Post on 22-Mar-2020
Predictive microwave device design by coupled electro-thermalsimulation based on a fully physical thermal model
W. Batty×+, C. E. Christoffersen∗, S. David×,A. J. Panks×, R. G. Johnson×, C. M. Snowden× and M. B. Steer∗,
×Institute of Microwaves and Photonics, ∗Dept. of Electrical and Computer Engineering,School of Electronic and Electrical Engineering, North Carolina State University (NCSU),
University of Leeds, Leeds LS2 9JT, UK. Raleigh, NC 27695-7914, USA.+Contact: tel. +44 113 2332089, fax +44 113 2332032, e-mail w.batty@elec-eng.leeds.ac.uk.
AbstractCoupled electro-thermal simulations are performed todemonstrate predictive design of microwave devices.These simulations are based on an original, fully physical,thermal impedance matrix approach, capable of describingcomplex 3-dimensional systems, whilst requiring no modelreduction for electro-thermal CAD. This thermal model isvalidated by thermal imaging of passive grid arrays repre-sentative of spatial power combining architectures. Fullyphysical simulations of power HEMT I-V characteristicsare presented, by coupling the thermal resistance matrixapproach to the Leeds Physical Model of MESFETs andHEMTs. Single-tone, two-tone and multi-tone harmonicbalance simulations are presented for a MESFET ampli-fier, by implementing the thermal impedance matrix ap-proach in microwave circuit simulator, Transim (NCSU).
I. Introduction
The importance of self-heating, and of mutual thermalinteraction between active elements, in power devicesand circuits, is well known. Hence predictive design,based on electro-thermal simulation, has been pursuedfor over 30 years. Until recently, the state of the artin time-independent thermal simulation of power FETsand MMICs, for coupled electro-thermal CAD, has beenrepresented by the hybrid finite element Green’s functionapproach of Bonani et al. This approach treated devicestructure such as surface metallisation, vias and partialsubstrate thinning. In time-dependent coupled electro-thermal CAD, thermal descriptions have been more prim-itive, and limited to simple rectangular multilayers. Workin this area is exemplified by that of Szekely et al., whogenerated a large range of semi-analytical thermal solu-tions for ICs, MCMs and microsystem elements. A vari-ety of thermal model reduction techniques have also beenemployed to make tractable the coupled electro-thermalsimulation problem on CAD timescales. The problem ofcompact model development for thermal networks is cur-rently a highly active area of research.The authors have progressed the state of the art, by pre-senting a thermal resistance matrix model capable of de-scribing, nearly exactly, 3-dimensional time-independentheat flow in complex device structures, in a fashion com-patible with electro-thermal CAD [1], [2]. This modelincludes description of surface fluxes and treats all ther-mal non linearities. More recently, the authors havepresented a thermal impedance matrix model, extendingthis description to treat the thermal time-dependent case,both steady-state and transient [3]. This time-dependentformulation allows interpretation of thermal subsystemsin terms of generalised multiport network parameters,without requiring model reduction. Circuit level electro-thermal simulation was achieved by implementation ofthis thermal impedance matrix model in a network basedmicrowave field and circuit simulator, Transim (NCSU).Fully physical electro-thermal device CAD, based on cou-pling of the thermal impedance matrix approach, tothe rapid, quasi-2-dimensional, Leeds Physical Model ofMESFETs and HEMTs, has been described by the au-thors elsewhere [4]. Application of the resulting fully
physical electro-thermal model to optimisation of powertransistor and MMIC design, by transient simulation,is described by David et al., (this conference, [5]). Incontrast, the aim of this paper is to apply the ther-mal impedance matrix model to examine design rules forpower devices embedded in amplifier circuits. This isachieved by electro-thermal harmonic balance and tran-sient simulation, particularly demonstrating thermal ef-fects on multi-tone intermodulation distortion and spec-tral regrowth. These represent an essential aspect ofdevice optimisation for narrowband digital modulationapplications such as CDMA for mobile communications.The ultimate intended application of the modelling capa-bility described here, is study and design of spatial powercombining systems for use as high power sources at mil-limeter wavelengths. The thermal model is therefore vali-dated by thermal imaging of passive grid arrays represen-tative of one form of quasi-optical system architecture.
II. Results
Figs. 1–3 demonstrate validation of the thermal model, bycomparison of simulation against thermal imaging, for apassive grid array representative of spatial power com-bining architectures. Figs. 4 and 5, demonstrate thatfully physical prediction of device performance can beachieved by combining the thermal resistance matrix ap-proach with the Leeds Physical Model, and can be usedfor electro-thermal optimisation of device design. Fig. 6depicts the simulated amplifier used for study of ther-mal effects on MESFET performance. Figs. 7 and 8 il-lustrate single-tone harmonic balance (HB) simulation.Figs. 9 and 10 illustrate two-tone HB, demonstrating in-termodulation distortion due to amplifier non linearity.Due to thermal inertia, thermal response is seen to bemuch greater at the 1 MHz difference frequency than atthe ∼1 GHz fundamental frequencies. Figs. 11 and 12 il-lustrate the impact of thermal effects on multi-tone IMD.
References
[1] W. Batty, A. J. Panks, R. G. Johnson and C. M. Snowden,‘Electro-thermal modelling and measurement for spatial powercombining at millimeter wavelengths,’ IEEE Trans. MicrowaveTheory Tech., vol. 47, no. 12, pp. 2574–2585, 1999.
[2] W. Batty, A. J. Panks, R. G. Johnson and C. M. Snowden,‘Electro-thermal modelling of monolithic and hybrid microwaveand millimeter wave IC’s,’ VLSI Design, vol. 10, no. 4, pp.355–389, 2000.
[3] W. Batty, C. E. Christoffersen, S. David, A. J. Panks, R.G. Johnson and C. M. Snowden, ‘Steady-state and transientelectro-thermal simulation of power devices and circuits basedon a fully physical thermal model,’ THERMINIC 2000, Bu-dapest, September 2000.
[4] S. David, W. Batty, A. J. Panks, R. G. Johnson and C. M.Snowden, ‘Fully physical coupled electro-thermal modelling oftransient and steady-state behaviour in microwave semiconduc-tor devices,’ 8th Gallium Arsenide Application Symp. (GAAS2000), paper GAAS/P1 (3), Paris, October 2000.
[5] S. David, W. Batty, A. J. Panks, R. G. Johnson and C. M.Snowden, ‘Electro-thermal modelling of microwave transistorsand MMICs for optimised transient and steady-state perfor-mance,’ submitted to this conference, EDMO 2000.
0 50 100 150 200 250 300 350 400Time (s)
290
300
310
320
330
340
350T
empe
ratu
re (
K)
AlN (simulation)
FR-4 (experiment)FR-4 (simulation)
Fig. 1. Central temperature rise with time at turn-on, of a 10×10passive grid array dissipating 2 W. Substrates: FR-4 (experi-ment and simulation) and AlN (simulation). Cooling is purelyby radiation and convection (no heatsink mounting). Agree-ment between theory and experiment is good, validating thethermal model.
t = 50 s
t = 200 s
t = 100 s
t = 250 s
t = 150 s
BELOW 300
300 - 304
304 - 309
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318 - 322
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336 - 340
340 - 345
ABOVE 345
Temperature (K)Fig. 2. Time dependent Inframetrics ThermaCam 280 measure-
ments of 10× 10 passive grid array: FR-4, 5× 5 cm2, dissipat-ing 2 W. Cooling purely by surface radiation and convection(no heatsink mounting).
t = 50 s
t = 200 s
t = 100 s
t = 250 s
t = 150 s
BELOW 300
300 - 304
304 - 309
309 - 314
314 - 318
318 - 322
322 - 327
327 - 332
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336 - 340
340 - 345
ABOVE 345
Temperature (K)Fig. 3. Time dependent thermal simulations of the 10× 10 passive
grid array: FR-4, 5 × 5 cm2, dissipating 2 W. Cooling purelyby surface radiation and convection (no heatsink mounting).Agreement between theory and experiment is good, validatingthe thermal model.
0 1 2 3 4 5 6 7 8
Vds (V)
0.0
0.2
0.4
0.6
0.8
Ids
(A)
Vg
-0.2 V
-0.4 V
-0.6 V
-0.8 V
-1.0 V
-1.2 V
-1.4 V
10-finger: GaAs die + 6um metal
Fig. 4. Electro-thermally simulated I-V characteristics of a 10-finger Filtronic power HEMT with 6 µm surface metallisationand adiabatic surface boundary conditions. Finger width is 400µm; substrate thickness is 75 µm; heatsink temperature is 300K. Thermal droop is predicted fully physically, based solely onspecification of device structure and material parameters.
BELOW 27
27 - 31
31 - 35
35 - 39
39 - 43
43 - 47
47 - 51
51 - 55
55 - 59
59 - 63
63 - 67
ABOVE 67
Fig. 5. Electro-thermally simulated interface temperature plot ofthe 10-finger Filtronic power HEMT with 6 µm surface met-allisation and no convective surface fluxes. Finger width is 400µm; substrate thickness is 75 µm; heatsink temperature is 300K. Bias point is (VDS , VG) = (3.5 V, -0.2 V); power dissipationis 2.8 W. Temperature varies from 27 ◦C to 67 ◦C. Tempera-ture variation along and between gate fingers implies spectralregrowth.
Thermal
300K
Vs
Vdd
Vbias
Thermal ground (0 K)
1-Port
Fig. 6. Schematic of the simulated MESFET amplifier with thermalcircuit. The MESFET is described by the Curtice-Ettenberg cu-bic model with symmetric diodes and capacitances. The MMICdie is described by thermal 1-port network parameters.
0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Time (us)
-0.01
-0.005
0.0
0.005
0.01
0.015
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0.03Id
s (A
)
2.94
2.95
2.96
2.97
2.98
2.99
3.0
3.01
Vds
(V
)
Fig. 7. Drain-source current ids (solid line) and drain-source voltagevds (dashed line) for a 5-finger power transistor, from single-tone HB analysis with fundamental frequency 10 MHz.
0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Time (us)
-0.08
-0.06
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-0.02
0.0
Pow
er (
W)
304.9
305.0
305.1
305.2
305.3
305.4
305.5
305.6
305.7
Tem
pera
ture
(K
)
Fig. 8. Power dissipation (solid line) and temperature variation(dashed line) for the 5-finger power transistor, from single-toneHB analysis with fundamental frequency 10 MHz.
105 106 107 108 109 1010
Frequency (Hz)
0.0
0.2
0.4
0.6
0.8
1.0
Pow
er (
W)
Fig. 9. Power dissipation in the frequency domain for a 50-fingerpower transistor, from two-tone HB analysis with fundamentalfrequency 1 GHz and difference frequency 1 MHz.
105 106 107 108 109 1010
Frequency (Hz)
0
2
4
6
8
10
12
14
16
Tem
pera
ture
Ris
e (K
)
Fig. 10. Temperature variation in the frequency domain for the 50-finger power transistor, from two-tone HB analysis with funda-mental frequency 1 GHz and difference frequency 1 MHz.
105 106 107 108 109 1010
Frequency (Hz)
0
50
100
150
200
250
300
Ids
(mA
)
Fig. 11. Current variation in the frequency domain for the 50-finger power transistor, from multi-tone HB analysis with 11fundamentals at frequency 0.5 GHz and difference frequencysteps of 0.5 MHz.
0.485 0.49 0.495 0.5 0.505 0.51 0.515 0.52Frequency (GHz)
0
10
20
30
40
50
60
Ids
(mA
)
Fig. 12. Current variation in the frequency domain for the 50-finger power transistor, from multi-tone HB analysis with 11fundamentals at frequency 0.5 GHz and difference frequencysteps of 0.5 MHz. Circles: without thermal effects. Crosses:with thermal effects.