Microelectronics Reliability 51 (2011) 560–565

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Microelectronics Reliability

journal homepage: www.elsevier .com/locate /microrel

RF small signal avalanche for bipolar transistor circuit design: Characterization,modeling and repercussions

Vladimir Milovanovic a,⇑, Ramses van der Toorn a, Ralf Pijper b

a Delft Institute of Microsystems and Nanoelectronics (DIMES), Delft University of Technology, Mekelweg 4, 2628CD Delft, The Netherlandsb NXP-TSMC Research Center, High Tech Campus 37, 5656AE Eindhoven, The Netherlands

a r t i c l e i n f o

Article history:Received 22 March 2010Received in revised form 12 October 2010Accepted 13 October 2010Available online 13 November 2010

0026-2714/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.microrel.2010.10.006

⇑ Corresponding author. Tel.: +31 (0) 152782431; fE-mail address: v.milovanovic@tudelft.nl (V. MilovURL: http://ectm.dimes.tudelft.nl (V. Milovanovic)

a b s t r a c t

In the face of increasing demands for high frequency and high output power of modern bipolar transistorcircuits, electronic circuit designers are exploring regimes of transistor operation that meet both require-ments and enter RF regimes, where impact ionization is significant. The present paper addresses AC/RFavalanche characterization techniques. Repercussions of avalanche breakdown on some important tran-sistor properties like unilateral power gain and the stability factor are introduced and demonstrated bymeasurements on modern industrial devices. On the basis of theoretical considerations and compactmodel simulations it is shown when avalanche can be expected to have significant impact on AC perfor-mance of bipolar transistors.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The millimeter wave (mmW) bands offer exciting opportunitiesfor various applications, such as short-range high data rate com-munications (e.g., the 60 GHz band), automatic cruise control andcollision avoidance systems through automotive radars (e.g., the77 GHz band) or passive imaging (e.g., the 94 GHz band) forsecurity screening. Therefore, the research and development of(monolithic) silicon-based solutions for such mmW applicationshas gained significant momentum in recent years.

Perhaps the most challenging building block at mmW frequen-cies is a power amplifier (PA). Driven by the requirements in termsof costs, integration and performance, integrated circuit designersstrive for implementation of such circuits using heterojunctionbipolar transistors (HBTs) available through the SiGe BiCMOS tech-nology. Due to the tradeoff between transit time and breakdownvoltage [1,2], the speed improvement of modern SiGe(:C) processeshas (partially) been achieved at the expense of reduced breakdownvoltages. For bipolar junction transistors (BJTs) in general, devicemetrics such as the unity current gain bandwidth fT, and the unitypower gain frequency fmax, increase as the collector-base bias volt-age VCB (and collector–emitter bias voltage VCE) is increased. In theface of increasing demands set upon power amplifiers for high fre-quency and simultaneous high output power, electronic circuitdesigners are exploring regimes of transistor operation that meetboth requirements and enter RF regimes, where impact ionization

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ax: +31 (0) 152787369.anovic)..

effects play significant role. Examples [3,4] of power amplifiersimplemented in SiGe:C BiCMOS technology and working in a 50–100 GHz range that exploit HBTs biased in the neighbourhood ofthe BVCEO (the open base collector–emitter breakdown voltage)[5] or even exceeding it by two to three [6] times, have been re-cently presented. Circuits containing bipolar transistors that areoperated above their BVCEO, but still always below BVCBO (thebase–collector p–n junction breakdown), are typically found inapplications, where high efficiency and large voltage swings are re-quired, that is, in RF power amplifiers for mobile wireless applica-tions. Specialized circuit topologies for biasing such circuits [7],tolerating output voltages above BVCEO have also been reported.It is known that the vast majority of BJTs appear to recover fromthe avalanche region without any visible permanent degradationin performance. However, in some highly scaled HBTs the hot car-riers generated in the process of impact ionization may damage asurface oxide leading to potential reliability issues.

For circuit designers that explore RF regimes in which ava-lanche breakdown may be expected to be significant, it is crucialto know the maximum usable transistor output voltage and itsdependence on driving conditions, as well as the repercussions ofworking in the avalanche regime on other transistor properties likevarious figures of merit for power gain and stability. Integrated cir-cuit designers rely on circuit simulator software to support theirdesign process using computer simulations. Compact models,which precisely describe the behavior of transistors in a mathe-matical way are essential in these simulations thanks to their effi-ciency. Consequently, accurate compact modeling of the AC/RFbehavior of bipolar transistors in the impact ionization regimehas become vital for the design of high speed Si and SiGe bipolarcircuits.

V. Milovanovic et al. / Microelectronics Reliability 51 (2011) 560–565 561

In general, studies of avalanche in bipolar transistors can begrouped in three classes, according to the regime in which a deviceis biased and the signal type by which it is driven. The first classwould then be the static, direct current (DC) class, in which in factno time-dependent signal is applied. This class is well-covered inliterature [8], which presents models [9–11] that describe devicebehavior well, at least in the so-called weak avalanche regime.The second class could be referred to as the small signal AC, wherea device is biased within the avalanche regime and a small alter-nating signal is applied. In the third class a transistor is biased out-side of the avalanche regime, but the applied AC signal is largeenough to put the device into the avalanche regime during signalswings or vice versa.

The present paper falls in the second class, extending the pastwork [12] of the first two authors. It focuses firstly on characteriza-tion of small signal AC bipolar transistor behavior in the impactionization regime on radio frequencies (RF), what is necessary toproceed with further research on this topic. Next, the effects of ava-lanche on some intrinsic transistor properties crucial for circuitdesigners, like unilateral power gain and Rollett’s stability factor,are addressed and analyzed on the basis of small signal equivalentcircuit analysis and compact model simulations. The dramaticrepercussions of impact ionization-induced influence on thesequantities is verified by RF measurements on modern high-endindustrial devices. Special attention is paid to explanation of phys-ics behind these phenomena.

Fig. 2. Full equivalent circuit schematics of Mextram 504.8, a physics-based,industrial world-standard compact model for vertical bipolar transistors. Theavalanche current source, central to this paper, is encased and highlighted.

2. Small signal AC avalanche characterization

2.1. Theoretical considerations

In a standard hybrid-pi small signal equivalent circuit of a bipo-lar junction transistor (BJT) shown in Fig. 1, the conductance gl inthe base–collector junction due to avalanche is represented by asimple resistor rl = 1/gl between the base and collector nodes. Astraightforward hand calculation (which solves port current equa-tions that are dependent on input voltages of the two-port networkdevice representation) shows that the avalanche conductance glimpacts the real parts of all four two-port admittance parametersof this equivalent circuit

y11 ¼ gp þ gl þ jxðcp þ clÞ; y12 ¼ �gl � jxcl; ð1Þy21 ¼ gm � gl � jxcl; y22 ¼ �go þ gl þ jxcl: ð2Þ

Imaginary unit is denoted by j. In this two-port network transistorrepresentation, base-emitter nodes are considered to form port 1and the collector–emitter nodes form port 2, hence together form-ing a common emitter configuration.

The real part of the y12 admittance parameter Rðy12Þ is equal tojust �gl. This suggests that in practice �Rðy12Þ might be an

Fig. 1. The hybrid-pi model of a bipolar junction transistor used for small signal ACanalysis complemented with the avalanche conductance gl, which is to becharacterized and whose effects on the characteristics are to be analyzed.

observable suitable to quantify and study avalanche in the smallsignal AC regime of transistor operation.

For accurate modeling of AC characteristics of modern indus-trial bipolar transistors in planar technologies, the hybrid-pi modelof Fig. 1 is too simple. The more extensive equivalent circuit that isa linear counterpart of the full equivalent circuit of Mextram [11](shown in Fig. 2 with highlighted avalanche current source), hasbeen demonstrated [14] to be adequate to this aim. Compared tothe hybrid-pi model in Fig. 1, the linearized circuit (of the model,with highlighted avalanche resistance) in Fig. 3 takes parasiticresistances and capacitances in the emitter, base and collector ofthe transistor into account. To limit the complexity of further anal-ysis of the circuit, input conductance gb and collector-substratecoupling effects have been neglected.

Using a computer algebra system, it can be shown that the realpart of the y012 admittance parameter of the linearized compactmodel two-port network circuit representation in common emitterconfiguration of Fig. 3 is given by

�R y012

� �¼ gl þ Oðx2Þ; ð3Þ

where x = 2pf is angular frequency. The symbol O(x2) denotes theadditional terms of at least second order in x. Because of space lim-itations, these terms cannot be represented here in full detail. Com-paring the circuits from Figs. 1 and 3, and the correspondingresulting expressions (1) and (3), however, it can be easily shownthat the O(x2) terms represent the effects from parasitic resistancesand capacitances (in combination with other model quantities liketransconductance).

Fig. 3. Linearized equivalent circuit of the model from Fig. 2, which has been usedas the basis in detailed small signal analysis. Substrate coupling is neglected. Theavalanche conductance, central to this paper, is highlighted.

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It should be emphasized that the effects of parasitics on Rðy012Þare of the second order as a function of frequency, as opposed to,for example, the first order contribution of base–collector capaci-tances to the Iðy12Þ in (1). On the basis of this observation, it canbe expected that, if the measurements are to be taken at suffi-ciently low frequencies and sufficiently high output bias voltages,the real part of y12 is going to be dominated by the avalanche con-ductance gl. Nonetheless, at sufficiently high frequencies or suffi-ciently low output voltages, the O(x2) parasitic terms willdominate Rðy012Þ.

Fig. 4. Measured (markers) and simulated (lines) real part of y12 parameter as afunction of frequency, for three values of the collector–emitter bias voltage (1.5 Vsquares and dash-dot line, 2.0 V diamonds and dashed line and 2.5 V circles andsolid line) of transistor [I] with BVCEO � 2.0 V. In an inset the correspondingmeasurements (dots) were performed on transistor [II] with BVCEO � 5.5 V forcollector–emitter voltages of 3 V, 5 V and 6 V. On lower frequencies and highervoltages avalanche conductance is clearly dominant for both of the processes. TheO(x2) effects become dominant over gl as the frequency is increased, however, theturnover point occurs later on RF device.

Fig. 5. Measured (markers) and simulated (lines) real part of y12 parameter as afunction of the collector current, for three values of the collector–emitter biasvoltage (1.0 V squares and dash-dot line, 1.5 V diamonds and dashed line and 2.0 Vcircles and solid line). In the subplot forward Early measurement (triangles) andsimulation (solid line) of the base current versus the applied collector–emitter biasvoltage are shown to indicate the avalanche breakdown point. Both measurementscorrespond to transistor [III]. In the medium current region, a complete change intrend of the Rðy012Þ admittance parameter (the 2.0 V curve crosses 1.0 V and 1.5 Vcurves) caused by avalanche is observed.

2.2. Experimental verification

The qualitative behavior of the real part of y12 admittanceparameter as a function of frequency and bias conditions, asexpected from the theoretical considerations of the previous sub-section, is indeed clearly observed in the measured data that wereobtained from three representative, state of the art industrialSiGe:C heterojunction bipolar transistors. Relevant properties ofthese HBTs are summarized in Table 1. Two high speed (HS)QUBiC4X BNX-type BiCMOS HBTs and one typical industrial highvoltage (HV) BiCMOS SOI HBT are used.

The measured (symbols) frequency sweeps in the main plot ofFig. 4, as well as of Figs. 7 and 9, are the ones of device [I] presentedfor several bias conditions: (VBE = 0.82 V, VCE = 1.5 V), (VBE = 0.81 V,VCE = 2.0 V) and (VBE = 0.81 V, VCE = 2.5 V). In the insets of the samefigures, frequency sweeps of another device [II] are presented forVCE = 3, 5, and 6 V, all for VBE = 0.85 V. These, and all other measure-ments in this paper were taken at room temperature. Also, all RFmeasurements were deembedded using the on-wafer open andshort structures for high speed devices and only the on-wafer openstructure for high voltage device.

For VCE well below BVCEO, it can be observed the O(x2) depen-dence of Rðy012Þ for all frequencies within the measurement range.This corresponds to a frequency dependence of Rðy012Þ induced byparasitic resistances and capacitances, conforming (3). For both de-vices it is observed that in the appropriate low frequency limit, forVCE approaching or above BVCEO; Rðy012Þ tends to a frequency inde-pendent value. Apparently it is dominated by gl in this regime ofoperation. In the high frequency limit, for the higher VCE valuesshown, parasitic effects are observed to dominate avalancheconductance.

Fig. 5 presents the bias sweep measurement (symbols) at fixedfrequency of f = 5.337 GHz for QUBiC4X BNX-type transistor [III] ofdifferent emitter size. Measurements shown in Figs. 6 and 8 arealso obtained from the same device.

It can be observed that in the medium current region, the effectsof bias cause a global increase of jRðy012Þj with increasing IC, due toa bias-dependence of various elements of the transistor equivalentcircuit. The drastic increase in jRðy012Þj for IC above roughly 2 mA isdue to the so-called base pushout or Kirk effect. It is well-knownthat the base pushout is postponed when VCE is increased and thistrend is clearly observed in the plot. The effect of avalanche onRðy12Þ is clearly recognizable in the collector current IC regimebetween roughly 30 lA and 1.5 mA, as it causes a dramatic in-crease in magnitude when VCE is increased from 1.5 V to 2.0 V.

Table 1Relevant facts about heterojunction bipolar transistors on which experimental verification is performed.

Device Transistor Type Process Application Emitter (lm2) BVCEO (V) Sweep In Figures

I QUBiC4X [13] NPN BiCMOS High speed 0.4 � 10.3 �2.0 Frequency Figs. 4, 7, 9II Typical industrial NPN BiCMOS SOI High voltage 0.4 � 0.8 �5.5 Frequency Figs. 4

0, 7

0, 9

0

III QUBiC4X [13] NPN BiCMOS High speed 0.4 � 1.0 �1.9 Bias Figs. 5, 6, 8

10−5

10−4

10−3

0

200

400

600

800

1000

Collector Current (IC) [A]

Uni

late

ral P

ower

Gai

n (G

U)

10−5

10−4

10−3

0

500

1000

IC [A]

GU

QUBiC4X high speed transistor [III]

frequencyf = 5.337 GHz

f = 5.337 GHz

Simulations:

avalanche off .

VCE =1.0 V ,1.5 V ,2.0 V .

EXAVL = 0

EXAVL = 1

Fig. 6. Measured (markers) and simulated (lines) unilateral power gain as afunction of the collector current, for three values (1.0 V, 1.5 V and 2.0 V) of thecollector–emitter bias voltage VCE. Symbols and curves correspond to those in Fig. 5.In an inset the same plot is repeated only in the simulations avalanche model ofMextram is turned off, thus giving a clear overestimate of the power gain forVCE = 2.0 V, where impact ionization effects cannot be neglected.

Fig. 7. Measured (markers) and simulated (lines) unilateral power gain as afunction of frequency of transistor [I], for three values (1.5 V, 2.0 V and 2.5 V) of thecollector–emitter bias voltage. In an inset the corresponding measurements (dots)were performed on transistor [II] for three values (3 V, 5 V and 6 V) of VCE. Cleardrop of the power gain caused by feedback effect of the avalanche conductance gl

on higher VCE and lower frequencies is observed.

Fig. 8. Measured (markers) and simulated (lines) stability factor k as a function ofthe collector current, for three values (1.0 V, 1.5 V and 2.0 V) of the collector–emitter bias voltage VCE. Symbols and curves correspond to those in Figs. 5 and 6, aswell as the change in trend of the observed variable in the middle current range,there Rðy12Þ and GU, respectively, and here of the k.

V. Milovanovic et al. / Microelectronics Reliability 51 (2011) 560–565 563

3. Small signal AC avalanche modeling

The curves in Fig. 5 demonstrate the capability of the model tosimulate effects of avalanche on AC characteristics. The inset of thefigure shows measured (symbols) and simulated (curve) data un-der DC bias conditions [15], more specifically, the DC base terminalcurrent IB for fixed base-emitter bias voltage VBE, as a function ofoutput voltage VCE. Observed decrease of the base current due toavalanche is neatly reproduced by the model simulations. Themain plot of Fig. 5 demonstrates that the combination of Mex-tram’s 504.8 (in further text simply referred to as the model) quasi-static avalanche model [16] and its extensive modeling of parasiticeffects [14] provides the capability to accurately simulate theeffects of impact ionization on the shown RF characteristics as well.Here also extended avalanche model is turned on by switching

EXAVL flag from 0 to 1. It enables taking into account the effectiveepilayer width decrease due to base widening. The effect of the ex-tended impact ionization modeling is observable in Figs. 5 and 6,which show that in the critical region of transition between middleto high current regime, setting the flag EXAVL = 1 gives slightlybetter fit.

In Fig. 4, it is shown that the dependence on frequency of Rðy012Þcan be simulated (curves) well by the model. The underestimationof Rðy12Þ in the low frequency limit for the VCE = 2.5 V curve is dueto the intentional underestimation of impact ionization in thestrong avalanche regime. Indeed, for the reasons of robustness ofconvergence in the context of general circuit simulations, the ava-lanche model is restricted to weak avalanche, (the case where car-riers generated in a process of impact ionization do not generateextra carriers).

4. Small signal AC avalanche repercussions

Expressions (1) and (2) show that in a two-port description ofthe small signal behavior of a bipolar transistor, avalanche is man-ifested in the real parts of all admittance parameters. In turn, thereal parts of admittances y are crucial ingredients of some funda-mental properties or invariants, of two-ports. In this section theimpact of avalanche on some of these is explored, namely, on theunilateral power gain GU, Rollett’s stability factor k, and the maxi-mum available power gain GMA.

4.1. Unilateral power gain

As an invariant and hence an intrinsic device property, unilate-ral power gain [17] is a central concept in two-port active devicecharacterization [18], as well as in (RF) analog circuit design. It isexpressed in terms of two-port network parameters by

GU ¼jc21 � c12j

2

4ðRðc11ÞRðc22Þ �Rðc12ÞRðc21ÞÞ; ð4Þ

where the immittances c can be substituted by impedance- (z),admittance- (y), hybrid- (h) or inverse hybrid- (g) parameters ofthe two-port transistor representation. As shown by expression(4), the unilateral power gain explicitly depends on the real partsof all four two-port transistor representation parameters.

Fig. 9. Measured (markers) and simulated (lines) frequency response of thestability factor k of transistor [I], for three values (1.5 V, 2.0 V and 2.5 V) of thecollector–emitter bias voltage VCE. In an inset the corresponding measurementswere performed on transistor [II] for three values (3 V, 5 V and 6 V) of VCE. Drasticincrease of stability caused by the avalanche conductance feedback effect can beobserved in the lower frequency region when entered into the impact ionizationregime. Symbols and curves correspond to those in Figs. 4 and 7.

564 V. Milovanovic et al. / Microelectronics Reliability 51 (2011) 560–565

Eq. (2) shows that, at lowest order in x;Rðy21Þ is the intrinsictransconductance of the transistor, gm. Since in the forward activemode of transistor operation, gm is a dominant quantity in bipolartransistors, and in view of the findings in the previous sectionsabout the sensitivity of Rðy12Þ to avalanche, (4) suggests that theunilateral power gain may be sensitive to avalanche too. Such sen-sitivity can indeed be observed on the cutting edge industrial bipo-lar transistors, as is demonstrated in Figs. 6 and 7. These figuresshow the measured (symbols) and the simulated (curves) unilate-ral power gain as a function of the collector current at fixed fre-quency and as a function of frequency at several biases,respectively.

In Fig. 6 it can be observed that for VCE = 1.0 V or 1.5 V, at fixedcollector current IC, the unilateral power gain increases withincreasing VCE. When VCE is further increased to 2 V, however, thegain drops dramatically. The physical mechanism behind this sen-sitivity is demonstrated in Fig. 6 by means of the compact modelsimulations. The curves in the main plot of this figure show the re-sult of the model simulations. The curves in the inset of the figurealso show the results of the model simulation, but with a modelparameter set that effectively suppresses avalanche effects alto-gether. These simulations clearly identify avalanche as the causeof the dramatic drop of GU when VCE is increased to 2.0 V. As a gen-eral observation, it should be noted that the underestimation ofavalanche leads to the overestimation of the transistor’s (unilate-ral) power gain at certain frequencies.

Also in Fig. 6 a sudden drop of the unilateral gain may be ob-served at relatively high current values. As this sharp change oc-curs at the very same current level as for Rðy12Þ in Fig. 5, itmight be expected that the same phenomenon is responsible forthis and that it is also the base pushout. However, it may be alsonoticed in Fig. 5 that there is a change in observed variable for fixedoutput voltage. For this change O(x2) effects are responsible, asthey include bias-dependent terms.

In Section 2.2 we learned that at sufficiently high frequencies,Rðy012Þmay be dominated by the parasitic effects that in such casesmask the influence of avalanche. These masking frequencies arehigher as the avalanche conductance is larger.

The conductance �Rðy12Þ represents a feedback inside anamplifying device. Due to the phase rotation of p between theintrinsic collector and base nodes this feedback is negative, there-fore the minus sign. As a result, power gain will drop with fre-quency, as follows from the feedback theory [19], when �Rðy012Þincreases with frequency due to the parasitic base and collectorresistance effects and their distribution over the base–collectorcapacitance, represented by the O(x2) term in (3). For bias condi-tions that are outside the avalanche regime (VCE = 1.5 V� BVCEO

for HS and VCE = 3.0 V� BVCEO for HV), this frequency dependenceis indeed observed in Fig. 7, which presents the measured (sym-bols) and the model simulated (curves) values of GU as a functionof frequency; results are shown for the same two representativeindustrial SiGe BiCMOS HBTs as in Fig. 4. The same figure showsthat, similar to �Rðy012Þ (Fig. 4), in the low frequency limit, GU issensitive to avalanche effects, while in the high frequency limit,this effect is masked by the (parasitic) resistance–capacitance con-tributions. In the low frequency limit and for VCE = 2.5 V, the im-pact of avalanche on GU is underestimated due to the intentionalrestriction of the avalanche model to weak avalanche.

A question of general interest is the following: up to whichoperating frequency are the avalanche effects actually dominantover the (distributed) parasitic resistance and capacitance effects?As explained in Section 2.1, the second order effects in (3) stronglydepend on the distributed parasitic base–collector capacitances. Asa result the frequency above which the unilateral power gain willstart to fall off with increasing frequency will depend on thesecapacitances. The lower the capacitances will be, the higher will

be the mentioned frequency. Therefore, as a result of the industrialtrend of decreasing the parasitic base–collector capacitance in or-der to increase the maximum oscillation frequency fmax, avalancheeffects can be expected to become more and more pronounced inRF characteristics and figures of merit of future high speed technol-ogy generations (as may be also concluded from the quantitativecomparison of devices [I] and [II] in this aspect).

Measurements at mmW frequencies can be both challengingand expensive, therefore it would be useful to be able to make arelatively accurate estimate of the frequency up to which the im-pact ionization effects are dominant over the higher order parasiticresistance and capacitance effects (and actually prevail) in the GU

characteristics. As such estimate one might choose the frequencypoint, where �20 dB/dec unilateral gain extrapolation of the de-vice, as biased with output voltage which does not correspond toexcessive impact ionization (low VCE) with input bias voltage keptat the same value, would meet the measured avalanche affectedunilateral gain at low frequencies.

4.2. Stability factor

Other important invariants, especially useful in analog (RF)integrated circuit design [20], are the stability factor,

k ¼ 2Rðc11ÞRðc22Þ �Rðc12c21Þjc12c21j

; ð5Þ

and the maximum available power gain GMA,

GMA ¼c21

c12

��������ðk�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffik2 � 1

qÞ : ð6Þ

In the last expressions the immittances c may also be substituted byimpedance- (z), admittance- (y), hybrid- (h) or inverse hybrid (g)transistor two-port network representation parameters, meaningk and GMA are the invariants.

The measurements (symbols) and the compact model simula-tions (curves) of the stability factor as a function of bias at fixedfrequency and as a function of frequency are shown in Figs. 8and 9, respectively. The influence of avalanche on the maximumavailable gain is similar to its influence on the unilateral powergain (of course, when defined for k P 1). In fact, when avalanche

V. Milovanovic et al. / Microelectronics Reliability 51 (2011) 560–565 565

influence is underrated, the maximum available power gain isovervalued. Repercussion of impact ionization on stability can alsobe explained in terms of the avalanche-induced negative feedback.Particularly, negative feedback tends to move transfer functionpoles further away from the right complex half-plane [19], thatis, the device becomes more stable.

5. Conclusion

To meet the increasing demands for high operating frequencyand high output power in modern bipolar transistor applications,circuit designers explore regimes of transistor operation close toor within the avalanche breakdown region.

In order to qualify and quantitatively model the effects occur-ring in the impact ionization regime, in the present paper this re-gime of operation is addressed, in which small signal bipolartransistor behavior is analyzed. The collapse of the unilateralpower gain due to the impact ionization effects, as quantified bythe avalanche-induced conductance gl, is demonstrated, physicalorigins of it are identified and the repercussions of avalanche onthe maximum available power gain, as well as on the stability fac-tor k, are addressed. The frequency dependence of these quantitiesis described and commented in detail. The concepts and analysesare illustrated by the RF measurements on modern industrial het-erojunction bipolar devices and by the corresponding computersimulations, employing the standard compact model for bipolartransistors. Though all examples in the paper were performedmeasuring and simulating NPN types, all physical concepts arequalitatively and quantitatively applicable to PNP type bipolarjunction transistors, as well.

It is found out that the effects of avalanche on AC characteristicsand figures of merit may be masked by higher order effects of par-asitic resistances and capacitances. However, according to the con-ducted analysis, trends in semiconductor industry imply thatavalanche effects tend to be dominant in the operating frequenciesof interest over parasitic effects in most modern and coming tech-nology generations.

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