Impact of the Emitter Stored Charge on RF Noise of JunctionBipolar Transistors.

Francesco Vitale1, Ramses van der Toorn1

1 Delft University of Technology, Electrical Engineering, Math and Computer ScienceMekelweg 4, 2628CD Delft, The Netherlands, F.Vitale@tudelft.nl

Abstract — In this paper a new noise model is pre-sented which accounts for the effect of the emitter storedcharge on the RF noise behavior of bipolar junction tran-sistors. The model is derived combining the general VanVliet noise model for bipolar transistors and the non-quasi-static (NQS) theory in quasi-neutral base and emitter re-gions. Model equations are then interpreted with the helpof a small-signal equivalent circuit of a bipolar transistorwhich includes additional circuit elements in order to takethe NQS effects in the base and in the emitter into account.It is shown finally that the emitter diffusion charge can havea considerable impact on the noise FOM’s of bipolar tran-sistors, compared to the impact of the NQS effects in thequasi-neutral base region.

Index Terms — Heterojunction bipolar transistors, semi-conductor device modeling, semiconductor device noise.

I. INTRODUCTION

Early calculations of the noise in bipolar junction tran-sistors date from the late 1950’s. The major results canbe found in the classical papers of Van der Ziel [1], [2]and Van Vliet [3]. In [3], a general expression is givenfor the noise in the impedance representation of a bipolartransistor in common base configuration:

SIαIβ = 2kT (Yαβ + Y ∗

βα)− δαβ2qIα ; (1)

here, α and β are the port indexes and δ is the Kroneckersymbol (if α = β then δαβ = 1 else δαβ = 0).

The derivation of the noise at the terminals of a bipolartransistor consists of two steps, as in any noise calcula-tion: first, the microscopic noise sources have to be de-termined. Second, the transfer from the location of thesemicroscopic noise sources to the external ports has to becalculated. This is not different from what happens whena compact model with an equivalent circuit is simulatedin a circuit simulator: the open-circuit noisy voltage in-duced on the external port α by a noise current generatorιij connected between the nodes i and j is calculated asthe transfer between the internal port j and the externalport α. This method and its evolution, known as the ad-joint approach [4], is very much related with the Green’sfunction approach extensively described in [3].

In principle, a compact model is quite capable of mod-eling most of the noise figures of merit, provided that theparameter extraction is done with a lot of attention puton the Y-parameters, so that the transfer from the internal

Figure 1: Small-signal model of bipolar transistors includingaddtional element counting for NQS effects.

noise sources to the external ports is done by the circuitsimulator in a proper way. Hence a good description ofthe admittance parameters of the transistor must be thefirst step for any good noise prediction.

It is known that compact models of bipolar transis-tors based on the charge-control principle are not capa-ble of modeling the device operation at high-frequencyproperly. Various models have been published which ac-count for NQS effects [5],[6],[7],[8],[9],[10] and in re-cent years noise models have been presented which de-scribe correlation combining the Van Vliet noise model(1) and the NQS theory in the base region. The emit-ter region has been always neglected in the noise the-ory, though it has been proved that the stored charge inthe emitter region has an impact on the high-frequencysmall signal characteristics of bipolar transistors [8],[11].In [12] was experimentally observed that the emitter dif-fusion charge has an impact on the noise figures of meritas well. Despite this it is common use in noise mod-eling either to neglect the emitter region or to nest theemitter diffusion charge together with the base diffusioncharge [13],[14].

The purpose of this paper is to show the impact ofthe emitter stored charge on the noise FOM’s of bipo-lar transistors. First a noise model is derived combin-ing the Van Vliet noise model (1) and the NQS modelof Seitchik [6] and Hamel [11]. The model equationsare then discussed and interpreted with the help of a lin-earized equivalent circuit of bipolar transistors which in-cludes an additional network in order to take NQS effectsin the base and emitter regions into account (Fig. 1). Thenoise model (1) is valid in the intrinsic transistor region;hence for a proper study of the effect of the emitter diffu-sion charge on RF noise and for a correct interpretationof data, the analysis is confined to the intrinsic transistoronly: all the parasitics, as well as the base-emitter and

978-1-4673-3021-3/12/$31.00 ©2012 IEEE

base-collector junction capacitances, are excluded fromthe model. It will be shown that the delay time associatedwith the emitter diffusion charge can have a considerableimpact on the noise figures of merit of bipolar transistors.

II. NOISE MODEL DERIVATION

The noise model (1) was derived for a common base con-figuration. In more recent theory of bipolar transistors itis common to work in a common emitter configurationby introducing the current ports [15]

ib = iep + ien − icn, ic = icn (2)

where iep, ien are respectively the hole and electronemitter current and icn is the electron collector current.These expressions for the base and the collector currentlead to:

y21 =∂ic

∂vBE

=∂icn∂vBE

(3)

y11 = ∂ib∂vBE

=∂iep∂vBE

+ ∂ien∂vBE

−∂icn∂vBE

=

= yb11e + yb

11b + yb21b = ye

11e + ye11b

(4)

where, following the notation given in [9], the subscripte/b indicates the region of the device - e.g. emitter orbase - and the superscript stands for ”common-base” (b)or ”common-emitter” (e).

Then the noise model (1) in common emitter configu-ration reads:

SIB = 4kTRe(y11)− 2qIB ,SIC = 2qIC ,SIBIC = 2kT (y∗

21− gm0) ;

(5)

here gm0 is the low frequency transconductance.In the low frequency limit, ye

11e is equal to the inputcommon emitter conductance gπ and ye

11b = jωgmτb,resulting in a frequency independent power spectral den-sity (PSD) at the input port (SIB = 2qIB). When theNQS effects in the base region are considered, the realpart of ye

11b is not zero anymore, but it contributes to theincrease of SIB with the frequency through a term that isa function of ω2. A common simplification is that ye

11e

is always set to Ipe/VT = gπ even at high frequencies,thus neglecting the NQS effect in the emitter region.

In order to include also the NQS effects of the emit-ter into the noise model (5), appropriate expressions ofy11 and y21 are needed, which can accurately model theinfluence of the stored charge in the base and emitter re-gion. Our starting point will be the NQS model presentedin [11], here rearranged as follows:

y11b = jωgm0τb

1 + jωτ2(6)

y11e = gπ + jωαegm0τe1 + jωτ3

(7)

y21 =gm0

1 + jωτ2exp(−jωτ1) (8)

where τb and τe are respectively the base and the emittertransit time and the delay times τ1, τ2 and τ3 are givenby

τ1 ≈ τ2 ≈

(1− αb)τb2

(9)

τ3 =(1− αe)αeβe

2(10)

The parameters αb and αe represent readily the fractionof the base and the emitter stored charge that is controlledby the small-signal base-emitter voltage.

For the sake of simplicity, equations (6)-(8) can be ap-proximated by the first terms of their Taylor expansionleading to

y11 = y11b + y11e ≃ gπ+

+ gm0[jω(τb + αeτe) + ω2(τbτ2 + αeτeτ3)](11)

y21 ≃ gm0[1− jω(τ1 + τ2)] (12)

Substituting (9)-(10) in (11)-(12) and then in equations(5) we get a new noise model that includes also the effectof the emitter stored charge:

SIB = 2qIB++ 2kTω2gm0[(1− αb)τ

2

b + αe(1− αe)βeτ2

e ]

SIC = 2qICSIBIC = −jω2kTgm0(1− αb)τb

(13)

III. EXPERIMENTAL RESULTS

In Fig. 1 shows the small-signal model that provides thebasis for our study of noise modeling. The grey part ofthe circuit includes precisely those ingredients of a tran-sistor model that are essential for our purpose here: thediffusion charges of the EB junction and the excess phasedelay associated with the transconductance gm. The cir-cuit of Fig. 1 is related to the equivalent circuit of the fullMextram model closely enough so as to make it possi-ble to obtain the parameter values for the circuit directlyfrom the operating point information of Mextram. Thisis demonstrated in Fig. 2, where ac-simulations on basisof the circuit of Fig. 1 are shown together with measuredadmittance parameters of a QUBiC4X [16] SiGe HBT;model parameters for the circuit were obtained directlyfrom corresponding Mextram operating point informa-tion.

For an interpretation of the noise model (13), we makeuse of the small-signal circuit representing the intrinsictransistor, illustrated in Fig. 1 (shaded box). This modelincludes an equivalent network that models correctly theexpressions (6)-(8) through the following small signal el-ements [11]:

rDB =(1 − αb)

2gm, CDB = gmτb (14)

rDE =(1 − αe)β

2αegm, CDE = αegmτe (15)

109

1010

1011

10−4

10−3

10−2

10−1

Y11

[A/V

]

109

1010

1011

10−6

10−4

10−2

Y12

[A/V

]

109

1010

1011

10−4

10−3

10−2

10−1

Y21

[A/V

]

freq [Hz]10

910

1010

1110

−6

10−4

10−2

freq [Hz]

Y22

[A/V

]

Figure 2: Admittance parameters as function of frequencyat fixed VBE = 0.82V and VCE = 1V . Symbols aremeasurements; solid lines are simulated Y-parameters of thesmall-signal circuit of Fig. 1. Data was measured dataon a QUBiC4X [16] SiGe HBT with an emitter size of0.4x10.3µm2.

Table 1: Small-signal parameter extracted from a 0.4x10.3µm2 SiGe HBT.

VCE = 1.0VVBE = 0.82V

gπ(µS) 163.2gm0(µS) 35β(−) 215τb(fs) 515τe(fs) 572

The small-signal parameters of the intrinsic block arelisted in Table (1).

From equations (13) it can be noticed that the increaseof SIB with the frequency is not only due to the NQS ef-fects in the base region but partly also to the delay associ-ated with the emitter diffusion charge. Since the emitterdelay time could be much larger than the base delay timefor polysilicon contact emitter, it is easily recognized thatthe impact of the emitter diffusion charge on SIB can bemore considerable than the impact of the base diffusioncharge, as Fig. 3 shows. Moreover any effect which in-fluences the PSD of the base noise current will have anobservable impact also on other noise figures of merit, asthe minimum noise figure Fmin, and the optimum noisesource admittance Yopt.

Two uncorrelated noise sources ιb and ιc have beenplaced in the intrinsic small-signal circuit, between theinternal node bi-ei and ci-ei. These noise sources arecharacterized by a PSD defined as:

ι2b = 2kTgpi∆f (16)

ι2c = 2kTgm∆f (17)

In practice, some correlation exists between these twonoise sources. An exact implementation of the noisemodel (13) has been implemented in the small-signal

0 1 2 3 4 5

x 1011

0

1

2

3

4

5x 10

−20 (a)

freq [Hz]

Sib

− 2

qIB [A

2 /Hz]

α

e = 0.65

αe = 0.75

αe = 0.85

0 1 2 3 4 5

x 1011

0

1

2

3

4x 10

−20

freq [Hz]

Sib

− 2

qIB [A

2 /Hz]

(b)

α

b = 0.65

αb = 0.75

αb = 0.85

Figure 3: (a) Analytical SIB− 2qIB versus frequency at fixed

αb = 0.75 and for three different values of αe. (b) AnalyticalSIB

− 2qIB versus frequency at fixed αe = 0.75 and for threedifferent values of αb.

model of Fig. 1. Details about the implementation ofthe correlation in our compact model will not be treatedhere.

The results of the circuit simulations are shown inFig. 4 and 5. Fig. 4 the impact of the emitter diffusioncharge: analytical data and circuit simulations matchonly when the effect of the emitter stored charge is takeninto account. Fig. 5 highlights the impact of the delay as-sociated with the emitter diffusion charge once more: theeffect of the base diffusion charge on the minimum noisefigure looks barely observable compared to the impact ofthe emitter region.

IV. DISCUSSION

In Fig. 5 we observe that the effect of the base chargedelay is negligible compare to that of the emitter diffu-sion charge. Nevertheless various noise models based onthe NQS theory in the base have been published, whichshow an observable impact of the base diffusion chargeon Fmin and Yopt [13], [14]. The reason for this is thatin these models the NQS theory in the base region is ap-plied to the total forward diffusion charge, making usein the model of global variables like Qtot = QE + QB

[13] or τf = τE + τB [14]. Hence the emitter diffusioncharge is nested in the base diffusion charge resulting ina observable effect and resulting in a proper noise predic-tion. This was observed in [12] where, by a modification

10−3

10−2

10−1

100

10−24

10−23

10−22

10−21

ω (τb + τ

e)

Sib

[A2 /H

z]

Figure 4: Simulated SIBversus the normalized frequency

ω(τb + τe): with base NQS effects and w/o emitter NQSeffects(◦), with both NQS effects (△). Symbols are from cir-cuit simulations, solid line is the analytical expression of SIB

from model (13).

10−2

10−1

100

101

0

2

4

6

8

10

12

ω (τb + τ

e)

Fm

in (

dB)

(a)

αe = 0.65

αe = 0.75

αe = 0.85

10−2

10−1

100

101

0

2

4

6

8

10

12

ω (τb + τ

e)

Fm

in (

dB)

(b)

αb = 0.65

αb = 0.75

αb = 0.85

Figure 5: (a) Minimum noise figure versus the normalized fre-quency ω(τb + τe) at fixed αb = 0.75 and for three differentvalues of αe. (b) Minimum noise figure versus the normalizedfrequency ω(τb+τe) at fixed αe = 0.75 and for three differentvalues of αb.

of the noise model, the effect of correlation on Fmin wasmuch less observable without counting the emitter diffu-sion charge in the noise model.

Finally a question may arise whether the VanVlietnoise model [3] is valid itself in the emitter region, sinceit has been derived in the base region only. To includethe emitter region in the Van Vliet noise model, a three-dimensional Langevin equation need to be solved for the

emitter minority carriers, following the same procedurein [3]. This issue was already addressed in [17], where itwas shown that, in order to include the noise induced bythe emitter minority carriers, the total SIB can be writtenas

SIB = 4kTRe(y11e + y11b)− 2qIB (18)

thus justifying the approach used in section II.

V. CONCLUSION

A noise model has been derived from the general VanVliet model which include the NQS effects related withthe quasi-neutral emitter region. The impact of the emit-ter diffusion charge on the noise properties of bipolartransistors has been then analyzed and discussed with thehelp of a small signal equivalent circuit whose parame-ters have been extracted from the admittance parametersmeasured on a NXP’s designed SiGe HBT. It has beenshown that the impact of the stored charge in the emittercan be considerable compared to the well known impactof the NQS effects in the base region, confirming the ob-servations given in [12].

ACKNOWLEDGMENT

Acknowledgements are due to TechAmerica CompactModel Council and to NXP Semiconductors.

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