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630 IEEE TR ASSAC TIONS o s ELECTROS DEVICES, VOL. ED-13, x os . 8/9, AUGUST/SEPTEMBER, 1966

Some New Aspects of Thermal Instability of the

Current Distribution in Power Transistors

F. BERGMANN AND D. GERSTNER

Abstract-An importantcharacteristic of secondbreakdown in

p-n junction s is the current onstriction to a small region. This may

becaused by a thermal eedbackmechanism, as discussed by

Scarle tt and Shockley, and by Bergmann and Gerstner.

A brief review of this theory is given, illustrated by experimental

results of a simple model arrangement consisting of three thermally

coupled transis tors. hessentialarameters influencing the

therma l stability of the cur ren t distribution are device geometry,

power density, and tempera ture d ependence of current.

I t is widely known that second breakdown occurs at high voltages

at a much lower power level than at low voltages. To allow a more

detailed discussion of this effect in view of thermal stability, we

determined experimentally the temperature coefficient of transistor

current for various Si planar transistors as a function of current,

voltage, and junction t emperature. The experimental procedure is

describ ed and the re sults are discussed.

Theexperimentalvalues of the emperature coefficient rangefrom 0.08 to 0.01 1 / "C . Thevalues forhigh currentsaremuch

lower than predicted by the theory of Ebers and Moll. It th us can

easily be understood why, in the case of high current, and low volt-

age, the thermaI stability of the current distribution is much better

than in the case of low current and high voltage.

INTRODUCTION

HE PHENOMENOK of second breakdown in

transistors and diodes is associated with a current

constriction to a small area [1]-/7]. In many cases

thismay becausedbya thermal feedbackmechanism

according to a theory proposed by Shockley and Scarlett

181, [9], and independently by Bergmann and Gerstner lo]in 1963. If the thermal eedback is overcritical, he current

distribution becomes unst'able,and small parts of the

transistor bear almost all of the current. This instability

can occur ndependently of possible diffusion defects of

the ransistor.Although he ransistor is loaded below

the theoreticalmaximum power dissipation,calculated

from the thermal resistance, local overheating (hot spots)

may occur. When a critical temperature is reached at a

hot spot, an intrinsic zone is formed which short circuits

the space charge region of the p-n junction [ l ], 1121. This

results in a typical voltage reduction over the transistor.

I n some cases evenmolten zones have been observed

[13], [14]. With reverse-bias conditions, in addiOion to t'hethermal effects, electrical fields have o be taken nto

account,but nevertheless the hermal nstability seems

to be an important featureof second breakdown.

The purposeof this paperis to point out the importance

of the essential parameters influencing the thermal sta-

The authors are with Telefunken Aktiengesellschaft, Heilbronn,Manuscript received December 7 , 1965.

Germany.

bility of the current distribution. These parameters aredevicegeometry, power density, nd emperature de-

pendence of current. Someexperimental esults on he

temperature coefficient of currentre presentedor

typical Si planar transistor configurations. These results

allow an interpreta tion of the fact that the thermal sta-

bility of the current distribution s much better in the

case of high current and low voltage than it s in the case

of low current and high voltage.

MODELDEMONSTRATIONF THERMALNSTABILITY

A large area HF power transistor can be regarded as a

parallel connection of many small area transistors. Actu-

ally power transistors are constructed in this way, e.g.,when annterdigitatedtructure (comb structure) is

used. The question is: how will thecurrentdistribute

itself amongst the single transistors?

Figure 1 shows a imple model arrangement [ lo ] to

measure the current istributionnhreeransistors

working inparallel. The hree ransistorswithin he

dashed ine epresentherea arge area ransistor.The

single collector currents J,,, J o , J,, of the transistor

parts are measured. The sum of these currents and the

common collector voltage VCEetermine the power load-

ing of the whole transist,or onfiguration. This power

loading is stabilized to a nearly constant value by means

of the emither resistor R, which is common to the tran-sistors of the model.

Figure 2 shows the measured currents J,,,J,,, J c sas a function of t, ime after application of power. At the

beginning the currents J c , , J c 2 , Jo areapproximately

equal o 10 mA. Thecurrent n 'ransistor 1 increases

steadily,whereas thecurrent n ransistor 2 decreases.

The current n ransistor3 a t first increases a small

amount, and then also decreases. Finally after 5 minutes,

transistor 1 carries 96 percent of the total current, which

implies also almost all of the supplied power,while the

remaining'ransistors arry less than 3 percent ach.

Throughout, hesum of thecurrents remainsapproxi-

mately onstant J , w 30 mA. Thus, fromonly ex-ternalvoltage VCR ndcurrent J , observations of our

power transistor model, the transistor seems to operate

well.

Under the special conditions of this model, transistor

1mas not dest'royed because the whole system was driven

far below its maximum allowableower dissipation.

Bu t under real, operational conditions of a power tran-

sistor when loaded near the theoretical maximum power

dissipation, alculated rom the hermal resistance, i t



1966 BERGMANN AND GERSTNER:HERMALNSTABILITY 63

1. 2. 3. I J C ,

Fig. 1. Arrangement for demonstration of currentdistribution nthree thermally coupled transistors.

A

0 2.5 5.0min

Time t

Fig. 2. Unstable currentdistribution among three ransistors nparallel or tw o different initia l conditions. At he right-handside, transistor 3 had been preheated.

may be tha t one part of the transistor would have burned

out.

It is important to note that this overloading of tran-

sistor 1 in our model arrangement is not predetermined

by adifferentelectricalcharacteristic of the transistor,

which would, orexample,correspond to aweakpoint

in the diffusion of the power transistor. This is demon-stratedat he ight-handside of Fig. 2. Here we had

preheated ransistor 3 a short whilebefore application

of the power. Now transistor 3ncreases its urrent

steadi ly and finally carries approximately 97 percent of

the otalcurrent , while transistors 1 and 2 retain he

remaining current.Thus,he urrentnstabilitys a

fundamental one, and can not be prevented by carefully

avoidingweakpoints n the ransis tor electricalstruc-

ture only.

This behaviorcanbeexplainedbya thermal feed-

backmechanism, which ismade possible by hevery

rapid increase of the collector current J , (approximately

equal to the emitter current J ,) with a rise in tempera-

ture.For abroad emperature range, this emperature

dependence may be pproximatedby an exponential

relation.

In our 3-transistor model the three transistors receive

the samevoltage V,, because theyare connected in

parallel. So a transistor tha t has a temperature slightly

higher than the others will bear more c,urrent than the

others.Thismeans he ransistor will dissipatemore

power, and if the emperature unbalance s not leveled

out either by hermal coupling t o the heat sink, or by

thermal coupling with ts neighbors, it will increase it s

temperature more than heothers,This n urn will

cause a further increase of the current, and so on. It is

not mportant how large the emperature difference or

the other differences between the various transistors are

at the beginning. When the feedback mechanism is over-

critical, the currentdistribution will beunstable,and

current crowding will occur.

STABILITYARAMETERS

From a quali tative discussion of our 3-transistor model,

three parameters can be predicted th at will influence the

thermalstability of currentdistribution n our model

or in a real large-area transistor.

A. Device Geometry.

Device geometry determines whether or not tempera-

ture differences between the various active parts of the

power transistor will be leveled out. If thehermal

couplingetween thehreeransistorsnd/orheir

thermal coupling to heheat sink sverystrong, the

temperature differences will be mall ven when thetransistorsdonotdissipate hesame power. Suppose,

as a limiting case, the whole transistor is concentrated at

one mathematical point; then no temperature differences

within this point would be possible.

B. Temperature Coe$icient of the Transistor Current.

A current nstability of the described type is only

possible when there is an increase of transistor current

with a rising temperature. Instability will be more serious

when the tempera ture coefficient of the transistor current

is high.

C . Power Level.

For a certain transistor system, thermal stability will

be better at a low rather han a t ahigh power level.

Suppose in our 3-transistor model, there is a temperature

unbalance tha t results in a 5 percent increase of current

for one transistor. At a power level of, say, 20 mW, this

means additional power of only 1 mW,whereas a t 200

mW this means 10 mW additional power.

For geometricallyimple transistortructuresnd

simple boundary conditions, the conditions for stable or

unstable current distribution can be calculated by solving

the differentialequation of heat conduction [lo], [ls].For a power transistor with a simple rectangular shape

with ength a , thickness h, the result of thestability

analysis is shown inFig. 3. At he op surface,a dis-

tributed heat source (e.g., a very fine interdigitated tran-

sistor structure),and at he undersurface, a flatand

perfect heat drain, have been assumed.

Again, here a re the three parameters that we already

know from the qualitative discussion. Using the stability

chart, (Fig. 3), it is possible to point o ut the relative im-

portance of theseparameters. Devicegeometry for this

transistor tructure s described by a,%, the ratio of

length o hickness of the ransistor crystal. This indi-



632 IEEE TRANSACTIONS ON ELECTRON DEVICES AUGUST/SEPTEMBER

cates th at in a large area ransistor, hermal coupling

depends on the greatestdistance between the active parts

of the ransistorand he thickness of the chip. The

temperaturedependence of t'he ransistorcurrent at th e

certain operating point is characterized by the tempera-

ture coefficient B, which is defined by

B = L % lJ C dT V B E - C O a S t .

This emperature coefficient depends on the semicon-ductormaterial bandgap), he operatingpoint of the

transistor (especially current density), and he junction

temperature. AT is the emperature difference between

the ransistor junctions and he heat sink. AT may be

calculated as he product of theheatproduced in the

collector unction, and he hermal resistancebetween

the transistor unctions and the heat ink. AT is a measure

fo r the power density at which the transistor is operated.

In the stability chartwe find three regions.

1 . Stable mgion, the lowpower region. In th is region,

stableoperation of transistors is possible, regardless of

their geometry (large or small area).

2. Conditionally stableegion. In this region, stableoperation is possible if the total power is limited; that is,

if the rans istor is stabilizedagainst thermal runaway.

As canbe seen from the stabilitychart, tabilization

against thermal runaway a t a certain value of B -AT can

be achieved only for suitably low values of a/h; that is,

only for transistors of sufficiently small area.

3. Unstable egion. In his region, thermal coupling

between the active part s of the transistor is oo weak.

Thus the current distributionn the transistor is unstable

and current crowding will occur. This type of instability

cannot be avoided by limiting the total dissipation to a

constant value,as, for example, by an emitter resistor.

Whencomparing he concept of thermal nstabilitywith experimental results on the phenomenon on second

breakdown, one finds tha t the thermal concept fits very

well the main features observed in forward-bias second

breakdown. A complete understanding of second break-

down, including reverse-bias second breakdown, has not

ye t been achieved 1161. But it is hoped that by proper

refinement of t he existing heories, further peculiarities

will be understood. An example is the emperature de-

pendence of triggering energy or of the delay time [5], [16].

It seems possible that this temperature dependence can

be explained by taking into account thevariation of heat

conductance with temperature, which is quite important,

for example, in silicon. Another well-known feature is

the depen.dence of forward-bias second breakdown be-havior on operating point (Fig. 4).As can be seen from

the lowest curve, which is for the dc case, the tendency

of the ransistor obedishrbedby unstable current

distribution ismuchhigher at highvoltages and low

currents than it s a t low voltages and high currents. For

example, n the 10 volt ange, this ransistormaybe

10distributed heat source

55

. ., , . . . . . . :. ;

b < a

.B.AT-Fig. 3. Stability chart for a power transistor of rectangular shape.

I I50 100 2

Col lectorvol tage V ---b

0

Fig. 4. Safe operating range of a power transistor.

loaded to approximately 100 watts, whereas at 100 volts

the power allowable is only 20 watts.

How can hisbe explained? We believe that t is a

consequence of thecurrentdependence of temperature

coefficient onransistor urrent.This arameter asalready been mentioned when we were discussing the

stabilitychart.Remember, for example, a reduction of

the temperature coefficient by, say, a factor of two will

allow theemperature difference, and, therefore, also

the power dissipation, o ncreaseby thesame actor

withoutchanging hestabilitybehavior of thecurrent

distribution. Indeed a current dependence of this temper-

ature coefficient can be predicted by t'he simple theory of

the junction ransistor, orexampleby he heory of

Ebers and Moll 1171. By this heory, one would expect

for reasonable current densities, a value of B = O . lO /OC ,

which means that the transistor current is increased by

10 percent when the junction temperature is increased by

1°C. Concerning the current dependence f B, this theorypredicts tha t B decreases by 2 . 3 / T ; hat is, about 0.007/"C

for a ten times increase in current density [8].Obviously

this heoreticalcurrentdependence of the emperature

coefficient B is too weak and would not explain the large

differences of current stability which are observed experi-

mentally.



1966 BERGMANN AND GERSTNER: THERMAL INSTABILITY 633

MEASUREMENTF TEMPERATURECOEFFICIENT

Since the transistor heory s based on many simpli-

fyingassumptions which are generally not fulfilled, we

havemeasured the emperature coefficients fo r silicon

planar transistors and their dependence on current level

and junction temperature.

In order to avoid instability of current distribution a t

too low power levels, we used small area transistors. Bu t

these transistors were similar to typical large area tran-

sistors when junction depth, base width, diffusion layer

sheet resistance, and so on, are considered.

On the right-hand side of Fig. 5, a sketch of our meas-

uring ircuit is given. The ransistors were put n a

thermostat, and for fixed collector currents J , the base

emitter voltage VB ,was measured with a high precision

digital voltmeter as a function of junction temperature

Ti.t should be mentioned th at the voltage drop over

the base resistance, which has a stabilizing influence, has

been subtracted from the measured values of VBE. hu s

the following considerations are also valid for open base

conditions, which are very mportant n practice. Toobtain he right value of Ti, e firstmeasured V B E t

several collector voltages for fixed collector current as a

function of case temperature T,. This measurement gave

aset of parallelcurves which could be extrapolated t o

zero dissipated power using the relation'

T i T,, +~- which has been derived in [ lS].cz - T c ,-- -C E l 1

v C E 2

In this way we obtained the set of curves shown on the

left-hand side of Fig. 5 for a 2 N 1613 transistor.

In order t o determine the emperature coefficient B,

this set of curves can be replotted in the manner shownin Fig. 6. This s a log plot of collector current J , against

junction temperature T i or constant base emitter volt-

age V B E . By graphical differentiation of these curves, th e

experimental values of the temperature coefficient B are

obtained. Throughout the whole curve set, it can be seen

that the slope is much less steep at high currents than itis at low currents, and that the lope is not very tempera-

ture dependent.

In Fig. 7, B has been plotted for two emperatures

(50 and 100°C) as a function of transistor current. For

comparison, two heoretical curves-the dot ted ones-

are given. These show the weak current and temperature

dependencementionedabove. In contrast o he theo-retical curves, the experimental values of B tend t o much

lower values when the current density is increased. Foran example, when J , is increased from 10 t o 100 mA, B

'or the determination of the thermal resistance between th e transis-1 This measurement procedure is actually a simple static method

;or junctions an d the case [18]. We noticed that the thermal resis-jances given by the dataheets were not accurateenough to calculate;he junction temperature from case temperature and power dissipa-ion, especially a t high power levels.

Tj -ig. 5. Base emitter voltage V B Evs. junction temperature Tifor various collector currents J c for a silicon planar ransistor2 N 1613.

mA

t lou7

1

".I , -0 50 - 100 150 200 "C

Tj -Fig. 6 . Collector current J c vs. unction temperature T i fo r a

silicon planar ransistor 2 N 1613. Parameter 1s base emittervoltage VBE.

-- heoretlca

0.00 !0.1 1 10 100mA

Jc

Fig. 7. Temperature coefficient B vs. collector current JC for asilicon planar transistor 2 N 1613.

decreases from 0.045 t o 0.015 according t o the 100°Ccurve;

tha t is, by about a factor of three.

Our experiments show that at high current densities,

the temperaturedependence of current is muchower tha n

predicted by theory . Thus itan be easily understood why,

in a large-area transistor a t acertain power level, the

stabilityagainst second breakdown is much better for

high current than for low current operation.

CONCLUSIONS

In large-area transistors, an instability of current dis-

tribution can occur due to a thermal feedback mecha-

nism. This type of instability which may initiate second

breakdownhas been demonstratedexperimentally na



634 IEEE TRANSACTIONS O K ELECTRON D E V I C E S AUGUST/SEPTEMBER

Fig. 8. Second breakdown proof power transistor.The large-area

resktor.device is divided into eight cells, each having a stabilizing emitter

simple model arrangement.There rehree ssential

parameters influencing the stabil ity of the current distri-

bution: deviceeometry, temperature dependence of

current, and power level.

In order to improvestabilityagainst second break-

down initiated by this thermal mechanism, th e following

precautions may be taken.

1) Device geometry should be designed so as to pro-

vide strong thermal coupling.

2) The temperature coefficient of current should be re-

duced or the single activeparts he ransistor s

composed of .

3) The power level should be reduced to a value which

assures stable current distribution.

The hird possibility does not seem to bevery atis-

factory, since it does not cure the inst’ability.I t is merely

a withdrawal from the dangerous high power region and

must be paid for by inconveniently high capacitance in

the ransistorandbyaddit ional yield problems when

producing such overdimensioned devices. But there is a

very promising possibility for he construction of a second

breakdown proof power transistor by combining the first

tm7o stability design concepts [19]. The large-area power

transistor is divided into single cells which are small

enough t o assurestabilitywithineach cell. Then hese

stable cells are combined to a large area configuration with

stabilizing emitter resistors for each cell. Of course, the

internal B within these cells is not influenced, but th at is

not necessary because the single parts are designed in an

undercritical size. Figure 8 shows, as an example, a power

transistor which is divided into eight small-area devices,

eachhaving a stabilizing emitter resistor. The resistors

in this example are evaporated KiCr resistors.

REFERENCES

[I] C. G. Thornton and C. D. Simmons, “A new high current modeof transistor operation,” IRE Trans. on Electron Devices, vol.ED-5 , pp. 6-10, January 1958.

[2] R. Greenburg, Breakdown oltagen power transistors,,’SemiconductorProducts, vol. 4, pp. 21-25, November 1961.

[3] J. Thire, ‘[Le PhhomBne de pincement sur les transistors depuissance en commutation,” Colloque Internat’l sur les Dis-positifs ci Shmiconducteurs, vol. I : Production, pp. 277-293,1961.

[41 F. Weitzsch. “ZumEinschnureffekt bei Trans istoren, die im-Durchbruchsgebietbetriebenwerden,” Arch. elektr. ‘ Ubertr.,vol. 16, pp . 1-8, January 1962.[5] H. A. Schafft and J. C. French, “Second breakdown in transis-

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Abraham. “Thermal breakdown in silicon z7-n

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[SI R. M. Scarlett and W. Shockley, “Secondary breakdown andjunctions,” Phys. Rev. , vol. 108, pp. 936-937, November 1957.

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Failure in Electronics, vol. 1, M . F. Goldberg and J. Vaccaro,

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schniiru!Ig bei Hochfrequenz-Leistungstransistoren,” Arch.electr. Obertr., vol. 17, pp. 467-475, October 1963.

[11] H. Melchior and M . J. 0. St rut t, “Secondary breakdown ntransistors.” Proc. IEEE (CorresDondence).vol. 52. nu. 439-440,April 1964:

[12] H. belchior and M. J. 0. Strutt, “On the initiation of secondbreakdown in diodes and transistors,” Scientia Electrica, vol. 10,

[13]A. C. English and H. M. Power, “Mesoplasma breakdown npp. 139-141, December 1964.

silicon junctions,” Proc. IEEE (Correspondence), vol. 51 , pp.500-501, March 1963.

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tember-October 1963.F. Weitzsch, ‘<ZurTheorie des zweiten Durchbruchs bei Transis-toren,” Arch.elektr.gbertr. , vol. 19, pp. 27-42, Jan uary 1955.H. A. Schafft and J. C. French, “A survey of second break-

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