782 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-17, NO. 9, SEPTEMBER 1970

0. Muller, “Recom,l$nation, thermal feedback and l/f-flicker noise in transistors, Arch. Elek. Ubertragung, vol. 24, pp. 169- 178, April 1970. L. D,. Yau and C. T. Sah, “On the ‘excess white noise’ in hIOS transistors,” Solid-state Electron., vol. 12, pp. 927-936, 1969. B. L. Jones and R. E. Hurlston, “VHF noise due to surface states in MOS devices,” Proc. IEEE (Letters), vol. 58, pp. 152- 153, January 1970. A. T. Brodersen and E. R. Chenette, “A superior low-noise amplifier,” Int. Solid-state Circuits Conf. Digest, pp, 164-165, 1970.

[89] R. Paul, Transistoren, 2nd ed. Berlin, 1969, ch. 19-21. (901 R. L. Pritchard, Electrical Chavartwisfics o,f Transis lo~s. Ne\\.

[91] I . F. Nicolayevskiy, “Thermal breakdown in transistors,“ Radio York: hlcGraw-Hill, 1967, ch. 9.

Engvg., vol. 24, no. 10, pp. 101-104, 1969. 1921 0. Siiiller, “Ultralinear UHF power transistors for CATV ap-

dications,“ Proc. IEEE, vol. 58, pp. 1112-1121, July 1970. .. [93] S . Noguchi and H. Morimura, “Solid-state inductance using

thermal effect and its application, Electron. Commun. Japan, vol. 52-C, no. 9, pp. 131-137,1969.

.~

Thermal Instability in Very Small p-n Junctions

Abstract-Thermally induced second breakdown is studied in very small 6- to lD-volt silicon diodes having uniform breakdown. The formation of a small high-current density region is observed optically at the onset of thermal breakdown. Incremental resistance measurements can be used to determine nondestructively the threshold current for thermal breakdown. The threshold temperature for thermal breakdown is measured using the avalanche voltage temperature coefficient. The voltage drop associated with thermal breakdown is shown to be due to a sudden change in active area of the junction rather than to melting of the crystal.

I . INTRODUCTIOK HERMALLY induced second breakdown usually has been investigated in large p-n junctions typical of those found in commercial diodes and

transistors. In such large-area p-n junctions, thermal breakdown occurs only in a small portion of the junc- tion, and the position of the high-current filament can wander, making repeatable measurements difficult [1]-[4]. By using guard ring diodes with a very small active area ( 7 X10-6 cm2) one can obtain uniform avalanche breakdown and reproducible thermal break- down. Such diodes are convenient for observing thermal breakdown since they require relatively small power levels and allow controlled and repeatable measure- ments.

11. OPTICAL OBSERVATIONS The cross-sectional structure of a typical diode is

shown in Fig. 1. The p-type guard ring has a sufficiently high breakdown voltage to insure that both conven- tional avalanche breakdown and second or thermal breakdown occur in the small 30-pm diameter circular

and May 1, 1970. This work was supported by the hTational Science Manuscript received February 9, 1970; revised March 23 , 1970

Foundation under Grant GK-1419. K. L. Chiang was with the University of lt’ashington, Seattle,

Wash. He is now with Fairchild Semiconductor, Palo Alto, Calif. P. 0. Lauritzen is with the Department of Electrical Engineering,

University of Washington, Seattle, Wash.

Guard si Ring n-’ypeJ Fig. 1. Cross-sectional view of diode structure.

active region. Some indiffusion of the heavily doped surface layer gives a graded junction profile. Aluminum metallization contacts only the edge of the heavily doped surface layer, allowing optical observation of the area directly above the active breakdown region.

The dc current-voltage characteristic of a typical diode is shown in Fig. 2 . T h e avalanche light emission in the same diode is shown in Fig. 3 as observed through a microscope a t various current levels. As the current in- creases, the light emission first becomes uniform across the junction area. Then the light becomes concentrated at the edge of the active region a t a current level of 150 mA just before thermal breakdown occurs. This non- uniform avalanche current flow is due to a higher tem- perature (and therefore a higher breakdown voltage) a t the center of the junction. As the current is increased above 150 mA, thermal breakdolvn occurs, the voltage drops suddenly, and the formation of a small high-cur- rent density filament is shown in the light emission photographs. If the dc current is increased further, the diameter of the current filament also increases slightly while the dc current-voltage plot exhibits a negative incremental resistance. When the current is decreased the filament diameter shrinks, and at a low enough cur- rent the diode switches back to the normal avalanche mode of operation.

CHIANG AND LAURITZEN: THERMAL INSTABILITY IN VERY SMALL p-n JUNCTIONS 783

50 i I I l i

V (VOLTS1

Fig. 2. The dc current-voltage plot of diode 802 showing the thermal breakdown region. The diode is mounted on a TO-46

which is in contact with a mixture of dry ice and acetone. header without cover. The header is connected to a copper bar

25 mA 50mA IO0 mA 125mA

150mA 175 mA IS0 mA 125 mP.

Fig. 3. Light emission from the reverse-biased diode 802 a t various current levels. The photographs were taken with identical ex- posure times following a left-to-right and then a top-to-bottom

region at high current (100-150 mA) is about 30 pm. sequence of current levels. The diameter of the light emission

The diodes are usually damaged slightly in the course of making such a dc trace around the hysteresis loop caused by thermal breakdown. This damage is indicated by the extra light emission appearing at the point where the current filament formerly occurred, and also by a “softness” of the initial breakdown knee appearing a t currents below 20 mA. This damage may result from a redistribution of impurities due to localized melting of the crystal. A given diode may be retraced into the thermal breakdown region many times without failure.

111. I N C R E M E N T A L RESISTANCE 11EASUREMENTS

When a p-n junction is biased into avalanche break- down, the avalanche current I A is determined by the diode spreading resistance R,,, the space-charge resis- tance R,, [ 5 ] , and the magnitude of the applied voltage V above the breakdown voltage VB(T) :

Roc (500 kHz) 2 -

Diode 668 TA = I92’K

‘ OO 40 .io I20 I60 200 i o 2800

- 4

I (mA1

Fig. 4. Electrical characteristics of diode 668 from zero current up to a current close to the threshold for thermal breakdown. Both dc and ac characteristics are plotted. The diode is mounted on a TO-46 header which is inserted in a copper block and im- mersed in a mixture of dry ice and acetone.

Here T is the operating junction temperature. The total equivalent series resistance R, = R,, i- Race Since the breakdown voltage has a positive temperature coeffici- ent and T increases due to Joule heating, the breakdoun voltage Vie will increase with avalanche current IA, giving rise to another component of incremental resis- tance due to this thermal mechanism.

Haitz, Stover, and Tolar [6] were able to determine the heat flow resistance or thermal resistance in aval- anche diodes using measurements of the incremental ac resistance a t various frequencies. At high frequencies the junction temperature remains constant and the resistance R, = R,,+R,, is measured, while at low fre- quencies the junction temperature varies with the ac driving signal and a larger incremental resistance is measured. \Ve have used a similar technique in deter- mining the mechanism for thermal instability a t high- current levels. Fig. 4 is a plot of the incremental ac resistance R,, of a typical diode as a function of dc current I. The dc voltage-current characteristic and the measurement circuit are also shown. In a high-fre- quency measurement R,, (500 kHz) is almost constant over a nide range of currents. At very low current levels R,, (500 kHz) increases greatly due to a decrease in active junction area caused by nonuniform current flow. This decrease in active area is also indicated by the optical observations (Fig. 3). The spreading resistance R,, is primarily due to the bulk resistivity of the sub- strate material and to confinement of the current flow path by the guard ring. Calculations indicate that about 20 percent of the total resistance R, is space-charge resistance and 80 percent is spreading resistance.

As the measurement frequency is lowered, the incre- mental resistance R,,(f) increases and eventually reaches a constant value [ 6 ] . For convenience in in- strumentation, a measurement frequency of 20 Hz n.as used for the ac data in Fig. 4. Due to a large thermal

784 IEEE TRANSACTIONS ON ELECTRON DEVICES, SEPTEMBER 1970

time constant, the final limiting low-frequency value of R,, is not attained until somewhat lower frequencies. The increase in R,,(20 Hz) with current shown in Fig. 4 is predicted by a simple thermal model. However, im- mediately before the threshold of thermal breakdown a sharp drop in Ra,(20 Hz) occurs. This drop in R,,(20 Hz) indicates the occurrence of a new mechanism of current flow. The fact that no change is observed in R,,(500 kHz) indicates that the new current is of thermal origin. The curves in Fig. 4 are not plotted beyond the maximum current indicated because a t higher currents the diode switches into thermal break- down; the slight damage which occurs makes it difficult to repeat the data precisely. Data of this type are ob- served on all the diodes measured. The sharp drop in Ra,(20 Hz) always occurs just before thermal break- down. Thus R,, can be used as a convenient and non- destructive indication of the thermal breakdolvn thresh- old current.

IV. TEMPERATURE ~ I E A S U R E M E N T S In order to identify the mechanism that triggers

thermal breakdown, an accurate junction temperature measurement should be obtained at the threshold of thermal breakdown. The temperature coefficient of the breakdown voltage can be used to conveniently measure temperature [6]. If the temperature coefficient is ( A V B ~ A T ) , the breakdown voltage can be expressed as

nhere T A is the ambient or external case temperature. Then eliminating I/,(T) from (1) and (2 ) me obtain

The breakdown voltage can be measured a t low currents to obtain I$ (TA) ; the resistance R,=R,,(500 kHz) is determined from a plot similar to Fig. 4. The tempera- ture coefficient (AV,/AT) can be obtained from the ex- perimental plot of low-current breakdolvn voltage versus temperature given in Fig. 5 . The da ta for (AV,/ A T ) must be extrapolated above 730'K since the diode packages cannot be safely heated above this tempera- ture. This extrapolation limits the accuracy of the tem- perature measurement especially since (AV,/AT) is not constant a t the higher temperatures.' The variation of (AV,/AT) xvith temperature shown in Fig. 5 is included in the calculation of AT. Equation ( 3 ) can be used to determine the junction temperature T since all the necessary parameters can be measured. Temperatures determined from this steady-state method, as well as temperatures obtained from a transient method, are

'The theoretical calculations of Croaell and Sze [7] predict a more constant value for ( A V ~ A T ) a t high temperatures.

3.0 ,' /'

I d -1.50 X K ) 400 600 800 1000 1200 I

TA ( O K ) -r

Fig. 5 . Breakdown voltage measured a t I=1 rnA as a function of diode temperature TA. The room temperature breakdown voltages for diodes 660, 803, and 11040 are 6.6, 7 . 7 , and 10.5 volts, re- spectively.

given in Table I. Different diodes were used for the data in Fig. 5 than were used for Table I, but their charac- teristics were essentially identical. Different diodes were used to avoid the possibility that darnage might occur in one experiment and affect the data in the other,

The transient method for junction temperature deter- mination does not require knowledge of the resistance R,. When a fast-risetime current pulse is applied to a diode, the initial breakdown voltage occurs a t Vg(TA) . The voltage rises until the diode approaches a steady- state thermal condition. If the pulse current is suffi- ciently high, a sharp drop in voltage occurs when the diode switches into the thermal breakdolvn mode. The pulse length can be carefully controlled to prevent the diode from remaining in thermal breakdown long enough to be damaged. Fig. 6 shows the current and voltage n.aveforms obtained with this technique. The junction temperature T a t t he threshold of thermal breakdown can be obtained from the voltage difference A V = V B ( T ) - V B ( T A ) shown in Fig. 5 and ( 2 ) . Good agreement between the steady-state method and the transient method is obtained. Both th is transient method and the steadp-state method described in the previous paragraph assume an extrapolated value of (AV,/AT) and uniform conduction across the junction area. A more accurate temperature measurement would be very desirable. The light emission photographs indi- cate that at the threshold of thermal breakdoivn, the avalanche current is concentrated at the edge of the active area. Thus the temperature in the junction center is slightly higher than indicated by the values in Table I.

CHIANG AND LAURITZEN: THERMAL INSTABILITY IN VERY SMALL p-n JUNCTIONS 785

TABLE I SUMMARY OF DIODE INFORMATION AND MEASUREMENT RESL-LTS

- Temperature at Thermal Breakdown

Substrate Temperature VB Device Concentratlon where R s e Steady-State Method Transient Method

ni(T) = N D a ~ ~ ~ : ~ ~ (ohms) (OK/watt) N D TA = 192'K TA = 300'K (c m-3) (OK)

A V B (volts) T(OK) AVB (volts) T(OK)

6732 668

788 812 101 103

2.5X1Ol8 2.5X10'8 2.5X1Ol8 2.5X1018 1.4X1018 1 .4X10I8

1100 1100

1100 1100 1000 1000

~~

6 . 4 6.53 7.6 7 . 7 9 . 6 9 .9

5 .5

10.3 5.25

9.55 8 . 2 9 . 8

440 440 370 400 300 350

2.14

2 . 5 2 . 2

3 . 4 2.4

3 . 8

1170 1200 1020 1000

1070 950

1.65

2.15 1.75

2 . 2 2 .6 2 . 7

1090 1140 1080 1090 910 960

W v

ol-

t (a> ( b )

Fig. 6. Transient techniques for junction temperatures measure- ment. (a) Z-V characteristic for a current step-function input. (b) Transient diode voltage waveform exhibiting the sudden voltage drop characteristic of thermal breakdown.

1:. ~ I O D E L FOR THERMAL INSTABILITY IVhen the temperature of the junction reaches the

point where the intrinsic concentration ni equals the doping concentration N D on the lightly doped side of the junction, the junction effectively vanishes and a large number of carriers becomes available for conduc- tion. Such a model based on the temperature for in- trinsic conduction a-as proposed by IIelchior and Strutt [8], and was also discussed by Weitzsch [ 2 ] . &'hen the temperature anywhere in the junction reaches the tem- perature for intrinsic conduction, the current tends to crowd into that high-conductance region of first in- trinsic and later molten silicon. The data in Table I indicate a threshold temperature which is approximately the temperature for intrinsic conduction, and which also decreases as expected with increasing breakdotvn voltage. Considering the approximations involved in determining the temperature, one can still reasonably conclude that the trigger temperature for thermal breakdown is associated with the temperature for intrinsic conduction.

A quantitative model for t he initial thermal instabil- ity condition can be derived by including a thermal or minority carrier diffusion component of current flow To(T) in addition to the avalanche current I A previ-

o'usly considered. The thermal component of current appears only at high temperatures and increases rapidly with increasing temperature. The total current I is de- fined as

I = ID i- I A . (4)

Equation (1) then must be rexvritten as2

The junction-to-ambient temperature difference T - TA is equal to the product of the junction-to-ambient heat flow resistance 0 and the power dissipated in the diode:

sumed constant and is given a new symbol 5'. Equation ( 7 ) can be differentiated to obtain the incremental dc resistance d T/' /dl. The thermal current I D is a strong function of temperature; its temperature coefficient (dID/dT) plays a crucial role in the high-temperature incremental resistance and is retained in the final ex- pression. Thus,

and the incremental resistance becomes

I D does not distort the field distribution within the space-charge 2 Equation (5) is valid when the thermally generated current

layer, as would be the case if ID were injected from both sides of the junction, If I D comes entirely from the lightly doped side, an ad- ditional term -ZD Rse must be added to (5). This additional terrn will modify (9), (12), and (13) by making

2R,, a I D S dT

G = 1 - - - - .

78 6 IEEE TRANSACTIONS ON ELECTRON DEVICES, SEPTEMBER 1970

SBVG dV

1 +-- R,

dI 1 - IS8G _ - - R, -

n-here

This quantity d L‘/dI is the dc incremental resistance a t operating temperatures below the onset of thermal breakdown. The term SOIG in the denominator is usually small compared to one and has little effect on d V / d I . In the numerator the term S8 VGIR, does have a value on the order of one, and it represents the contri- bution of thermal effects to the incremental resistance.

3Iost of the quantities in (9) can be measured directly; the heat f lo~v resistance O = ( T - TA/I’I) is determined from the temperature measurements de- scribed in Section IV; the thermal current I D can be very roughly approximated using the expression for minority carrier diffusion current I D = A ~ ( D / T ) ” * ( ~ ~ ~ / N D ) where the usual symbols are employed for the junction area A , electronic charge q, diffusion constant D , lifetime T ,

intrinsic carrier concentration n;, and doping concen- tration L V ~ . Using this form for I D and experimental values for 7 = 0.5 ,us and , u p = 2 . 3 X lo9 T-2.7 [9], dl’/dI is calculated from (9) and plotted in Fig. 4 along with d V j d I measured by graphically differentiating the ex- perimental dc current-voltage curve. The theoretical d V / d I exhibits the sharp decrease in incremental resistance a t high-power levels show-n by Rae(20 Hz). The experimental d l ’ / d I curve does not show this de- crease a t high currents and this discrepancy is thought to be due to the relative inaccuracy of a graphical differentiation as compared to an ac measurement.

Equation (9) is derived under the assumption of uni- form current flow over a constant area. Thus it Ivould not be valid for currents at the threshold of thermal breakdonm. An additional instability is created by the variation in active area. We can include this effect by setting up the equations in such a manner that area becomes a variable. The specific dependence of each term on the junction area A can be expressed as follon-s:

xvhere the quantities I’D, K’,,, K’,,, 8’ are not functions of area A . The exponents -11 and N include the effects of deviation from a one-dimensional model for the heat flon- resistance and spreading resistance. For a one- dimensional model _If and N equal 1 ; for a three- dimensional model -11 and N equal 1!’2.

Substituting (10) into ( 7 ) Ive differentiate allolving V and A to vary while holding the total current I con- stant. In differentiating I D , both the area and tempera- ture variation must be included as follolvs:

Solving ford I/’dd n-e obtain

This expression is very similar in form to (9). The term SBIG in the denominator is usually small and has little effect. In the numerator (1 - -Vl)Rsp/Rs is less than one and NGVSO/R, is on the order of one. At low currents dT’ /dA is negative; thus if the area A is allowed to in- crease, the diode voltage Vwill decrease. Since the maxi- mum area is limited by the diode geometry, a stable operating condition is maintained. Hou-ever, a t high currents and high temperatures when the condition

G < 0 or (Rsc/’S) ( d I ~ i d T ) > 1 (13)

is reached, d 17/dA can become positive. Then operation is unstable and the active area will decrease along with the voltage, causing the diode to sxvitch rapidly to a small-area, low-voltage state. This model explains the sudden drop in voltage observed at the onset of thermal breakdolvn. 3Ielting of the crystal should rapidly follow the formation of the small-area, high-current region, but melting is not necessary to produce the sudden drop in voltage. Sote that the identical condition for in- stability, (13), occursin both (9) and (12).

Dumin [ lo ] proposes a different model for thermal breakdown in his work on thin-film silicon-on-sapphire diodes. Thermal breakdown occurs in his diodes \Then the injected avalanche carrier concentration becomes comparable to the background doping density. Dumin’s model is not applicable to the bulk p-n junction diodes used in our experiments nhere thermal breakdown oc- curs when the injected avalanche carrier concentration is still txvo orders of magnitude below the background doping density.

VI. CONCLUSION These measurements shoxv that initial thermal break-

down or second breakdown in small, low-voltage p-11 junctions is caused by the temperature in a small area approaching the level \\-here intrinsic conduction be- comes possible. The simultaneous observation by both optical and electrical methods is particularly con- venient in these small-area uniform breakdou-n diodes \\.here junction parameters are accurately known.

Further independent investigations are necessary to verify the threshold temperature by improving the accuracy of the temperature measurements. A better mathematical model for the initiation of thermal break- down would also be desirable.

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-17, NO. 9, SEPTEMBER 1970 787

Incremental resistance measurements should be con- sidered as a convenient and nondestructive technique for determining second-breakdon-n threshold currents in power devices.

REFERENCES [I ] 1. Tauc and ‘4. Abraham, “Thermal breakdown i n Si p-11

[ Z ] F. \\Teitzsch, “X discussion of some known physical models for ]unction,” Phys. Rev., vol. 108, pp. 936-937, November 1957.

second breakdown,” IEEE Trans. Electron Devices, vol. ED-13, pp. 731-734, Sovember 1966.

[3] X. C. English and H . A I . Power, “Mesoplasma breakdown in silicon junctions,” Proc. IEEE (Correspondence), vol. 51, pp. 500-501, March 1963.

[4] A. C. English, “Physical investigation of the mesoplasma,“

September 1966. IEEE Trans. Electron Devices, vol. ED-13, pp. 662-667, August/

[j] lY. Shockley, “Problems related to p-n junctions in silicon,“ Solid-State Electron., vol. 2, pp. 35-67, 1961.

[6] R. H. Haitz, H. L. Stover, and N. J. Tolar, “A metbod for heat flow resistance measurements in avalanche diodes, IEEE

[7] C. R. Crowell and S. M. Sze, “Temperature dependence of Trans. Electron Deaices, vol. ED-16, pp. 438-444, May 1969.

avalanche multiplication in semiconductors,” Appl. Phys.

181 H. M:fchior and M . J . 0. Strutt, “Second breakdown in trans- Lett., vol. 9, pp. 242-244, September 15, 1966.

istors, Proc. IEEE (Correspondence), vol. 52, pp. 439-440,

[9] H . F. \Volf, “Silicon semiconductor data ,” Int. Series of Mono- April 1964.

graphs on Semiconductors, vol. 9, H. K. Henisch, Ed. Kew York: Pergamon, 1969.

[ lo] D. J . Dumin, “Emission of visible radiation from extended plasmas in silicon diodes during second breakdown,“ IEEE Trans. Electron Devices, vol. ED-16, pp. 479-485, May 1969.

Thermal Fatigue in Silicon Power Transistors G. -4. L,L\NG, B. J. FEHDER, ASD W. D. WILLIAMS

Abstract-In silicon power transistor applications, thermal cycling of the transistor may activate a failure mechanism called thermal fatigue. This phenomenon is caused by the mechanical stresses set up by the differential in the thermal expansions of the various materials used in the assembly and heat sink of the transis- tor. Thermal fatigue often results in cracking of the silicon pellet or failure at the silicon mounting interface.

This paper discusses the two types of interfaces encountered in power-transistor chip mounting. In type I (hard-solder) systems, the stress-strain relationship is treated in the elastic region. In type I1 (soft-solder) systems, the stress-strain relationship is plastic in that at least one component exhibits material flow. For the type I sys- tems, a method is suggested for calculation of the forces acting at each interface. For type I1 systems, an empirical approach to pre- dicting the number of cycles to failure is given.

Accelerated testing techniques for thermal-fatigue evaluation are suggested, and a method of predicting performance for various mounting systems is given. This method uses an equation of the form N=Aoe(70!H).

This paper combines an analytical approach to the design of power transistors with an empirically derived method of predicting failure under conditions of thermal fatigue.

INTRODUCTION

I N silicon power transistor applications, thermal cycling of the transistor as a result of power dissi- pation causes a failure mechanism called thermal

fatigue [ l ] , [ 2 ] . This phenomenon, which results from mechanical stresses set u p by the differences in thermal expansion of the various materials used in power- transistor fabrication, often results in cracking of the silicon transistor pellet or failure a t the silicon mounting interface.

The authors are with RCX Solid State Division, Somerville, X. J. Manuscript received February 9, 1970; revised May 1, 1970.

08876.

llIany applications of power transistors result in stringent thermal-fatigue requirements. For example, an automobile radio output stage may require a device to withstand a total of 5000 cycles of 55OC case-tem- perature change over a period of five years. Power sup- ply applications usually subject a transistor to a change in case temperature greater than 6OoC. \&’hen the power to a load is switched, the number of cycles is deter- mined by the application; a typical requirement for the life of a computer power supply is 5000 cycles with a case-temperature variation of 65OC.

This paper reviews the design considerations neces- sary to produce a thermal fatigue-resistant power tran- sistor. The paper is organized as follows:

I. Device Design Considerations A. Type I (Hard-Solder) Systems B. Nature of Thermal Fatigue C. Type I1 (Soft-Solder) Systems D. Redesign of a Type I1 (Soft-Solder) Device

11. Accelerated Thermal-Fatigue Testing

I I I. Conclusions.

The analytical treatment of the hard-solder systems is used to give the reader a feeling for the order of mag- nitude of the stresses produced by the thermal mismatch of the multimaterial structures. This discussion is fol- lowed by a brief consideration of the nature of thermal fatigue. Empirical data from soft-solder-mounted tran- sistors is used to predict the number of cycles to failure under conditions of thermal fatigue. An accelerated thermal-fatigue test is also described.