t USAELRDL Technical Report 2311

" A METHOD OF BASIC TEMPERATURE COMPENSATION IN TRANSISTORS

p •Richard L. Broyden

*-- ;

MAY8 1961

February 1963

UNITED STATES ARMY

ELECTRONICS RESEARCH AND DEVELOPMENT LABORATORY

FORT MONMOUTH, N.J.

U. S. ARMY ELECTRONICS RESEARCH AND DEVELOPIE2MIT LABORATORYFORT MONMOUTH, NEW JERSEY

February 1963

USAELRDL Technical Report 2311 has been prepared under the super-vision of the Director, Electronic Components Department, and is publishedfor the information and guidance of all concerned. Suggestions or criti-cisms relative to the form, contents, purpose, or use of this publicationshould be referred to the Commanding Officer, U. S. Army ElectronicsResearch and Development Laboratorl, Fort Monmouth, New Jersey, Attn: Chief,Semiconductor and Microelectronics Branch, Solid State and Frequency ControlDivision.

J. M. K1JBROUGH, JR.Colonel, Sigmal CorpsCommanding

OFFICIAL:HOWARD W. KILLAMMajor, SigCAdjutant

DISTRIBUTION:Special

QUALIFIED REQUESTERS MAY OBTA2•COPIES OF THIS RPORT FROM AKITA.

THIS REPORT HAS BEZI RELEASED TO =1IPOFFICE OF TECHNICAL SERVICES, U. S.DEPAR12TN OF C04.=IRCE, WAS! T0I.10 25,D. C., FOR SATL TO THE G=ERA PUBLIC.

A M! 0D OF BASIC TBWEM U OCWPENSATIM 3I TRAISISTO0S

Richard L. fraYden

DA Task Nr. 3A99-21-003-01

ABSTRACT

A semiconductor device complex, consisting of a diode-transistorcombination, that effectively compensates for normal transistor gainvariations as a function of temperature has been developed underSignal Corps Contract DA 36-039 SC-87276, Hoffmn Electronics Corpor-ation. This device has the characteristics of the normal transistor,except that in the range of OOC to 70°C the h., changes by less than10%. 7he complex device is in a single transiltor package and may betreated circuit-vise as if it were an ordinary NPN silicon transistor.

In this report a direct comparison is made between the new deviceand an electronically similar commercially available transis-or. Inaddition, a simple technique called a-slope analysis is presented thatgives a method of pinpointing the dominant leakage effects in bothplanar and mesa transistors and to vhat extent these effects occur.

U. S. APM ELBCTRONCS RESEARCH AND DEVEOPMEGT IABORATORYFORT NODtfl, NEW JERSEY

i

ABSTRACT -

OIASSARTINIUCIU1

DISCUSICN

14-slope Analarsis1

Technicue of Compensation 5

Experimental Results 6

cOczaUMoi 6

FJ CE 6

FIGURES

1. D.C. current gain vs temperature for constant values ofcollector current(Experimental Boffman Transistor No.607) 7

2. D.C. current gain vs temperature for constant values ofcollector current(Experimental Hoffman Transistor No.608) 8

3. D.C. current gain vs temperature for constant values ofcollector current for a 2N702 9

4. Normalized hFE vs temperature for constant values of 1C(Eperimental Hoffman Transistor No.6o7) 10

5. Normalized hFE vs temperature for constant values of 1 C(Experimental Hofman Transistor No.608)

6. Normalized hFE vs temperature for constant values of 1Cfor a 2702 1

7- Magnified view of physical structure of experimentaltemperature insensitive transistor 13

8. An isometric pictorial of the experimental HoffmanTemperature Insensitive Transistor i4

9. Slope constant m as a function of the ratio Yj of basecurrents fro the type ma 2 to m - 1 15

10. Slope constant m as a function of the ratio T of basecurrents from the type ma 2 to m - 1 (for both aplanar and a mesa structure) 16

ii

GLOSSARY

h FE D.C. current gain

S Surface recombination velocity

PN Hole concentration in emitter region

Dli Diffusion constant of electrons in base region

LB Diffusion length of el ectrons in base region

WD Width of depletion layer

W B3ase width

A Cross-sectional area of the conduction path

V E Bitter Base Voltage

q 1.6 x 10-19 coulomb

kc 1.38 x 10-23 watt sec/0C

IT Lifetime for holes injected into highly n-type specimen

orno Lifetime for electrons injected into highly p-type specimen

T Temperature in Ok

AS Effective surface area for recombination

W E Width of emItter region

Dp Diffusion constant of holes in emitter region

Np Electron concentration in base region

ni Intrinsic concentration

A METHOD OF BASIC TUEATUEE COMMESATION I TRANSISTORS

The problem of the variation of a transistor's parameters with tempera-ture has long been a serious one for circuit designers and has led to ex-tensive circuit manipulations in an attempt to reduce the effects of thesevariations on a system's performance. Because of this, a contract wasawarded to the Hofftan Electronics Corporation1 to study this problem. Thespecific objectives of this contract were:

1. to make a thorough study of the problem of desiging a tempera-ture insensitive transistor.

2. to fabricate practical transistors that would have less than10 percent current-gain variation between OOC and 700 C.

This report is an evaluation of the experimental transistor models thatwere submitted at the end of the contract to support the theory developedunder the contract.

DISCUSSION

One of the major contributions of this contract was the develOpmeet ofa simple analytical tool called m-slope analysis. With this analyticaltechnique it was possible to pinpoint which leakage effects were dcainantin both a double-diffused mesa and a planar transistor.

Fbr a complete understanding of this analytical technique the follow-

ing derivation is offered.

M-slo.e Analysis

The original starting point of this analysis was the Websterequation for dc current gain. During the course of the contract, twoadditional terms were adsded to the Webster equation which accounted forthe effects of emitter space-charge recombination and surface leakage. Thecomplete expression for the current gain of a transistor was shown to be:

s c r c(o t1F [W1S +FEE FESP + LrE hF

wh e e 7h _ s . . . . . . . . f a ce t e rm

(b;ýE ...... 00 9.... 0 emitter efficiency term

/h I-E-SP *....*........ 0 space charge recombination term

1

(hFE)B . . . . . . . bulk recombination term

)L ............. Cutler-Bathsurface leakage term.

Equation (1) can also be expressed as

1 = (IB)S + (IB)E + (IB)SP + (IB)B + (IB)L (2)h FE

whereIC = collector current

(IB)i = base current components due to the various effects(i = S, E, SP, B, L).

The collector current Ic and the various base current components(IB)i depend on the dimensionless quantity, V,

where V = qVEkT

and = A exp•V (3)where

A, = qNpDN l&w

(IB)s - A2 exp V (5)where

A2 - SWAS A, (6)DNA

(IB)E = A3 exp V (7)

whereA3 qP1NDP (8)

WE

(IB) = A4 exp V (9)2

whereA= qNi Wd (10)

(C po + ono)

(IB)B = A5 exp V (.1)

2

where 1 (5 - 2 T (12)

(BL-A6 exp y [A - AB exp - 13

where L(2ok j 1

1v >> r. 1S•., DO) 2 (17)

Thne total base cu~rrent is

(IB) total-u{IB)S + (I3)E + (I3)sp + (IB)B + (IB)L]. (18)

Sysubstitutin equations (5), (7), (9), (U), (13)4 ineqation(18), the following equation is attained:(I) to [( )A+ A 5 (e1V + )

+A8 " - ex p( (19)

also A6 e xp + B3[A - A exp V M2(22

The b-Ae + A6S- 3 + ( + +. (21)

Btuation (20) can be e(,ressed b() an equation of the foie

= B v (•)

where the value of a is related to the particular mechanism contributingto the base current in the voltage range under consideration.

• Derivation of this equation can be found in the 3rd QuarterlyReport, Signal Corps Contract DA. 36-339, $0-87276,Hoffman Electronics Corporation, pp. 2-17.

+[ 2 3

Therefore,

B, Bexp V - B2 Bexp2B3O Vm + [A7A XPf.(3

Neglecting the s-all term of equation (23)

B, ep 2 Btexp + .3 ep V(24i)

Equation (24) contains the constant unknown factor B1 . To solve thisequation for the slope constant m, a second equation is needed. Thisequation can be obtained by differentiation of equation (24).

1 VY D2 B, exp Lr ex V

+ Be exp V. (25)

Using equation (24) and (25) to eliminate the unknown factor, B1,

r E Vý]% l3 +_1 2 exp Ym B3

B2 + expVB3 (26)

Assuming a is independent or almost independent of V, equation(26) becomes:

1 + expVm2

2B (27)

The term B2 exp Y represents the base current caused by surface

leakage and space-charge recombination, and the term Bý exp V is the basecurrent caused by surface reccobination, bulk recombination and the majoritycarrier flow into the emitter. The ratio of both current components charac-terizes the kind of base current.

,~B 2x' Vx (28)B3 exp V B

or2 (29)

"33Substituting equation (29) into equation (27) gives a simple expression

for m: 1

•+ii

or

m•TB+l.

2 (30)

The slope constant m is plotted as a function of T1 in Fig. 9.

At once a method of isolating which surface effects are predominantin a given transistor suggests itself. If the values of m are plotted onFig. 9 for different current levels the - values are readily obtainable.If n is less than one, the major effect is surface recombination at highcurrent levels and emitter space-charge recombination at low current levels.If the values of n are greater than one, the major effect is surfaceleakage at high current levels and emitter space-charge recombination atlow current levels. This technique of analysis could be extremelyvaluable in analyzing surface passivization techniques on transistors andcould prove a useful tool in both research and production control.

Fig. 10 shows the average values of m plotted for planar and mesastructures at both high and low values of current. It is seen that inplanar devices, surface recombination plays a dominant role in the variationof.h (dc current gain) at high current levels; while at low currentleve , surface recombination and emitter space-charge recombination areboth important, with emitter space-charge recombination becoming more impor-tant as the current is reduced to still lover values.

In the double-diffused mesa transistor, Cutler-Bath leakage currentis the dominant cause of temperature-gain variation. At very low currentlevels, a combination of both the Cutler-Bath leakage current and emitterspace-charge recombination current becomes important, with the emitterspace-charge recombination current gradually becoming the dominant factoras the current level is still further reduced.

Technique of Compensation

It has long been known that planar transistors have a greatertemperature-gain variation than geometrically equivalent mesa structures.The reason for this, it was found, is that mesa transistors have a greatermount of leakage current than planar types, and this extra leakage

current serves to control the temperature-gain variation of the mesa transis-tor. Also, because of the inherently excessive amounts of leakage current,mesa transistors have overall lover current gains than equivalent planartypes. Utilizing this conclusion, it seemed apparent that the solution forcontrolling the current gain of a planar transistor would li.• in introduc-ing a controlled leakage path in the transistor.

The approach used to create this leakage path was the inclusion of adiode between the emitter and base of an ordinary, medium-power NPNsilicon planar transistor. The effect of this diode would be to divertsome of the base current of the transistor, thereby effectively loweringthe current gain. This shunting effect would become Ino.1easingly pre-dominant as the temperature increased so as to offset the inherent increase

5

in gain of the transistor. Since the inclusion of this diode would effect-ively reduce the actual current gain of the transistor, as well as controlthe gain, special high gain transistor units were produced so that when thediode was introduced the overall current gain of the transistor would bea reasonable value. The actual photographs of the physical structure of theexperimental transistors, along with a pictorial view, are shown in Figs.7 and 8.

Experimental Results

Upon receiving the experimental transistor models, the dc current gainwas monitored over a temperature range of -250 C to 1000C. Although theinitial specification called for no more than a ten percent variation ofbFZ over the range of O°C to 700 C, experiments were conducted to observehow these transistors performed beyond the temperature limits imposed by theoriginal specifications. Figs. 1 and 2 show the variation of hFE for two ofthese experimental devices at various values of collector current. As acontrol, a 2N702 transistor was selected to show the temperature-gainvariation of a similar type of commercially available transistor. Fig. 3shows the temperature gain variation of the 2N702 at different values ofcollector current. Next, the normalized current gain versus temperature(Figs. 4, 5 and 6) were plotted for all three units. For these normalizedcurves onl the normalized current gains for the two extreme values ofcollector current were used. Mis was done because normalized values ofcurrent gain for the in-between values of collector current lie somewherebetween the normalized gains of the highest value of collector current usedand the lowest value of collector cumrent used. It can be seen from thesenormalized curves that the experimental transistors offer an improvementin gain control of about 150%. Also, the experimental models offer betterthan the ten percent compensation called for by the original specifications.

CONCLUSION

The final conclusion of this study is that gain compensation intransistors is indeed possible and that, with a further understanding of thetransictor structure and better methods of building and controlling sur-faces, high gain temperature-compensated devices over wide current rangeswill becme possible.

R~' CE

1. USAELRDL Contract DA 36-039 SC-87276, "Temperature InsensitiveTransistor," May 1961-May 1962.

6

00

70- -- -- -- -

c2 5MA50

FIG. 1

40

30

DG.CWREN- GAIN Vs TE MP-RATREFOR ONST\Nl VALUES0F COLECTOR URERT

EXFERINENTAL H)FFNAN rRANSIST)R No. 607

TE PERTUR IN 0

20-0 ; 40* 600 800* lo

90 HFE____ __ _ _

60__ ____ __

40 o__ _______

30__ __ ______

DW~0 CRE TEAl PERATUE 0C - -UR

'R0 600SAN 800 100C F

900-

7--

FIG.3

30-4

VI: I

~0. 5

-d DO. CURRENF GAIN VTEMPERATURE

3- 0F CONýTNTVA-UqS DF IICOLLOO7R CLRR:-N- FOR N702

I EMFIERAIURE I N4(f -20o 00a 2e 4e 600 80e 100

9

* HMAT THCAT 2!FC

1,4

NORMA IZED iFEVs TEMPE ATURE1.3FO G TA ' AIS _0 f

1.2FIG. 4

1.0

EXPERIWENlAL HOFFMAN TRANSISI R No.6C7

0.7

-4(f -2?f 2(f 40" 6(r a10

HFE AT T

HFE AT 2

1.4

1.3

NORMALIZED -IFEVs TEMPERATURE2 FOR CC NSTA T VALUES (,F If

FIG. 5

VCE:5V lc:

.i;;,20MA

0.9

0.8EXPERIMENTAL HOFFMAN TRANSI, TOR No 608

0.7

TEIMPERATUi E IN Q__0°-40" -20p 0o o0" 40 6e 80" 10

11

H~q•AT"I

•.V IAT 2't 1A

NN MAL ZED FE Vs TE MPER ATUREF()R COR C STAN VALUES CIF Ic

FOR A 2NY02

1.2

0.00Vcv 5V

FIG. 6

0.7

I TEMIERATURE IN _C

400 -20Q 00 200 4W0 600 80 1Q00°

t

iiIii

13

a wnma

0

00 LLWcr0 Ha.0

zOILz<H< cW

Cr <)

4 ':1LLJ

zCIL

1J&

0 \E--4

!N

0

N

0

cmI4 I.

33

15

IAr

040

-4 F4 P

.436

'Gel I26

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