Integrated circuits and components for bandgap references and temperature transducers

1

integrated circuits

gerard cm. meijer

Integrated Circuits and Components for

Bandgap References and

Temperature Transducers

Gerard CM. Meijer

Electronics Research Laboratory

(Dissertation Delft 18 march 1982),

Department of Electrical Engineering,

Delft University of Technology,

Delft, The Netherlands.

B i b l i o t h e e k TU D e l f t

C 8 6 3 1 6 9

A c k n o w l e d g e m e n t

Many people p a r t i c i p a t e d i n the work described i n t h i s d i s s e r t a t i o n and i t i s a pleasure f o r me to be able to take t h i s o p p o r t u n i t y to thank a l l of them f o r the e n t h u s i a s t i c and s k i l l f u l way i n which they d i d t h e i r work.

In p a r t i c u l a r , I would l i k e to mention Frans A. D i e t z Kees P. Duijverman Gerard de Haan

George J . van Heerden Hans G. Kerkhoff Ralph K r u i d e r i n g Peter C. Schmale Jan B. Verhoeff Kees V i n g e r l i n g Klaas van Zalinge

who examined and designed IC's during the course of t h e i r Master's degree study;

F r i t s J . de Jong Wim de Koning Paul K. Nauta Linus Smit Leo Wubben who f a b r i c a t e d the i n t e g r a t e d c i r c u i t s ; Bram van der Enden G i j s K. Steenvoorden Fred F. van Leeuwen who f a b r i c a t e d the t h i c k - f i l m c i r c u i t s ;

Wil G.M.M. Straver who performed many measurements;

Corlex A.M. Boon A l b e r t C. van der Woerd

who gave v a l u a b l e suggestions f o r improving t h i s p u b l i c a t i o n s Susan Massotty

who reviewed the E n g l i s h i n t h i s d i s s e r t a t i o n ; Mr. G. van B e r k e l

Mr. W.Th.J. van Kan Mr. W.J.P. van Nimwegen who made the large number of drawings,

O l f i e n van den Broeke Renate de Jong

who typed the d r a f t s ; and

H i l d a Verwest who typed the f i n a l v e r s i o n .

I I

INTEGRATED C I R C U I T S AND COMPONENTS FOR BANDGAP REFERENCES AND TEMPERATURE TRANSDUCERS

page

1. General i n t r o d u c t i o n 1

2. Components f o r IC bandgap references and temperature transducers 3

2.1 I n t r o d u c t i o n 3 2.2 The b i p o l a r npn t r a n s i s t o r i n the forward a c t i v e mode 3

2.2.1 The I_(V_„) c h a r a c t e r i s t i c 3 2.2.2 The temperature dependence of the base-emitter v o l t a g e 4

2.2.3 The temperature dependence of the current gain h ^ 6

2.2.4 Base-width modulation e f f e c t s 6 2.2.5 Matching of npn t r a n s i s t o r s operated at equal v o l t a g e s 7

2.2.6 N o n - i d e a l i t y of the PTAT v o l t a g e 9 2.3 The l a t e r a l pnp t r a n s i s t o r 10 2.4 R e s i s t o r s 11 2.4.1 P r o p e r t i e s of r e s i s t o r s 11 2.4.2 Trimming of r e s i s t o r s 12 2.5 The Seebeck e f f e c t 13

3. I n t e r a c t i o n s w i t h regard to power d i s s i p a t i o n and mechanical s t r e s s 15

3.1 I n t r o d u c t i o n 15 3.2 The e f f e c t of power d i s s i p a t i o n ; thermal response time 15

3.3 Thermal gradients i n the c h i p 17

3.4 Mechanical s t r e s s 18

4. Bandgap references 19 4.1 I n t r o d u c t i o n 19 4.2 An a c c u r a t e , s t r a i g h t f o r w a r d implementation of the b a s i c c i r c u i t 20

4.2.1 Design c o n s i d e r a t i o n s 20 4.2.2 Temperature and v o l t a g e dependence of the c u r r e n t t r a n s f e r f a c t o r 21

of a pnp current m i r r o r 4.2.3 P r a c t i c a l r e a l i z a t i o n 23 4.3 An a l l - n p n c o n f i g u r a t i o n 24 4.3.1 Design c o n s i d e r a t i o n s and p r i n c i p l e 24 4.3.2 R e a l i z a t i o n 26 4.3.3 Performance 27 4.4 A c i r c u i t w i t h high-order compensation of the temperature dependence 27

4.4.1 Design c o n s i d e r a t i o n s and p r i n c i p l e s 27 4.4.2 Curvature c o r r e c t i o n by applying temperature-dependent r e s i s t o r s 27

4.4.3 Curvature c o r r e c t i o n by l i n e a r i z i n g V (T) 29 4.4.4 R e a l i z a t i o n 30 4.5 P r e c i s i o n and c a l i b r a t i o n 32 5. M o n o l i t h i c temperature transducers 5.1 I n t r o d u c t i o n 5.2 A s i n g l e - t r a n s i s t o r temperature sensor 35 35 35

page

5.3 PTAT temperature sensors 36 5.3.1 An accurate PTAT current source 36

5.3.2 A v o l t a g e or current output 37 5.4 IC temperature sensors w i t h an i n t r i n s i c bandgap reference 38

5.5 Comparison of IC temperature sensors w i t h respect to long-term s t a b i l i t y and p r e c i s i o n

5.6 A general-purpose temperature transducer w i t h a f u l l y c a l i b r a t e d output c u r r e n t 41

5.6.1 P r i n c i p l e 41 5.6.2 The i n f l u e n c e of base currents and temperature dependence of r e s i s t o r s 42

5.6.3 Experimental r e s u l t s 43 5.7 A micropower e a s y - t o - c a l i b r a t e temperature transducer implemented w i t h d i f f u s e d 44

r e s i s t o r s

5.7.1 Design c o n s i d e r a t i o n s 44 5.7.2 Influence of temperature dependence of the r e s i s t o r s and f i n i t e 45

c u r r e n t g a i n f a c t o r

5.7.3 P r a c t i c a l r e a l i z a t i o n 46 5.7.4 Thermocouple c o l d - j u n c t i o n compensation 47

5.8 An accurate small-range temperature transducer 48 5.8.1 Design c o n s i d e r a t i o n s and b a s i c c i r c u i t 48

5.8.2 P r a c t i c a l r e a l i z a t i o n 49 5.8.3 C a l i b r a t i o n and r e s u l t s 50 5.9 A temperature sensor w i t h b i n a r y output, a d j u s t a b l e t r i p p o i n t and trimmable 51

h y s t e r e s i s

5.9.1 Design c o n s i d e r a t i o n s and b a s i c c i r c u i t 51

5.9.2 P r a c t i c a l r e a l i z a t i o n 52

6. Survey and conclusions 54

Appendix A Measurements of the temperature dependence of the I^iV^^) c h a r a c t e r i s t i c s 57 — — —C—-BE

of i n t e g r a t e d b i p o l a r t r a n s i s t o r s

Appendix B Accurate d e s c r i p t i o n of temperature e f f e c t s i n I (V ) c h a r a c t e r i s t i c s 61 C—-BE

References • 63

1. GENERAL INTRODUCTION

Voltage references are a p p l i e d i n data a c q u i s i t i o n systems, voltage r e g u l a t o r s and a l a r g e v a r i e t y of measurement equipment. With a l l of these

a p p l i c a t i o n s the magnitude of an unknown voltage i s determined by measuring i t s r a t i o w i t h respect to a reference v o l t a g e .

The magnitude of the reference voltage has to be known every time and under a l l circumstances i n which the measurement has to be performed. Un-c e r t a i n t y about i t s value d i r e Un-c t l y l i m i t s the accuracy of the measurement. Therefore, a v o l t a g e reference should supply a v o l t a g e w i t h a very low temperature c o e f f i c i e n t , a great l o n g and s h o r t -term s t a b i l i t y , a low i n t e r n a l r e s i s t a n c e and an i n s e n s i t i v i t y to thermal and mechanical shocks. Nowadays, g e n e r a l l y bandgap or zener references are a p p l i e d .

In bandgap references the output v o l t a g e i s o b t a i n -ed by adding a c o r r e c t i o n v o l t a g e V (T) to the base-emitter v o l t a g e V (T) of a b i p o l a r t r a n s i s t o r

(the reference t r a n s i s t o r ) i n order to cancel i t s temperature dependence.

Since the i n t r o d u c t i o n of t h i s p r i n c i p l e i n 1971 by Widlar [1.1] a l o t of m a t e r i a l has been published about bandgap references and a l a r g e number of commercial products i n which these references have been a p p l i e d have become a v a i l a b l e . Bandgap references have to compete w i t h zener r e f e r e n c e s . The main advantages of bandgap references concern t h e i r low supply v o l t a g e , low power d i s s i p a t i o n and good long-term s t a b i l i t y . A s u r p r i s i n g l y high p r e c i s i o n can be achieved w i t h bandgap r e f e r e n c e s . The temperature c o e f f i c i e n t (TC) of a base-emitter v o l t a g e i s r a t h e r h i g h : c i r c a 3000 ppm/°C. The TC of the output v o l t a g e of the best bandgap references i s l e s s than 2 ppm/°C. This means that the r e d u c t i o n i n TC i s over a f a c t o r of 11)00!

This high order o f compensation has to be maintained over a period of many months and under v a r i o u s e x t e r n a l circumstances without r e c a l i b r a t i o n . The c a l i b r a t i o n has to be performed during production i n a simple, inexpensive way.

In f a c t , the r e a l i z a t i o n of accurate bandgap references c l e a r l y demonstrates the amazing r a t e of p r e c i s i o n achieved w i t h analog IC ' s . The c o r r e c t i o n voltage V (T) needed to compensate f o r the TC of the

base-emitter v o l t a g e of the reference t r a n s i s t o r i s i n the same order of magnitude as V i t s e l f . There

BE

f o r e , demands w i t h respect to accuracy are as s t r i n g e n t f o r the c o r r e c t i o n v o l t a g e as f o r the V of the reference t r a n s i s t o r . The only v o l t a g e

BE

w i t h the d e s i r e d thermal behavior which i s accurate enough to be used f o r t h i s purpose i s the

d i f f e r e n c e AV of the base-emitter v o l t a g e s of a BE

matched p a i r of t r a n s i s t o r s operated at unequal e m i t t e r - c u r r e n t d e n s i t i e s . This d i f f e r e n t i a l voltage i s p r o p o r t i o n a l to the absolute temperature

(PTAT) when the r a t i o p ( p ^ 1) of the c u r r e n t d e n s i t i e s i s constant.

In bandgap references s i g n a l s w i t h a r e l a t i v e l y high TC are generated and processed i n a h i g h l y accurate way. The same type of component and c i r c u i t s can be used f o r the implementation of IC

temperature transducers. For the l a s t few years

these temperature transducers have provided a welcome s o l u t i o n f o r many temperature measurement problems. They d e l i v e r an accurate e l e c t r i c a l output s i g n a l i n the temperature range from -55 C to +150°C.

During the course of the work presented i n t h i s d i s s e r t a t i o n a number of new, accurate c i r c u i t s f o r bandgap references and temperature transducers have been developed. The l i m i t a t i o n s w i t h respect to accuracy have been i n v e s t i g a t e d .

Much emphasis has had to be put on the thermal behavior of components and c i r c u i t s , and many second-order e f f e c t s a l s o had to be taken i n t o account.

To achieve high accuracy not only the components and c i r c u i t s but a l s o the layout had to be c a r e -f u l l y designed i n order to optimize the matching of components and to minimize the e f f e c t s of thermal gradients and mechanical s t r e s s .

A b r i e f o u t l i n e of the m a t e r i a l found i n t h i s d i s s e r t a t i o n i s given below.

The c o n s i d e r a t i o n s of and the i n v e s t i g a t i o n s i n t o the p r o p e r t i e s of the a p p l i e d components and the i n f l u e n c e of t h e r m a l - e l e c t r i c a l i n t e r a c t i o n and mechanical s t r e s s have been c l u s t e r e d i n Chaps. 2. and 3.

The reader who i s mainly i n t e r e s t e d i n the c i r c u i t designs may omit these chapters and simply adopt

2 the main r e s u l t s d e r i v e d from these c o n s i d e r a t i o n s . In Chapter 2 the p r o p e r t i e s of the components used f o r the generation and a m p l i f i c a t i o n of the b a s i c s i g n a l s i n bandgap r e f e r e n c e s and temperature transducers are d i s c u s s e d .

In Chapter 3 the temperature r i s e of the chip due to i n t e r n a l power d i s s i p a t i o n i s considered. With the r e s u l t s of these c o n s i d e r a t i o n s values are found f o r the maximum admissible power d i s s i p a t i o n of temperature transducers. Furthermore, both e m p i r i c a l and c a l c u l a t e d data are presented about the temperature g r a d i e n t s caused by i n t e r n a l d i s s i p a t i o n i n the c h i p . These data are important f o r an optimal design of the layout of the c h i p . This chapter a l s o i n c l u d e s the i n f l u e n c e of mechanical s t r e s s on c i r c u i t performance. I t w i l l be argued that t h i s s t r e s s i s the dominant source of inaccuracy i n many w e l l - d e s i g n e d c i r c u i t s . In Chapter 4 accurate bandgap-reference c i r c u i t s developed during the course of t h i s work are presented.

In Chapter 5 v a r i o u s methods of using b i p o l a r t r a n s i s t o r s to sense the temperature are d i s c u s s e d . Much a t t e n t i o n has been paid to accuracy, c i r c u i t s i m p l i c i t y and m i n i m i z i n g the e f f o r t needed to c a l i b r a t e the d e v i c e s . There i s a l a r g e v a r i e t y of temperature-transducer a p p l i c a t i o n s . The demands f o r s p e c i f i c a p p l i c a t i o n s can b e t t e r be met by s p e c i a l c i r c u i t d e s i g n s . Examples of such s p e c i a l designs are d e s c r i b e d .

In Chapter 6 the main c o n c l u s i o n s of t h i s work are summarized.

2. COMPONENTS FOR IC BANDGAP REFERENCES AND TEMPERATURE TRANSDUCERS

I n t r o d u c t i o n

The f a v o r a b l e p r o p e r t i e s of IC bandgap references and temperature transducers are due to the h i g h l y p r e d i c t a b l e and time-independent way i n which the base-emitter v o l t a g e of a b i p o l a r t r a n s i s t o r i s r e l a t e d to the temperature.

For t h i s reason b i p o l a r technology has been s e l e c t e d to f a b r i c a t e the devices. Bandgap references

f a b r i c a t e d i n MOS technology [2.1] are l e s s accurate and t h e r e f o r e l e f t out of c o n s i d e r a t i o n i n t h i s work.

In t h i s chapter f i r s t l y the p r o p e r t i e s of the most important component the b i p o l a r npn t r a n s i s t o r -are d e a l t w i t h .

The c o n s i d e r a t i o n s about the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c and the temperature dependence of the base-emitter v o l t a g e of the b i p o l a r t r a n s i s t o r presented i n Sections 2.2.1 and 2.2.2 provide the t h e o r e t i c a l b a s i s f o r the c i r c u i t designs d e a l t w i t h i n t h i s d i s s e r t a t i o n . For high accuracy second-order e f f e c t s , such as base-width modulation and temperature dependence of the current g a i n which are discussed i n Sections 2.2.3 and 2.2.4, a l s o have to be taken i n t o account.

Mismatch of npn t r a n s i s t o r s and n o n i d e a l i t i e s of PTAT v o l t a g e s , as d e a l t w i t h i n Sections 2.2.5 and 2.2.6, are d e c i s i v e f o r the accuracy of the d e v i c e s . In S e c t i o n 2.3 the p r o p e r t i e s of l a t e r a l pnp

t r a n s i s t o r s a r e d i s c u s s e d . I t i s shown that the n o n i d e a l i t i e s i n t h e i r p r o p e r t i e s are so large that they cannot be used i n the b a s i c reference and sensor c e l l s . However, i n the supporting

e l e c t r o n i c s l a t e r a l pnp's are very u s e f u l , e s p e c i a l -l y f o r -l e v e -l s h i f t i n g .

R e s i s t o r s are used f o r v o l t a g e - t o - c u r r e n t conversion and f o r s e t t i n g the a m p l i f i e r g a i n . Their

p r o p e r t i e s have been d e a l t w i t h i n S e c t i o n 2.4. F i n a l l y , some a t t e n t i o n i s paid to the Seebeck e f f e c t . I t i s shown that i n the design of the r e s i s t o r layout t h i s e f f e c t has to be taken i n t o account.

Fig. 2.1 Sign conventions for bipolar'npn transistors.

amplify the b a s i c s i g n a l s . I n t h i s s e c t i o n the d.c. behavior of these t r a n s i s t o r s i s considered, w i t h emphasis on the temperature dependence of t h e i r p r o p e r t i e s . In our a p p l i c a t i o n s the t r a n s i s t o r s are u s u a l l y operated a t low v o l t a g e s and low currents i n order to o b t a i n high accuracy and to minimize power d i s s i p a t i o n .

Therefore, no a t t e n t i o n has been paid to e f f e c t s such as h i g h - l e v e l i n j e c t i o n and avalanche m u l t i p l i c a t i o n . The s i g n conventions used f o r

t r a n s i s t o r voltages and c u r r e n t s are shown i n F i g . 2.1.

2.2.1 The I _ ( V _ _ ) c h a r a c t e r i s t i c C DL

The main p r o p e r t i e s of b i p o l a r t r a n s i s t o r s a p p l i e d f o r bandgap references and temperature transducers are revealed by the well-known equation f o r the c o l l e c t o r current 1^ [2.2] :

BE

qV

XC = H e X P

i

kT /'

where

T = the absolute temperature, V = the base-emitter v o l t a g e ,

BE

q = the e l e c t r o n charge, k = the Boltzmann constant, and Ig i s given by (2.1) 2 2 -q n i V B _(2.2) 2.2 The b i p o l a r npn t r a n s i s t o r i n t h e f o r w a r d a c t i v e mode

In bandgap references and temperature transducers b i p o l a r npn t r a n s i s t o r s a r e used to generate and

w i t h Ag = the e m i t t e r - j u n c t i o n area, n. = the i n t r i n s i c c a r r i e r c o n c e n t r a t i o n i n the l base, D = the e f f e c t i v e m i n o r i t y - c a r r i e r d i f f u s i o n B

4 Q = the charge represented by the net number of

B

doping atoms i n the n e u t r a l base per u n i t area.

The charge Q can be w r i t t e n as B

(2.3)

where N i s the net base-doping d e n s i t y and x„ and

B E

x^ represent the boundaries of the n e u t r a l base r e g i o n on the e m i t t e r and the c o l l e c t o r s i d e , r e s p e c t i v e l y . These boundaries depend on the j u n c t i o n v o l t a g e s . This causes the base-widening e f f e c t which w i l l be discussed i n S e c t i o n 2.2.4. The q u a n t i t y Q„/q i s o f t e n c a l l e d the Gummel number.

B

The base current i s at low current l e v e l s dominated by mechanisms such as surface recombination and recombination i n the d e p l e t i o n r e g i o n s . At t h i s c u r r e n t l e v e l the base current i s p r o p o r t i o n a l to exp (qV /mkT), where the n o n i d e a l i t y f a c t o r m i s

BE

between 1 and 2 L2.3]. Due to the n o n i d e a l i t y of the base current the temperature dependence of the

l„(V-,„) c h a r a c t e r i s t i c can be p r e d i c t e d w i t h L B E

greater p r e c i s i o n than that of the I„(VTJ_,) E B E

c h a r a c t e r i s t i c .

At moderate c u r r e n t l e v e l s the base current 1^ i s mainly due to i n j e c t i o n of holes from the base i n t o the e m i t t e r . Then m = 1 and i t holds that L2.4]

^ Í E V E ^VB E I (2.4) where n._ = the i n t r i n s i c c a r r i e r c o n c e n t r a t i o n i n the I E e m i t t e r , a constar

Gummel number f o r the e m i t t e r ,

G_ = a constant which i s c a l l e d the e f f e c t i v e

D = the e f f e c t i v e m i n o r i t y - c a r r i e r d i f f u s i o n

E

constant i n the e m i t t e r .

2 ^ 2 ^ 2 _ _ T h e _ t e m g e r a t u r e _ d e g e n d e n c e _ o f _ t h e

To c a l c u l a t e the temperature dependence of the base-e m i t t base-e r v o l t a g base-e V wbase-e considbase-er thbase-e tbase-empbase-eraturbase-e

BE

dependence of the terms of (2.1) and (2.2). From [2.5] we have 2 3 ni = T exp(-qVg/kT), Dg = (kT/q)uB, (2.5) (2.6) where

y = the e f f e c t i v e value of the m o b i l i t y of B

e l e c t r o n s i n the base,

Vg = the bandgap v o l t a g e of the base m a t e r i a l .

The base charge Q a l s o depends somewhat B

on the temperature because of the temperature dependence of the boundaries x and x„. However,

E C

c a l c u l a t i o n s showed that t h i s e f f e c t i s n e g l i g i b l e i n a l l p r a c t i c a l cases d e a l t w i t h i n t h i s

d i s s e r t a t i o n .

The m o b i l i t y u and the bandgap v o l t a g e V are

B g r e l a t e d to the temperature i n a n o n l i n e a r way. When

we make the common approximations [ 2 . 5 ] : u * T

MB

vg O -a T'

(2.7)

(2.8)

where n and cc are constants and V _ i s the e x t r a -gO

polated bandgap v o l t a g e at 0 K, and then s u b s t i t u t e (2.5) and (2.6) i n (2.1) and (2.2) and n e g l e c t i n g the E a r l y e f f e c t i t i s found t h a t :

kT (2.9)

where

C = a constant, n = 4-n.

An accurate d e s c r i p t i o n of the temperature dependence of the I„(VD„) c h a r a c t e r i s t i c i s very

C B E

important f o r the designers of bandgap references and temperature transducers.

In a p p l y i n g approximations (2.7) and (2.8) we found i t necessary to check the v a l i d i t y of (2.9). For t h i s purpose we performed the measurements described i n Appendix A. The emperical values V „ = 1166 mV and fi = 3.72 were found from these

gO

measurements. These values d i f f e r c o n s i d e r a b l y from those expected on the b a s i s of p h y s i c a l

c o n s i d e r a t i o n s . T s i v i d i s [2.6] showed that t h i s i s mainly due to the poor approximation (2.8) f o r the V (T) dependence and presented a more a c c u r a t e , p h y s i c a l l y based a n a l y s i s . However, even w i t h t h i s a n a l y s i s the r e s u l t i n g equations found are not as accurate as i s d e s i r e d i n bandgap reference a p p l i c a t i o n s .

In Appendix B i t i s shown that equation (2.9) w i t h emperical values f o r n and VgQ can provide the

V g O ' l T l - m ) - ^

, k T , T - T r , T ,

Fig. 2.2 The base-emitter voltage V versus the temperature T. The curvature is

exaggerated in order to indicate the characteristic points clearly.

r e q u i r e d accuracy. For t h i s reason and a l s o because of i t s s i m p l i c i t y we w i l l use t h i s equation to describe the temperature dependence of the I (V )

C DD c h a r a c t e r i s t i c .

To examine spread i n V _ and n a number of measurements have been performed on t r a n s i s t o r s located on d i f f e r e n t chips on one wafer and having a l a r g e range of b i a s c u r r e n t s . The small spread found was w i t h i n the range determined by the measurement accuracy, which amounted t o 0 . 0 3 K. These measurement r e s u l t s confirm the accuracy of

( 2 . 9 ) w i t h the best f i t t i n g values f o r V ^ Q and n. Tó develop the equations f o r V (T) we consider two

BE

temperatures: an a r b i t r a r y temperature'T and a s p e c i f i e d r e f e r e n c e temperature T . A p p l y i n g ( 2 . 9 ) for each temperature, one can d e r i v e the f o l l o w i n g equation: VB E( T ) = V ' - T - > + f W " i f & r r H r + — I n q IC( T ) ( 2 . 1 0 )

For p r a c t i c a l reasons i n many of the c i r c u i t s d e a l t w i t h i n t h i s d i s s e r t a t i o n the c o l l e c t o r c u r r e n t i s made p r o p o r t i o n a l to some power of T:

( 2 . 1 1 ) S u b s t i t u t i n g t h i s i n ( 2 . 1 0 ) g i v e s : T T V (T) = V ( 1 - — ) + — V (T ) BE^ ; gO^ T ; T B E ^ V & r r . .kT . T - ( n - m ) — I n — . q T ,-( 2 . 1 2 )

As w i l l become c l e a r i n the f o l l o w i n g chapters i t i s convenient to express V (T) as the sum of a

B E

Fig. 2.2 The nonlinearity n(k/q)(T-T -Tin T/T ) of V (T) versus the temperature

t(°ffl

constant term, a term p r o p o r t i o n a l to T, and higher-order terms i n such a way that the l i n e a r terms represent the tangent to the V (T) curve f o r T =T

BE r ( f i g . 2 . 2 ) . We o b t a i n from ( 2 . 1 2 ) : kT VB E( T ) = {V _+(n-m)—-) -gO q XT where + (n-m)-(T-T -T In q r kT r X = V8 T r ( 2. 1 3 ) ( 2 . 1 4 )

To o b t a i n an impression of the magnitude of the d i f f e r e n t terms o f ( 2 . 1 3 ) and ( 2 . 1 4 ) we s u b s t i t u t e V ^ Q = 1 1 6 6 mV, n = 3 . 7 2 , and f o r example m = 0

(I„ i s c o n s t a n t ) , T = 3 2 3 K and VD„(T ) = 6 3 0 mV;

L r BE r then we f i n d f o r the constant:

kT

V n + n

gO q

1 2 6 9 . 5 mV

and f o r the l i n e a r term:

X = 1 . 9 8 mV/K.

The n o n l i n e a r i t y i n V ( T ) , which i s represented by

D E

the l a s t term i n ( 2 . 1 3 ) , i s p l o t t e d i n F i g . 2 . 3

against the temperature t i n °C f o r v a r i o u s v a l u e s of (n-m).

For r e l a t i v e l y small temperature changes

AT= T - T^ << T^ ( 2 . 1 3 ) can be approximated w e l l by the f i r s t three terms of i t s Taylor expansion, which r e s u l t s i n

VB E( T )

kT kT / \ 2

+ (n - m ) ~ - XT H| ( n - m ) - ^ l ^

6 1IL.1L - £HE £ _ d e E e ^ d e n c e _ o f _ t h e c u r r e n t g a i n h U £ k The i n t r i n s i c c a r r i e r c o n c e n t r a t i o n n.„ i n the lE e m i t t e r i s e x p o n e n t i a l l y r e l a t e d to the bandgap v o l t a g e i n the emitter i n a way s i m i l a r to that given by (2.5) f o r the i n t r i n s i c c a r r i e r

c o n c e n t r a t i o n n^ i n the base. Because of the heavy emitter doping the bandgap v o l t a g e i n the e m i t t e r i s an amount AV lower than that i n the base [ 2 . 5 ] .

S

The temperature dependence of the common-emitter-current g a i n f a c t o r h „ i s , a t moderate common-emitter-current

FE

l e v e l s , m a i n l y due to t h i s e f f e c t Q?.8_|. When t h i s i s

taken i n t o account i t can be c a l c u l a t e d from (2.1), (2.4) and (2.5) that

FE exp

-qAV

kT (2.16)

I f a Taylor expansion a t T = T i s performed on (2.16), then i t f o l l o w s f o r AT = T - Tf << kT 2/(qAV ) t h a t : qAV AT hF E 3 r (2.17) FE 2.2.4 B a s e - w i d t h m o d u l a t i o n e f f e c t s

The base charge (L given by (2.3) depends on the

B

boundaries x^ and of the n e u t r a l base r e g i o n . These boundaries i n turn depend on the j u n c t i o n v o l t a g e s .

An increase i n V__ or a decrease i n V w i l l cause

L B B E

an increase i n the corresponding d e p l e t i o n - l a y e r widths. As a consequence of t h i s base-width modulation e f f e c t the d e p l e t i o n - l a y e r charge

increases and the base charge Q decreases. In [2.9] Jespers presents a c a l c u l a t i o n of t h i s e f f e c t f o r changes of V__. When we extend t h i s

L B

c a l c u l a t i o n s to i n c l u d e changes of V as w e l l

B E

[2.10] we f i n d f o r the base charge Q_(V„„,V„„)

B C B B E

- t ( t )

Fig. 2.4 Common emitter-current gain ft versus the temperature for various current levels. VVC B 'VB E > - QB0 (. A,C 0 CB CC( Vc b > dV "CO cb A,E 0 E0 b e } ' <2-1 8) where %0 - % for VCB " VB E = 0 V> Cc( Vc^ ) = the c o l l e c t o r j u n c t i o n capacitance f o r a F i g u r e 2.4 shows t y p i c a l c h a r a c t e r i s t i c s of h versus the temperature f o r i n t e g r a t e d npn t r a n s i s t o r s f a b r i c a t e d i n a conventional IC

process. These curves f i t w e l l f o r those p r e d i c t e d

by (2.16) f o r AVg = 40 mV. For a number of

t r a n s i s t o r s f a b r i c a t e d on d i f f e r e n t wafers, we

found values f o r 'x d h^/dT w i t h i n the range VA,E

of 0.005/°C up to 0.006/°C. b i a s v o l t a g e Vc b, Cg(V^e) = the e m i t t e r j u n c t i o n capacitance f o r a Vb e ' 0 V, b i a s v o l t a g e v b e, • °Cf0r Vc b - CE f o r Vb e = 0 V, CO CE0 VA C = % 0 ^CC 0 w^ ^c l 1 *-s called the E a r l y v o l t a g e ,

For small changes i n v__ and vnii of the j u n c t i o n

v o l t a g e s when Vc b = VC B + vCB and Vb £ = VB E + vg g

i t i s found from (2.18) f o r the base charge V v c b ' V that: VVc b 'Vb e > ~- Q B ^ C B ' V I ' VCB VB E \ V V i . c yI , E . ; where = V. ""CO I,C A,C CC( VC B) ., CE 0 and I.E A,E CE( VB E) (2.19) (2.20)

Taking i n t o account that the l a s t two terms of the right-hand s i d e of (2.19) are always small compared to u n i t y , we d e r i v e from (2.1), (2.2) and (2.19) for the c o l l e c t o r current I_(V , ,V, ) that

C cb' be

CB B E

I,C I.E _(2.21)

I_(V ) c h a r a c t e r i s t i c s . For t r a n s i s t o r f a b r i c a t e d w i t h today's technology the l a s t terms i n (2.18) and (2.19) can be neglected i n a l l p r a c t i c a l s i t u a t i o n s d e a l t with i n t h i s d i s s e r t a t i o n .

2 ^ 2 . 5 _ _ M a t c h i n g _ o f _ n g n _ t r a n s i s t o

Fig. 2.5 The parameter Vj „ can be found in the IQ(VQE) characteristic by determining where the tangents to the curves inter-sect with the horizontal axis.

Fig. 2.6 The parameter „ of a bipolar transistor versus the collector-base voltage.

The parameter V can be found from the 1 , C

c h a r a c t e r i s t i c s by determining where BE

the tangents to the curves i n t e r s e c t w i t h the h o r i z o n t a l a x i s ( F i g . 2.5). This parameters has to be measured at r a t h e r low current l e v e l s ; otherwise s e l f - h e a t i n g e f f e c t s have to be taken i n t o account [2.11].

Values of V versus the bias v o l t a g e V„„

i- , C C B

measured f o r a t y p i c a l IC t r a n s i s t o r are shown i n F i g . 2.6.

^Measurement of VT „ of a forward biased t r a n s i s t o r

I,E

i s somewhat complicated. From (2.20) i t i s seen that t h i s parameter can be determined from ^, which can be measured f o r the i n v e r s e l y operated t r a n s i s t o r and from C„_/C„(V__), which can be

E U E B E

measured as described i n L2.12]. For a t y p i c a l IC t r a n s i s t o r we measured V, _ - 25 V. We d i d not

A,E

measure the capacitance r a t i o C /C (V ). When we estimate i t as a f a c t o r of [2.12], we f i n d

VI , E ~~ 8 V ^

With these values of V and V the e f f e c t of

A,E I , E

base-width by the emitter-base d e p l e t i o n l a y e r i s small as compared to other n o n - i d e a l i t i e s i n the

Due to the occurrence of mismatches the c o l l e c t o r -current r a t i o p = T-Q]I^-Q2 °^ t w o s uP Po s e c' l y

i d e n t i c a l t r a n s i s t o r s operated at equal v o l t a g e s d e v i a t e s s l i g h t l y from u n i t y . This non-unity l i m i t s the a t t a i n a b l e performance of many b a s i c i n t e g r a t e d c i r c u i t s such as current m i r r o r s and d i f f e r e n t i a l a m p l i f i e r s . The c o l l e c t o r - c u r r e n t r a t i o p i s d i r e c t l y r e l a t e d to the input o f f s e t v o l t a g e V c c , where o f f s e t V ,, - — I n p. o f f s e t q (2.22)

In npn t r a n s i s t o r s mismatches are mainly caused by: - V a r i a t i o n s i n the doping p r o f i l e , which cause

base-load mismatches as w e l l as b u l k - r e s i s t a n c e mismatches.

- V a r i a t i o n s i n the t r a n s i s t o r geometry as a consequence of the l i m i t e d r e s o l u t i o n of the p h o t o l i t h o g r a p h i c process. This causes e m i t t e r -area mismatches.

- Temperature g r a d i e n t s and v a r i a t i o n s i n

mechanical s t r e s s . These e f f e c t s w i l l be discussed i n Chap. 3.

- V a r i a t i o n s i n leakage c u r r e n t s .

The matching of components gets b e t t e r the more c l o s e l y together the components are p o s i t i o n e d or the l a r g e r they are. We performed a l a r g e number of measurements to o b t a i n e m p i r i c a l data about the magnitude and the temperature c o e f f i c i e n t s of the c o l l e c t o r - c u r r e n t mismatches.

F i r s t l y , Straver [2.13] tested a wafer c o n t a i n i n g p a i r s of t r a n s i s t o r s with rectangular and c i r c u l a r emitters having areas of 20 ym x 25 ym,

20 um x 50 ym and 20 ym x 100 ym and diameters of 25.2 ym, 35.7 ym and 50.5 ym, r e s p e c t i v e l y . A microphotograph of a chip i s shown i n F i g . 2.7. The measurement set-up i s p i c t u r e d i n F i g . 2.8. A t o t a l of 67 chips have been t e s t e d . By d e l e t i n g the r e s u l t s of the 10% worst cases, the standard d e v i a t i o n a(AI^,/I(-,) of the c o l l e c t o r - c u r r e n t

500 1000 1500 2000 6000 — ((jm!) Emitter area

Fig. 2.7 Miarophotograph of a chip containing transistor pairs with various geometries.

Fig. 2.8 Measurement set-up for the determination of collector-current mismatches

shown i n F i g . 2.9 f o r v a r i o u s e m i t t e r areas. In a d d i t i o n , t r a n s i s t o r p a i r s formed from c r o s s -connected segments of a quad of t r a n s i s t o r s have been t e s t e d ( F i g . 2.10).

Such p a i r s are o f t e n a p p l i e d to reduce the i n f l u e n c e of thermal gradients (see Chap. 3 ) . However, w i t h respect to c o l l e c t o r - c u r r e n t matching the observed improvement i n d i c a t e d i n F i g . 2.9 i s not b e t t e r than was expected from the l a r g e t o t a l e m i t t e r area.

The c o l l e c t o r - c u r r e n t r a t i o p of a p a i r of

t r a n s i s t o r s operated a t equal b i a s v o l t a g e s i s a l s o temperature dependent. At l a r g e current l e v e l s (1^ > 200 uA) t h i s i s mainly due to mismatches o f the e m i t t e r and base bulk r e s i s t a n c e s . At low current l e v e l s ( 1 ^ < 100 nA) unequal leakage currents are r e s p o n s i b l e f o r t h i s phenomenon. From measurements taken a t high and low current l e v e l s , r e s p e c t i v e l y , the i n f l u e n c e of these e f f e c t s at moderate c u r r e n t l e v e l s can be c a l c u l a t e d . However, i t has been found that a t moderate current l e v e l s (1 uA < 1^ < 100 uA) the measured temperature dependence i s much l a r g e r than can be explained on the b a s i s of the e f f e c t s of bulk r e s i s t a n c e s and leakage c u r r e n t s .

The measurements have been performed w i t h the s e t -up shown i n F i g . 2.8. T y p i c a l measurement r e s u l t s

Fig. 2.9 Observed standard deviation in the mismatch distribution of collector currents of transistor pairs and a

transistor quad with various geometries.

Fig. 2.10 Pair of transistors formed from cross-connected segments of a quad.

p ( t ) - p ( 4 0 ° C ) p(40°C)

(ppm)

lE per emitter = 10 liA

/ / / ^.., -f -20 0 2 b ~ ~ ^ As • ^ 6 0 8 0 / 100 — / / / • t(°C) 800 600 400 200 0 -200 -400 -600 -800 -1000 -1200 -1400

Fig. 2.11 Normalized collectro-current ratio (p) versus the temperature.

are depicted i n F i g . 2.11, which represents the r e l a t i v e change of the c o l l e c t o r - c u r r e n t r a t i o p w i t h respect to i t s value a t t = 40°C versus the

temperature t(°C) f o r s i x c h i p s .

A remarkable phenomenon observed d u r i n g these measurements i s the occurrence of a h y s t e r e s i s e f f e c t f o r successive heating and c o o l i n g c y c l e s , shown i n F i g . 2.12. The measurement r e s u l t depicted i n t h i s f i g u r e have been found f o r a p a i r of

t r a n s i s t o r s a f f l i c t e d w i t h a strong h y s t e r e s i s e f f e c t . A t a lower l e v e l t h i s e f f e c t has a l s o been found f o r the other d e v i c e s . The h y s t e r e s i s e f f e c t can p o s s i b l y be explained by the occurrence of mechanical s t r e s s a t the A l - S i 0 2 ~ S i i n t e r f a c e s [Sect. 3.4].

Fig. 2.12. Hysteresis effect of the

collector-current ratio (p) for successive heating and cooling cycles.

2^2^6__Non = i d e a l i ty__of _ t h e _ P T A T _ v o 1 t a g e

When two t r a n s i s t o r s are operated at a constant r a t i o r (r ^ 1) of t h e i r e m i t t e r - c u r r e n t d e n s i t i e s , the d i f f e r e n c e AV i n t h e i r base-emitter v o l t a g e s

B E

i s p r o p o r t i o n a l to the absolute temperature (PTAT). This PTAT v o l t a g e i s a b a s i c s i g n a l f o r bandgap references and temperature transducers. Non-i d e a l Non-i t Non-i e s of t h Non-i s s Non-i g n a l l Non-i m Non-i t the accuracy of well-designed devices.

When we assume that n. and D„ are equal f o r both l B t r a n s i s t o r s , then w i t h (2.1) i t i s found t h a t : I„ AV = V - V BE BEI BE2 kT , C 1QB 1 ^ 2 — I n q I ' m m , :

Fig. 2.13 Microphotograph of a chip containing two transistor pairs with emitter-area ratio 1:8.

C2

(2.23)

Fig. 2.14 The deviation A T of the PTAT voltage

from pure proportionality with T for six nominally identical transistor pairs.

In t h i s equation the numerical s u b s c r i p t s correspond to those of the t r a n s i s t o r s .

For t r a n s i s t o r s w i t h i d e n t i c a l d i f f u s i o n p r o f i l e s and operated a t equal c o l l e c t o r - b a s e v o l t a g e s we f i n d from (2.3) w i t h x CI C2 Xç that "E2

% l . ,

+ X

E1 V

X)DX XE 2C NB ^x^d x (2.24)

Even though i n the approximation i n (2.24) the i n f l u e n c e of base-width modulation by the (unequal) base-emitter v o l t a g e s i s n e g l e c t e d , the e r r o r made by t h i s approximation i s small when compared to the observed n o n - i d e a l i t i e s i n AV_„ discussed i n t h i s

B E

s e c t i o n .

With (2.23) and (2.24) we have

AV _BE kT ,—- In - ; — IC 1AE 2

q ^ 2 ^ 1

(2.25)

E m p i r i c a l l y , the v a l i d i t y of (2.25) has been tested w i t h the measurement set-up described i n Appendix A f o r npn t r a n s i s t o r p a i r s w i t h an e m i t t e r - a r e a r a t i o of (20 urn x 60 pm) : (8 x 20 um x 60 um) . A microphotograph of these t r a n s i s t o r s i s shown i n F i g . 2.13. The c o l l e c t o r c u r r e n t s were adjusted u n t i l they were equal and ranged from 10 uA up to

100 uA. The d e v i a t i o n AT of AV__(T) from pure

B E

p r o p o r t i o n a l i t y has been c a l c u l a t e d from measured values of AV and T by means of the equation:

BE

MB E< T'

(2.26)

where T denotes a reference temperature.

T y p i c a l r e s u l t s of these measurements are shown i n F i g . 2.14 versus the temperature t i n °C f o r

t = 40°C. The c u r r e n t dependency of t h i s d e v i a t i o n was found to be s m a l l . The d e v i a t i o n A T shown i n F i g . 2.14 turned out to be l a r g e r than what can be

10

explained by the i n f l u e n c e of bulk r e s i s t a n c e s , leakage c u r r e n t , base-width modulation or i n t e r n a l power d i s s i p a t i o n . P o s s i b l y , mechanical s t r e s s i s r e s p o n s i b l e f o r the d e v i a t i o n [Sec. 3.4].

2.3 The l a t e r a l pnp t r a n s i s t o r

L a t e r a l pnp t r a n s i s t o r s have a bad r e p u t a t i o n because of t h e i r low c u r r e n t gain h ^ and low c u t -o f f frequency f^,. L i t t l e kn-own i s that a l s -o the L(V„_) c h a r a c t e r i s t i c s are a l s o f a r from i d e a l .

C BE

F i g u r e 2.15 shows these c h a r a c t e r i s t i c s as measured f o r a G312 breadboard component of P h i l i p s and a CA3096 a r r a y t r a n s i s t o r of RCA, and f o r comparison, those f o r an npn t r a n s i s t o r of the type CA3046 (RCA) .

The CA 3096 t r a n s i s t o r c o n s i s t s of seven

t r a n s i s t o r s connected i n p a r a l l e l . This and the d i f f e r e n c e i n doping p r o f i l e s e x p l a i n s why the two l a t e r a l pnp's behave d i f f e r e n t l y . The d e v i a t i o n s A VB E of the IC(V B E) c h a r a c t e r i s t i c s from the i d e a l

can be d e s c r i b e d by kT r AV = V - V - — In — BE BE BE.ref q I (2.27) C,ref 100 f! M lr e f .

Fig. 2.16 The deviation àV of the IJVBE)

characteristic from the ideal one and d(AK__J/dl„ versus J ~ .

DL L> c

e m i t t e r - s e r i e s r e s i s t o r r = d(AV„„)/dl„ whose E BE C values are shown i n F i g . 2.16.

The n o n - i d e a l i t i e s i n the I_(V ) c h a r a c t e r i s t i c s L BE

are so large that l a t e r a l pnp t r a n s i s t o r s cannot be a p p l i e d to generate accurate PTAT s i g n a l s . In one respect the l a t e r a l pnp has an advantage: Due to the low e m i t t e r doping and the consequent l i t t l e bandgap narrowing i t s c u r r e n t - g a i n f a c t o r h_„ i s l e s s temperature-dependent than that of the

r E

where r e f denotes the base-emitter v o l t a g e f o r npn t r a n s i s t o r s . T y p i c a l values f o r the temperature

a c e r t a i n reference v a l u e I„ . of the c o l l e c t o r C,ref

current ( F i g . 2.15).

These n o n - i d e a l i t i e s of the I„(V__,) c h a r a c t e r i s t i c s C BE

are mainly due to a h i g h - l e v e l i n j e c t i o n mechanism and to the i n f l u e n c e of the e m i t t e r - b u l k r e s i s t a n c e . We can model t h i s e f f e c t by a current-dependent

c o e f f i c i e n t of h„_ as measured f o r the G 312 r E

breadboard components ( P h i l i p s ) are l i s t e d i n Table 2.1.

The base-width modulation e f f e c t (see S e c t i o n 2.2.4) can be c h a r a c t e r i z e d by a s i n g l e parameter V

1 ,C whose magnitude as measured f o r a G 312 i s shown

'be

(mV)

Fig. 2.15 The IQ(V^ characteristics of two different types of lateral pnp transistors and an npn transistor.

Table 2.1

Temperature coefficient of the current-gain factor hp-g of lateral pnp transistors FE at 25°C FE hF E 6 T 10 uA 100 uA 1 mA 32 34 9 4 X 10_ 4/°C 11 X io"4/°c 16 X 10- 4/°C •i,c (V) G 312 lateral pnp

Fig. 2.17 The base-width-modulation parameter V of a lateral pnp transistor versus the collector-base voltage.

IC

i n F i g . 2.17 versus the c o l l e c t o r - b a s e v o l t a g e . For a number of wafers measurements were made on the c o l l e c t o r - c u r r e n t matching of p a i r s of pnp t r a n s i s t o r s operated at equal b i a s v o l t a g e s . We observed c o n s i d e r a b l e d i f f e r e n c e s i n the mismatches f o r d i f f e r e n t wafers. However, f o r the best wafers the mismatches were comparable to those of the npn t r a n s i s t o r s [2.14].

2 . 4 R e s i s t o r s

P r o p e r t i e s o f _ r e s i s t o r s

In bandgap references and temperature transducers s p e c i a l a t t e n t i o n has to be paid to the q u a l i t y of the r e s i s t o r s , which perform important tasks i n the c i r c u i t r y . They are a p p l i e d f o r v o l t a g e t o -c u r r e n t -conversion and f o r s e t t i n g the a m p l i f i e r g a i n . Furthermore, by trimming the r e s i s t o r s , the devices can be c a l i b r a t e d .

The main types of r e s i s t o r s a p p l i e d f o r IC bandgap references and temperature transducers are:

1) T h i c k - f i l m r e s i s t o r s . These r e s i s t o r s , which are f a b r i c a t e d on a ceramic s u b s t r a t e , are a p p l i e d because they have a low temperature

c o e f f i c i e n t , e x c e l l e n t matching, a wide range of a v a i l a b l e sheet r e s i s t a n c e (from 10H /D to 1 Mfl/D), and lend themselves to l a s e r trimming. Their main disadvantage i s the r e l a t i v e l y h i g h c o s t of f a b r i c a t i n g and t e s t i n g the h y b r i d c i r c u i t s .

2) T h i n - f i l m - o n - s i l i c o n r e s i s t o r s . The p r o d u c t i o n cost of devices made w i t h t h i s technology i s much l e s s than that of h y b r i d s because trimming and t e s t i n g can be performed on the wafer. As compared to t h i c k - f i l m r e s i s t o r s a disadvantage i s the l i m i t e d range of s h e e t - r e s i s t a n c e values (100 a/D to 2 kfi/LJ").

3) B a s e - d i f f u s e d r e s i s t o r s . These r e s i s t o r s are f a b r i c a t e d w i t h standard IC technology, which makes them very a t t r a c t i v e i n view of the low production c o s t s . An e x c e l l e n t long-term s t a b i l i t y i s reported [2.15]. Their main d i s -advantages concern the high temperature and v o l t a g e dependence, and the l i m i t e d trimming p o s s i b i l i t i e s , which w i l l be d i s c u s s e d i n d e t a i l i n t h i s s e c t i o n and i n S e c t i o n 2.4.2,

r e s p e c t i v e l y . The sheet r e s i s t a n c e cannot be f r e e l y chosen but i s determined according to the IC process a p p l i e d .

In order to a c q u i r e nummerical data concerning t h e i r p r o p e r t i e s the v a r i o u s types of r e s i s t o r s ,

f a b r i c a t e d w i t h standard technology, have been t e s t e d . The main measurement r e s u l t s are l i s t e d i n Table 2.2. The matching data i n t h i s t a b l e concern the p r o p e r t i e s of nominally i d e n t i c a l r e s i s t o r s located as c l o s e l y to each other as p o s s i b l e . Note that d i f f u s e d r e s i s t o r s match almost as w e l l as t h i c k - and t h i n - f i l m r e s i s t o r s . Short d i f f u s e d r e s i s t o r s match l e s s w e l l than long ones, due to the r e l a t i v e l y l a r g e r i n f l u e n c e of the S i - A l c o n t a c t .

The temperature c o e f f i c i e n t 6_, = R (dR/dT) of d i f f u s e d r e s i s t o r s s t r o n g l y depends on the

temperature as shown i n F i g . 2.18. The temperature dependence of t h i n - f i l m r e s i s t o r s has been found to be l i n e a r i n T.

D i f f u s e d r e s i s t o r s are voltage-dependent because of the i n f l u e n c e of d e p l e t i o n - l a y e r - w i d t h

modulation. S m a l l - s i g n a l values R of base-sp

d i f f u s e d (sp) r e s i s t o r s have been measured as a f u n c t i o n of the b i a s v o l t a g e a p p l i e d to the ( e p i t a x i a l ) i s l a n d . The v o l t a g e c o e f f i c i e n t 6„ = R ' (dR /dV . ) of the r e s i s t o r f o r b i a s

V sp sp epi-sp

Table 2.2

Summary of resistor properties measured for various types of IC resistors

R e s i s t o r type S i z e : l e n g t h width (ym x ym) Sheet r e s i s t a n c e (0/0) Absolute t o l e r a n c e (%) Matching t o l e r a n c e (%) Temperature c o e f f i c i e n t (TC) (ppm/°C) d i f f e r e n c e i n TC's of matched r e s i s t o r s (ppm/°C)

Base d i f f u s e d 40 x 80 200 ± 20 ± 1.2 See Fig.2.18 ± 30

100 x 20 200 ± 20 ± 0.7 II II II ± 5 500 x 20 200 ± 20 ± 0.2 tl II II ± 5 Base p i n c h 6000 ± 50 3500 Nichrome 100 x 20 200 ± 2 0 ± 0.7 50 t o 100 ± 2 on s i l i c o n 750x 15 200 ± 2 0 ± 0.7 50 t o 100 ± 2 30 x 60 200 ± 2 0 ± 0.7 50 t o 100 ± 2 Thick f i l m 1000x1000 1000 ± 1 0 ± 1 . 5 30 ± 2 Dupont 500 x 500 1000 ± 1 0 ± 2.0 30 ± 2 comp. 1731 -20 0 20 40 60 80 100 » - l ( ° C )

Fig. 2.18 The temperature coefficient

&T = (dR/dt) of diffused resistors

versus the temperature.

versus the b i a s v o l t a g e V . f o r three v a l u e s epi-sp

of the temperature. An important item not mentioned i n Table 2.2 i s the long-term s t a b i l i t y of matching p r o p e r t i e s . To measure t h i s one needs to observe a l a r g e number of components over a long period of time, under p r e s c r i b e d c o n d i t i o n s . U n f o r t u n a t e l y , we had no o p p o r t u n i t y o f perform these measurements. A few data about the long-term s t a b i l i t y of

r e s i s t o r s are reported i n l i t e r a t u r e . I n [2.16] f o r m o n o l i t h i c t h i n - f i l m r e s i s t o r networks i t i s mentioned- that the absolute d r i f t i s l e s s than

1000 ppm per 1000 hrs (at 125°C) and that the d r i f t of the r a t i o o f two r e s i s t o r s i s l e s s than

100 ppm per 1000 hours (at 125°C). For t h i c k - f i l m r e s i s t o r s i n [2.17] an absolute d r i f t of t y p i c a l l y 500 ppm (2000 hrs a t 70°C) i s r e p o r t e d . With respect t o d i f f u s e d r e s i s t o r s i t i s argued i n [2.15] that t h e i r long-term s t a b i l i t y i s b e t t e r 400 0 2 4 6 8 10 ^ V ,p i_ ,p( V )

Fig. 2.19. The voltage coefficient

6V ~ Rsk (dRs.p'/dVe i-s ) °f base~

dtffuseu resvstoriPassu function of

the bias voltage V ._ between the resistor and the reJsis^or island.

than that of t h i n - f i l m r e s i s t o r s . However, no data have been g i v e n .

2^_4 • 2 _ _ T r i m m i n g _ o f _ r e s i s t o r s

C a l i b r a t i o n of bandgap references and temperature transducers i s performed by trimming one o r more r e s i s t o r s .

T h i c k - and t h i n - f i l m r e s i s t o r s can be laser-trimmed, o and can thus achieve an absolute accuracy of 1 / of the r e s i s t o r v a l u e . A microphotograph of a l a s e r -trimmed t h i c k - f i l m r e s i s t o r i s shown i n F i g . 2.20. D i f f u s e d r e s i s t o r s can be trimmed by s h o r t

Fig. 2.20 A laser-trimmed thick-film resistor.

Fig. 2. 21 Adjustment of resistors is achieved by a) blowing-up interconnections b) short-circuiting zener diodes.

by blowing-up i n t e r c o n n e c t i o n s ( f u s a b l e - l i n k trimming) ( F i g . 2.21).

The zener-zap method i s p r e f e r a b l e because i t does not have the disadvantages mentioned by E r d i [2.18] for the f u s a b l e - l i n k method, namely that metal regrowth due to e l e c t r o m i g r a t i o n and thermal expansion may occur, that wafer t e s t probes d e t e r i o r a t e q u i c k l y and that blown metal i n t e r -connections are u n s i g h t l y and t h e r e f o r e o f t e n un-acceptable.

In the zener-zap method a l a r g e c u r r e n t i s passed through an emitter-base diode i n the avalanche mode, which destroys the j u n c t i o n and produces a h i g h l y r e l i a b l e short c i r c u i t [2.18]. Some precautions have to be taken to avoid damaging the sp-epi j u n c t i o n , as w i l l be explained now. The zener-diode bulk r e s i s t a n c e i s r a t h e r high. For emitter-base diodes w i t h a 20 ym * 20 ym e m i t t e r s i z e the zener s e r i e s r e s i s t o r amounts to about 150fi. This s e r i e s r e s i s t o r i s an order of magnitude l a r g e r than that of a forward-biased

a) b)

Fig. 2.22 Current-flow paths for a diode in a) the zener mode

b) the forward-biased mode.

Fig. 2.23 With zener zapping of the breakdown voltage ^(m)cER °^ ® can be excee^er^'

which causes tne collector-base junction of Qg to be destroyed.

diode because of the d i f f e r e n t c u r r e n t - f l o w paths ( F i g . 2.22). The emitter-base zener diodes make part of ( p a r a s i t i c ) npn t r a n s i s t o r s as shown i n F i g . 2.23 f o r two r e s i s t o r s and two diodes. The c o l l e c t o r s have been connected to a p o s i t i v e v o l t a g e i n order to prevent the c o l l e c t o r - b a s e j u n c t i o n s of going i n t o conduction.

Because of the high s e r i e s r e s i s t o r r the zener B

v o l t a g e V of Q. a t l a r g e c u r r e n t l e v e l s may

E B I

exceed the breakdown v o l t a g e V, . of Q„

( , B R ) C E R c

(Fig. 2.23). In t h i s case the c o l l e c t o r - b a s e j u n c t i o n of (¡2 w i l l be destroyed.

This u n d e s i r a b l e e f f e c t can be avoided by d e s i g n i n g the zener diodes w i t h a s m a l l e r s e r i e s r e s i s t o r or by s h o r t - c i r c u i t i n g the unused B-E j u n c t i o n s during zener-zap trimming. In the l a t t e r case the

p a r a s i t i c breakdown occurs a t a v o l t a g e V, > V,

(BR)CES (BR)CER'

2.5 The S e e b e c k e f f e c t

In the l a y o u t design of the p r e c i s i o n c i r c u i t s discussed i n t h i s d i s s e r t a t i o n the Seebeck e f f e c t has to be taken i n t o account, e s p e c i a l l y when temperature g r a d i e n t s i n the c h i p are to be expected. The Seebeck e f f e c t occurs when the j u n c t i o n s a and b of two m a t e r i a l s ( f o r instance

14

£7

Al

Fig. 2.24 The Seebeak effects in an IC.

s i l i c o n and aluminum) are at d i f f e r e n t

temperatures Tj and 1^ ( F i g . 2.24). In t h i s case a v o l t a g e Vg which i s p r o p o r t i o n a l to the

temperature d i f f e r e n c e Tj - i s generated. There-f o r e one can w r i t e :

Vs - « ( ! , - T2) , (2.28)

where a denotes the Seebeck c o e f f i c i e n t . In S i - A l couples the value of a depends on the doping c o n c e n t r a t i o n of the s i l i c o n and can be as l a r g e as 1.4mV/K, which i s i n the same order of magnitude as the temperature c o e f f i c i e n t s of a base-emitter v o l t a g e .

A chip c o n t a i n i n g i n t e g r a t e d thermocouples of A l and a l l d i f f e r e n t types of S i was designed by Kerkhoff [2.19]. For these thermocouples the Seebeck c o e f f i c i e n t s have been measured and are l i s t e d i n Table 2.3.

E s p e c i a l l y w i t h long r e s i s t o r s temperature gradients can induce undesired Seebeck v o l t a g e s . This w i l l be i l l u s t r a t e d w i t h the s t r u c t u r e of F i g . 2.25. One of the A l - S i j u n c t i o n s of a r e s i s t o r i s l o c a t e d c l o s e to a p o w e r - d i s s i p a t i n g component ( f o r instance a t r a n s i s t o r ) . As w i l l be d e a l t w i t h i n S e c t i o n 3.3 the temperature d i f f e r e n c e Tj - T_ between the

Fig. 2.25 In the resistor a Seebeck voltage is generated by temperature gradients caused by power dissipation in the transistor. r e s i s t o r contacts amounts to T2 " ?h C . •

0

(2.29) 2nk where k = the thermal c o n d u c t i v i t y of s i l i c o n , P^= the d i s s i p a t e d power. I f , f o r i n s t a n c e , Tj = 70 um, = 1000 ym and Ph = 10 mW, then w i t h k = 140 W/mK i t i s found that Tj - T2 = 0.14°C. S u b s t i t u t i o n of t h i s value i n (2.28) w i t h a = 950 yV/K gives f o r the Seebeck v o l t a g e :

Vg = 0.134 mV.

In a s e n s i t i v e part of the c i r c u i t r y such a v o l t a g e may be unacceptable. This e f f e c t can be minimized by c a r e f u l l y designing the l a y o u t , f o r instance by p l a c i n g the r e s i s t o r contacts c l o s e to each other.

Table 2.3

Seebeck coefficients of Al-Si thermocouples for different types of doped silicon

Type of s i l i c o n Sheet r e s i s t a n c e (fl/D) Layer t h i c k n e s s (ym) <x(yV/K)

sn 10 1.9 - 2 1 0 sp 200 2.6 + 950

dn 8 4 340 dp 5 12 + 610

n-epi 1250 8 -1420 s = shallow, d = deep, n = n-type s i l i c o n , p = p-type s i l i c o n .

3. INTERACTION WITH REGARD TO POWER D I S S I P A T I O N AND MECHANICAL STRESS

3 . 1 I n t r o d u c t i o n

Power d i s s i p a t i o n i n the c h i p gives r i s e to a

temperature increase i n the c h i p . Such a temperature r i s e c o n t r i b u t e s d i r e c t l y to the absolute e r r o r of a temperature sensor. Bandgap references are i n s e n s i t i v e to uniform temperature changes i n the c h i p . However, these devices a r e , l i k e temperature transducers, very s e n s i t i v e to thermal g r a d i e n t s , which can e a s i l y be caused by i n t e r n a l power d i s s i p a t i o n .

This s e l f - h e a t i n g e f f e c t can be c h a r a c t e r i z e d by a thermal model. A simple model i s shown i n F i g . 3. 1 , i n which 8 i s the thermal r e s i s t a n c e between the

JB

emitter j u n c t i o n and the b u l k of the c h i p , 9 i s

B C

the thermal r e s i s t a n c e between the bulk of the chip and the case, 6 i s the thermal r e s i s t a n c e between

CA

the case and i t s surroundings, C i s the thermal c a p a c i t y of the chip and C^, i s the thermal c a p a c i t y of the case. The power source i s represented by the c u r r e n t source P w h i l e the ambient temperature w i t h respect to a c e r t a i n references i s represented by the v o l t a g e source T^.

The v a l i d i t y of t h i s model w i l l be discussed i n S e c t i o n 3.2. Although i t w i l l appear to be u s e f u l for q u a l i t a t i v e a n a l y s i s of s e l f - h e a t i n g e f f e c t s the model i s not s u i t a b l e f o r p r e d i c t i n g temperature g r a d i e n t s i n the c h i p . In S e c t i o n 3.3 a simple manner of c a l c u l a t i n g these g r a d i e n t s from e m p i r i c a l and t h e o r e t i c a l data i s shown.

Not only t h e r m a l - e l e c t r i c i n t e r a c t i o n but a l s o

bulk of

junction the chip case ambient

1 I

Fig. 3.1 Simple thermal model.

m e c h a n i c a l - e l e c t r i c i n t e r a c t i o n can cause d e v i a t i o n s i n the behavior of t r a n s i s t o r s . The magnitude of mechanical s t r e s s and i t s i n f l u e n c e on base-emitter v o l t a g e s w i l l be discussed i n Section 3.4.

3.2 The e f f e c t o f power d i s s i p a t i o n ; t h e r m a l r e s p o n s e t i m e

We can get a good idea of the thermal behavior of IC's by measuring the thermal step response of chips mounted i n d i f f e r e n t types of packages. The temperature changes i n the chip can be determined from the values of the base-emitter v o l t a g e s . A t y p i c a l r e s u l t , observed f o r a CA 3046 npn-t r a n s i s npn-t o r array i n a DIL package i s shown i n F i g . 3.2(a).

The layout of the array i s given s c h e m a t i c a l l y i n F i g . 3.2(b). The upper s o l i d curve of F i g . 3.2(a) represents the r e l a t i v e temperature change AT^ of

_ATj_ AP, AP, 10 10 10 10 10 1 10 time (a) J a E El a i 1 1 1 (b)

Fig. 3.2 (a) Temperature rise AT of the base-emitter junctions as caused by a power step AP^ in the collector dissipation of Q^.

16

the e m i t t e r j u n c t i o n of r e s u l t i n g from a power step AP^ i n the c o l l e c t o r d i s s i p a t i o n of that t r a n s i s t o r . Roughly, the temperature r i s e can be broken down i n t o two components, v i z . , a f a s t one and a slow one. The f a s t e f f e c t i s concerned w i t h the t r a n s i s t o r geometry. The slow e f f e c t i s

dependent on the thermal p r o p e r t i e s of the package. The lower curve of F i g . 3.2(a) represents the temperature change AT^ of caused by a power step APj i n the d i s s i p a t i o n of Q^.

Note that t h i s curve p a r a l l e l s the upper curve f o r time >1 ms and represents the slow e f f e c t mentioned above, In p l a s t i c packages, between chip and

ambient the heat i s mainly transported by thermal c o n d u c t i v i t y of the metal leads. The broken curves i n F i g . 3.2(a) represent measurement r e s u l t s f o r a s i m i l a r chip mounted i n an outwardly i d e n t i c a l DIL package but having a d i f f e r e n t metal c o n s t r u c t i o n i n t e r n a l l y . A c o n s i d e r a b l e d i f f e r e n c e i n thermal impedances i s found. For times longer,than 10s the temperature r i s e depends on the thermal

r e s i s t a n c e between the package and i t s surroundings, which i s i n f l u e n c e d by the presence of assembling m a t e r i a l , c o o l i n g b o d i e s , a i r v e l o c i t y , e t c . The time response shown i n F i g . 3.2 d e v i a t e s c o n s i d e r a b l y from the e x p o n e n t i a l behavior to be expected from the model of F i g . 3.1. However, f o r our a p p l i c a t i o n s i t i s not i n t e r e s t i n g to improve the accuracy of the model at the p r i c e of l a r g e r complexity. From S e c t i o n 3.1 i t f o l l o w s that we mainly need the model f o r two purposes:

a) To p r e d i c t the r i s e of the chip temperature i n the s t a t i o n a r y case. For t h i s purpose we can omit the c a p a c i t o r s i n the model of F i g . 3.1 b) To p r e d i c t the time response o f f a s t temperature

transducers. Fast temperature transducers are made by mounting the c h i p s i n s p e c i a l packages w i t h low thermal r e s i s t a n c e s and c a p a c i t a n c e s . In t h i s p a r t i c u l a r case u s e f u l r e s u l t s are obtained w i t h the simple model of F i g . 3.1.

Table 3.1 Thermal resistances for various types of packages in still air.

Tt RCA trans i s CA 3046 ermal r e s i s t a r or a r r a y CA 3045 ce (°C/W) P h i l i p s br components G007-DIL eadboard G007-SOT Type o f package 9J B °BC °CA 14-pens DIL (plas t i c ) 62 72 18 14-pens DIL (ceramic) 62 50 14 16-pens DIL (plas t i c ) 62 124 17 T0-74 (kovar) 62 40 35 SJ A !52 126 203 137

Fig. 3.3 Chip mounted on an epoxy PCB for measurement on the thermal properties of uncovered chips in air streams.

A d e t a i l e d study of the thermal p r o p e r t i e s of

diebond, bonding w i r e s and the c o n s t r u c t i o n of the package has been performed by F.A. D i e t z [ 3 . 1 ] . A summary of h i s measurement r e s u l t s f o r d i f f e r e n t types of packages i s g i v e n i n Table 3.1.

To study the l i m i t a t i o n s to the response time o f f a s t temperature sensors Duyverman [3.2] i n v e s t i g a t -ed the thermal p r o p e r t i e s of unpackag-ed chips placed i n an a i r stream w i t h a s p e c i f i e d v e l o c i t y . For these measurements a temperature-sensor chip which measures 2 mm x 1mm x0.2mm has been glued on a grooved p r i n t e d - c i r c u i t board ( F i g . 3.3). For a i r v e l o c i t i e s > 1 m/s the thermal response to a step change i n the power d i s s i p a t i o n on the chip agreed w e l l w i t h those p r e d i c t e d by the simple model of

F i g . 3.1 w i t h C„ = 0 Ws/ C and 6D„ 0 C/W. The

observed magnitudes of the thermal conductance between the chip and ambient and the thermal time constant T = eD. x C „u are shown i n F i g . 3.4 versus

T(S) 9B A(mW/°C)

(m/s)

Fig. 3.4 Thermal conductance and thermal time constant of the sensor chip positioned in an air stream versus the air velocity v.

m < ? ,at'>at.on

Fig. 3.5 Fast thermal response is maintained and some mechanical protection is obtained by gluing a dummy chip on the temperature-sensor chip.

the a i r v e r l o c i t y v. The small response time means that the IC temperature sensor i s a p p l i c a b l e f o r very f a s t temperature measurements.

The time constant i s o n l y s l i g h t l y dependent on the chip area because w i t h i n c r e a s i n g area the thermal conductance as w e l l as the thermal capacitance i n c r e a s e s . For a low response time the chip i s etched as t h i n as i s p e r m i s s i b l e from,the p o i n t of view of mechanical s t r e n g t h . G e n e r a l l y , temperature-sensor chips are mounted i n s p e c i a l types of

packages to o b t a i n mechanical and chemical

p r o t e c t i o n together w i t h good thermal p r o p e r t i e s . In [3.3] Analog Devices s p e c i f i e s the thermal p r o p e r t i e s of temperature sensors i n two types of packages i n v a r i o u s thermal environments. The time constants of these devices are about 30 times l a r g e r than those of the unpackaged chips so that f u r t h e r improvement of these sensors w i t h respect to response time seems to be p o s s i b l e . An i n t e r e s t i n g device can be obtained by g l u i n g a piece of s i l i c o n on the sensor chip ( F i g . 3.5) i n order to o b t a i n some mechanical p r o t e c t i o n of the c h i p . The thermal time constant of such a device i s only 2 times that of the s i n g l e unprotected c h i p .

3 . 3 T h e r m a l g r a d i e n t s i n t h e c h i p

The accuracy of bandgap references as w e l l as of temperature transducers can e a s i l y be s p o i l e d by temperature g r a d i e n t s over the c h i p . Temperature gradients caused by i n t e r n a l power d i s s i p a t i o n have been e x p e r i m e n t a l l y i n v e s t i g a t e d by measuring the temperature d i f f e r e n c e of two t r a n s i s t o r s caused by a power step AP i n a t h i r d t r a n s i s t o r . An example of such a step response has been shown i n F i g . 3 . 6 f o r a CA 3 0 4 6 t r a n s i s t o r a r r a y .

I t has been found that these thermal g r a d i e n t s are

s

È

8 < ~' 6 D3

m

_°,

m m

W

I — 1 -(s)

Fig. 3.6 Temperature differences of transistors Q„ and caused by a power step AP^ in the dissipation of on a CA 3046 array. Inset: basic layout of the CA 3046 array.

Fig. 3.7 Half-spherical heat source at the surface of a half space.

h a r d l y i n f l u e n c e d by the thermal p r o p e r t i e s of the package and surroundings. The magnitude of t h i s e f f e c t can be c a l c u l a t e d i n a r e l a t i v e l y simple way. For the case i n which the heat source i s h a l f

s p h e r i c a l and l o c a t e d at the surface of a h a l f space ( F i g . 3.7) and the heat i s e x c l u s i v e l y transported v i a conduction i n t h i s h a l f space, a thermal

d i f f e r e n t i a l r e s i s t a n c e e,(r.,r„) i s found f o r two p o i n t s located a t d i s t a n c e s and r ~ from the center of the source f o r which i t holds that i n the s t a t i o n a i r y case [ 3 . 4 ] : 3d( r , , r2) = A ( T ( r , ) - T ( r2) ) ÂP = 1 / 1 1 2 i r k ' I T j r ^ ,(3.1)

where k' = the thermal c o n d u c t i v i t y of s i l i c o n (=, 140 W/mK at T = 300 K) .

For t r a n s i s t o r a r r a y s the thermal d i f f e r e n t i a l r e s i s t a n c e s c a l c u l a t e d w i t h (3.1) d i f f e r l e s s than 25% from those found e m p i r i c a l l y [ 3 . 5 ] .

When the layout i s designed Eq. 3.1 can be used to make a rough e s t i m a t i o n of the e f f e c t of d i s s i p a t i n g components on the most s e n s i t i v e c i r c u i t p a r t s . When t h i s e f f e c t i s too l a r g e , the layout can be optimized by choosing a more symmetrical p o s i t i o n