically seen by GaAs

and Si oscillators.

6.2 Future Paths

Trying to make progress in an entire field of study which is not completely under-

stood and making three difficult-to-use measurement systems work allows room for

improvement. To improve noise figure, gate leakage needs to be controlled, but first

it needs to be understood. This is no doubt the pursuit of many champions of GaN

research because of its implications for reliability and power performance. It would

also be of interest to look at bias dependence of ion-implanted GaN HEMTs to see

if it improves the curve typically seen for minimum noise figure versus drain-source

current. As thick-cap HEMTs do not need passivation, they are an interesting device

with possible industry applications. Their noise figure performance at large current

biasings was better than any other measured by the author. A better understanding

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could be pursued.

The work on low-frequency noise studies was only started and could be greatly

expanded upon. In particular, while few researchers have even reported the drain low-

frequency noiseVds dependence, none have attempted to explain it. As this seems to

be directly linked to the measured phase noise of oscillators, it is strongly suggested

it be studied in depth.

There are many ways to try to improve phase noise. The oscillators presented here

were relatively simple. More-sophisticated circuits should be undertaken and with

smaller devices than those presented here or in other works. The researchers whose

work has been discussed were designing with high power in mind. Before these cir-

cuits can be attempted, the circuit model needs to be improved. There are several

shortcomings. First, the ADS circuit model predicts that minimum noise figure ver-

sus drain source current is flat, which is a glaring problem (see figure 3.7). Dynamic

source and drain resistances must be included along with self-heating effects. Gate

leakage is not included in the model and should be added. The attempt at using

an ADS symbolically-defined device to generate a voltage-controlled low-frequency

noise current source was not successful, as the simulator appeared to use the DC bias

instead of the varying large-signal voltage of the oscillation. A custom ADS compo-

nent might be required, which could involve a few hundred lines of code. With these

deficiencies corrected, it might be possible to more closely simulate phase noise and

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possibly better understand why a field plate helps the phase noise performance.

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AADS Files

An ADS project that contains files used in this work can be downloaded at

http://my.ece.ucsb.edu/sanabria/research/ADSNoiseTemplate.zap

or by contacting the author [email protected]. The downloaded file will need

to be unarchived in ADS. The project contains files necessary to:

1. Extract and optimize the small-signal parameters, as well as to simulate a small-signal model of the transistor for S-parameters

2. Simulate noise figure with either the correlated noise or Pospieszalski model

3. Extract the noise variables for the correlated noise model

Steps explaining how to do each of these functions with the project are presented in

the next three sections. Example files for each are provided in the project.

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APPENDIX A. ADS FILES

A.1 Small-Signal Extraction

To extract the small-signal model, three S-parameter measurements are needed:

those of the device, a shorted-pads version of the device, and an open channel version

of the device. For more details, refer to§ 2.3. It may also be useful to measure

extrinsic parasitic resistances through another means (such as Hall measurements).

The S-parameter measurements will then need to be imported intoindividual ADS

data sets.

Once the data is correctly in the ADS project, open the data display file

templatesmall signal parameterextraction.dds

The middle of the first page of the dds file should look like figure A.1. This is where

the S-parameters for the device, open, and short are entered. Example data sets are

currently entered (Hongtaoopen, Hongtaoshort, d021218FC1...). Once these are en-

tered, turn to the next page in the data display (its shortcut key combination isAlt,

p, e). Plots for the small-signal extrinsic capacitances are displayed, along with two

markers per graph. The plots should be relatively flat, except maybe at very low fre-

quencies (less than 1 GHz). Move the markers to a suitable range of values for each

parameter. An average will be calculated for these (and the rest of the small-signal

parameters). Continue through the next two pages for the parasitic resistance and in-

ductances. Then advance two pages to theintrinsic parameters graphspage. Here

there may be larger variations in the parameters. Choose values that make sense, and

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Figure A.1: First page oftemplatesmall signal parameterextraction.dds.

narrow the range close to the target frequency. Advancing to the next page shows the

calculated small-signal parameters. These can be entered into a small-signal model of

the transistor. Two have already been provided in the project:

templateHEMT smallsignaland PospieszalskiNoisemodel.dsn

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templateHEMT smallsignaland PucelNoisemodel.dsn

Simply substitute your values into one of these and save it as a new file. Once the

small-signal parameters have been entered, the sub-circuit containing the network can

be simulated for S-parameters. Open the schematic file

templateSparametersextractionoptimization.dsn

Here there is one of the small-signal files in a subnetwork, an S-parameter simulation

block, optimization blocks, and a Data Access Component for identifying an ADS

data set. This is shown in figure A.2. Leave the deactivated components out of the

simulation. Exchange the subnetwork with the circuit to be simulated, and simulate.

This will call the previous data display window. If ADS asks to change the data set,

answer “yes.” Go to theverificationpage. Here, S-parameters for the simulation are

compared to the data set used for extraction. The fit should be good, but not excellent.

The parameters can be optimized to the data. In the schematic window, enter the

ADS data set into the Data Access Component that was used for the extraction. Ac-

tivate all components in the schematic, then simulate. The simulation window will

display the final optimized small-signal parameters. Theverificationpage of the data

display window will show S-parameters for both the initial and optimized values. En-

ter the optimized values in the circuit sub-network. Deactivate the optimization blocks

again, and simulate. The agreement on theverificationpage of the data display win-

dow of the simulated and measured S-parameters should be excellent.

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Figure A.2: Schematic used for simulating S-parameters of the small-signal circuitand for optimization.

A.2 Noise Figure Simulation

Open the project, and then open the circuit schematic file

templatenoisefigure measure.dns

You should now be at the window shown in figure A.3. The subnetwork

templateHEMT smallsignaland PucelNoisemodel

contains a small-signal model for a HEMT that includes noise sources and noise vari-

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ables for a Correlated Noise (CN) model. How to obtain the noise variables from

noise parameter measurements and small-signal parameter values is discussed in the

next section. This subnetwork can also be substituted with

templateHEMT smallsignaland PospieszalskiNoisemodel.dsn

which contains a small-signal model of a HEMT and noise sources and noise vari-

ables for the Pospieszalski model. The Pospieszalski noise variables are obtained from

noise parameter measurements and small-signal parameters with the Matlab code in

Figure A.3: Schematic used for simulating noise parameters.

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appendix C.

Returning to the circuit schematic, simulating brings up the data display

templatenoisefigure viewer.dds

Page 3 of this data display (use the shortcutAlt, p, eto navigate through the pages)

contains noise and gain circles on Smith Charts, the noise parameters, stability factor,

and noise figure for a 50Ω termination compared to NFmin versus frequency. The

other pages of the display also contain useful information for design.

A.3 Correlated Noise Model Extraction

To extract the noise variables for this type of noise model, the small-signal param-

eters need to be determined and entered into a circuit as explained in the first section

of this appendix. In particular, have all the small-signal parameters entered into the

variable (VAR) block of the circuit network


Measured noise parameters are also needed to determine the noise variables. Once

setup, open the circuit schematic

templateparasitic matrix for correlation extraction.dsn

which is shown in figure A.4. Here, there are two networks simulated for S-parameters.

They correspond to the intrinsic and extrinsic parameters, respectively. If the small-

signal network listed above was used, itsVARblock can just be pasted into this design

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and the previous one deleted.

Simulating should bring up the data display

templatenoisecorrelation extraction.dds

A screen shot of it is shown in figure A.5. The noise parameters will need to be entered

into the equations inside theChange Thesebox. Once this is done, theCpd unnorm

box andCextwill be the desired results:Cpd unnorm(1,1)is the gate noise in units

of A2/Hz, Cpd unnorm(2,2)is the drain noise in units of A2/Hz, Cpd unnorm(1,2)

andCpd unnorm(2,1)are the cross-correlation terms (not used here), andCext is the

correlation between the gate and drain noise. Entering these back into the secondVAR

block in


will allow for simulation of the noise parameters.

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Figure A.4: Schematic used for extracting correlated noise model noise variables.

Figure A.5: Data display used for extracting correlated noise model noise variables.

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BMatlab Code for Noise

Parameter Modeling

THIS Matlab script computes all four of the noise parameters as developed in§ 2.6,displays them in different formats, and plots minimum noise figure versus fre-

quency. This should facilitate the model’s use for other researchers. A copy of the filecan be obtained by contacting the author [email protected].

% NF.m% NF and other noise parameters including gate leakage, but not Cgd.% Chris Sanabria, 12/03/04

clear all;close all;

% Variables (change)

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APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING

Igs = 6e-6; % Gate leakagerge = 3.03; % Gate resistancers = 6;gmi = 0.033;ri = 8;cgsi = 0.21e-12;rds = 1000; % Drain-source resistance. Only used for a gain calculation

% and not for noise prediciton.

G = 2/3; % Gamma, use 2/3

f = [5e9 10e9]; % Operating frequency or frequenciesZo = 50; % Reference impedance for calculating reflection coefficientTa = 290; % Kelvin. This is the input temp., NOT the channel temp.!

% Constantsq = 1.6022e-019;k = 1.3807e-023;w = 2*pi*f;

% Intermediates that may changerin = rge + ri + rs;gm = gmi./(1+gmi.*rs);cgs = cgsi./(1+gmi.*rs);

% Intermediate variables (no changing)wt = gm./cgs; % That’s right, no 2pi.a = gm.*G.*(w./wt).ˆ2;b = q.*Igs./(2.*k.*Ta);xgs = -1./(2.*pi.*f.*cgs);

% Optimum input impedance (reflection coefficient) for noiseXopt = 1./(w.*cgs).*a./(a+b);Ropt = sqrt(rin./(a+b) + a./(a+b).*rin.ˆ2 + a.*b./((a+b).ˆ2.*(w.ˆ2.*cgs.ˆ2)));Zopt = Ropt + j.*Xopt;Gamopt = (Zopt-Zo)./(Zopt+Zo);

% Minimum Noise Figure

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APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING

rg = Ropt;xg = Xopt;Fmin = 1 + rin./rg + b./rg.*(rg.ˆ2+xg.ˆ2) + a./rg.*(abs(rin+rg+j.*(xg - 1./(w.*cgs)))).ˆ2;

% Noise resistance% First calculate NF at Zo, then use NFmin and NF @ Zo to get rnrgzo = real(Zo);xgzo = imag(Zo);Fzo = 1 + rin./rgzo + b./rgzo.*(rgzo.ˆ2 + xgzo.ˆ2) + a./rgzo.*(abs(rin+rgzo+j.*(xgzo -1./(w.*cgs)))).ˆ2;Rn = Zo.*(Fzo - Fmin).*(abs(1 + Gamopt)).ˆ2./(4.*abs(Gamopt)); % noise resistance(not normalized)

% Gainav @ NFmin. Will not be accurate because Cgd is not includedGav = abs(-(rds./2).*(wt./w).*j./((rg+rin) + j.*(xgs + xg))).ˆ2;

% Display outputsdisp([’Fmin = ’ num2str(Fmin)])disp(’ ’)NFmin = 10*log10(Fmin);disp([’NFmin (dB) = ’ num2str(NFmin)])

% disp([’|Zopt| = ’ num2str(abs(Zopt))])% disp([’|Zopt| = ’ num2str(abs(Zopt))])% disp(’ ’)% disp([’phase Zopt = ’ num2str(angle(Zopt)/pi*180)])% disp(’ ’)

disp([’r n = ’ num2str(Rn./Zo)])disp([’|Gammaopt| = ’ num2str(abs(Gamopt))])disp([’phase Gammaopt = ’ num2str(angle(Gamopt)/pi*180)])disp([’Gain av [dB] = ’ num2str(10.*log10(Gav))])

% Some plottingfigure;plot(f./1e9,NFmin,’r’)xlabel(’Frequency [GHz]’)ylabel(’NF min [dB]’)

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CMatlab Code for Pospieszalski Noise

Parameter Modeling

THIS Matlab script calculates the two noise temperatures for the Pospieszalskinoise model as discussed in§ 2.5.3. Because this involves solving a pair of

quadratic equations, it returns two sets of noise temperatures. The temperatures thatare negative in value are non-physical and should not be used.

% noisetemps.m% Uses Pospieszalski’s model to get the two noise temperatures. You need to% have taken noise figure measurements and have extracted a small signal% model. Because the solving is for a pair of quadratic equations, there% are two sets of solutions. Ignore the negative temperature pair.% Chris Sanabria, March 2003

clc;format compact

%Input these:

freq = 10e9; % HzNFmin = 2.03; % dBrn = .755; % NOT ohms, the normalized valuegamopt= 0.609*exp(j*54.4/180*pi); % Complex Reflection Coefficientft = 22.1e9; % In Hz. Pospieszalski defines this as gm/(Cgs*2*pi), but the% author finds that the measured ft can work better.Cgs = .258e-12; % Faradsrgs = 7.46; % Same as Ri

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APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING

rds = 1155; % Ohmsgm = .032; %STo = 290; % Kelvin

% Intermediate Equations

gds = 1/rds;Rn = rn*50;gn = 1/Rn;Zopt = (1+gamopt)/(1-gamopt)*50;Xopt = imag(Zopt);Ropt = real(Zopt);Tmin = (10ˆ(NFmin/10)-1)*To;N = Ropt/Rn;

% Solve the equations

[Td Tg] = solve(’Roptˆ2 = (ft/freq)ˆ2*rgs/gds*Tg/Td+rgsˆ2’,...’Tmin = 2*freq/ft*sqrt(gds*rgs*Tg*Td+(freq/ft)ˆ2*rgsˆ2*gds...ˆ2*Tdˆ2) + 2*(freq/ft)ˆ2*rgs*gds*Td’,’Td’,’Tg’);

% Values are currently in Kelvin

disp(’Values in Kelvin’);Td = eval(Td)Tg = eval(Tg)disp(’ ’);disp(’ ’);

% Values are now in degrees C

disp(’Values in Celcius’);Td C = Td - 273.15Tg C = Tg - 273.15

% Check the validty

disp(’ ’)disp(’ ’)disp(’Validity Check’)

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APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING

check = 4*N*To/Tmin;

(1<= check) && (check< 2)

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