Self-heating in BJT circuit parameter extraction

Solid-State ElectronicsVol. 35, No. 5, pp. 677-679, 1992 Printed in Great Britain. All rights reserved

0038-1101/92 $5.00+ 0.00 Copyright © 1992 Pergamon Press pie

S E L F - H E A T I N G IN BJT C I R C U I T P A R A M E T E R EXTRACTION MICHAEL REISCH SIEMENS AG, Corporate Research and Development, Otto-Hahn-Ring 6, 8 Miinchen 83, Fed. Rep. Germany

(Received 20 May 1991; in revised form 1 September 1991) Abstract--Due to the finite thermal resistance between the surface and backside of semiconductor wafers, self-heating effects may influence the results of parameter measurements in temperature-controlled waferprobe stations. This paper discusses the impact on the determination of the Early voltage and the emitter series resistance. Furthermore, a novel method for the extraction of the thermal resistance from the input characteristics of a bipolar transistor is presented.

I. INTRODUCTION Some circuit parameters of bipolar junction transistors (BJTs) are known to be strongly temperature dependent. Waferprobe stations for BJT measurements therefore generally are equipped with a thermal control unit that keeps the temperature on the backside of the wafer constant. However, due to the finite thermal resistance between the device and the heat sink, self-heating effects may still lead to deviations of extracted parameters from their isothermal values, as is shown in the following section. 2. THERMAL EFFECTS ON BJT OUTPUT CONDUCTIVITY Figure 1 shows measured output characteristics of a self-aligned BJT[1] (Ae= 1 6 x 16/1m) determined with the temperature of the wafer backside held constant (_+0.3°C)t. The Early voltages I?A included in the figure were determined by a least-square fit to the experimental data in the interval 1V -%
. f Oqb ~ l V , ~ q b ' f dqb ~-1 V A ~ qb _ ~7~bc / v ; \-ff'~b~ J V~

(1)

Re "-V~Ic- Rb " Ib } ,

(3)

one obtains for the apparent Early voltage VA determined by experiment: ~ f 0 ln[,c]']

vA \ 0v~b )v~ . ( 0q b ~ - I

VA

0,

(2)

ov~o \ov~)~ \-D--~)~ ~V. >

1

0 ln[Ic]

~4

0T

0T

Re

0/~

0Vo~ V~ 0V~b' (4)

considering that for Vb~ = c o n s t . (OIb/OVcb) ~ 0 as long as carrier multiplication in the BC diode is negligible. Since:

\Measurements were performed with V~ = const, rather than 1b =const., since in the second method the operational point of the emitter-base diode and thus the collector current is affected by a possible generation current (e.g. due to impact ionization) in the base-collector diode. ssE 35I~E

Ic = l'( T) " exp{ Vbe

1

and therefore OVA __ ( 0 q b "/

since the normalized base charge qb increases both with Vbe and V~. In Fig. 2 experimentally determined values VA are plotted vs V~ for transistors of different geometry. For small values of V~, the increase of VA with V~ expected from (2) is indeed observed. The decrease of 1?A with Vb¢ for larger values of Vb~ is seen to be essentially dependent on the area of the transistor and rather independent of emitter stripe width, i.e. base charge modulation effects or base series resistance effects fail to explain this phenomenon. The effect is explained by means of a finite thermal resistance Rth between the wafer surface and the backside of the wafer. Since the data points of the output characteristic are each determined for a different value of dissipated power--which approximately increases in proportion to Vcb--the local temperature of the device will increase with Vcb. Due to the exponential temperature dependence of the collector saturation current l , ~ e x p [ - E g / k . T] even small temperature changes imply significant changes in the slope of the output characteristic[4,5]. From:

OT O -~¢b~b[Rth'lc 677

" Veel,~Rth'I¢>O,

(5)

678

MICHAEL REISCH

the apparent value of the Early voltage 17A will be smaller than VA and decrease with increasing values of I~ because of self-heating. In Fig. 2 for values of V~ smaller than some 0 . 6 5 . . . 0.7 V (dependent on transistor size) the value of I¢ and hence the value of OT/OVcba r e too small to cause significant deviations from the behaviour predicted by the G u m m e l - P o o n model. For larger values of Vb~ the second term on the RHS of (4) gains significance and results in the observed deviations of l?A from the expected behaviour. The third term is negligibly small for the measurement conditions chosen and the devices investigated. If this term would dominate, it would lead to a reduction of 1/VA and hence to an increase in the apparent Early voltage in contrast to what is observed experimentally. It is possible to extract R~h from the slope of the output characteristics of the bipolar transistor by using formula (4). This approach, however, is rather cumbersome, and not very precise; a better method is presented in Section 3. In principle all those parameter extraction procedures will be affected by self-heating that employ fitting of a curve to a set of data points that corresponds to different operating points with different values of dissipated power. The effect is negligible for small values of dissipated power, as is e.g. the case with the extraction of the saturation current from the log[I~] vs V~ plot, which is evaluated in the low-level injection regime. Procedures that employ large currents, such as the d.c. method for the extraction of the emitter series resistance considered in the following, do not fulfil this requirement, and must be investigated for errors due to self-heating.

/ J 45 [Vl

*

40

"

". , ~''~'~.

[a} ° ° --=15 aVue

35

30 i 0.5

0,4

EFFECTS OF

ON

THE

I 06

; 0,7

Vbe

t

[Vl

i 08

•

Fig. 2. Extrapolated Early voltage I7"A vs V~ for BJTs of different geometry: (a) A,= 16 × 16#m; (b) finger structured A~= 128 × 2pm; and (c) A~= 2 x 8 pm.

resistances Re, R b is Ning's method[6], which considers the deviation of the measured base current: /b = /b~(T) ' exp[(Vb~ -- R~" I~ -- R b /b)/VT],

(6)

from the "ideal base current" /b.id = Ib~(To)'exp[Vb~/VT].

(7)

The value of Ib,(To) is determined from the ideal portion of the input characteristics in the low-level injection regime. Both I b and Ib.,dare determined with the wafer backside temperature held constant at To. If self-heating effects may be neglected T = TO and Re, Rb are determined from the slope and ordinate of the line fitted to the points VT- Icl'ln[lb,id/lb] plotted vs /3 ~, since then: VT ln~'lb,~d~ =

3. T H E R M A L

.(b)

T

EXTRACTION

Re+Rb

Ro+-7--

(8)

Re, R b

A widely employed d.c. measurement method for the determination of the emitter and base series

0,10

200 [,uA]

0,05

150

[04V

1OC

37,95 V

!

to.. 3B23V

---~

5C

~ -

'

---

3 B,70 V

.05 - -

39,25V 0

I

o

:~

;

,; Vce

8

tvl lO - 0.10

I~

Fig. 1. Measured output characteristics and extrapolated Early voltages I7Aof a self-aligned BJT with temperature on wafer backside held constant. The curves correspond to different values of V~ in the interval 0.65 V < V~ < 0.71 V.

Fig.

2

3

Mob

P

4

[Vl

3. [Ib(V~, Vcb) - I b ( V ~,O)]/lb(V ~,0) VS Feb for V~=0.6V and Vb~=0.8V (Ae=2 x 32#m).

Self-heating in BJT circuit parameter extraction 02

0.1

l Ib

...::....,.....

::;..

-OJ

-0'20

l" "'~

°°°

,

10

! i

.I I

t

20 30 /.0 Ap ~,

50 [mWl

Fig. 4. [lb(V~, V~b)--Ib(V~,O)]/Ib(V~,O ) VS changes of dissipated power A P = P ( V ~ , V ¢ b ) - P ( V ~ , O ) for two different emitter geometries: (a) 16× 16/~m; and (b) 128 × 2 pro, finger structure. The thermal resistance values indicated in the figure are extracted from the slope of the resulting straight line in the submultiplication regime. For nonnegligible self-heating, the assumption T = TOno longer holds, and (8) has to be modified to:

Re+Rb

Vvo. ln~'lb,id~

V,o { v~ F.~ ) AT T k. ro To'

(9)

up to first-order in AT~To, since Ib~(T) ~ e x p [ - Eg/k • T]. With AT = T - To proportional to the power dissipated we obtain for the error 6R, imposed onto the extracted emitter series resistance by the extra term in (9):

k(E,

aRe : -- q" k 7 %

VToj

/~+l

x Rth'---ff--. Vb~; Vb¢ = 0.

(10)

This error is independent of I~ and proportional to &h' For fl >> !, Vb, = 0.8 V we obtain

6R~/Rth~ 1 0 - 3 f ~ . W K

I,

i.e. errors due to self-heating will be tolerable for thermal resistances of the order of 100 K W 1

4. EXTRACTIONOF THE THERMAL RESISTANCE Re~ A rather direct procedure for the extraction of Rth is obtained by monitoring the Ib vs Vcb curve. For transistors with negligible thermal generation in the base-collector diode [Ib(0, V~b)~ 0] and if self-heating can be neglected, the base current:

lb(V~, ToO =/b(Vbe, 0)+Ib(0, Vcb)"b[1 --

1 / M . ] ' I c,

(11)

679

is independent of Vcb up to the onset of carrier multiplication[7]. This is demonstrated in Fig. 3a, where the relative change of Ib as a function of Vcb is plotted for Vb~= 0.6V. Virtually no changes are observed until the onset of nonnegligible carrier multiplication in the base-collector diode. A different result is obtained for Vbo= 0.8V (Fig. 3b). Here AIUIb shows an approximately linear increase with Vcb until carrier multiplication becomes dominant. This increase is explained by the increasing power dissipation in the device, which is essentially proportional to Vcb. For the extraction of Rth the relative change AIb/l b of the base current is plotted vs the change in dissipated power P(Vt~, Vcb)--P(Vbe, O) where P ( V ~ , Vcb) = Vbe' Ib + Vce" Ic. This is illustrated in Fig. 4 for two different emitter geometries. For the slope of the resulting straight line in the submultiplication regime one obtains:

L

( A l b ' ] - - c ln[Ib] -- Rth "c31n[lb~]

op \ *u }

~P

or

(12)

'

which is easily resolved for Rth with the result:

Rth ~ Eg ~qq T Vbe " OP \ lh }

(13)

The only assumption inherent to this procedure is that the thermal generation current in the basecollector diode is negligible, as is the case for wellprocessed devices.

5. SUMMARY Self-heating effects in bipolar transistors may introduce measurement errors even in temperature-controlled waferprobe-stations. Affected are parameter extraction procedures that employ fitting of data measured at different operating points. The thermal resistance that is used for the characterization of the coupling between the device and the heat sink can be determined from the Ib(Vcb ) characteristic (V~ held constant) in the submultiplication regime. The extraction procedure described provides a fast method for the determination of Rth for all transistors that show a negligible leakage current in the base-collector diode.

Note--During review of this paper, results similar to those presented in Section 3 of this paper have been published by T. M. Liu et al., 1EEE Trans. Electron Devices 38, 1845 (1991). REFERENCES

1. H. Kabza et al., IEEE Electron Device Lett. 10, 344 (1989). 2. I. A. Getreu, Modeling the Bipolar Transistor. Elsevier, New York (1978). 3. H. C. de Graaff, In Process and Device Modeling (W. L. Engl (Ed.), p. 413. Elsevier, Amsterdam (1986). 4. R. L. Pritchard, Electrical Characteristics of Transistors. McGraw-Hill, New York (1978). 5. O. Mfiller, A.E.CL 17, 13 (1963). 6. T. H. Ning and D. D. Tang, IEEE Trans. Electron Devices ED-31, 409 (1984). 7. M. Reisch, Solid-St. Electron. 33, 189 (1990).