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The effects of stress on gallium arsenide device characteristics Peng, Harry W. 1988

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THE EFFECTS OF STRESS ON GALLIUM ARSENIDE DEVICE CHARACTERISTICS by HARRY W. PENG A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of E l e c t r i c a l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA January 1988 © Harry W. Peng, 1988 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the The U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permi s s i o n . Department of E l e c t r i c a l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: January 1988 ABSTRACT For VLSI a p p l i c a t i o n s , i t i s e s s e n t i a l t o have c o n s i s t e n t d e v i c e c h a r a c t e r i s t i c s f o r d e v i c e s f a b r i c a t e d on d i f f e r e n t f a b r i c a t i o n runs, on d i f f e r e n t wafers, and e s p e c i a l l y a c r o s s a s i n g l e wafer. MESFETs f a b r i c a t e d on GaAs have been found t o have an o r i e n t a t i o n dependence i n t h e i r t h r e s h o l d v o l t a g e and other c h a r a c t e r i s t i c s . For MESFETs with gate l e n g t h l e s s than 2 urn, changing the d e v i c e o r i e n t a t i o n can so s i g n i f i c a n t l y a l t e r the d e v i c e c h a r a c t e r i s t i c s t h a t i t must be c o n s i d e r e d d u r i n g the t r a n s i s t o r d e sign stage. The causes f o r the o r i e n t a t i o n dependence i n the d e v i c e c h a r a c t e r i s t i c s have been suggested to be the p i e z o e l e c t r i c p r o p e r t y of GaAs and s t r e s s i n the s u b s t r a t e . S t r e s s produced by the e n c a p s u l a t i n g d i e l e c t r i c f i l m generates a p o l a r i z a t i o n charge d e n s i t y i n the s u b s t r a t e . I f the magnitude of the p o l a r i z a t i o n charge d e n s i t y i s l a r g e enough to a l t e r the channel doping p r o f i l e , then the d e v i c e c h a r a c t e r i s t i c s are changed. In t h i s t h e s i s , the e f f e c t s of s t r e s s on GaAs MESFET de v i c e c h a r a c t e r i s t i c s were s t u d i e d by m o d e l l i n g and experimental works. In the m o d e l l i n g p a r t , p o l a r i z a t i o n charge d e n s i t i e s under the gate of an en c a p s u l a t e d MESFET were c a l c u l a t e d by u s i n g the so c a l l e d d i s t r i b u t e d f o r c e model and the edge c o n c e n t r a t e d model. The d i s t r i b u t e d f o r c e model i s a much b e t t e r model because i t d e s c r i b e s more r e a l i s t i c a l l y the s t r e s s d i s t r i b u t i o n i n the f i l m and i n the s u b s t r a t e . I t should p r o v i d e a much more a c c u r a t e c a l c u l a t i o n of the i i . induced p o l a r i z a t i o n charge d e n s i t y . The r e s u l t s show that the p o l a r i z a r i t i o n charge d e n s i t i e s c a l c u l a t e d by the two models have s i m i l a r d i s t r i b u t i o n p a t t e r n , but the magnitudes are very d i f f e r e n t . With an i d e n t i c a l set of c o n d i t i o n s , a much l a r g e r p o l a r i z a t i o n charge d e n s i t y i s p r e d i c t e d by the edge c o n c e n t r a t e d model. In a d d i t i o n , the d i s t r i b u t e d f o r c e model d i s t i n g u i s h e s d i f f e r e n t f i l m s by a "hardness" val u e , based on t h e i r e l a s t i c p r o p e r t y , whereas the edge c o n c e n t r a t e d model does not. A f i l m with a l a r g e r "hardness" v a l u e i s p r e d i c t e d to generate a l a r g e r p o l a r i z a t i o n charge d e n s i t y . Two types of f i l m were c o n s i d e r e d , S i C ^ and S i g N 4 . Using bulk f i l m c h a r a c t e r i s t i c s , the c a l c u l a t i o n s showed th a t S i 0 2 f i l m i s "harder" than S i g N 4 f i l m . I f an equal b u i l t - i n s t r e s s value i s assumed, then a l a r g e r p o l a r i z a t i o n charge d e n s i t y i s p r e d i c t e d f o r S i C ^ than f o r SigN^ e n c a p s u l a t e d s u b s t r a t e s . In the experimental p a r t , s t r e s s was a p p l i e d to t e s t d e v i c e s by bending s t r i p s of GaAs wafers i n a c a n t i l e v e r c o n f i g u r a t i o n . MESFETs t e s t e d were o r i e n t e d i n the [ 011 ] or the [01T] d i r e c t i o n . Both s t a t i c s t r e s s and t i m e - v a r y i n g s t r e s s were a p p l i e d . In the s t a t i c s s t r e s s experiment, the changes i n the b a r r i e r h eight and the C-V p r o f i l e were measured. I t was found t h a t , with equal s t r e s s a p p l i e d , Schottky b a r r i e r s with a l a r g e r i d e a l i t y f a c t o r showed a l a r g e r change i n the b a r r i e r height.. i i i In the t i m e - v a r y i n g s t r e s s experiment, attempts were made to measure the e f f e c t of the p o l a r i z a t i o n charge d e n s i t y on d e v i c e c h a r a c t e r i s t i c s by measuring changes i n the d r a i n - s o u r c e c u r r e n t . iv Table of Contents ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS x i i 1 . I n t r o d u c t i o n 1 2. O r i e n t a t i o n Dependence i n GaAs MESFETs: I t s causes and A p p l i c a t i o n s . 4 2.1 I n t r o d u c t i o n and H i s t o r y 4 2.2 Schottky B a r r i e r Height Change wi t h A p p l i e d S t r e s s 11 2.3 E f f e c t s of D i s l o c a t i o n s on Device C h a r a c t e r i s t i c s 13 2.4 P i e z o e l e c t r i c P r o p e r t y of GaAs 17 2.5 L a t e r a l D i f f u s i o n of Dopants During Annealing ...17 2.6 A p p l i c a t i o n s of the P i e z o e l e c t r i c E f f e c t 20 3. T h e o r e t i c a l C a l c u l a t i o n s of the P o l a r i z a t i o n Charge D e n s i t y 23 3.1 P o l a r i z a t i o n Charge D e n s i t y 23 3.2 P o l a r i z a t i o n Charge D e n s i t y i n GaAs C a n t i l e v e r ..25 3.3 Between F i l m Edges 27 3.3.1 F i l m S t r e s s 27 3.3.2 C a l c u l a t i o n s by Edge Concentrated model ...31 3.3.3 C a l c u l a t i o n s by the D i s t r i b u t e d Force Model 33 3.4 D i s c u s s i o n 38 4. Experimental I n v e s t i g a t i o n of S t r e s s on Device C h a r a c t e r i s t i c s 58 4.1 I n t r o d u c t i o n 58 4.2 E l a s t i c a l l y L i n e a r G a l l i u m A r s e n i d e C a n t i l e v e r s .59 4.3 S t a t i c S t r e s s Experiment 61 v 4.3.1 Background 61 4.3.2 Experimental Method 64 4.3.3 R e s u l t s 66 4.4 Time-Varying S t r e s s Experiment 71 4.4.1 Experimental Procedures 74 4.4.2 Comments on the R e s u l t s 75 4.5 C a l c u l a t i o n s of the B a r r i e r Height S h i f t due to F i l m S t r e s s 79 5. C o n c l u s i o n s and Suggestions f o r Future Work 81 REFERENCES 84 APPENDIX A . .89 APPENDIX B 93 APPENDIX C 94 v i L i s t of T a b l e s 1 T h e o r e t i c a l expected changes due to s t r e s s . . . . 62 2 Comparison of b a r r i e r h e i g h t s h i f t with r e s u l t s o b tained by Kusaka et al 69 v i i L i s t of F i g u r e s 2.1 Te s t d e v i c e o r i e n t a t i o n used by Lee et al. [3] 5 2.2 O r i e n t a t i o n dependence i n t h r e s h o l d v o l t a g e observed by Lee et al. [3] 5 2.3 Asbeck et a/.'s t h e o r e t i c a l (a) and experimental (b) r e s u l t s [4] 9 2.4 T h r e s h o l d v o l t a g e versus gate l e n g t h with S i 0 2 o v e r l a y e r (Ohnishi et a/. [11]) 9 2.5 T h r e s h o l d v o l t a g e versus gate l e n g t h with S i 3 N 4 o v e r l a y e r (Ohnishi et a/. [11]) 9 2.6 Mechanisms a f f e c t i n g d e v i c e c h a r a c t e r i s t i c s . . . 10 2.7 Changes i n the b a r r i e r h e i g h t versus s u r f a c e s t r a i n (Kusaka et a/. [14]) 12 2.8 D i s l o c a t i o n p r o x i m i t y e f f e c t on t h r e s h o l d v o l t a g e (Miyuzawa and Hyuga [20]) 15 2.9 O r i e n t a t i o n and p r o x i m i t y e f f e c t s of d i s l o c a t i o n on t h r e s h o l d v o l t a g e (Miyuzawa and I s h i i [21 ]) . 15 2.10 D i s l o c a t i o n g e n e r a t i o n a t S i ^ N . f i l m edge (Isomae [15]) 7 ? 16 2.11 L a t e r a l s t r e t c h of the n + l a y e r d u r i n g a n n e a l i n g (Ohnishi et a / . [ l 2 J ) 19 2.12 Gate l e n g t h dependence of t h r e s h o l d v o l t a g e f o r lamp and furnace annealed samples (Ohnishi et al. [ 12]) 19 2.13 Gate l e n g t h dependence of K value f o r d i f f e r e n t t h i c k n e s s of o v e r l a y i n g f i l m (Onodera e l 0 / . [31]) 22 3.1 D e f i n i t i o n of MESFET d i r e c t i o n showing new and o l d r e f e r e n c e frames, (a) [01T] MESFET • and (b) [01 1 ] MESFET 26 3.2 T r a n s f o r m a t i o n m a t r i c e s (a) [01T] and (b) [011] MESFET 26 3.3 C a n t i l e v e r c o o r d i n a t e r e f e r e n c e d e f i n i t i o n . . . . 26 3.4 Coordinate r e f e r e n c e frame f o r f i l m window . . . 32 v i i i 3.5.1 E C M - P o l a r i z a t i o n charge d e n s i t y L Q= 0.2 Mm and d f= 0.2Mm 41 3.5.2 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 0.2 Mm and d^= 0.5*xm 41 3.6.1 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 0.5 um and d^- 0.2MID 42 3.6.2 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 0.5 um and d^= 0.5*im 42 3.6.3 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 0.5 /xm and d^= I.OMITI 43 3.7.1 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 1.0 Mm and d f= 0.2Mtn 43 3.7.2 E C M - P o l a r i z a t i o n charge d e n s i t y LQ- 1.0 M*n and d^= 0.5nm 44 3.7.3 E C M - P o l a r i z a t i o n charge d e n s i t y L G= 1.0 Mm and d^= 1.0Mm 44 3.8 S t r e s s d i s t r i b u t i o n i n SiO- f i l m d e p o s i t e d on GaAs 45 3.9 S t r e s s d i s t r i b u t i o n i n S i , N . f i l m d e p o s i t e d on GaAs 45 3.10.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 0.2 Mm, and d f= 0.2 Mm 46 3.10.2a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 0.2 Mm, and d j = 0.5 Mm 46 3.10.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N 4 f i l m , L Q= 0.2 Mm, and d f= 0.2 Mm 47 3.10.2b D F M - P o l a r i z a t i o n charge d e n s i t y Si^Ng f i l m , L G= 0.2 Mm, and d f= 0.5 Mm 47 3.11.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 0.5 Mm, and d^= 0.2 Mm 48 3.11.2a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 0.5 Mm, and d f= 0.5 Mm 48 3.11.3a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 0.5 Mm, and d f= 1.0 Mm 49 3.11.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N 4 f i l m , LQ- 0.5 Mm, and d^= 0.2 Mm 49 i x 3.11.2b D F M - P o l a r i z a t i o n charge d e n s i t y SigN^ f i l m , LQ= 0.5 Mm, and dj= 0.5 ium 50 3.11.2c D F M - P o l a r i z a t i o n charge d e n s i t y S i j N ^ f i l m , LQ= 0.5 Mm, and dj= 1.0 nm 50 3.12.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i G ^ f i l m , L Q= 1.0 Mm, and d^= 0.2 urn 51 3.12.2a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , LQ= 1.0 Mm, and d^ = 0.5 Mm 51 3.12.3a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L G= 1.0 nm, and d^ = 1.0 Mm 52 3.12.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N ^ f i l m , LQ- 1.0 *tm, and d^= 0.2 Mm 52 3.12.2b D F M - P o l a r i z a t i o n charge d e n s i t y Si-jN^ f i l m , LQ= 1.0 Mm, and d^= 0.5 Mm 53 3.12.3b D F M - P o l a r i z a t i o n charge d e n s i t y S i ^ N ^ f i l m , LQ= 1.0 Mm, and d^= 1.0 Mm 53 3.13.1 P o l a r i z a t i o n charge d e n s i t y a t midgate L G= 0.2 Mm, and d^= 0.2 Mm 54 3.13.2 P o l a r i z a t i o n charge d e n s i t y a t midgate L G = 0.2 Mm, and d^= 0.5 Mm 54 3.14.1 P o l a r i z a t i o n charge d e n s i t y a t midgate LQ= 0.5 Mm, and d^= 0.2 Mm 55 3.14.2 P o l a r i z a t i o n charge d e n s i t y a t midgate LQ= 0.5 Mm, and dj= 0.5 Mm 55 3.14.3 P o l a r i z a t i o n charge d e n s i t y a t midgate L G= 0.5 Mm, and d^= 1.0 Mm 56 3.15.1 P o l a r i z a t i o n charge d e n s i t y a t midgate L G = 1.0 Mm, and d f= 0.2 Mm 56 3.15.2 P o l a r i z a t i o n charge d e n s i t y a t midgate L G= 1.0 Mm, and d^= 0.5 Mm 57 3.15.3 P o l a r i z a t i o n charge d e n s i t y a t midgate L G = 1.0 Mm, and dj= 1.0 Mm . 57 4.1 F a b r i c a t e d d e v i c e o r i e n t a t i o n 60 4.2 Experimental set-up f o r e l a s t i c i t y t e s t 60 4.3 Load versus d e f l e c t i o n 62 4.4.a S t a t i c t e n s i l e s t r e s s a p p l i e d t o DUT 65 X 4.4.b S t a t i c compressive s t r e s s a p p l i e d t o DUT 65 4.5.1 C-V p l o t : no s t r e s s / c o m p r e s s i v e s t r e s s ( i d e a l i t y f a c t o r 1.3) 67 4.5.2 C-V p l o t : no s t r e s s / c o m p r e s s i v e s t r e s s ( i d e a l i t y f a c t o r 1.3) 67 4.6.1 C-V p l o t : p e r p e n d i c u l a r MESFETs ( i d e a l i t y f a c t o r 1.09) 68 4.6.2 C-V p l o t : p a r a l l e l MESFETs ( i d e a l i t y f a c t o r 1.09) 68 4.7 A t y p i c a l doping p r o f i l e p l o t 69 4.8 Time-varing s t r e s s mechanical set-up 73 4.9 Time-varying s t r e s s measurement set-up 73 4.10 Measured s i g n a l without mercury probes 76 4.11 Mercury c o n t a c t s 76 4.12 Measured s i g n a l with mercury c o n t a c t s 77 4.13 Es t i m a t e d changes i n b a r r i e r h eight due to f i l m s t r e s s 80 5.1 Co o r d i n a t e d e f i n i t i o n f o r a p o t e n t i a l f i e l d around an elementary d i p o l e 89 x i ACKNOWLEDGEMENTS v I would l i k e to thank my s u p e r v i s o r , Dr. L. Young, f o r h i s support and guidance throughout t h i s work. Mr. H. Kato i s t o be thanked f o r f a b r i c a t i n g the MESFETs used i n the experiments, and f o r demonstrating the op e r a t i o n of some of the l a b o r a t o r y equipment. I would a l s o l i k e to s p e c i a l l y thank Mr. D. Hui f o r many u s e f u l d i s c u s s i o n s , and f o r h i s a s s i s t a n c e i n the l a b o r a t o r y . H e l p f u l d i s c u s s i o n s were a l s o p r o v i d e d by D. Sut h e r l a n d , P. Matz, and E. S w i t l i s h o f f . x i i 1. INTRODUCTION The development of GaAs i n t e g r a t e d c i r c u i t s began with the B u f f e r e d FET Logic (BFL) and the Schottky Diode FET Log i c (SDFL), which are a l l - d e p l e t i o n mode t r a n s i s t o r l o g i c s . BFL and SDFL are q u i t e s u i t a b l e f o r LSI designs but t h e i r power consumption i s too l a r g e f o r VLSI. The most promising candidate f o r VLSI and ULSI i n GaAs i s the D i r e c t Coupled FET Lo g i c (DCFL), because i t has the lowest power consumption and the s i m p l e s t c i r c u i t r y [ 1 ] , In a d d i t i o n , i t r e q u i r e s only one power supply whereas the ot h e r s r e q u i r e two. The p r i c e f o r these advantages i s an i n c r e a s e i n process complexity. DCFL uses both enhancement and d e p l e t i o n mode t r a n s i s t o r s . I t i s s i m i l a r t o the NMOS l o g i c i n s i l i c o n . The l o g i c l e v e l swing f o r DCFL i s only about 0.5 V. It i s l i m i t e d by the enhancement mode MESFETs. A s t r i n g e n t c o n t r o l of the t h r e s h o l d v o l t a g e of the enhancement d e v i c e s i s c r u c i a l to the o p e r a t i o n of DCFL, because any d e v i a t i o n i n the t h r e s h o l d v o l t a g e i s d i r e c t l y t r a n s l a t e d t o a d e t e r i o r a t i o n i n the n o i s e margin. I t has been suggested that the standard d e v i a t i o n of the t h r e s h o l d v o l t a g e f o r the enhancement mode MESFETs should not be g r e a t e r than 25 mV [ 2 ] . The t h r e s h o l d v o l t a g e f o r GaAs MESFETs i s p r i m a r i l y dependent on the doping p r o f i l e , because the b a r r i e r h e i g h t i s pinned at about 0.8 eV by the s u r f a c e s t a t e s . In 1980, Lee et al. [3] re p o r t e d an o r i e n t a t i o n dependence i n the t h r e s h o l d v o l t a g e f o r d e v i c e s with gate l e n g t h l e s s 1 2 than 2 Mm. The observed changes i n the t h r e s h o l d v o l t a g e are so s i g n i f i c a n t that the o r i e n t a t i o n of a d e v i c e must be c o n s i d e r e d d u r i n g the t r a n s i s t o r d e sign stage. I t i s important to understand the causes f o r the o r i e n t a t i o n dependence i n the d e v i c e c h a r a c t e r i s t i c s , because the device o r i e n t a t i o n can a f f e c t the y i e l d of the enhancement MESFETs and p o s s i b l y the f u t u r e of DCFL f o r GaAs VLSI. The causes f o r the o r i e n t a t i o n e f f e c t have been suggested to be the p i e z o e l e c t r i c p r o p e r t y of GaAs and s t r e s s generated i n the s u b s t r a t e by the o v e r l a y i n g d i e l e c t r i c f i l m [ 4 ] . The work performed i n the present t h e s i s i n v o l v e d t h e o r e t i c a l c a l c u l a t i o n s of the p o l a r i z a t i o n charge d e n s i t y i n the channel of an enc a p s u l a t e d MESFET and experimental measurements of the e f f e c t s of s t r e s s on d e v i c e c h a r a c t e r i s t i c s . In the t h e o r e t i c a l p a r t , p o l a r i z a t i o n charge d e n s i t i e s were c a l c u l a t e d by two methods. The f i r s t method i s c a l l e d the edge c o n c e n t r a t e d method. I t has been the method used i n a l l r e p o r t e d works to date. The second method i s c a l l e d the d i s t r i b u t e d f o r c e method. I t i s a s u p e r i o r model, because i t d e s c r i b e s more r e a l i s t i c a l l y the s t r e s s d i s t r i b u t i o n i n the f i l m and i n the s u b s t r a t e . I t was developed by Hu [5] f o r c a l c u l a t i n g s t r e s s i n the s u b s t r a t e near a f i l m edge. I t was a p p l i e d t o f i n d the p o l a r i z a t i o n charge d e n s i t y i n the s u b s t r a t e between two f i l m edges. The d i f f e r e n c e s between the two models and the c a l c u l a t e d r e s u l t s , are given i n chapter 3. In the experimental p a r t , the d e v i c e c h a r a c t e r i s t i c s were measured with and without 3 s t r e s s a p p l i e d . The s t r e s s was produced by bending s t r i p s of GaAs wafers i n a c a n t i l e v e r c o n f i g u r a t i o n . Both s t a t i c s t r e s s and t i m e - v a r y i n g s t r e s s were a p p l i e d . The experimental methods and r e s u l t s are given i n chapter 4. A l i s t of c o n c l u s i o n s and suggestions f o r f u t u r e works i s given i n chapter 5. In the next chapter, the h i s t o r y of the works performed on the t o p i c , the o r i e n t a t i o n dependence i n GaAs MESFET d e v i c e c h a r a c t e r i s t i c s , and a survey of the l i t e r a t u r e on v a r i o u s mechanisms t h a t can a f f e c t metal-semiconductor i n t e r f a c e c h a r a c t e r i s t i c s are g i v e n . 2. ORIENTATION DEPENDENCE IN GAAS MESFETS: ITS CAUSES AND APPLICATIONS 2.1 INTRODUCTION AND HISTORY In 1980, Lee et al. [3] r e p o r t e d an o r i e n t a t i o n dependence i n GaAs MESFET t h r e s h o l d v o l t a g e . In t h e i r experiment, they used MESFETs with 1.0 Mm gate l e n g t h and o r i e n t e d i n 5 d i f f e r e n t d i r e c t i o n s ( f i g u r e 2.1). The t h i c k n e s s of the e n c a p s u l a t i n g S i ^ N 4 f i l m was 1.0 Mm. The r e s u l t i s reproduced i n f i g u r e 2.2. Based on p r e v i o u s works which had shown that s t r e s s at the i n t e r f a c e of e p i t a x i a l l a y e r of InGaAs or GaAsP on GaAs s u b s t r a t e was d i f f e r e n t f o r the [011] and [ O l T ] d i r e c t i o n s [ 6 , 7 ] , and that s t r e s s enhanced the d i f f u s i o n of dopants i n GaAs [8,9], Lee et al. suggested that the magnitude of the s t r e s s produced i n the s u b s t r a t e by the S i g N 4 cap was a l s o d i f f e r e n t f o r d i f f e r e n t c r y s t a l d i r e c t i o n s . Thus, the d i f f u s i o n r a t e of an enc a p s u l a t e d sample was b e l i e v e d t o be o r i e n t a t i o n dependent. The d i f f e r e n c e i n the t h r e s h o l d v o l t a g e , f o r MESFETs which were i d e n t i c a l except t h e i r o r i e n t a t i o n , was suggested t o be due to d i f f e r e n t amount of dopants that had d i f f u s e d i n t o the channel from the d r a i n and the source r e g i o n s , d u r i n g a n n e a l i n g . The l a r g e r the number of dopants d i f f u s e d i n t o the channel the g r e a t e r the change r e s u l t e d i n the doping p r o f i l e , assuming t h a t the d i f f u s e d dopants 4 5 F i g u r e 2.2 O r i e n t a t i o n dependence of t h r e s h o l d v o l t a g e observed by Lee et al. [ 3 ] , 6 were a c t i v a t e d . The r e s u l t was an i n c r e a s e i n the t h r e s h o l d v o l t a g e . The l a r g e s t stress-enhanced d i f f u s i o n r a t e was determined to be i n [011] d i r e c t i o n . The v a l i d i t y of Lee et al. 's theory was put i n doubt when Yokoyama et al. [10] p u b l i s h e d t h e i r f i n d i n g s i n 1983. Yokoyama el al . used MESFETs with gate l e n g t h v a r y i n g from 1.1 to 1.6 urn and o r i e n t e d i n [011] and [ O l T ] d i r e c t i o n s . T h e i r experiment showed t h a t MESFETs o r i e n t e d i n the [ O l T ] d i r e c t i o n had the l a r g e s t t h r e s h o l d v o l t a g e . Using the model proposed by Lee et al. , Yokoyama et at. 's r e s u l t showed that the p r e f e r r e d stress-enhanced d i f f u s i o n d i r e c t i o n i n GaAs should be the [ O l T ] d i r e c t i o n , which c o n t r a d i c t e d Lee et c/.'s r e s u l t . In 1984, a new theory based on the p i e z o e l e c t r i c p r o p e r t y of GaAs was proposed by Asbeck et al. [ 4 ] . When a d i e l e c t r i c f i l m i s d e p o s i t e d over a MESFET, two f i l m edges p a r a l l e l t o the width of the gate are c r e a t e d . I t i s w e l l known that l a r g e s t r e s s i s generated i n the s u b s t r a t e near f i l m edges [40-42], Asbeck et al. proposed that t h i s s t r e s s generates a p o l a r i z a t i o n charge d e n s i t y under the gate. The magnitude of the p o l a r i z a t i o n charge d e n s i t y i s l a r g e enough to change the doping p r o f i l e . Consequently, the d e v i c e c h a r a c t e r i s t i c s are a l t e r e d . F u r t h e r support f o r the p i e z o e l e c t r i c model was t h a t the d e v i c e c h a r a c t e r i s t i c s were found to change as the f i l m was t h i n n e d by e t c h i n g . T h i n n i n g the d i e l e c t r i c f i l m reduces the s t r e s s i n the s u b s t r a t e , hence i t decreases the p o l a r i z a t i o n charge d e n s i t y i n the c h annel. The e t c h i n g process was performed a f t e r a n n e a l i n g 7 and was not performed at h i g h temperature. The stress-enhanced d i f f u s i o n model would have p r e d i c t e d no change i n the d e v i c e c h a r a c t e r i s t i c s , because no dopant d i f f u s i o n should have taken p l a c e . However, the p i e z o e l e c t r i c model alone c o u l d not e x p l a i n the observed changes i n the d e v i c e c h a r a c t e r i s t i c s . F i g u r e 2.3 shows Asbeck et al. 's t h e o r e t i c a l and experimental p l o t s of the t h r e s h o l d v o l t a g e versus gate l e n g t h f o r the [011] and [01T ] MESFETs. The p i e z o e l e c t r i c model p r e d i c t e d an equal but o p p o s i t e s h i f t i n the t h r e s h o l d v o l t a g e f o r the [011] and [01T] MESFETs. The experimental r e s u l t showed a l a r g e t h r e s h o l d v o l t a g e s h i f t f o r the [011] MESFETs but only a s m a l l t h r e s h o l d v o l t a g e s h i f t f o r the [01T] MESFETs. Asbeck et al. suspected t h a t other mechanisms, such as s t r e s s r e l a x a t i o n by d i s l o c a t i o n g e n e r a t i o n at the f i l m edge, were a t work. Ohnis h i et al. [11], i n 1985, combined the s h o r t channel e f f e c t and the p i e z o e l e c t r i c model to e x p l a i n the observed changes i n the d e v i c e c h a r a c t e r i s t i c s . The short channel e f f e c t i s the l a t e r a l s t r e t c h of the n + dopants i n t o the channel from the d r a i n and source regions d u r i n g thermal a n n e a l i n g . T h i s causes an i n c r e a s e i n the dopant c o n c e n t r a t i o n at the two ends of the channel. I t can be i n t e r p r e t e d as an i n c r e a s e i n the e f f e c t i v e channel depth [12]. With a deeper e f f e c t i v e channel depth, the t h r e s h o l d v o l t a g e i s i n c r e a s e d ( i n the n e g a t i v e d i r e c t i o n ) . " The p i e z o e l e c t r i c model, as d e s c r i b e d by Asbeck et al. , causes a 8 p o l a r i z a t i o n charge d e n s i t y to be generated i n the channel. I f the s i g n of the p o l a r i z a t i o n charge d e n s i t y i s p o s i t i v e , the e f f e c t i v e channel depth i s f u r t h e r i n c r e a s e d and the t h r e s h o l d v o l t a g e becomes more n e g a t i v e . I f the s i g n of the p o l a r i z a t i o n charge d e n s i t y i s n e g a t i v e , i t c o u n t e r a c t s the short channel e f f e c t by d e c r e a s i n g the e f f e c t i v e channel depth. T h e r e f o r e , the channel doping p r o f i l e i s m o d i f i e d by an induced p o l a r i z a t i o n charge d e n s i t y and the l a t e r a l s t r e t c h of the n + l a y e r . F i g u r e s 2.4 and 2.5 show the experimental r e s u l t s o b tained by Ohnishi et al . . The f i g u r e s show t h r e s h o l d v o l t a g e as a f u n c t i o n of gate l e n g t h , d i e l e c t r i c l a y e r t h i c k n e s s , and the type of d i e l e c t r i c f i l m . I t was found t h a t S i 0 2 f i l m had the op p o s i t e e f f e c t on the t h r e s h o l d v o l t a g e t o S i 3 N 4 f i l m , because S i 0 2 f i l m was found to be i n t e n s i l e s t r e s s and SigN^ f i l m was found t o be i n compressive s t r e s s [ 1 1 ]. The d i f f e r e n c e i n the s t r e s s s i g n caused o p p o s i t e p o l a r i t y of p o l a r i z a t i o n charge d e n s i t y t o be generated. The d i s c r e p a n c y between the r e s u l t s obtained e a r l i e r by Lee et al. and Yokoyama et al . were a l s o c l a r i f i e d . They used d i f f e r e n t e n capsulant. Lee et al. used S i 0 2 but Yokoyame et al. used S i g N ^ Chen et al. [13],- i n 1987, modelled the combined e f f e c t of the l a t e r a l s t r e t c h of the n + r e g i o n s and the p i e z o e l e c t r i c e f f e c t . The t h e o r e t i c a l c a l c u l a t e d s h i f t i n the t h r e s h o l d v o l t a g e agreed w e l l with t h e i r experimental r e s u l t s . They a l s o observed that the s t r e s s s i g n f o r a 9 |v T Hl »TH I \ C o i q _ 1.0 0.8 O R l I 1 1 2 5 10 GATE LENGTH (,,ml (a) (b) F i g u r e 2.3 Asbeck el c/.*s (a) t h e o r e t i c a l (b) experimental r e s u l t s [ 4 ] . and a -2 0.1 1 1 • | 1 M», d(Si02)(nm) ' 1 ' i " " 1200 - tw^, , . 600 - ^ c r S 0 Jr/f ' 600 ' / o (OlT) " 1 m (011) . 1200 ' i • • i , . ^  . 1.... 1 10 Gate length (pm) F i g u r e 2.4 T h r e s h o l d v o l t a g e versus gate S i O , o v e r l a y e r (Ohnishi et al l e n g t h with [ 1 1 ] ) . 8. o o I 5 - i rrrm— ' • • i • nt d(Si3NA Hnm) - 1000 500 0 500 f v*- . 1000 f o • (OiT) " (011) i .,,.1 0.1 1 10 Gate length (pm) t F i g u r e 2.5 Th r e s h o l d v o l t a g e versus gate l e n g t h with Si.,N A o v e r l a y e r (Ohnishi et al. [ 1 1 ] ) . OBSERVED CHRNGES IN DEVICE CHRRRCTERISTICS ( FOR DEVICE WITH GRTE-LENGTH LESS THRN 2 urn) ORIENTATION INDEPENDENT EFFECTS _L n LAYER LHTERRL STRETCH FILM STRESS BRRRIER HEIGHT CHRNGES WITH STRESS CONDUCTION BRND SHIFT ION IMPLRNTRTION STRRGGLE DIFFUSION DURING RNNERLING PIEZOELECTRIC PROPERTY OF GaAs ORIENTRTION DEPENDENT EFFECTS DISLOCRTION GENERATION DISLOCRTION PROXIMITY AND ORIENTATION STRESS ENHANCED ACTIVATION Figure 2.6 Mechanisms a f f e c t i n g device c h a r a c t e r i s t i c s o 11 d i e l e c t r i c f i l m was dependent on the method of d e p o s i t i o n . PECVD-Sigl^ f i l m was found to be i n t e n s i l e s t r e s s but s p u t t e r e d - S i j ^ f i l m was found to be i n compressive s t r e s s . Although the p i e z o e l e c t r i c model combined with the l a t e r a l s t r e t c h of the n + l a y e r can e x p l a i n reasonably w e l l the o r i e n t a t i o n dependence i n the d e v i c e c h a r a c t e r i s t i c s , other mechanisms do e x i s t . Some of them are l i s t e d i n f i g u r e 2.6. In the f o l l o w i n g s e c t i o n s , a b r i e f d i s c u s s i o n of each i s g i v e n . 2.2 SCHOTTKY BARRIER HEIGHT CHANGE WITH APPLIED STRESS The e l e c t r i c a l p r o p e r t i e s of Schottky c o n t a c t s between metal and GaAs under mechanical s t r e s s have been s t u d i e d by Kusaka et al. [14,15]. They f a b r i c a t e d diodes on (111)Ga and ( T T T)As s u r f a c e s . The wafers were then glued to s t e e l c a n t i l e v e r s and s t r e s s e d by bending the c a n t i l e v e r s . For n-type GaAs, the b a r r i e r h e i g h t was found to be l i n e a r l y r e l a t e d to the s u r f a c e s t r a i n ( f i g u r e 2.7) which can be expressed by ^ b n = - 3 ' 6 7 e s u r f ( e V ) ( 2 ' 1 ) where e s u r f i s the a p p l i e d s u r f a c e s t r a i n at the Schottky i n t e r f a c e . The cause f o r the b a r r i e r height s h i f t has been suggested t o be s t r e s s - i n d u c e d change i n the energy l e v e l of the c o n d u c t i o n band minimum [15-19], Zurawsky et al. [16] measured the s h i f t i n the conduction band minimum and 12 -6 -A -2 0 2 4 SURFACE STRAIN (1x10"*) F i g u r e 2.7 Changes i n the b a r r i e r h eight v e r s u s _ s u r f a c e s t r a i n , x represent diodes on the ( T T T ) s u r f a c e and o represent diodes on the (111) surface(Kusaka et a / . [ 1 4 ] ) . the s h i f t i n the valence band maximum with h y d r o s t a t i c p r e s s u r e a p p l i e d t o GaAs samples. They found t h a t the energy of the conduction band minimum i n c r e a s e d with h y d r o s t a t i c -7 2 pre s s u r e by 1.22x10 meV m /N. The energy of the valence band maximum d i d not change with p r e s s u r e . The r e l a t i o n s h i p between the e f f e c t s of h y d r o s t a t i c p r e s s u r e and u n i a x i a l compressive s t r e s s on the energy of the conduction band has been modelled by P o l l a k and Cardona [18], u s i n g a quantum mechanical model. The model was t e s t e d by Kusaka et al. [15] and good agreement between t h e o r e t i c a l and experimental r e s u l t s was ob t a i n e d . 13 2.3 EFFECTS OF DISLOCATIONS ON DEVICE CHARACTERISTICS Many works have been p u b l i s h e d on the e f f e c t s of d i s l o c a t i o n s on d evice c h a r a c t e r i s t i c s [20-23], Miyuzawa and Hyuga [20] have shown that there i s a c o r r e l a t i o n between the p r o x i m i t y of d i s l o c a t i o n s and GaAs MESFET t h r e s h o l d v o l t a g e ( f i g u r e 2.8). They found that the c l o s e r a d i s l o c a t i o n was to a MESFET's channel the l a r g e r the s h i f t i n the t h r e s h o l d v o l t a g e was observed. A 5±2 mV per Mm of l i n e a r change i n the t h r e s h o l d v o l t a g e was found f o r d i s l o c a t i o n - g a t e s e p a r a t i o n l e s s than 50 Mm. They a l s o found a c o r r e l a t i o n between the sheet c a r r i e r c o n c e n t r a t i o n and the p r o x i m i t y of d i s l o c a t i o n s . A l a r g e sheet c a r r i e r c o n c e n t r a t i o n value was measured i n a r e g i o n which had a l a r g e number of d i s l o c a t i o n s ; and a s m a l l sheet c a r r i e r c o n c e n t r a t i o n value was found i n a d i s l o c a t i o n f r e e r e g i o n . To e x p l a i n t h e i r o b s e r v a t i o n s , they proposed t h a t d i s l o c a t i o n s might have a f f e c t e d the a c t i v a t i o n e f f i c i e n c y of the implanted dopants. R e c e n t l y , Otsuki [24] presented a theory that p r e d i c t s the a c t i v a t i o n of S i - i m p l a n t s i n GaAs i s s e n s i t i v e t o the s t r e s s present d u r i n g a n n e a l i n g . The theory p r e d i c t s t h a t S i dopants are more l i k e l y to become donors under compressive s t r e s s and a c c e p t o r s under t e n s i l e s t r e s s . He compared the a c t i v a t i o n of implanted S i i n samples t h a t were annealed with and without Si^N^ cap. SigN^ has been found to be i n t e n s i l e s t r e s s at temperatures around 825°C [8,25]. The major purpose of the S i g N 4 cap i s to prevent the degradation of the GaAs s u r f a c e . From 14 O t s u k i ' s paper i t i s not c l e a r whether any steps were taken to prevent the o u t g a s s i n g of As d u r i n g a n n e a l i n g . I f As atoms were l o s t , a l a r g e r number of the implanted S i atoms would be expected to be found i n As s i t e s , which was what Otsuki found. S t r e s s f i e l d s are known to e x i s t near d i s l o c a t i o n s [25,27], For example, the magnitude of the s t r e s s around an edge d i s l o c a t i o n v a r i e s with the r a d i a l d i s t a n c e and angle, measured from the d i s l o c a t i o n [26,27]. If the a c t i v a t i o n of S i i s s e n s i t i v e to s t r e s s , as proposed by O t s u k i , then the s h i f t i n the t h r e s h o l d v o l t a g e near a d i s l o c a t i o n would be dependent on both the d i s t a n c e between the d i s l o c a t i o n and the gate, and t h e i r o r i e n t a t i o n . Miyazawa and I s h i i [21] have observed such an o r i e n t a t i o n and a p r o x i m i t y r e l a t i o n s h i p ( f i g u r e 2.9). However, more works are needed to determine the r e l a t i o n s h i p between d i s l o c a t i o n s and the a c t i v a t i o n of dopants, because the mechanisms i n v o l v e d are not w e l l understood. For l i q u i d - e n c a p s u l a t e d C z o c h r a l s k i grown c y s t a l s , some d i s l o c a t i o n s are generated as the boule i s being p u l l e d out of the melt. The d i s l o c a t i o n d e n s i t y has a t y p i c a l "W" shape a c r o s s the c r y s t a l [28]. The main cause f o r the g e n e r a t i o n of the d i s l o c a t i o n s has been i d e n t i f i e d as thermal v a r i a t i o n a c r o s s the boule c a u s i n g s t r e s s i n the c r y s t a l . Isomae [29] has shown th a t i t i s p o s s i b l e t o generate d i s l o c a t i o n s at f i l m edges [40-42]. In h i s experiment, small square pads of d i e l e c t r i c f i l m were d e p o s i t e d on S i s u b s t r a t e s . 1 5 0.2 . 0.1 o 0 -0.1 -0.2 O 00 -+-50 100 150 * • Oislance from etch p i t . pm •1* o inside cellular walls • c lose to ' F i g u r e 2.8 D i s l o c a t i o n p r o x i m i t y e f f e c t on t h r e s h o l d v o l t a g e (Miyazawa and Hyuga [ 2 0 ] ) . Vth <110> F i g u r e 2.9 O r i e n t a t i o n and p r o x i m i t y e f f e c t s of d i s l o c a t i o n on t h r e s h o l d v o l t a g e (Miyazawa and I s h i i [ 2 1 ] ) . 16 X XX XX XX A X X X O A A X O O A A 900 1000 1100 1200 Temperature PC) F i g u r e 2.10 D i s l o c a t i o n g e n e r a t i o n at Si,N. f i l m edge, o denotes no d i s l o c a t i o n , x denotes many, and xx denotes a l o t (Isomae [ 1 5 ] ) . The s u b s t r a t e s were then heated i n an oven to h i g h temperatures. He found that the number of d i s l o c a t i o n s generated at the f i l m edges i n c r e a s e d with temperature and f i l m t h i c k n e s s ( f i g u r e 2.10). Although the s u b s t r a t e used was s i l i c o n , the same concept should apply to GaAs. If new d i s l o c a t i o n s are generated at f i l m edges i n GaAs s u b s t r a t e s , the e f f e c t of these d i s l o c a t i o n s on the d e v i c e c h a r a c t e r i s t i c s i s an i n c r e a s e i n the t h r e s h o l d v o l t a g e . E c V o o in * 100 U Z 17 2.4 PIEZOELECTRIC PROPERTY OF GAAS During the f a b r i c a t i o n of GaAs d e v i c e s , s t r e s s may be u n i n t e n t i o n a l l y produced in the s u b s t r a t e by thermal bonding, c o n t a c t a l l o y i n g , and d i e l e c t r i c e n c a p s u l a t i n g [ 4 ] . These s t r e s s e s may produce a p o l a r i z a t i o n charge d e n s i t y i n the s u b s t r a t e . I f the magnitude of the p o l a r i z a t i o n charge d e n s i t y i s l a r g e enough to a l t e r the doping p r o f i l e , then the d e v i c e c h a r a c t e r i s t i c s are changed. The s t r e s s generated by the e n c a p s u l a t i n g d i e l e c t r i c f i l m i s of c o n s i d e r a b l e i n t e r e s t , because f o r two f i l m edges that very c l o s e t o g e t h e r , as i n the case of e n c a p s u l a t e d MESFETs with gate l e n g t h l e s s than 2 Mm, the p o l a r i z a t i o n charge d e n s i t y generated under the gate i s l a r g e enough to change the d e v i c e c h a r a c t e r i s t i c s . 2.5 LATERAL DIFFUSION OF DOPANTS DURING ANNEALING Io n - i m p l a n t a t i o n of dopants has been shown to be s u p e r i o r over d i f f u s i o n processes f o r p u t t i n g i m p u r i t i e s i n t o GaAs s u b s t r a t e s . To remove the r a d i a t i o n damage caused by i o n - i m p l a n t a t i o n and to a c t i v a t e the dopants, thermal a n n e a l i n g i s r e q u i r e d . During the a n n e a l i n g p r o c e s s , the implanted dopants w i l l d i f f u s e . I f the dopants d i f f u s e i n t o the channel of a MESFET and are a c t i v a t e d , then the d e v i c e c h a r a c t e r i s t i c s are a f f e c t e d . O h n i s h i et al. [12] compared the l a t e r a l s t r e t c h of dopants i n samples t h a t were annealed by a lamp or i n a f u r n a c e . Lamp a n n e a l i n g was performed by u s i n g a h i g h 18 i n t e n s i t y lamp to heat the s u b s t r a t e to a h i g h temperature about 900 to 1000°C, f o r a s h o r t d u r a t i o n about 10 seconds. The furnace annealed samples were heated i n an oven to about 750 to 850°C f o r about 5 minutes. Ohnishi et al. found that the l a t e r a l s t r e t c h of the n + dopants from the d r a i n and the source r e g i o n s was much l a r g e r f o r the furnace annealed than f o r the lamp annealed samples. F i g u r e 2.12 shows the e f f e c t on the t h r e s h o l d v o l t a g e by the two d i f f e r e n t methods of a n n e a l i n g . The s h o r t e r the gate, the g r e a t e r the p e n e t r a t i o n of the dopants r e l a t i v e t o the channel l e n g t h , hence the l a r g e r the e f f e c t . A pre-anneal s t r e t c h of 100 nm was determined by e x t r a p o l a t i o n . I t was b e l i e v e d to be the t r a n s v e r s e s t r a g g l e of i o n - i m p l a n t a t i o n . (The t r a n s v e r s e s t r a g g l e i s the s i d e p e n e t r a t i o n of implants under the edge of a mask.) The l a t e r a l s t r e t c h of the n + dopants was found to i n c r e a s e with h i g h e r a n n e a l i n g temperature and longer d u r a t i o n ( f i g u r e 2.11). S a d l e r and Eastman [30] have shown that the l a t e r a l s t r e t c h of the n + l a y e r has no o r i e n t a t i o n p r e f e r e n c e . They used a c a p l e s s a n n e a l i n g system, where InAs was used to p r o v i d e an a r s e n i c over p r e s s u r e . S e v e r a l d i f f e r e n t gate l e n g t h MESFETs which were o r i e n t e d i n the [011] and [01T] d i r e c t i o n s were used i n t h e i r experiment. They found that the t h r e s h o l d v o l t a g e i n c r e a s e d with d e c r e a s i n g 19 400 0 10 50 100 500 (sec) -5300 x u §200 V— </> or >oof<: U ( t . T ) :JdP:„2 • 2D*(T)t 860 1000'C 4R£« 100 nm "0 50 100 15.0 20.0 250 SQUARE ROOT OF ANNEALING TIME (sec"2) F i g u r e 2.11 L a t e r a l s t r e t c h of the n l a y e r d u r i n g a n n e a l i n g (Ohnishi et al. [12]). 1.0 tu o < o > o _ l o X if) UJ tr x •1.0 •2.0 LA FET (900'C. 5" sec) o» d*-F.A.FET ( 750 *C. 900 sec ) -l 1 : i i_ 0 1.0 2.0 3.0 4.0 GATE LENGTH (urn ) 50 F i g u r e 2.12 Gate l e n g t h dependence of t h r e s h o l d v o l t a g e f o r lamp and furnace annealed samples (Ohnishi et al. [12 ] ) . 20 gate l e n g t h f o r a l l MESFETs. In summary, stress-enhanced l a t e r a l d i f f u s i o n of dopants d u r i n g a n n e a l i n g i s not, as i t was f i r s t b e l i e v e d to be, the cause f o r the o r i e n t a t i o n dependence i n GaAs MESFET d e v i c e c h a r a c t e r i s t i c s , but the l a t e r a l s t r e t c h of the n + l a y e r does s i g n i f i c a n t l y change the d e v i c e c h a r a c t e r i s t i c s f o r MESFETs with gate l e n g t h l e s s than 2 urn, r e g a r d l e s s of i t s o r i e n t a t i o n . 2.6 APPLICATIONS OF THE PIEZOELECTRIC EFFECT When the o r i e n t a t i o n e f f e c t i n GaAs MESFETs was f i r s t observed, i t was c o n s i d e r e d to be u n d e s i r a b l e because MESFETs f a b r i c a t e d i n d i f f e r e n t d i r e c t i o n s would have a l a r g e r standard d e v i a t i o n i n the t h r e s h o l d v o l t a g e than i f they were a l l f a b r i c a t e d i n the same d i r e c t i o n . The p r e f e r r e d d e v i c e o r i e n t a t i o n was suggested to be i n the d i r e c t i o n that showed the minimum o r i e n t a t i o n e f f e c t , which was i n the d i r e c t i o n with the s m a l l e s t p i e z o e l e c t r i c e f f e c t . On (lOO)GaAs s u r f a c e s , the l a r g e s t changes i n the d e v i c e c h a r a c t e r i s t i c s due to the p i e z o e l e c t r i c e f f e c t have been observed f o r MESFETs o r i e n t e d i n the <110> d i r e c t i o n s . The s m a l l e s t p i e z o e l e c t r i c e f f e c t s have been observed f o r MESFETs o r i e n t e d i n the <100> d i r e c t i o n s . With the demand f o r f a s t e r c i r c u i t s and higher packing d e n s i t y , the gate l e n g t h of the d e v i c e s t a r t e d to decrease. The s h o r t e r gate l e n g t h d e v i c e s show a s h i f t i n i n the t h r e s h o l d v o l t a g e and a d t - t e r i a t i o n i n the d e v i c e performance. The cause f o r the 21 t h r e s h o l d v o l t a g e s h i f t and the d e t e r i o r a t i o n i n the device performance has been suggested to be the l a t e r a l s t r e t c h of the n + l a y e r . One remedy i s to generate a n e g a t i v e p o l a r i z a t i o n charge d e n s i t y i n the channel to counter the e f f e c t due to the l a t e r a l s t r e t c h of the n + l a y e r . F i g u r e s 2.2 and 2.3 show that by p r o p e r l y s e l e c t i n g the device o r i e n t a t i o n , the type of d i e l e c t r i c o v e r l a y e r , and the t h i c k n e s s of the o v e r l a y e r , the t h r e s h o l d v o l t a g e can be made independent of the d e v i c e gate l e n g t h . Onodera et al. [31] have measured the changes i n the K v a l u e f o r MESFETs with d i f f e r e n t gate l e n g t h and d i f f e r e n t t h i c k n e s s of d i e l e c t r i c f i l m . For a MESFET o p e r a t i n g i n the s a t u r a t e d r e g i o n , the d r a i n c u r r e n t can be d e s c r i b e d f a i r l y w e l l by the so c a l l e d "square law", where the d r a i n c u r r e n t i s p r o p o r t i o n a l to the square of ( V G - V T ) . The constant of p r o p o r t i o n a l i t y , the K v a l u e , i s expressed as K = ^ — 2 (2.2) 2 a e f f L g where Z i s the gate width, &e£f i s the e f f e c t i v e channel depth, L i s the gate l e n g t h , c i s the p e r m i t t i v i t y of g s GaAs, and un i s the e l e c t r o n m o b i l i t y i n GaAs. An i n c r e a s e i n the e f f e c t i v e channel depth, by equation 2.2, causes the K value to decrease, which causes the transconductance gain to decrease. Onodera et al. [31] have shown t h a t by u t i l i z i n g the p i e z o e l e c t r i c e f f e c t , the K v a l u e can be improved. F i g u r e 2.13 shows t h a t S i O , cap can be used to 22 improve the K value f o r [011] MESFETs. The t h i c k e r the f i l m used, the l a r g e r the K value was o b t a i n e d . T h e r e f o r e , the p r e f e r r e d d e v i c e o r i e n t a t i o n f o r small gate l e n g t h MESFETs f a b r i c a t e d on (lOO)GaAs s u r f a c e s i s dependent on the type of d i e l e c t r i c encapsulant, but the d e v i c e s should be o r i e n t e d i n the <011> d i r e c t i o n . to.o 5.0 tOU] FET > > i 0.5-1 1 " •>* 05 10 5.0 10.0 GATE LENGTH . L 8 (urn) F i g u r e 2.13 Gate l e n g t h dependence of K v a l u e f o r d i f f e r e n t t h i c k n e s s of o v e r l a y i n g f i l m (Onodera et al. [31 ] ) . 3. THEORETICAL CALCULATIONS OF THE POLARIZATION CHARGE DENSITY 3.1 POLARIZATION CHARGE DENSITY GaAs belongs t o c r y s t a l c l a s s 43m. The p i e z o e l e c t r i c modulus elements i n matrix n o t a t i o n are [32] 0 0 0 d14 0 0 0 0 0 0 d25 0 (3.1) 0 0 0 0 0 d 3 6 where d 1 4 = d 2 5 • d 3 6 - 1.63x10 e l e c t r o n charges/N at room temperature [33], The g e n e r a l form of the p o l a r i z a t i o n v e c t o r P" i s given by P i = d i j a j ( i = 1 ' 2 ' 3 ; j=1,2,...,6). (3.2) where d^j are the p i e z o e l e c t r i c moduli elements and the are the s t r e s s components i n matrix n o t a t i o n . The c a l c u l a t i o n s of the p o l a r i z a t i o n charge d e n s i t i e s i n the channel of MESFETs f a b r i c a t e d on ( l O O)GaAs s u r f a c e and o r i e n t e d i n the [011] or [ O l T ] are d e s c r i b e d i n t h i s c h a p t e r . F i g u r e 3.1 shows the d e f i n i t i o n of a [ O i l ] MESFET, a [ O l T ] MESFET, the o l d , and the new r e f e r e n c e axes. The o l d axes are l a b e l e d without a prime and the new axes are l a b e l e d with a prime. The t r a n s f o r m a t i o n m a t r i c e s from the o l d to the new axes are given i n f i g u r e 3.2. The p i e z o e l e c t r i c modulus elements i n the new r e f e r e n c e frame can be found by a p p l y i n g the t r a n s f o r m a t i o n law 23 24 d i j k ' " a i l a j m a k n dlmn (3.3) The p i e z o e l e c t r i c modulus elements i n the new re f e r e n c e frame i n matrix n o t a t i o n are 0 0 0 0 0 0 -d/2 d/2 0 0 d 0 -d 0 •0 0 0 0 [011] MESFET (3.4.1 ) 0 0 0 0 0 0 d/2 -d/2 0 0 d -d 0 0 0 0 0 0 [011] MESFET (3.4.2) where d= 1.63x10 e l e c t r o n charges/N. The non-zero P* components i n the new r e f e r e n c e frame f o r [011] MESFET are P 2 = d a 2 3 (3.5) P 3 = 0.5 d ( o 2 2 - au) The same equations apply f o r [ O l T ] MESFETs, but the s i g n i s op p o s i t e f o r each component of P. The d i p o l e moment per u n i t volume can be i n t e r p r e t e d as a volume charge d e n s i t y which i s equal t o the negative of the divergence of P* pz (3.6) 25 The d e r i v a t i o n of equation 3.6 i s given i n appendix A. Pois s o n ' s equation f o r a p i e z o e l e c t r i c m a t e r i a l under s t r e s s i s then expressed as 2 1 = (p + p ) (3.7) P Equation 3.7 can be used t o f i n d the e f f e c t of the p o l a r i z a t i o n charge d e n s i t y on d e v i c e c h a r a c t e r i s t i c s . 3.2 POLARIZATION CHARGE DENSITY IN GAAS CANTILEVER In t h i s s e c t i o n the p o l a r i z a t i o n charge d e n s i t y i n a GaAs c a n t i l e v e r i s d e r i v e d as a f u n c t i o n of the d e f l e c t i o n a t the f r e e end. The c o o r d i n a t e r e f e r e n c e frame f o r a GaAs c a n t i l e v e r i s as d e f i n e d i n f i g u r e 3.3. The non-zero s t r e s s components i n a c a n t i l e v e r with a loa d W a p p l i e d at the f r e e end are giv e n by [34,35] a11 W x1 x3 Z2 a13 , , (3.8) -W ( - x 3 2 ) 2 I 2 where W i s the l o a d , x1 i s the p o s i t i o n measured along the beam s t a r t i n g at the f r e e end, d g i s the t h i c k n e s s of the beam, I 2 i s the second moment of area about the x2 a x i s , [100] [100] [^001] [100]' [010] [001] [010] [001] (a) noo]'- • - [oioi [001]' (b) F i g u r e 3.1 D e f i n i t i o n of MESFET d i r e c t i o n showing new and o l d r e f e r e n c e frames, (a) [ O l T ] MESFET and (b) [011] MESFET. 0 1 1 -iz 0 0 1 /2 Ii 0 -1 0 0 -1 _ \ 41 0 1 0 (a) (b) F i g u r e 3.2 Tra n s f o r m a t i o n m a t r i c e s (a) [011] and (b) [011] MESFET. F i g u r e 3.3 C a n t i l e v e r c o o r d i n a t e r e f e r e n c e d e f i n i t i o n , 27 and x3 i s the p o s i t i o n measured from the n e u t r a l a x i s . (Along the n e u t r a l a x i s the s t r a i n i n the beam i s zero.) The amount of d e f l e c t i o n can be expressed as a f u n c t i o n of the a p p l i e d l o a d [36] 3 L J W 6 = (3.9) 3 E s l2 where 6 i s the d e f l e c t i o n at the f r e e end, L i s the l e n g t h of the beam, and E i s the Young's modulus of the beam. The p o l a r i z a t i o n charge d e n s i t y i n the beam at x3=L i s found by combining equations 3.8 and 3.9 and t a k i n g the divergence. The r e s u l t i s ± 3 d_ E 5 P p z = V 5 — { 3 ' 1 0 ) pz 2 L z The p o s i t i v e s i g n i s f o r [011] MESFETs and the negative s i g n i s f o r [ O l T ] MESFETs. 3.3 BETWEEN FILM EDGES 3.3.1 FILM STRESS A uniform l a y e r of t h i n f i l m d e p o s i t e d on a s u b s t r a t e i s u s u a l l y i n a s t a t e of s t r e s s . The causes f o r the s t r e s s are not w e l l understood, but they have been c l a s s i f i e d i n t o two g e n e r a l c a t e g o r i e s . The f i r s t cause i s due to the d i f f e r e n c e i n thermal expansion c o e f f i c i e n t between the f i l m 28 and the s u b s t r a t e . The s t r e s s measurement i s u s u a l l y performed at a temperature which i s d i f f e r e n t from the temperature at which the f i l m i s d e p o s i t e d . The change i n temperature and the d i f f e r e n c e i n the thermal expansion r a t e between the f i l m and the s u b s t r a t e produce s t r e s s at the i n t e r f a c e . The second category has been l a b e l e d " i n t r i n s i c p r o p e r t i e s " , which i n c l u d e s a l l other causes such as d e p o s i t i o n p r o c e s s , d e p o s i t i o n r a t e , d e p o s i t i o n temperature, s u r f a c e l a y e r p r o p e r t i e s , i n t e r f a c i a l d e f e c t s , and other unknown causes [9,37,38]. Some of the e a r l i e r works on s t r e s s i n t h i n f i l m s were c a r r i e d out by Stoney [39]. He determined the s t r e s s i n t h i n f i l m s by measuring the amount of bending i n e n c a p s u l a t e d s u b s t r a t e s . H i s model has been accepted as the b a s i s f o r determining s t r e s s i n t h i n f i l m s [9,37-41]. For an uniform f i l m d e p o s i t e d on a s u b s t r a t e , the s t r e s s i n the f i l m can be expressed as [40] of = ^ ^ (3.11) 1 6 r d f ( 1 - us ) where i s the s t r e s s i n the f i l m , E g i s the Young's modulus of the s u b s t r a t e , d g i s the t h i c k n e s s of the s u b s t r a t e , r i s the r a d i u s of c u r v a t u r e of the bent s u b s t r a t e , and v i s the Poisson's r a t i o of the s u b s t r a t e . 29 The r e l a t i o n s h i p between the s t r e s s i n the f i l m and the maximum s t r e s s i n the s u b s t r a t e (at the i n t e r f a c e ) can be expressed as [40] • f • - • . . » » ( 3 - , 2 ) Most e n c a p s u l a t i n g f i l m i s about 2 to 3 orders of magnitude t h i n n e r than the s u b s t r a t e , thus the s t r e s s i n the s u b s t r a t e produced by an o v e r l a y i n g f i l m i s very s m a l l . However, at f i l m d i s c o n t i n u i t i e s , the s t r e s s i n the s u b s t r a t e i s g r e a t l y i n t e n s i f i e d by the "edge f o r c e " [5,42], The o r i g i n of the "edge f o r c e " can be understood by c o n s i d e r i n g the d i f f e r e n c e i n p r e s s u r e on a t h i n s t r i p of f i l m near an edge. I f the t h i c k n e s s of the f i l m i s assumed to be very s m a l l , then the v e r t i c a l v a r i a t i o n of the s t r e s s i n the f i l m i s n e g l i g i b l e . In other words, an uniform b u i t - i n s t r e s s , a , e x i s t s everywhere i n the f i l m . For a l a y e r of uniform f i l m on top of a s u b s t r a t e t h a t extends to i n f i n i t y i n both h o r i z o n t a l d i r e c t i o n s , the body f o r c e on a s t r i p of f i l m , which i s given by the d i f f e r e n c e i n s t r e s s on the two o p p o s i t e s u r f a c e s , i s zero everywhere. I f a t h i n s t r i p of f i l m with t h i c k n e s s dx at x=0 i s removed, the net body f o r c e per u n i t l e n g t h on the s t r i p at x=±0 i s then equal t o d ^ a Q on one s i d e and zero on the other s i d e . T h i s f o r c e i s then t r a n s m i t t e d to the s u b s t r a t e [42], and i t i s c a l l e d the "edge f o r c e " , F ( f i g u r e 3.4). 30 The d i f f e r e n c e between the edge con c e n t r a t e d model and the d i s t r i b u t e d f o r c e model l i e s i n the treatment of the s t r e s s d i s t r i b u t i o n i n the f i l m near an edge. In the edge c o n c e n t r a t e d model, the s t r e s s i n the f i l m i s assumed to be equal t o aQ everywhere. A l i n e f o r c e , F g = d ^ a 0 , then e x i s t s at the f i l m edge. In the d i s t r i b u t e d f o r c e model, s t r a i n r e l a x a t i o n i n the s u b s t r a t e and a complementary amount of s t r a i n r e l a x a t i o n i n the f i l m i s assumed [ 5 ] . For r e a l m a t e r i a l s under s t r e s s , some r e l a x a t i o n must occur [42]. T h e r e f o r e , the d i s t r i b u t e d f o r c e model i s a more r e a l i s t i c model than the edge c o n c e n t r a t e d model. The r e l a t i o n s h i p between the s t r a i n i n the s u b s t r a t e and the s t r a i n i n the f i l m i s expressed as [5] e s 1(x1 ,0) = e f ^ 1 ( x 1 ) - e o (3.13) The f i r s t s u b s c r i p t " s " denotes s u b s t r a t e and the s u b s c r i p t " f " denotes f i l m . The second s u b s c r i p t denotes the s t r e s s component, i n matrix n o t a t i o n . The f o r c e near the f i l m edge i s then d i s t r i b u t e d over a small r e g i o n near an edge. The f o r c e d e n s i t y f u n c t i o n , SF S/9X, i s expressed as [5] 31 3.3.2 CALCULATIONS BY EDGE CONCENTRATED MODEL The s t r e s s i n the s u b s t r a t e due to an "edge f o r c e " t a n g e n t i a l to the s u b s t r a t e s u r f a c e has been c a l c u l a t e d by B l e c h and Meieran [42]. T h e i r r e s u l t were used by Asbeck et al . [ 4 ] , Chen et al.[13], and Onodora et al. [32] to c a l c u l a t e the p o l a r i z a t i o n charge d e n s i t y i n the s u b s t r a t e . The c o o r d i n a t e r e f e r e n c e frame used i n the c a l c u l a t i o n i s shown i n f i g u r e 3.4. The s t r e s s components i n the s u b s t r a t e are given by [4] -2 x 1 3 ° 1 if ( ( x 1 2 + x 3 2 ) 2 -2 x1 °2 = "s F s ( 2 2 * v 5 5 x 1 z + x 3 z -2 x1 x 3 2 (3.15) ° 3 Tr ( ( x 1 2 + x 3 2 ) 2 -2 x 1 2 x3 ° 5 = * F s ( ( X1 2 + x 3 2 ) 2 32 and the p o l a r i z a t i o n charge d e n s i t y i s expressed as [4] x1.x3.(x1? - 0.53 x3?) <>pz= 3 9 0 ° o d f [ .6 r1 (3.16) x 1 2 x 3 2 ( x l 2 " 0.53 X32,) 4 1 DRAIN F i g u r e 3.4 Coordinate r e f e r e n c e f o r a f i l m window. 33 Contour p l o t s of the p o l a r i z a t i o n charge d e n s i t y i n the s u b s t r a t e c a l c u l a t e d by u s i n g equation 3.16. are shown i n f i g u r e s 3.5 to 3.7. A b u i l t - i n s t r e s s value of a Q=5.0xlO N/m was used i n the c a l c u l a t i o n s . In each f i g u r e , the p l o t window i s 1.0 am long and 0.5 urn wide. The c e n t e r of the gate i s a l i g n e d with the c e n t e r of the p l o t . The top edge of the p l o t corresponds to the s u r f a c e of the s u b s t r a t e . Only the p o l a r i z a t i o n charge d e n s i t y under the gate i s p l o t t e d . F i g u r e 3.5 shows the p o l a r i z a t i o n charge d e n s i t y under a 0.2 urn gate with 0.2 and 0.5 urn t h i c k o v e r l a y i n g f i l m . F i g u r e 3.6 shows the p o l a r i z a t i o n charge d e n s i t y under a 0.5 Mm gate with 0.2, 0.5, and 1.0 Mm t h i c k o v e r l a y i n g f i l m . F i g u r e 3.7 shows the p o l a r i z a t i o n charge d e n s i t y under a 1.0 Mm gate with 0.2, 0.5, and 1.0 Mm t h i c k o v e r l a y i n g f i l m . 3.3.3 CALCULATIONS BY THE DISTRIBUTED FORCE MODEL Hu [5] has o u t l i n e d a numerical method f o r c a l c u l a t i n g the s t r e s s i n the s u b s t r a t e near a s i n g l e f i l m edge based on the d i s t r i b u t e d f o r c e model. H i s method was a p p l i e d to c a l c u l a t e the p o l a r i z a t i o n charge d e n s i t y between two f i l m edges. From equation 3.13, the s t r e s s at the s u r f a c e of the s u b s t r a t e can be expressed as [5] 0 S ^ x ^ x S ) = H [ a f j U l ) - oQ] (3.17) 34 where H i s the "hardness" value and i t i s expressed as E_ ( 1 - *>2 ) H = — £ (3.18) E £ ( 1 - V \ ) a .(x1,x3) i s the s t r e s s i n the s u b s t r a t e , E i s the Young's modulus of the s u b s t r a t e , E^ i s the Young's modulus of the f i l m , v i s the Poisson's r a t i o of the s u b s t r a t e , i s the Poisson's r a t i o of the f i l m , ^ ( x l ) i s the s t r e s s i n the f i l m , and oQ i s the uniform b u i l t - i n s t r e s s i n the f i l m . The s t r e s s component i n the s u b s t r a t e i s found by s u b s t i t u t i n g the f o r c e d e n s i t y f u n c t i o n f o r the edge f o r c e i n equation 3.15 and convolute [5] 2d f « do- .(u) o(x1,x3) = - J G(x1-u,x3) i-tJ du (3.19) 7T 0 9U where G(x1-u,x3) i s the l a s t term i n any one of the equations i n 3.15, and a(x1,x3) i s the corre s p o n d i n g s t r e s s element i n the s u b s t r a t e . To f i n d the s t r e s s component i n the s u b s t r a t e i t i s necessary t o f i n d the s t r e s s d i s t r i b u t i o n i n the f i l m which i s s o l v e d by combining equations 3.17 and 3.19 and s o l v e f o r x3=0. 35 The s t r e s s i n the f i l m i s then expressed as 2d. » So* ,(u) of .(x1 ) = o-r , i o JTH 0 3u (x - u) du (3.20) The above equation was s o l v e d n u m e r i c a l l y by a f i n i t e d i f f e r e n c e technique. The g r i d p o s i t i o n s used i n the c a l c u l a t i o n were s e l e c t e d such that the g r i d spacing i n c r e a s e d e x p o n e n t i a l l y from the edge. The the same g r i d p o s i t i o n s were used by Hu [ 5 ] : The optimum v a l u e s f o r p and q have been determined by Hu to be 0.001 and 1.2, r e s p e c t i v e l y . The boundary c o n d i t i o n s were = q( - 0.5) (3.21) -f o r s u f f i c i e n t l y gf,1j+1 " g f , 1 j (3.22) = o o + I i r H j = 1 x1. - 0 . 5 ( x 1 j + x 1 j + 1 ) The summation can be w r i t t e n as a matrix equation ioff,}= [M]" 1 { Y } (3.22) 36 where [M] i s a (N-1)x(N-1) matrix with elements 1 1 it H M. •= + 6: ' 1 3 x1.-0.5( x1. ,+x1 .) x1 i-0.5( x1. + 1+x1.) 1 D 2 (3.24) The elements i n the v e c t o r {Y^} are given 7T H 1 Y. = - — = = = (3.25) 1 2 x1 i~0.5( x1 N +,+x1j) where of . . and x1. are d e f i n e d as t, 1 1 I °f,M= a f , U / a c (3.26.1) ^ 1 i = x 1 i / d f (3.26.2) Bulk Young's modulus and Poisson's r a t i o f o r S i 0 2 and S i 3 N 4 were used i n the c a l c u l a t i o n . The va l u e s a r e : E ( S i 0 2 ) = 7 . 1 7 X 1 0 1 0 N/m2, E ( S i 3 N 4 ) = 2.2X10 1 2 N/M2, v(SiO 2)=0.16, and i>(Si 3N 4)=0.27 [43,44]. P l o t s of the s t r e s s d i s t r i b u t i o n f o r S i 0 2 and S i 3 N 4 f i l m s are shown i n f i g u r e s 3.8 and 3.9, r e s p e c t i v e l y . (The s t r e s s d i s t r i b u t i o n p l o t f o r the edge c o n c e n t r a t e d case would be a step f u n c t i o n : f o r x1£0, a f=1.) The s t r e s s components represented by equation 3.19 can be expressed i n matrix form s i m i l a r to equation 3.23 {a(x1,x3)} = [ B ] { a f > 1 } + {C} (3.27) 37 For example, the matrix elements B.. and C f o r {oc} are 1J 1 D given by 2 -1 3 7T [ x i ! - 0.5( x1^_ 1 + x l ^ ) 3 ' x3  { [ x i : - 0.5( x 1 j _ 1 + x 1 j ) ] 2 + x 3 2 } 2 [x1^ - 0.5( x 1 . + 1 + x 1 . ) ] 2 x3 _1 1. { [ x i ! - 0.5( x 1 j + 1 + x 1 j ) ] 2 + x 3 2 } 2 ) (3.28) C i -[ x i ! - 0.5( x 1 N + 1 + x 1 N ) ] 2 x3 { [ x i ! - 0.5( x 1 N + l + x 1 N ) ] 2 + x 3 2 } 2 ) x1^ without the prime corresponds to the g r i d p o i n t s given by e quation 3.22. x1^ with the prime corresponds to the p o i n t s where the s t r e s s a^(xl!,x3) was c a l c u l a t e d . A f t e r the s t r e s s m a t r i c e s were generated, the p o l a r i z a t i o n components were found by u s i n g equation 3.5. The p o l a r i z a t i o n charge d e n s i t y , p__, was found by u s i n g equation 3.6. The pz d e r i v a t i v e s were e v a l u a t e d by using c e n t r a l d i f f e r e n c e s . The computer programs used to c a l c u l a t e the p o l a r i z a t i o n charge d e n s i t y were w r i t t e n i n HP-BASIC and ran on a HP-9816 computer. A l l program l i s t i n g s are i n c l u d e d i n appendix C. The r e s u l t s are p l o t t e d i n f i g u r e s 3.10 to 3.12. F i g u r e 3.10 shows the p o l a r i z a t i o n charge d e n s i t y under a 0.2 Mm gate 38 with a 0.2 and 0.5 Mm t h i c k o v e r l a y i n g f i l m . F i g u r e 3.11 shows the p o l a r i z a t i o n charge d e n s i t y under a 0.5 um gate with a 0.2, 0.5 and 1.0 Mm t h i c k o v e r l a y i n g f i l m . F i g u r e 3.12 shows the p o l a r i z a t i o n charge d e n s i t y under a 1.0 Mm gate with a 0.2, 0.5, and 1.0 Mm t h i c k o v e r l a y i n g f i l m . Each f i g u r e i s a l s o d i v i d e d i n t o two p a r t s , a and b. Part a i s f o r S i 0 2 f i l m and part b i s f o r S i g N 4 f i l m . 3.4 DISCUSSION Hu [5] has p o i n t e d out that w i t h i n 5d £ from a f i l m edge the s t r e s s v a l u e s c a l c u l a t e d by the edge c o n c e n t r a t e d model are s i g n i f i c a n t l y l a r g e r than the v a l u e s c a l c u l a t e d by the d i s t r i b u t e d f o r c e model. The d i f f e r e n c e i s g r e a t e r f o r " s o f t e r " f i l m s . The gate l e n g t h of the MESFETs used i n a l l of the r e p o r t e d works [3,4,10,11,13,32,45-48] are l e s s than 2 urn and the t h i c k n e s s of d i e l e c t r i c f i l m l a y e r v a r i e s between 0.2 to 1.0 Mm. The r a t i o of gate l e n g t h over the f i l m t h i c k n e s s i s much l e s s than 5, hence a d i f f e r e n c e i n p o l a r i z a t i o n charge d e n s i t y value c a l c u l a t e d by the two methods i s expected. F i g u r e s 3.5 to 3.7 show the r e s u l t s o b t a i n e d by the edge c o n c e n t r a t e d model, and f i g u r e s 3.10 to 3.12 show the r e s u l t s c a l c u l a t e d by the d i s t r i b u t e d f o r c e model. The two set of p l o t s have s i m i l a r p o l a r i z a t i o n charge d e n s i t y d i s t r i b u t i o n p a t t e r n , but the magnitude i s much l a r g e r f o r the edge c o n c e n t r a t e d model case. As a f i r s t approximation i n determining the e f f e c t of the induced p o l a r i z a t i o n charge d e n s i t y on the t h r e s h o l d 39 v o l t a g e , an one-dimensional p e r t u r b a t i v e assumption has been used by Asbeck et al. , Onodera et al. , and Chen et al. . In the assumption, the induced p o l a r i z a t i o n charge d e n s i t y under the e n t i r e channel i s assumed to be equal to the d i s t r i b u t i o n p r o f i l e at midgate. The p o l a r i z a t i o n charge d e n s i t y p r o f i l e at midgate c a l c u l a t e d by the edge c o n c e n t r a t e d model and by the d i s t r i b u t e d model f o r S i 0 2 and S i ^ N ^ f i l m s are shown i n f i g u r e s 3.13, 3.14, and 3.15 f o r gate l e n g t h of 0.2, 0.5, and 1.0 Mm, r e s p e c t i v e l y . These p l o t s c l e a r l y show that the e r r o r i n making the edge c o n c e n t r a t e d assumption r e s u l t s i n p r e d i c t i n g a much l a r g e r p o l a r i z a t i o n charge d e n s i t y i n the channel. The e f f e c t of the p o l a r i z a t i o n charge d e n s i t y on d e v i c e c h a r a c t e r i s t i c s i s determined by e v a l u a t i n g the f i r s t moment of the p o l a r i z a t i o n charge d e n s i t y . As r e s u l t , the edge c o n c e n t r a t e d model would p r e d i c t a much l a r g e r change i n d e v i c e c h a r a c t e r i s t i c s than the d i s t r i b u t e d f o r c e model. As p o i n t e d out by Asbeck et al. , the one dimensional p e r t u r b a t i v e assumption should underestimate the changes i n the d e v i c e c h a r a c t e r i s t i c s , because the p o l a r i z a t i o n charge d e n s i t y i s l a r g e r near the two ends of the gate than at the middle. However, Chen et al. and Onodera el al. o b t a i n e d good agreement between t h e o r e t i c a l and experimental r e s u l t s u s i n g the edge c o n c e n t r a t e d model and the one dimensional p e r t u r b a t i v e assumption. To f i t the . t h e o r e t i c a l data to the e x p e r i m e n t a l data, they used the f i l m s t r e s s value as a f i t t i n g parameter. The f i l m s t r e s s value which p r o v i d e d the 40 best s o l u t i o n was i n the same order of magnitude as the e x p e r i m e n t a l l y measured v a l u e , but a c c o r d i n g t o Asbeck a l a r g e r f i l m s t r e s s v alue should have been used. The r e s u l t s o b t a i n e d i n the present work showed that the edge c o n c e n t r a t e d model had overestimated the p o l a r i z a t i o n charge d e n s i t y p r o f i l e and a l a r g e r s t r e s s value was not needed. In the m o d e l l i n g of the p i e z o e l e c t r i c e f f e c t , Chen et al. [13] and Onodera et al. [49] used a l a r g e r b u i l t - i n s t r e s s v a l u e f o r S i 0 2 f i l m than f o r SigN^ f i l m i n order to f i t the experimental data to the t h e o r e t i c a l d a t a . However, the measured s t r e s s v alue f o r Si^N^ f i l m was found to be j u s t as l a r g e or l a r g e r than S i 0 2 f i l m [25,51]. The d i s t r i b u t e d f o r c e model showed that the magnitude of the induced p o l a r i z a t i o n charge d e n s i t y depends on the "hardness" of the o v e r l a y i n g d i e l e c t r i c f i l m . The "harder" the f i l m the l a r g e r the p o l a r i z a t i o n charge d e n s i t y i s generated. I t was c a l c u l a t e d that S i 0 2 f i l m i s "harder" than S i 3 N 4 f i l m . Using bulk f i l m c h a r a c t e r i s t i c s v a l u e s , the hardness value of S i 0 2 on GaAs i s 1.715 and the hardness value of SigN^ on GaAs i s 0.566. Q u a l i t a t i v e l y , the t h e o r e t i c a l r e s u l t s o b t a i n e d by the d i s t r i b u t e d f o r c e model agreed b e t t e r with the experimental data than the r e s u l t s o b t a i n e d by the edge c o n c e n t r a t e d model. P o l a r i z a t i o n C h a r g e D e n s i t y . CECM) F i g u r e 3.5.1 E C M - P o l a r i z a t i o n charge d e n s i t y Lg= 0.2 p and d^= 0.2MHI. P o l a r i z a t i o n Charge D e n s i t y . (ECM) Contour: Mtn- SxlB17, M»x- S x i e 1 7 , Step- 5 x l B l B ch&rgas/'en9 F i g u r e 3.5.2 E C M - P o l a r i z a t i o n charge d e n s i t y L_= 0.2 Mm and d f= 0.5Mm. P o l a r i z a t i o n Charge Density. CECM) F i g u r e 3.6.1 E C M - P o l a r i z a t i o n charge d e n s i t y L_= 0.5 urn and d f= 0.2vm. P o l a r i z a t i o n Charge D e n s i t y . (ECM) Contour: Min- - 8 x l B 1 6 . fUx- XB 1 6. Step- 5 x l 0 1 5 ch»rge*/cip3 F i g u r e 3.6.2 E C M - P o l a r i z a t i o n charge d e n s i t y L^= 0.5 Mm and df- 0.5Mm. P o l a r i z a t i o n Charge D e n s i t y . (ECM) F i g u r e 3 . 6 . 3 E C M - P o l a r i z a t i o n c h a r g e d e n s i t y L r = 0 . 5 um a n d d f = 1.Oum. P o l a r i z a t i o n Charge Density (ECM) Contour: Mtn- - I B 1 6 . M*x- I B 1 6 , Stop- I B 1 5 chtrgit/cm 3 F i g u r e 3 . 7 . 1 E C M - P o l a r i z a t i o n c h a r g e d e n s i t y L r = 1 . 0 Mm a n d d f = 0.2Mm. P o l a r i z a t i o n Charge D e n s i t y (ECM) C o n t o u r : M i n - - 2 x I 0 1 S , Max- 1 0 1 S , S t e p - 1 0 1 5 c h « r g e s / c m ' F i g u r e 3.7.2 E C M - P o l a r i z a t i o n charge d e n s i t y L„= 1.0 <un and df= 0.5M H I . P o l a r i z a t i o n Charge D e n s i t y (ECM) C o n t o u r : M i n - - 4 x l 0 1 6 , Max- I B 1 6 , S t e p - Z x l B 1 5 e h a r g e « / c m 3 F i g u r e 3.7.3 E C M - P o l a r i z a t i o n charge d e n s i t y 1.0 Mm and drB 1.0MHI. 45 o in H C tn •n m e L. o z F i l m t h i c k n e s s i s h. F i l m h a r d n e s s M - 0.5S5G, F i l m s t r e s s |So|- 1 . 0 E+9 Nm~2. 0 A 6 P o s i t i o n F r o * Edge Cx/h) F i g u r e 3.9 S t r e s s d i s t r i b u t i o n i n o v e r l a y i n g S i , N . f i l m on GaAs. 3 3 4 P o l a r i s a t i o n Charge D e n s i t y (DFM) ,16 C o n t o u r : M l n - - 8 x i e i H , M*x« 4 x l B 1 S , S t e p - 4 x l 8 A a c h » r g e s / c m ,15 F i g u r e 3.10.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i O j f i l m , LQ= 0.2 Mm, and d^= 0.2 Mm. P o l a r i z a t i o n Charge D e n s i t y (DFM) Contour: M1n- -12xlB 1 B. Max- 4 x l B 1 B . Stop- 4 x l 0 1 S chtrgas/ea 3 F i g u r e 3.10.2a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , LQ= 0.2 Mm, and d f= 0.5 Mm. 47 P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M l n - - 4 . 8 x l B l e . H » x - 4 x l B 1 6 . S t e p - 4 x l 0 1 5 c h ^ r g e s / e m 3 1  F i g u r e 3.10.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N 4 f i l m , L G= 0.2 wn, and d £= 0.2 um. P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M l n - - B x l B 1 S , f1»x- 4 x l B 1 S , S t e p - 4 x l 0 1 5 e h * r g e « x c r a 3 F i g u r e 3.10.2b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N 4 f i l m , LQ= 0.2 ttm, and d f= 0.5 »m> F i g u r e 3.11.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i 0 2 f i l m , L Q= 0.5 nm, and d f= 0.2 Mm. P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M1n- - 5 x i e l S . Max- X B 1 S , S t e p - 2 x l B I S c h a r g e s / c m 3 F i g u r e 3.11.2a D F M - P o l a r i z a t i o n charge d e n s i t y SiO~ f i l m , L r= 0.5 urn, and df«= 0.5 ftm. P o l a r i z a t i o n Charge Density (DFM) Contoupi Mln- - 3 x l B 1 6 , Max- 18 1 B, Step- 2 x l 0 1 S ehargas/'e*3 1 1 F i g u r e 3.11.3a D F M - P o l a r i z a t i o n charge d e n s i t y S i C ^ f i l m , Lg= 0.5 *an, and dj= 1.0 inn, P o l a r i z a t i o n Charge D e n s i t y CDFM) F i g u r e 3.11.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i j N ^ f i l m , LQ- 0.5 Mm, and d f= 0.2 um. P o l a r i z a t i o n Charge Density (DFM) F i g u r e 3.11.2b D F M - P o l a r i z a t i o n charge d e n s i t y S i , N . f i l m , L r= 0.5 Mm, and d f= 0.5 Mm P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M J n - - 5 x l 0 1 6 , Max- 1 0 1 6 , S t e p - 2 x l 0 1 S c h a r g e e / c m ' F i g u r e 3.11.2c D F M - P o l a r i z a t i o n charge d e n s i t y Si,N. f i l m , L r= 0.5 Mm, and d f= 1,0 p P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M l n - - 1 0 1 6 , Max- 1 0 1 6 , S t e p - 1 0 1 S c h a r g e s / c m F i g u r e 3.12.1a D F M - P o l a r i z a t i o n charge d e n s i t y S i O , f i l m , L r= 1.0 tim, and d f= 0.2 put. P o l a r i z a t i o n Charge D e n s i t y <DFM) C o n t o u r : M l n - - I B 1 6 , Max- 1 0 1 6 , S t o p - 1 0 1 5 c h a r g e s / c m F i g u r e 3.12.2a D F M - P o l a r i z a t i o n charge d e n s i t y S i O , f i l m , L r= 1.0 urn, and d f= 0.5 iun. P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M i n - - 2 x l 0 1 6 , Max- I 0 l f i . S t e p - I B 1 5 chergee^cm F i g u r e 3.12.3a D F M - P o l a r i z a t i o n charge d e n s i t y SiO- f i l m , L r= 1.0 urn, and d f= 1.0 nm. P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M i n - - 1 B 1 S , Max- I B 1 6 , S t e p - I B 1 5 e h . r g e s / c m F i g u r e 3.12.1b D F M - P o l a r i z a t i o n charge d e n s i t y S i , N . f i l m , L r= 1.0 jim, and d f= 0.2 um 53 P o l a r i z a t i o n Charge D e n s i t y (DFM) C o n t o u r : M ! n - - i e l S . Max- 1 8 1 6 , S t o p - I B 1 5 c h a r g o s ^ c a i 3 F i g u r e 3.12.2b D F M - P o l a r i z a t i o n charge d e n s i t y s i 3 N 4 f i l m » L G = 1.0 Mm, and d f= 0.5 Mm. P o l a r i z a t i o n Charge Density (DFM) F i g u r e 3.12.3b D F M - P o l a r i z a t i o n charge d e n s i t y S i 3 N 4 f i l m , LG«= 1.0 Mm, and dr= 1.0 Mm. o r * —5 . * • * • I t • ' * * ' * * ' *—* • * * u B .1 .2 .3 .4 .5 Depth Cum) F i g u r e 3.13.1 P o l a r i z a t i o n charge d e n s i t y a t midgate L R= 0.2 Mm, and d f= 0.2 Mm. Depth (urn) F i g u r e 3.13.2 P o l a r i z a t i o n charge d e n s i t y a t midgate L r= 0.2 Mm, and d f= 0.5 Mm. X u 8 .2 . 3 D e p t h Cum) F i g u r e 3.14.1 P o l a r i z a t i o n charge d e n s i t y a t midgate L Q= 0.5 Mm, and d f= 0.2 um. r—r—r—p—r—T- i i i . 2 . 3 .4 D e p t h (um) F i g u r e 3.14.2 P o l a r i z a t i o n charge d e n s i t y at midgate L G= 0.5 Mm, and d^= 0.5 p . .5 u 0 .2 . 3 D e p t h (urn) F i g u r e 3.14.3 P o l a r i z a t i o n charge d e n s i t y at midgate L Q= 0.5 Mm, and d f= 1.0 Mm. < E u \ M O en t. «s J C u CO < (3 M c o o o CD 4. 0 JC o .8 -> 1 1 1 1 1 1 1 1 1 1 1 1 1 v 1 J 1 1 1——i— ECM F i g u r e 3.15.1 P o l a r i z a t i o n charge d e n s i t y at midgate L Q= 1.0 Mm, and d f= 0.2 Mm. 0 -1 .2 .3 . 4 D e p t h (uin) F i g u r e 3.15.2 P o l a r i z a t i o n charge d e n s i t y at midgate Lg= 1.0 um, and d^= 0.5 um. D e p t h ( u r n ) F i g u r e 3.15.3 P o l a r i z a t i o n charge d e n s i t y at midgate Lr= 1.0 Mm, and d f= 1.0 Mm. 4. EXPERIMENTAL INVESTIGATION OF STRESS ON DEVICE CHARACTERISTICS 4.1 INTRODUCTION The o r i e n t a t i o n dependence i n GaAs MESFET device c h a r a c t e r i s t i c s has been observed by many r e s e a r c h groups: Asbeck ei al. at Rockwell I n t e r n a t i o n a l [3,4,45,46], Onedera et al. at F u j i t s u L a b o r a t o r i e s [10,11,32], Chen et al. a t Honeywell [13], Yamasaki et al. at Nippon Telegraph and Telephone [47], and Magerlein et al. at IBM [48]. These authors s t u d i e d the changes i n the d e v i c e c h a r a c t e r s i t c s by s t r e s s generated by "edge f o r c e s " at d i s c o n t i n u i t i e s i n the e n c a p s u l a t i n g d i e l e c t r i c f i l m . In the present work, s t r e s s i n the s u b s t r a t e was generated by bending s t r i p s of GaAs c a n t i l e v e r s . The advantage i s that an uniform p o l a r i z a t i o n charge d e n s i t y i s generated i n the channel of a d e v i c e under t e s t (DUT). The changes i n the d e v i c e c h a r a c t e r i s t i c s can then be a c c u r a t e l y c a l c u l a t e d by e v a l u a t i n g the f i r s t moment of the p o l a r i z a t i o n charge d e n s i t y , whereas the p o l a r i z a t i o n charge d e n s i t y generated by "edge f o r c e s " has a complex d i s t r i b u t i o n p a t t e r n and some approximation method i s needed. MESFETs used i n the present work were f a b r i c a t e d by i o n - i m p l a n t i n g 2 9 S i at a dose of 3 . 0 X 1 0 1 2 c m - 2 at 125 keV 13 -2 f o r the channel r e g i o n s and 1.0x10 cm at 125 keV f o r the n + r e g i o n s . Furnace anneal at 825°C f o r 25 minutes was used to a c t i v a t e the dopants and to r e p a i r the r a d i a t i o n damage. 58 59 Ohmic c o n t a c t s f o r the d r a i n and source regions were made by d e p o s i t i n g Au/Ge and a l l o y e d at 425°C f o r 2 minutes. L a s t l y , A l was evaporated f o r the gate e l e c t r o d e s . A f t e r the d e v i c e s were f a b r i c a t e d , the e n c a p s u l a t i n g l a y e r of Si-^N^ was completely removed by r e a c t i v e ion e t c h . The wafers were then cut i n t o 1.0 cm wide s t r i p s . Two batches of MESFETs were f a b r i c a t e d and t e s t e d . MESFETs i n the f i r s t batch had a t y p i c a l i d e a l i t y f a c t o r of 1.3, and they were a l l o r i e n t e d i n the same d i r e c t i o n . MESFETs i n the second batch had a t y p i c a l i d e a l i t y f a c t o r of 1.09, and they were o r i e n t e d i n the two <110> d i r e c t i o n s ( f i g u r e 4.1). 4.2 ELASTICALLY LINEAR GALLIUM ARSENIDE CANTILEVERS The model used to c a l c u l a t e the p o l a r i z a t i o n charge d e n s i t y i n a GaAs c a n t i l e v e r , equation 3.10, assumes that the beam m a t e r i a l i s e l a s t i c a l l y l i n e a r . The s t i f f n e s s c ^ , i n the [011] r e f e r e n c e frame, has been e v a l u a t e d to be 1 1 2 1.0x10 N/m . The purpose of t h i s experiment was to determine the maximum d e f l e c t i o n that c o u l d be a p p l i e d at the f r e e end u n t i l the beam no longer deformed l i n e a r l y . The experimental set up i s i l l u s t r a t e d i n f i g u r e 4.2. Incremental loads were added to bend the c a n t i l e v e r . A f t e r each lo a d was added, the d e f l e c t i o n at the f r e e end was measured wi t h a t r a v e l l i n g microscope. Weights were added u n t i l the c a n t i l e v e r broke, which o c c u r r e d f o r l o ads 60 SECONDARY FLAT (001) PRIMARY FLAT F i g u r e 4.1 Device O r i e n t a t i o n . P U L L E Y G a A s C A N T 1 L T V E R WEIGHTS F i g u r e 4.2 Experimental set-up f o r e l a s t i c i t y t e s t , 61 g r e a t e r than 6.0 N. The break l i n e was a t the f i x e d end of the beam and i t was p a r a l l e l to the (011) s u r f a c e . (The cleavage planes i n GaAs are the (011) and the (111) c r y s t a l p l anes [40].) F i g u r e 4.3 shows a p l o t of the a p p l i e d l o a d versus the f r e e end d e f l e c t i o n . The experimental data p o i n t s and the t h e o r e t i c a l l i n e c a l c u l a t e d by using equation 3.9 are p l o t t e d on the same graph. The experimental r e s u l t agreed w e l l with the t h e o r e t i c a l v a l u e s . The c a n t i l e v e r s were found to deform l i n e a r l y u n t i l they broke. T h e r e f o r e , equations 3.9 and 3.10 are v a l i d , as long as the d e f l e c t i o n a p p l i e d does not cause any p h y s i c a l damage to the GaAs c a n t i l e v e r s . 4.3 STATIC STRESS EXPERIMENT 4.3.1 BACKGROUND Va r i o u s s t r e s s r e l a t e d e f f e c t s on GaAs MESFET de v i c e c h a r a c t e r i s t i c s were d i s c u s s e d i n chapter 2. For a MESFET l o c a t e d at the f i x e d end of a s t r e s s e d c a n t i l e v e r , the Schottky b a r r i e r h e i g h t and the p o l a r i z a t i o n charge d e n s i t y under the gate are expected to be d i f f e r e n t f o r the s t r e s s e d and the u n s t r e s s e d s t a t e s . Table 1 shows the s u r f a c e s t r a i n and the magnitude of the induced p o l a r i z a t i o n charge d e n s i t y f o r v a r i o u s c a n t i l e v e r d e f l e c t i o n s . The s u r f a c e s t r a i n was c a l c u l a t e d by using equation 3.8.1 arid 3.9. _ i E x p e r i m e n t a l S e t a . 3 I T 1 S 1 1 1 1 I I — T h e o r e t i c * ! L i n e . 1 1 1 1 1 1 1 1 1 1 1 1 1 r-4 r -3 h ~4 J u —1 1 1 1_ 3 4 Load at F r e e End ( N e w t o n s ) F i g u r e 4.3 T y p i c a l l o a d versus d e f l e c t i o n f o r GaAs c a n t i l e v e r . D e f l e c t i o n a 1 c 1 Pp 2 (Surface) (Surface) (xl=L) (xl0~ 2m) (N/m2) e~/cm 3 0.0030 5.7X10 7 5.6X10"4 6 . 8X 1 0 1 1 0.010 1.9X10 8 1.9X10" 3 2 . 3 X 1 0 1 2 0.015 2.9X10 8 2 . 9 X 1 0 - 3 3 . 4 X 1 0 1 2 Table 1. T h e o r e t i c a l expected changes due to s t r e s s . 63 The p o l a r i z a t i o n charge d e n s i t y was c a l c u l a t e d by using equation 3.10. The Schottky b a r r i e r height was determined by c a p a c i t a n c e - v o l t a g e (C-V) and c u r r e n t - v o l t a g e (I-V) measurements. For an u n i f o r m l y doped sample, the b a r r i e r 2 h e i g h t can be determined from the y - i n t e r c e p t of 1/C p l o t t e d a g a i n s t the a p p l i e d v o l t a g e , V, [49] kT r2 n KT fai ( V - V. .- ) (4.1 .a) and kT N *bn = V b i + l n I " 5 — I (4.1.b) ND where C i s the measured c a p a c i t a n c e per u n i t a r e a , V ^ i s the b u i l t - i n v o l t a g e , and i s the e f f e c t i v e d e n s i t y of s t a t e s i n the conduction band. For moderately doped semiconductors, the I-V c h a r a c t e r i s t i c s f o r a forward b i a s e d metal-semiconductor j u n c t i o n , where V>3kT/q, can be expressed as [49] J = A V e x p ( -L^) exp( S i ) (4.2) kT kT where * s t n e z e r o - f i e l d b a r r i e r h e i g h t , <f>s^ i s the ** Schottky b a r r i e r l o w e r i n g , A i s the e f f e c t i v e Richardson c o n s t a n t , k i s the Boltzmann c o n s t a n t , and J i s the 64 c u r r e n t d e n s i t y . The b a r r i e r height i s expressed as * * o kT , A T . *bn = ~5 l n ( ] ( 4-3 ) where J g i s the e x t r a p o l a t e d c u r r e n t d e n s i t y at zero v o l t , and ^>Vin i s the Schottky b a r r i e r h e i g h t , which i s i s sum of the z e r o - f i e l d b a r r i e r h e i g h t and the Schottky b a r r i e r l o w e r i n g . The i d e a l i t y of the b a r r i e r i s d e f i n e d as q 3V n = (4.4) kT 9 ( l n J) 4.3.2 EXPERIMENTAL METHOD The 1.0 cm wide s t r i p s of GaAs wafers were p l a c e d between two g l a s s p l a t e s and clamped t i g h t l y t o g e t h e r . A de v i c e under t e s t (DUT) was p l a c e d as c l o s e t o the edge of the g l a s s p l a t e s as p o s s i b l e while s t i l l a l l o w i n g t e s t probes t o make e l e c t r i c a l c o n n e c t i o n s to the DUT. The width of the gate was p a r a l l e l t o the bending a x i s . T y p i c a l l e n g t h of the c a n t i l e v e r s was about 1.0 cm. Both t e n s i l e and compressive s t r e s s were a p p l i e d by d e f l e c t i n g the f r e e end of the c a n t i l e v e r with a micrometer. F i g u r e 4.4.a shows the mechanical set-up used t o apply t e n s i l e s t r e s s , and f i g u r e 4.4.b shows the mechanical set-up used t o apply compressive 65 T E S T P R O B E S F i g u r e 4 .4 .a S t a t i c t e n s i l e s t r e s s a p p l i e d t o DTJT. TEST PROBES JUL F i g u r e 4.4.b S t a t i c compressive s t r e s s a p p l i e d t o DUT. 66 s t r e s s t o the DUT. A l l DC d e v i c e c h a r a c t e r i s t i c s were measured with a HP-4145A Semiconductor Parameter A n a l y z e r . The C-V c h a r a c t e r i s t i c s were measured with a HP-4175A Mult i f r e q u e n c y LCR Meter at 1.0 MHz. The LCR meter was c o n t r o l l e d by a HP-9816 computer. The d e p l e t i o n l a y e r c a p a c i t a n c e was measured with the source and the d r a i n grounded and the b i a s v o l t a g e a p p l i e d to the gate. Measurements were made be f o r e , d u r i n g , and a f t e r s t r e s s was a p p l i e d . 4.3.3 RESULTS C-V measurements showed t h a t s t r e s s d i d indeed a f f e c t the metal-semiconductor i n t e r f a c e . For a f i x e d b i a s v o l t a g e , the c a p a c i t a n c e i n c r e a s e d when t e n s i l e s t r e s s was a p p l i e d , and i t decreased when compressive s t r e s s was a p p l i e d , r e g a r d l e s s of the d e v i c e o r i e n t a t i o n . The i d e a l i t y f a c t o r d i d not change with s t r e s s . The r e s u l t s are c o n s i s t e n t with the data o b t a i n e d by Kusaka et al. [15]. F i g u r e 4.5 and 4.6 show some t y p i c a l C-V curves with and without s t r e s s being a p p l i e d to MESFETs with i d e a l i t y f a c t o r of 1.09 and 1.3, r e s p e c t i v e l y . The s h i f t i n the curves with s t r e s s can be i n t e r p r e t e d as as a s h i f t i n the b u i l t - i n v o l t a g e , because the s h i f t i n the v o l t a g e was uniform f o r a l l c a p a c i t a n c e v a l u e s . The amount of s h i f t was found to be dependent on the q u a l i t y of the i n t e r f a c e . MESFETs with good i d e a l i t y f a c t o r , 1.09, showed a s m a l l e r s h i f t i n the curves than f o r MESFETs with l a r g e r i d e a l i t y f a c t o r , 1.3 ( t a b l e 2 ) . i c «; ?3 J » n 198? I b . 3 r — i 1——i 1 IB r-r—'—r- "~l 1 I 1— I I 1 I ~i—i—i—i i 1 5 . 5 15 1 4 . 5 14 «—'—•—•—•—I—i—i—i—i. I ,— ,—,—,— i , • . • . 12 •14 . I B B i * s V o l t a g e (V) . IB .2 F i g u r e 4.5.1 C-V p l o t ; no s t r e s s / compressive s t r e s s ( i d e a l i t y f a c t o r 1.3). 1 3 . 2 5 13 12. 75 1 2 . 5 1 2 . 2 5 12 12 Jf lN 198? -> 1 • 1 1 1 1 i -i r~ i i i i p -i—i—J—J—i i i i i I, i . i • * • • • • » • • • • . 12 . 14 . I E B i a s V o l t a g e (V ) . 18 . 2 F i g u r e 4.5.2 C-V p l o t ; t e n s i l e s t r e s s / no s t r e s s ( i d e a l i t y f a c t o r 1.3). 20 F e b 198? r " I I -1 - T • | f I f • '"T | - r f - "1 1— T-—j 1 1 - T - - -T 0 . 8 2 .04 . 0 6 . 08 . 1 Bi»s Voltage XV) F i g u r e 4.6.1 C-V p l o t ; p e r p e n d i c u l a r MESFET ( i d e a l i t y f a c t o r 1.09). 5 4 I " 1 1 1 1 1 — i i i 1 1 i i i I i i i i I i t t i i . 05 . 06 . 0 7 . 08 . 0 9 . 1 B i a s V o l t a g e (V) F i g u r e 4.6.2 C-V p l o t ; p a r a l l e l MESFET ( i d e a l i t y f a c t o r 1.09). S t r e s s o, (N/m^) R X 1 0 8 A.* b n(meV) Kusaka et al. T h i s Experiment n=1.02-1.13 n=1.09 n=1.3 1.3±0.2 1.9±0.2 5.1 7.5 1.110.1 1.8+0.1 3.3±0.2 5.510.2 Ta b l e 2. Comparison of b a r r i e r h e i g h t s h i f t with r e s u l t s o b t a i n e d by Kusaka et al. . D o p i n g P r o f i l e S A M P L E - BRTCH Z: P e r p e n d i c u l a r T , r P l o t t e d on 1? Feb 1987 1.E.+ IH p——i 1 r— -j r — i 1 r "i i r- -j 1 i i i | 1 1 -i 1" j l.E+17 l.E+15 r l.E+14 - j i I i i - i 1 i i i i * 1 ' p . 2 . 3 D e p t h ( m i c r o n ) .5 F i g u r e 4.7 A t y p i c a l doping p r o f i l e p l o t . 70 A change i n c a p a c i t a n c e f o r a f i x e d gate b i a s v o l t a g e means that the d e p l e t i o n l a y e r depth i s changed. The change i n the d e p l e t i o n l a y e r depth, W 2 - W 1 ' c a n ^ e c a l c u l a t e d by using the f o l l o w i n g e q u a t i o n : C - c2 w, - w = A e_( — (4.5) C C l2 1 where A i s the gate e l e c t r o d e area, C2 and C1 are the measured c a p a c i t a n c e s with and without s t r e s s , w2 and w^  are the c o r r e s p o n d i n g d e p l e t i o n l a y e r depth, and c i s the p e r m i t t i v i t y of GaAs. For a c a n t i l e v e r d e f l e c t e d by 0.15 mm and the DUT b i a s e d at zero v o l t , the d e p l e t i o n l a y e r f o r MESFETs with i d e a l i t y of 1.09 was found to change i n the order of 0.1 nm. The change i n the d e p l e t i o n l a y e r depth f o r MESFETs with i d e a l i t y f a c t o r of 1.3 was found to be about 10 times l a r g e r . The e f f e c t of the induced p o l a r i z a t i o n charge d e n s i t y on the changes i n the d e p l e t i o n l a y e r depth was n e g l e c t e d because the expected p o l a r i z a t i o n charge d e n s i t y f o r a c a n t i l e v e r d e f l e c t e d by 0.15 mm i s c a l c u l a t e d to be about 12 3 10 charges per cm ( t a b l e 1 ) , which i s about 4 to 5 o r d e r s of magnitude smal l e r than the peak doping c o n c e n t r a t i o n i n the c h a n n e l . The doping p r o f i l e f o r the t e s t d e v i c e s has a 17 3 peak i n the order of 10 charges per cm and a p r o j e c t e d s t r a g g l e about 0.15 Mm ( f i g u r e 4.7). F i n a l l y , the s t r e s s - i n d u c e d changes i n the b a r r i e r height and the p o l a r i z a t i o n charge d e n s i t y caused no 71 measurable changes i n the d e v i c e I-V c h a r a c t e r i s i t c s . 4.4 TIME-VARYING STRESS EXPERIMENT The o b j e c t i v e of t h i s experiment was to observe the e f f e c t of the induced p o l a r i z a t i o n charge d e n s i t y on the d r a i n - s o u r c e c u r r e n t . With a low frequency t i m e - v a r y i n g s t r e s s a p p l i e d , the induced p o l a r i z a t i o n charge d e n s i t y should f o l l o w the s t r e s s with the same phase and frequency. By equation 3.10, the p o l a r i z a t i o n charge d e n s i t y can be expressed as Consequently, the t i m e - v a r y i n g p o l a r i z a t i o n charge d e n s i t y should modulate a smal l AC s i g n a l on the d r a i n c u r r e n t . I f an uniform doping p r o f i l e i s assumed, the d r a i n c u r r e n t f o r a MESFET o p e r a t i n g i n the l i n e a r r e g i o n can be expressed as P pz s i n ut (4.6) [49] I 2 2 3 z V N e f f a [ — ( y 22 - y 2> -DS (4.7) where y 2 and y 1 are the d e p l e t i o n l a y e r depths at the two ends of the channel. They are given by [51] 72 ( V N + V_+ V. . ) . / 9 y 2 = a [ _ 5 G b i _ }l/2 (4.8.1) V P (vG+ vu,) y. = a [ ^ b i _ _ ]1/2 (4.8.2) P and the p i n c h - o f f v o l t a g e i s d e f i n e d « N e f f a 2 V D = — 4.8.3 For a d e f l e c t i o n of 6„ = 30 Mm, which was the value max measured f o r the experimental set-up, the change i n the b a r r i e r h eight can be n e g l e c t e d . The only s t r e s s dependent v a r i a b l e i s then the e f f e c t i v e doping c o n c e n t r a t i o n , which i s equal to the sum of the a c t i v a t e d doping c o n c e n t r a t i o n and the p o l a r i z a t i o n charge d e n s i t y , N e f £ = N D+ N p Z « The change i n the d r a i n - s o u r c e c u r r e n t can be expressed as 21° i D S - D S N s i n ut (4.9) ND where 1°^ i s the d r a i n c u r r e n t c a l c u l a t e d with N e f f = N n * S u b s t i t u t i n g numerical v a l u e s i n t o equation 4.9, a c u r r e n t change of 0.2 uk peak to peak was expected. The change i n c u r r e n t was measured as a v o l t a g e drop a c r o s s a 100 ohm r e s i s t o r , hence the expected s i g n a l magnitude was i n the tens of MV. 73 STEEL PROTECTIVE PLATE 0.051 r»m THICK OFF-CENTER SHftFT DRIVEN BY A DC MOTOR F i g u r e 4.8 Time-varying s t r e s s mechanical set-up. \ GaAs CANT1LIVER \ y, fr4 T Lock-In Analyzer "GS 4 1 ' 1. E6&G 5Z04-Ref Input " O S F i g u r e 4.9 Time v a r y i n g s t r e s s e l e c t r i c a l measurement set-up. 74 4.4.1 EXPERIMENTAL PROCEDURES A t i m e - v a r y i n g s t r e s s was generated by d e f l e c t i n g the c a n t i l e v e r with a camshaft. The cam motion was produced by r o t a t i n g a c y l i n d r i c a l s h a f t whose a x i s of r o t a t i o n was s l i g h t l y m i s a l i g n e d with i t s l o n g i t u d i n a l a x i s of symmetry. A c e n t e r hole s l i g h t l y l a r g e r than the diameter of a DC motor's r o t o r s h a f t was f i r s t d r i l l e d i n a c y l i n d r i c a l rod. Three through h o l e s , spaced about 120° a p a r t , were d r i l l e d r a d i a l l y i n the c y l i n d r i c a l s h a f t i n t e r s e c t i n g the center h o l e . The three h o l e s were then tapped. Screws were i n s e r t e d to secure the rod onto the DC motor's r o t o r s h a f t . The alignment of the ce n t e r a x i s of the rod with i t s r o t a t i o n a l a x i s were a d j u s t e d by the three r a d i a l screws. The f r e e end of a c a n t i l e v e r was then p l a c e d on top of the camshaft and a v e r t i c a l o s c i l l a t o r y d e f l e c t i o n was generated. A microscope with a c a l i b r a t e d s c a l e i n the eyepiece was used to measure the f r e e end d e f l e c t i o n . An EG&G P r i n c e t o n A p p l i e d Research 5204 Lock-In A m p l i f i e r was used t o measure the change i n the v o l t a g e a c r o s s the load r e s i s t o r . The e l e c t r i c a l measurement set-up i s i l l u s t r a t e d i n f i g u r e 4.9. The r e f e r e n c e s i g n a l t o the l o c k - i n a m p l i f i e r was generated by an opto-tachometer. A s i n g l e blade chopper was a t t a c h e d to the r o t o r s h a f t . Each time the blade passed between the s l o t of an o p t o - c o u p l e r , a f l i p - f l o p was t o g g l e d . The output of the f l i p - f l o p was connected t o the r e f e r e n c e input of the l o c k - i n a m p l i f e r . The schematic diagram of the opto-tachometer i s i l l u s t r a t e d i n appendix B. 75 Because a s i n g l e blade was used, the output of the tachometer was 1/2 of the c a n t i l e v e r d e f l e c t i o n r a t e . Frequency do u b l i n g was performed by i n t e r n a l c i r c u i t s i n the l o c k - i n a m p l i f i e r . 4.4.2 COMMENTS ON THE RESULTS A very l a r g e s i g n a l , g r e a t e r than 400 mV peak to peak, was d e t e c t e d while the t i m e - v a r y i n g s t r e s s was a p p l i e d . The s i g n a l was about 4 o r d e r s of magnitude l a r g e r than the value c a l c u l a t e d from the model. F i g u r e 4.10 shows the observed s i g n a l . The top t r a c e i s the output s i g n a l from the opto-tachometer, and the bottom t r a c e i s the v o l t a g e measured a c r o s s the 100 ohm l o a d r e s i s t o r . A d e t a i l e d a n a l y s i s r e v e a l e d t h a t the s i g n a l was a c t u a l l y n o i s e , generated by the movement of the probe t i p s on top of the c o n t a c t pads. With the t i m e - v a r y i n g s t r e s s a p p l i e d , the d e f l e c t i o n at any p o s i t i o n along the c a n t i l e v e r was l i n e a r l y r e l a t e d t o the d i s t a n c e from the f i x e d end, with the maximum d e f l e c t i o n at the f r e e end. The v e r t i c a l movement of the c a n t i l e v e r caused the probe t i p s t o move r e l a t i v e to the s u r f a c e of the wafer. T h i s n o i s e was s i g n i f i c a n t l y reduced when small drops of mercury were p l a c e d between the probe t i p s and the c o n t a c t pads, forming f l e x i b l e c o n t a c t s ( f i g u r e 4.11). The diameter of the mercury d r o p l e t s was about 100 76 F i g u r e 4.11 Mercury c o n t a c t s . F i g u r e 4.12 Measured s i g n a l with mercury d r o p l e t s . 78 to 150 /im. With the mercury d r o p l e t s i n p l a c e , the s i g n a l measured a c r o s s the l o a d r e s i s t o r i s shown i n f i g u r e 4.12. The top t r a c e i s the output from the opto-tachometer, and the bottom t r a c e i s the v o l t a g e measured a c r o s s the loa d r e s i s t o r . The n o i s e due to the movement of the probe t i p s was s i g n i f i c a n t l y reduced. The l o c k - i n a m p l i f i e r was then used i n an attempt to e x t r a c t the s i g n a l due to the induced p o l a r i z a t i o n charge d e n s i t y . A 10 (iV s i g n a l , which was w i t h i n the expected magnitude, was de t e c t e d f o r a short d u r a t i o n a f t e r the t i m e - v a r y i n g s t r e s s was a p p l i e d . Then i t dis a p p e a r e d . Viewing through a microscope, the mercury d r o p l e t s were v i b r a t i n g when the t i m e - v a r y i n g s t r e s s was a p p l i e d . From time t o time a d r o p l e t would be shaken out of p o s i t i o n and the c o n t a c t broken. Furthermore, the contact s u r f a c e was observed to be coated with mercury oxide a short p e r i o d a f t e r the d r o p l e t s were p l a c e d on the pads. The co n t a c t i n t e g r i t y was f u r t h e r degraded by the a d s o r p t i o n of the Au from the Au/Ge ohmic c o n t a c t s i n t o the mercury. The i n t e g r i t y of the mercury c o n t a c t was a major problem, which might e x p l a i n the poor r e p r o d u c i b i l i t y of the experiment. The i d e a l s o l u t i o n i s t o r e d e s i g n the t e s t p a t t e r n s to al l o w the e l e c t r i c a l c o n n e c t i o n s t o the DUT be made v i a exte n s i o n pads t h a t do not move when t i m e - v a r y i n g s t r e s s i s a p p l i e d . The e x t e n s i o n pads would be l o c a t e d on the o p p o s i t e s i d e of the c a n t i l e v e r . A new s t r e s s stage i s a l s o needed to allow the probe t i p s t o make co n t a c t t o these e x t e n s i o n pads. 79 4.5 CALCULATIONS OF THE BARRIER HEIGHT SHIFT DUE TO FILM  STRESS The s t a t i c s t r e s s experiment showed that the Schottky b a r r i e r h e i g h t s h i f t e d under e x t e r n a l l y a p p l i e d s t r e s s and the change can be i n t e r p r e t e d as a change i n the b u i l t - i n v o l t a g e . In t h i s s e c t i o n , the s h i f t i n the b a r r i e r height due to s t r e s s produced by f i l m edges and i t s e f f e c t on the t h r e s h o l d v o l t a g e was estimated. The d i s t r i b u t e d f o r c e model was used to c a l c u l a t e the s t r e s s i n the s u b s t r a t e between two f i l m edges. As a f i r s t a pproximation, the component at the midgate value was used i n the c a l c u l a t i o n . The midgate s t r e s s component, ', i s p l o t t e d as a f u n c t i o n of gate l e n g t h and f i l m t h i c k n e s s f o r S i 0 2 and S i 3 N 4 f i l m ( f i g u r e 4.13). Estimated changes i n the b a r r i e r h e i g h t were e v a l u a t e d by using equation 2.1. The magnitude of the b a r r i e r h e i g h t change i s l a b e l e d on the r i g n t - h a n d o r d i n a t e a x i s of f i g u r e 4.13. The c a l c u l a t i o n s showed t h a t , f o r MESFETs with gate l e n g t h l e s s than 0.2 Mm and with f i l m t h i c k n e s s g r e a t e r than 1.0 Mm, the e f f e c t of s t r e s s on the b a r r i e r h e i g h t should cause a l a r g e enough change i n the t h r e s h o l d v o l t a g e that can be separated from the e f f e c t s due to the p i e z o e l e c t r i c p r o p e r t y of GaAs and the l a t e r a l s t r e t c h of the n + l a y e r . The gate l e n g t h s of the t e s t d e v i c e s used by Chen et al. and Onodera et al. were a l l g r e a t e r than 0.5 Mm. T h e r e f o r e , the s h i f t i n the b a r r i e r h eight due to s t r e s s was n e g l i g i b l e . F i g u r e 4.13 E s t i m a t e d changes i n the b a r r i e r h e i g h t due t o f i l m s t r e s s . 5. CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK The o b j e c t i v e s of t h i s t h e s i s were to study the e f f e c t s of s t r e s s on GaAs MESFET d e v i c e c h a r a c t e r i s t i c s . P o l a r i z a t i o n charge d e n s i t i e s were c a l c u l a t e d by the edge c o n c e n t r a t e d model and the d i s t r i b u t e d f o r c e model. I t was found that the two models p r e d i c t e d s i m i l a r p o l a r i z a t i o n charge d e n s i t y d i s t r i b u t i o n p a t t e r n but the magnitude c a l c u l a t e d u s i n g the edge c o n c e n t r a t e d model was much l a r g e r than that u s i n g the d i s t r i b u t e d f o r c e model. Furthermore, the d i s t r i b u t e d model showed that the magnitude of the p o l a r i z a t i o n charge d e n s i t y was dependent on the "hardness" of the o v e r l a y i n g f i l m . The "hardness" of S i 0 2 and S i 3 N 4 f i l m s were e v a l u a t e d and S i 0 2 was found to be "harder" than S i 3 N 4 . The model p r e d i c t e d t h a t i f S i 0 2 f i l m i s used, a l a r g e r change i n the d e v i c e c h a r a c t e r i s t i c s i s expected than i f S i 3 N 4 f i l m i s used as encapsulant. T h i s r e s u l t i s c o n s i s t e n t with the r e p o r t e d experimental d a t a . The model used i n a l l of the r e p o r t e d works to date has been the edge c o n c e n t r a t e d model. The r e s u l t s o b tained i n the present work with the d i s t r i b u t e d f o r c e model p r o v i d e d some i n s i g h t s and a b e t t e r understanding of the e f f e c t of f i l m edges on the d i s t r i b u t i o n of the p o l a r i z a t i o n charge d e n s i t y i n the gate of an encapsulated MESFET. The experiments performed i n t h i s t h e s i s showed that the Schottky b a r r i e r h eight i n c r e a s e d with compressive s t r e s s and i t decreased with t e n s i l e s t r e s s . The s h i f t was found to be l a r g e r f o r Schottky b a r r i e r s with a l a r g e r 81 82 i d e a l i t y f a c t o r . T h e o r e t i c a l c a l c u l a t i o n s were performed t o p r e d i c t the b a r r i e r h e i g h t s h i f t f o r a Schottky gate s t r e s s e d by an encapsulated d i e l e c t r i c l a y e r . The c a l c u l a t i o n showed that the change i n the t h r e s h o l d v o l t a g e due to the b a r r i e r h eight s h i f t can be n e g l e c t e d compared to the p i e z o e l e c t r i c e f f e c t and the l a t e r a l s t r e t c h of the n + l a y e r f o r d e v i c e with gate l e n g t h g r e a t e r than 0.5 um. Attempts were made to measure the e f f e c t of the induced p o l a r i z a t i o n charge d e n s i t y by a p p l y i n g a t i m e - v a r y i n g s t r e s s . Although some encouraging r e s u l t s were obta i n e d , there was a r e p r o d u c i b i l i t y problem due to poor e l e c t r i c a l c o n n e c t i o n s . For f u t u r e works, some suggestions are given below: 1. To e l i m i n a t e the n o i s e problem encountered i n the ti m e - v a r y i n g s t r e s s experiment, a new mask set and a new s t r e s s stage are needed, such t h a t the e l e c t r i c a l c o n n e c t i o n s to the d e v i c e under t e s t are made v i a ex t e n s i o n pads l o c a t e d at some p o s i t i o n s where there i s no v i b r a t i o n . 2. Devices with gate l e n g t h l e s s than 0.2 Mm and encapsulants with t h i c k n e s s g r e a t e r than 1.0 Mm should be f a b r i c a t e d t o observe the p r e d i c t e d changes i n the de v i c e c h a r a c t e r i s i t c s due to s t r e s s - i n d u c e d b a r r i e r h e i g h t s h i f t . 83 3. F u r t h e r study on the e f f e c t of a d i s l o c a t i o n on the a c t i v a t i o n of the implanted dopants are needed. 4. An experiment s i m i l a r to the one performed by Isomae [15] should be performed to observe the g e n e r a t i o n of d i s l o c a t i o n s at f i l m edges i n GaAs s u b s t r a t e s . REFERENCES 1. K. Lehovec and R. Zuleeg, " A n a l y s i s of GaAs FET's f o r I n t e g r a t e d L o g i c , " IEEE Trans, on E l e c t r o n Devices, V o l . ED-27, No. 6, pp. 1074-1091, 1980. 2. G a l l i u m Arsenide Techonology, Ed. D. F e r r y , Howard W. Sams and Co., I n d i a n a p o l i s , 1985. 3. C P . Lee, R. Zucca, and B.M. Welch, " O r i e n t a t i o n E f f e c t s on P l a n a r GaAs Schottky B a r r i e r F i e l d - E f f e c t T r a n s i s i t o r s , " App. Phys. L e t t . , V o l . 37, No. 3, pp. 311-313, 1980. 4. P.M. Asbeck, C P . Lee, and M.F. Chang, " P i e z o e l e c t r i c E f f e t c s i n GaAs FETs and T h e i r Role i n Orientation-Dependent Device C h a r a c t e r i s t i c s , " IEEE Trans. E l e c t r o n D evices, V o l . 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Proto, " D i s l o c a t i o n s and the P i e z o e l e c t r i c E f f e c t i n I I I - V C r y s t a l s , " J . Appl. Phys., V o l . 48, No. 7, pp. 3008-3013, 1977. 27. J.P. H i r t h abd J . Lothe, Theory of D i s l o c a t i o n s , 2nd ed., John Wiley and Sons, New York, pp. 30-95, 1982. 28. R. B l u n t , S. C l a r k , and D. S t i r l a n d , " D i s l o c a t i o n D e n s i t y and Sheet R e s i s t a n c e V a r i a t i o n Across S e m i - I n s u l a t i n g GaAs Wafers," IEEE Trans. Microwave Theory and Techniques, V o l . MTT-30, No. 7, pp. 943-948, 1982. 29. S. Isomae, " S t r e s s i n S i l i c o n and S i 3 N 4 / S i 0 2 F i l m Edges and V i s c o e l a s t i c Behavior of SiO~ F i l m , J . Appl. Phys., V o l . 52, No. 4, pp. 2782-2791, 1981. 30. R.A. Saddler and L.F. Eastman, " O r i e n t a t i o n E f f e c t Reduction Through Capless Annealing of S e l f - A l i g n e d Planar GaAs Schottky B a r r i e r F i e l d - E f f e c t T r a n s i s t o r s , " A p p l . Phys. L e t t . , V o l . 43, No. 9, pp. 865-867, 1983. 31. T. Onodera, T. O h n i s h i , N. Yokoyama, and J.H. N i s h i , "Improvement i n GaAs MESFET Performance Due to P i e z o e l e c t r i c E f f e c t , " IEEE Trans. E l e c t r o n Devices, V o l . ED-32, No. 11, pp. 2314-2318, 1985. 32. J.F. Nye, P h y s i c a l Property of C r y s t a l s : T h e i r  R e p r e s e n t a t i o n by Tensors and M a t r i c e s , Claredon Press, Oxford, pp. 33-38,110-130, 1979. 33. M. Neuberger, Handbbook of E l e c t r o n i c M a t e r i a l s , V o l 2:  I I I - I V Semiconductor Compounds, IFI/Plenum, New York, pp. 45-63, 1971. 34. S.P. Timoshenko and K. Goodier, Theory of E l a s t i c i t y , 3rd ed., Mc Graw H i l l , New York, 1970. 35. A.S. Saada, E l a s t i c i t y : Theory and A p p l i c a t i o n s , Pergamon Press, New York, 1974. 36. R. Neathery, A p p l i e d S t r e n g t h of M a t e r i a l s , John Wiley, New York, 1982. 37. R.W. Hoffman, "The Mechanical P r o p e r t i e s of T h i n Condensed F i l m s , " P h y s i c s of T h i n F i l m , V o l . 3, Academic Pr e s s , New York, pp. 211-273, 1966. 38. L. E c k e r t o v a , P h y s i c s of Thin F i l m , 2nd ed., Plenum Pre s s , New York, pp. 202-213, 1986. 87 39. G. Stoney, "The Tension of M e t a l l i c F i l m s Deposited by E l e c t r o l y s i s , " Proc. Roy. Soc. (London), V o l . A82, pp. 172-175, 1909. 40. R. Jaccodine and W. S c h l e g e l , "Measurement of S t r a i n s at S i - S i 0 9 I n t e r f a c e , " J . Appl. Phys., V o l . 37, No. 6, pp. 2429-2534, 1966. 41. P. K i r k b y , P. Selway, and L. Westbrook, " P h o t o e l a s t i c Waveguides and T h e i r E f e e c t on Strip-Geometry GaAs/ G a n _ x A l As L a s e r s , " J . Appl. Phys., V o l . 50, No. 7, ppi'4567-3579, 1979. 42. I. Blech and E. Meieran, "Enhanced X-Ray D i f f r a c t i o n from S u b s t r a t e C r y s t a l s C o n t a i n i n g D i s c o n t i n u o u s Surface F i l m s , " J . Appl. Phys., V o l . 38, No. 7, pp. 2913-2919, 1967. 43. Handbook of M a t e r i a l S c i e n c e : Volume I I . Metals,  Composites, and R e f r a c t o r y M a t e r i a l s , Ed. C. CRC Press Inc., C l e v e r l a n d , pp. 331, 332, 357, 382-384, 1974. 44. Handbook of Tables f o r A p p l i e d E n g i n e e r i n g S c i e n c e , 2nd ed., Ed. R. Bolz and G. Tuve, CRC Press Inc., C l e v e r l a n d , pp. 162, 163, 187, 1973. 45. C. Chen, A. P e c z a l s k i , M.Shur, and H. Chung, " O r i e n t a t i o n and Ion-Implanted Transverse E f f e c t i n S e l f - A l i g n e d GaAs MESFET's," IEEE Trans, on E l e c t r o n D e vices, V o l . ED-34, No. 7, pp. 1470-1481, 1987. 46. C P . Lee, M.F. Chang, P.M. Asbeck, L.D. Hou, R. Vahrenkamp, and G. K i r k p a t r i c k , " O r i e n t a t i o n Dependence of Device U n i f o r m i t y i n GaAs I n t e g r a t e d C i r c u i t , " S e m i - I n s u l a t i n g I I I - V M a t e r i a l s Rah-Nee-Ta 1984, Ed. D.C. Look and J.S. Blakemore, Shiva P u b l i s h i n g , Natwich, England, pp. 347-353, 1984. 47. K. Yamasaki, K. A s a i , and K. Kuramada, "GaAs LS.I-Directed MESFET's with S e l f - A l i g n e d Implantation f o r n -Layer Technology (SAINT)," IEEE Trans, on E l e c t r o n D e vices, V o l . ED-29, No. 11, pp. 1772-1776, 1982. 48. J . M a g e r l e i n , D. webb, A. C a l l e g a r i , J . Feder, T. F r y x e l l , H. G u t h r i e , P. Hoh, J . M i t c h e l l , A. Poerence, S. S c o n t r a s , G. S p i e r s , and J . Greine-r, " C h a r a c t e r i z a t i o n of GaAs S e l f - A l i g n e d R e f r a c t o r y - G a t e Metal-Semiconductor F i e l d - E f f e c t T r a n s i s t o r (MESFET) I n t e g r a t e d C i r c u i t s , " J . A p p l . Phys., V o l . 61, No. 8, pp. 3080-3092, 1987. 49. S.M. Sze, P h y s i c s of Semiconductor Devices, John Wiley and Sons, New York, pp. 245-361, 1981. 50. S o l i d - S t a t e Magnetic and D i e l e c t r i c Devices, Ed. H.W. Katz, Wiley, New York, pp. 6-10, 1959. 88 51. R.W. Hornbeck, Numerical Methods, Quantum P u b l i s h o r , New York, pp. 16-23, 1975. 52. C. Mogab, P. P e t r o f f , and T. Sheng, " E f f e c t of Reactant N i t r o g e n Pressure on Micro S t r u c t u r e and P r o p e r t i e s of R e a c t i v e l y Sputtered S i l i c o n N i t r i d e F i l m s , " J . Electorchem. S o c , V o l . 122, p. 185, 1975. APPENDIX A P o l a r i z a t i o n Charge D e n s i t y [50] F i g u r e 5.1 Coordinate D e f i n i t i o n f o r a p o t e n t i a l f i e l d around an elementary d i p o l e . The e l e c t r i c a l p o t e n t i a l at p o i n t P due to a s i n g l e d i p o l e can be c a l c u l a t e d by summing the c o n t r i b u t i o n due to each charge -q q 1 0 p = ( + ) (A.1) 1 2 1 , 47re o <3 12" 11 *p = ( — — ) (A.2) o 2 1 where , 7 d 2 1^ = r + - r d cos 6 (A.3) 89 90 A2 2 2 ° l ; = r + + r d* cos 6 (A.4) ^ 4 If p o i n t P i s f a r away, r>>d, then 1 1 = r - + r d cos 6 (A.5) 1 1 * r + + r d cos 6 (A.6) Hence 1 2-1 1 = d cos 6 (A.7) 1 2 1 1 =* r 2 (A.8) S u b s t i t u t i n g equations A.7 and A.8 i n t o A.2: q d cos 6 * p = 5 — ( A .9 ) 4 i r e ^ r z o Equation A.9 can be r e w r i t t e n i n v e c t o r form by c o n s i d e r i n g p=qS p . y Q / r ) ( A > 1 0 ) 0 P = ~T7e— 91 For a volume of d i p o l e s , the d i p o l e moment per u n i t volume i s expressed as F-=pn, where n i s the number of d i p o l e s per u n i t volume. The p o t e n t i a l at a p o i n t P i s c a l c u l a t e d by 1 <t>v = / F - V O / r ) dv (A.11) o Using the f o l l o w i n g i d e n t i t y : 1 V - ( P V r ) = — V - P + F - V O / r ) (A.12) r the p o t e n t i a l at p o i n t P can be expressed as 1 P" V - P <t>p = [ / V-( — ) dv - f dv ] (A. 13) 47rc Q r r Using the divergence theorem, the f i r s t i n t e g r a l can be expressed as a s u r f a c e i n t e g r a l : 1 P-dS V-P" 4 = ( J - J dv ) (A. 14) 4ire D r r The p o t e n t i a l at p o i n t P due i s equal to the sum of two components: 1) a volume charge d e n s i t y equals t o (-V-P), and 2) a s u r f a c e charge d e n s i t y equal t o the normal component of P" at the s u r f a c e of the d i e l e c t r i c . 92 The d i p o l e moment per u n i t volume generated by the p i e z o e l e c t r i c e f f e c t can be i n t e r p r e t e d as a volume charge d e n s i t y of type 1 above. The p o l a r i z a t i o n charge d e n s i t y i s then d e f i n e d as P p z = - V-P (A.15) The Poisson's equation i n s i d e the d i e l e c t r i c becomes 2 1 Vz<p = — (p - p n_) (A.16) P vo Id 4564 4584 M0C7B11 CHOPPER 2K2 T 4584 10> POWER-UP RESET OPTO-TACHOMETER BY- HARRY PENG AUG 1987 APPENDIX C 10 REM 20 REM program name: d i s t f 30 REM 40 REM This program uses the equations given by S.M. Hu 50 ' REM to calculate the d i s t r i b u t e d f i l m s t ress. 60 REM 70 REM The film stress i s for a one edge s e m i - i n f i n i t e 80 REM fi l m . 50 REM 100 REM by: Harry Peng A p r i l 1987 110 REM 120 REM 130 REM 140 REM the X g r i d positions are given by the following equation: 150 REM 160 REM < i ) 170 REM Xi ( P - l ) 180 REM « q • ( -0.5 > 190 REM h < ) 200 REM ( P - l ) 210 •REM 220 «EM 230 OPTION BASE 1 240 REAL P,0,H,Addl,Add2,Deltaij.Const 250 INTEGER Inum,Inuma,Irow,Jcol,Ielem 2G0 REAL Esio,Esin,Egaas,Usio,Vsin,Vgaas,Rvalue,Es,Ef,<Js,Vf 270 PIM Xnorm(1:100),Y(100 >,M(100,100 ),A$[1],Stress(100 ) 280 >.REM 290 REM 300 REM 310 REM Assign constant values T -in REM 330 REM 340 REM 350 Esio -7.2E+10 ! N/(cm*cm) 360 Esi n •=2.1E+11 ! N/(cm»cm) 370 Egaes=1.2E+ll 1 N/(cin>cm> 380 Vsio -.16 390 Vsin -.25 400 Vgaas c.23 410 Qo.0001 ! fission Q 420 H-2. E-7 ! Assign layer thickness 430 H$«VAL$(H) 440 P - l . 2 ! Assign P. 450 ! f i n a l value used to Hu 460 REM 470 REM #••*••»•••••*#••*•»••#•#*»»**»•••»** 480 REM • 490 REM request overlayer type. User input 3* 95 500 REM 510 REM ••***••»••»••****•*•»•*•»•*****•**** 520 REM 530 Inl=!input layer type 540 INPUT 'Input overlayer ""0""<Si02> or ""N""(Si3N4 )", A$ 550 IF A$m = "o" OR A$m-"0" THEN ! Overlayer i s Si02 560 Ef-Esio 570 Vf-Vsio 580 Filmtype$«"Si02" 590 SOTO Contl 600 END IF 610 IF A$[l]-"n" OR A$m«"N" THEN ! Overlayer is Si3N4 620 Ef=Esin 630 Vf-Ysin 640 Filmtype$-"Si3N4" 650 GOTO Contl 660 END IF 670 GOTO Inl 680 Contl:( the substrate i s assumed to be GaAs 690 DISP "Running" 700 Es-EQaas 710 Ys-Ugaas 720 Kvalue-(Es»<l-Vf*2))/(Ef*(l-Us"2)> ! Evaluate K value 730 K$«UALS(Kvalue> 740 Const-PI*Kvalue/2 ! Evaluate Const 750 REM 760 REM «*#....•••..#..•. 770 REM 780 REM request user to enter Inum, dimension of matrix 790 REM 800 REM •*•«•«••#••••••••••••»•••••»««*• • 810 REM 820 INPUT "Input N number for XKMAX 99):",Inum 830 Inum-INT(Inum) 840 Inuma"Inum+l 850 REDIM Xnorm(1 = Inuma >,Y< 1 = Inum-1>,M(Inum-1,Inum-1 ),Stress(Inum-1> ! REDIMEN SION MATRICES 860 REM 870 REM ••#••#•••••••#*•«**••••••••••••••••••• 880 REM 890 REM generate Xnorm Values Xi/h 1 to Xnorm+1 900 REM 910 REM •**«••#»•**»•**•*••*»••**«*•*•**•••*»* 920 REM 930 FOR 1 = 1 TO <Inuma) ! generate Xnorm vector 940 Xnormd >-(<<PAI-l )/(P-l ))-.5)»Q 950 NEXT I 960 REM •*•«•••••*•••«*»•*•»•*••••#*••«•***»• 970 REM . 980 REM generate Y vector 96 990 REM 1032 REM • * 1010 FOR Ielem=l TO Inum-1 1020 Addl»l/(Xnorm(Ielem >-.5*< Xnorm(Inum+1>+Xnorm(Inum))) 1030 Y(Ielem>-Const-Addl 1040 NEXT Ielem 1050 REM 10G0 REM • 1070 REM i860 REM generate M matrix elements 1090 REM 1100 REM ••****•*»•*#**#»•*»*•**«••**•*•**•*»* 1110 REM 1120 FOR Irow-2 TO Inum 1130 FOR Jcol-2 TO Inum 1140 Addl-l/<Xnorm<Irou >-.5»(XnormtJcol-1 )+Xnorm(Jcol>)) 1150 Add2-l/<Xnorm<Iroui)-.5*<Xnorm(Jcol>+Xnorm(Jcol + 1))) 1160 D e l t a i j - 0 1170 IF Ir o w J c o l THEN 1180 Del t a i j - 1 1190 END IF 1200 M(Iroui-1,Jcol-1 >-Addl-Add2+(Deltaij*Const) 1210 NEXT Jcol 1220 NEXT Irou 1230 REM 1240 REM •* •••*« 1250 REM 12B0 REM Calculate nomalized stress vector 1270 REM 1280 REM ...» 1290 REM 1300 PRINT " Now doing matrix inversion !" 3 31C MAT M- INv(M) 1320 PRINT " Matrix inversion completed " 1330 MAT Stress" M*Y 1340 REM 1350 REM • «•*. •«••••».*•* 1360 REM 1370 REM store data. No re-save Is allowed. 1380 REM 1390 REM Datavalue contains Xnorm 1 to Inum 1400 REM stress 1 to Inum-1 1410 REM ««•••»••»••*••»•*«•••*»**•»*•**#*•**»#****• 1420 REM 1430 DIM Linel$[S0],Unitl$[30],Line2$[50],Unit2$t303 1440 DIM Title$C80],Sample$[801,Xtitle$[50],Ytitle$tS0],Xunit$[3C],Yunit$[30J 1450 DIM DSC 11 ],Datavalue(100,2 ) 1460 INTEGER Xeuto,Yauto- ^ 1470 REAL Xfnan,Xmin,Ymax,Ymin,Logx,Logy,Dl,D2,Ul,U2,Ndata 1480 REDIM Datavalue(Inum,2 ) 1490 Ndata»Inum 1500 FOR 1-1 TO Ndata-1 ! transfer data into Datavalue 1510 Datavalue(I,l )-Xnorm(I ) 1520 Datavalue(I,2)-Stress(I) 1530 NEXT I 1540 Datevalue<Ndata,1>-Xnorm<Ndata> 1550 Xmin=Datavalue(1,1 ) 1560 Xmax-Datavalue(Ndata-l,1> 1F70 Ymin»Detavelue(1,2> 1580 Ymax»MAX(Stress<»>> 1590 Title$="Stress Value in the Film. Distributed Force Method.* 1600 SampleS="6aAs Substrate." 1610 Y t i t l e S - " S t r e s s Normalized" 1620 X t i t l e S - ' P o s i t i o n From Film EdQe" 1530 Xunit$«"x/h" 1640 Yunit$«*S/So" 1650 LlnelS-'Film thickness is h«="&H$&" m." 1660 Line2$-"Film type i s "&FilmtypeS&" K »"&KS 167e Unitl$="" 1680 Unit2$="" 1690 DIM Msu5$(2HH] 1700 MsusSd )-":HP9133,702" 1710 Msus$(2)-"=HP9133,700" 1720 PRINT T i t l e s 1730 Save_data : ! Routine to save the data onto a f i l e 1740 INPUT "Save onto which file<<10 characters>",Fil$ 1750 INPUT "Which device (1) F l e x i b l e , (2> Winchester",D 1760 ON ERROR 60T0 Err_hendle 1770 DISP "Running" 1780 CREATE ASCII "6"&Fil$&Msus$<D ),20 1790 ASSI6N BF i l e TO "6"&Fil$&Msus$<D ) 1800 OUTPUT 8File;TitleS,D$ 1810 OUTPUT SFileiSampleS 1820 OUTPUT e F i l e ; X t i t l e $ , X u n i t $ 1830 OUTPUT S F i l e ; Y t i t l e $ , Y u n i t $ 1840 OUTPUT ©FileiXauto.Xmin.Xmax,Yauto.Ymin.Ymax,Ndata 1850 OUTPUT «File;Dl,Ul,Linel$,Unitl$ 1860 OUTPUT *File;D2,U2,Line2$,Unit2$ 1870 REDIM 0atavalue(Ndeta,2> 1880 OUTPUT §File;Dataveluet* ) 1890 OUTPUT 9File;Logx,Logy 1900 ASSI6N BF i l e TO • 1910 GOTO Fin 1920 ! Routine to handle f i l e input/output error 1930 Err_handle;SELECT ERRN 1940 CASE 53 1950 PRINT "Improper f i l e neme.";CHR$(129>&Fi1$&CHR$<128> 1960 BEEP 1970 CASE 54 1980 PRINT " F i l e e x i s t s elready." 98 1990 BEEP 2000 CASE 56 2010 PRINT " F i l e name i6 undefined in the storage unit." 2020 BEEP 2030 CASE 83 2040 PRINT CHR$<129)&°The storage unit i s write protected"&CHR$(128) 2050 BEEP 2060 CASE ELSE 2070 PRINT 'Error ";ERRN 2080 BEEP 2090 END SELECT 2100 GOTO Save_data 2110 Fin: DISP "Program Completed" 2120 END 99 IB REM 20 REM 30 REM program name: sigma2a 40 REM 50 REM This program uses the equations given by S.M. Hu 60 REM to c a l c u l a t e the stress tensor elements in the 70 REM substrate. Three stress tensors are calculated 80 REM Sx, Sz, and Sxz. 30 REM 100 REM 110 REM 120 REM 1 f i l m 130 REM o > X 140 REM I 150 REM substrate U Z 160 REM 170 REM The stress in the film must had been evaluated 180 REM end stored in e f i l e . 190 REM The user i s requested to enter the X and Z ranges. 200 REM The r e s u l t i s store in a user s p e c i f i e d f i l e . 210 REM 220 REM by: Harry Peng A p r i l 1987 230 REM 240 REM 250 OPTION BASE 1 260 DIM LinelS[50],UnitlS[30],Line2$[50],Unit2$r303 270 DIM Title$t80 3,Sample$[80],Xtitle$[501,Ytitle$t50],XunitS[30],Yunit$[30 ] 280 DIM D $ [ l l l 290 REAL Xmax,Xmin,Ymax,Yroin.Logx,Logy 300 REAL Datavalue(500,2),Dl,D2,Ul,U2 310 INTE6ER Ndata,Not_used,Xauto,Yauto.Filelength 320 DIM Msus$(2Hll] 330 DIM Stresszx<200,200),B(200,200),C(200),Tenp<200) 340 DIM Xpnorm(200),Xnorm(150),Filmstress(150> 350 REAL Zmin,Zmax,Zstep,Xpmin,Xpmax,Xpstep,Ipmin,Ipmax,Addl,Add2 360 INTE6ER Ielem,Irow,Jcol,Stresstype,Zcount,Ipnum,Xsel,Ndatal,Ndata2 370 REM ) 380 REM •»••• • ..*«.•.•...... 390 REM 400 REM get normalized f i l m stress data from memory 410 REM 420 REM •..•.•*.••....•*•.....•« •••••••»• 430 REM 440 DISP "Running" 450 MsusSd )-":HP9133,702" 460 MsusS(2>-":HP9133,700" 470 6et_data : I Routine to get the data from a f i l e 480 INPUT "Specify normalized f i l m stress f i l e name",Fil$ 490 INPUT "Which device (1) F l e x i b l e , (2) Winchester",D 100 500 DISP "Running" bifc ON ERROR 60T0 Err_handle 520 ASSIGN B I n f i l e TO "6"&Fil$&MsusS(D) 530 Title$="" 540 Samples-"" 550 Y t i t l e S - " " 560 X t i t l e S - " " 570 Xunit$="" 580 Yunit$»"" 590 LinelS="" 600 Line2$«="" 610 Unitl$="" 620 Unit2S="" 630 ENTER B l n f i l e ; T i t l e S , D $ 640 ENTER Blnfile;Samples 650 ENTER B l n f i l e : X t i t l e $ , X u n i t S 660 ENTER B l n f i l e ; Y t i t l e $ , Y u n i t $ 670 ENTER Blnfile;Xauto,Xmin,Xmax,Yauto,Ymin,Ymax,Ndata 680 ENTER B l n f i l e i D l , U l , L i n e l $ , U n i t l $ 690 ENTER Blnfile;D2,U2,Line2$,Unit2$ 700 REDIM Datavalue(Ndata,2) 710 ENTER 8Infile;Datevalue<•) 720 ENTER Blnfile;Logx,Logy 730 ASSIGN B I n f i l e TO * 740 GOTO Contl 750 ! Routine to handle f i l e input/output error 760 Err_handle= SELECT ERRN 770 CASE 53 780 PRINT "Improper f i l e name.";CHRS(129>fcFil$&CHR$<128> 790 BEEP 800 CASE 56 810 PRINT " F i l e name i s undefined in the storage unit." 820 BEEP 830 CASE ELSE 840 DI5P "STOPPED! Error ";ERRN 850 BEEP 860 STOP 870 END SELECT 880 60T0 6et_data 890 REM 900 REM ..*•••• * « • • 910 REM 920 REM 930 Contl: ! 940 I r e t r i e v e f i l m s t r e s s value 950 ! 950 FOR Ielem=l TO Ndata-1 I divide Datavalue into two f i l e s : 970 Xnorm(Ielem )-Datavalue(Ielem,1 ) ! Xnorm and (Ndata) 980 Filmstress(Ielem )-Datavalue<Ielem,2> . ! Filmstress(Ndata-1 ) 990 NEXT Ielem 101 1000 Xnorm(Ndata)-Datavalue<Ndata,l ) 1010 ! 1020 INPUT "Specify depth Z/h parameters <Min «0>:<Max, Step>*,Zmax,Zstep 1030 Zmax-ABS(Zmax ) 1040 Zstep-ABS(Zstep> 1050 Zmin-0 1060 INPUT "Specify Stress component (1) Sx, <2) Sz, (3) Sxz, or <4> Sy",Str esstype 1070 Cont2= ! 1080 PRINT 1090 PRINT * 1100 PRINT "X parameter options:" 1110 PRINT * (1) user specify step for -ve X values ONLY!" 1120 PRINT " (2) self-generated steps for X" 1130 INPUT "Input X parameter option",Xsel 1140 IF Xsel-1 THEN 1150 INPUT "Specify Xmin and Xstep",Xmin,Xstep 1160 Ipnum«INT(ABS(Xmin)/XstepHI 1170 IF Ipnum>199 THEN 1180 PRINT "X parameter out of range Ipnum max i s 149" 1190 PRINT "Respecify X parameter" 1200 GOTO 1150 1210 END IF 1220 FOR Ielem=l TO Ipnum 1230 Xpnorm(Ielem >-(-1»ABS<Xmin > >+((Ielem-1 )»ABSCXstep>) 1240 NEXT Ielem 1250 DISP "Running" 1260 ELSE 1270 INPUT "Specify X/h parameters: (Min, Max>",Xpmin,Xpmax 1280 IF (Xpmin<-200 OR Xpmax>200) THEN 1290 PRINT "X parameter out of range. Xmin >-200 , Xmex<200" 1300 Cont3: PRINT "respecify X/h parameters" 1310 BEEP 1320 60T0 Cont2 1330 END IF 1340 DISP "Running" 1350 Ipmin-0 ! f i l l i n g the x natix 1360 Ipmax-0 1370 REPEAT I fin d Ipnum for -ve x's 1380 Ipmin=Ipmin+l 1390 UNTIL Xnorm(Ipmin»ABS(Xpmin) 1400 REPEAT ! fin d Ipnum for +ve x's 1410 Ipmax»Ipmax+l 1420 UNTIL Xnormdpmax )>ABS(Xpmax ) 1430 FOR Ielem-Ipmin TO 1 STEP -1 ! f i l l the beginning with -ve 1440 Xpnorm(Ipmin-Ielem+1 )—l»Xnorm(Ielem) ! x numbes. 1450 NEXT Ielem 102 1460 FOR Ielem«l TO Ipmax ! add the +ve x's 1470 XpnormfIpmin+Ielem >»Xnorm(Ielem ) 1460 NEXT Ielem 1490 Ipnum-Ipmax+Ipmin 1500 IF Ipnum>149 THEN 1510 PRINT "Ipnum too big.",Ipnum 1520 60T0 Cont3 1530 END IF 1540 END IF 1B50 FOR Ielem-2 TO Ipnum+1 I f i l l s 1st row of stresszx 1560 Stresszx<1,Ielem )*Xpnorm(Ielem-1 ) ! which contains Xpnorm 1570 NEXT Ielem 1580 REDIM Xnorm(Ndata ) ,Filmstress<Ndata-1>,B(Ipnum,Ndata-1 ),C(Ipnum),Temp( I pnum ) 1590 ! 1600 Zcount«2 1610 PRINT "Start c a l c u l a t i n g stress tensor elements " 1620 FOR Znorm-Zmin TO Zmax STEP Zstep 1630 FOR Irow-1 TO Ipnum 1640 FOR Jcol-2 TO Ndata-1 1650 ! generate B matrix 1660 SELECT Stresstype 1670 CASE 1 I solve for Sx 1680 Addl-((XpnormtIrow >-.5«(Xnorm<Jcol-1 )+Xnorm(Jcol>> >"3)/ (< (Xpnormf Irow>-.5«(Xnorm<Jcol-1 )+Xnorm(Jcol ) > >*2+Znorm*2 )"2 > 1690 Add2«((Xpnorm(Irow>-.5»(Xnorm<Jcol>+Xnorm(Jcol+1>>>"3>/ < ( ( Xpnorm< Irow )-. 5«( Xnorm( Jcol )+Xnorm< Jcol + 1 )) r2+Znorm*2 )"2 ) 1700 CASE 2 ! solve for Sz 1710 Addl-(< Xpnorm(Irow>-.5*(Xnorm(Jcol-1)+Xnorm( Jcol)))*Zno rm"2 >/<<(XpnormfIrow )-.5*(Xnorm(Jcol-1 )+Xnorm(Jcol> > )"2+Znorm*2)"2) 1720 Add2-((Xpnorm(Irow >-.5*(Xnorm< Jcol )+Xnorm(Jcol + 1)>)«Zno rm*2 >/< <(Xpnorm(Irow )-.5»(Xnorm<Jcol )+Xnorm< Jcol + 1)) )'2+Znorm*2)"2> 1730 CASE 3 I solve for Sxz 1740 Addl-((Xpnorm<Irow )-.5*(Xnorm< Jcol-1)+Xnorm( Jcol)))*2*Z norm >/(< <Xpnorm(Irow )-.%*(Xnorm<Jcol-1>+Xnorm(Jcol>)>*2+Znorm"2 >"2 > 1750 Add2-((Xpnorm(Irow )-.5*(Xnorm(Jcol>+Xnorm( Jcol + 1>))"2*Z norm )/(((Xpnorm(Irow )-.5»(Xnorm( Jcol>+Xnorm(Jcol + 1 )) )*2 + Znorm"2 )"2 ) 1760 CASE 4 ! solve for Sy 1770 Addl-.23*(Xpnorm(Irow >-.5«(Xnorm(Jcol-1)+Xnorm( Jcol>))/ (<Xpnorm(Irow )-.5*(Xnorm(Jcol-1 )+Xnorm(Jcol)) )*2+Znorm"2) 1780 Add2-.23*(Xpnorm(Irow )-.5«(Xnorm(Jcol)+Xnorm( Jcol+1)))/ ((Xpnorm(Irow >-.5*<Xnorm(Jcol )+Xnorm(Jcol + 1 )) )*2+Znorm*2 > 1790 END SELECT 1800 BUrow.Jcol-l >«=(-2/PI >*(Addl-Add2 ) 1810 NEXT Jcol 1820 SELECT Stresstype ! generate C matrix 1830 CASE 1 ! solve for Sx 1840 C(Irow )-(2/PI>•<(Xpnorm(Irow )-.5»<Xnorm(Ndata )+Xnorm< Ndata -1> > >A3 >/(((XpnormtIrow )-.5»(Xnorm<Ndata )+Xnorm(Ndata-1))r2+ZnorrT2K2) 1850 CASE 2 103 18B0 C(Irow )-(2/PI )•<(Xpnorm(Irow )-.5»<Xnorm<Ndata >+Xnorn<Ndata -i))Wnorm'2 )/<< <Xpnorm<Irow >-.5«<Xnorm<Ndata >+Xnorm(Ndata-1> > >"2+Znorm"2 >"2) 1870 CASE 3 1880 C(Irow )-(2/PI>*< <Xpnorm<Irow >-.5*(Xnorm<Ndata>+Xnorm<Ndata -1))>*2«Znorm )/(< <Xpnorm<Irow )-.5*(XnormtNdata )+Xnorm<Ndata-1 )) >*2+Znori>i*2>*2) 1890 CASE 4 -1900 C(Irow >-<2/PI>»(Xpnorm<Irow >-.5*(Xnorm(Ndata >+Xnorm(Ndata-1 >) )/< (XpnormC Irow)-. 5* (Xnorm< Ndata >+Xnorm<Ndata-1 )) >*2+Znorm*2 ) 1910 END SELECT 1920 NEXT Irow 1930 PRINT "pass matrix generation f o r Znorm-",Znorm 1940 MAT Temp- B'Filmstress 1950 MAT Temp- Temp+C 1960 Stresszx(Zcount,1 )«Znorm ! f i r s t column contains Znorm 1970 FOR Ielem-2 TO Ipnum+1 ! put result into stresszx 1980 Stresszx(Zcount,Ielem )-Temp(Ielem-1> !looses last TEMP's datum 1990 PRINT "stresszx",Zcount,Ielem,Stresszx(Zcount,Ielem) 2000 NEXT Ielem 2010 Zcount-Zcount+1 2020 NEXT Znorm 2030 IF Zcount-3 THEN 2040 Z$-" Z - "&UAL$(Znorm-Zstep) 2050 ELSE 2060 ZS-" Z - "&UALS(Zmin>&" TO *&UAL$(Zmax) 2070 END IF 2080 REM 2090 REM •••• • • •••• 2100 REM 2110 REM store r e s u l t into a user s p e c i f i e d f i l e 2120 REM 2130 REM «*»••#«#*••#••• «••* 2140 REM 2350 DIM Oatastore(150,150) 2160 REDIM Datastore(Zcount-1,Ipnum+1 ) 2170 FOR Irow-1 TO Zcount-1 2180 FOR Jcol-1 TO Ipnum+1 2190 Datastore(Irow,Jcol )-Stresszx(Irow,Jcol ) 2200 NEXT Jcol 2210 NEXT Irow 2220 ! Datavalue(Ielem,1>-Xpnorm(Ielem) 2230 ! Datavalue(Ielem,2 )-Temp<Ielem ) 2240 ! NEXT Ielem 2250 Filelenoth-INT<(Zcount-1.0 >»(Ipnum+1.0 >«8.0/256.0 >+6 2260 Save_data= ! Routine to save the date onto a f i l e 2270 INPUT "Save onto which filet<10 characters )",Fil$ 2280 INPUT "Which device <1> F l e x i b l e , (2) Winchester",D 2290 ON ERROR GOTO Err2 2300 Ndatal-Ipnum+1 2310 Ndata2-Zcount-l 2320 Xmin-Xpmin 10** 2330 Xmax-Xpmax 7340 Ymin-MIN(Temp<«>> 2350 Ymax«=MAX(Temp< * )) 2360 Ndata"=Ipnum-l 2370 SELECT Stresstype 2380 CASE 1 2390 Tit l e $ - " S t r e s s Values for Sx"&Z$ 2400 CASE 2 2410 Title$«*Stress Values for Sz"&Z$ 2420 CASE 3 2430 Ti t l e $ - " S t r e s s Values for Szx"&Z$ 2440 END SELECT 2450 Ytitle$="Normailzed Stress Value <S/So)" 2460 Xtitle$="Position from Film Edoe (x/h)" 2470 XunitS="x/h" 2480 Yunit$-="S/So" 2490 CREATE BDAT "6"&Fil$&Msus$<D ) ,Filelength 2500 ASSIGN C F i l e TO "6"&Fil$&Msus$(D> 2510 OUTPUT e F i l e ; T i t l e $ , D * 2520 OUTPUT «File;Semple$ 2530 OUTPUT e F i l e ; X t i t l e $ , X u n i t S 2540 OUTPUT GFile; Y.titleS, YunitS 2550 OUTPUT eFile;Xauto,Xmin,Xmax,Yauto,Ymin,Ymax )Ndatal,Ndata2 2560 OUTPUT e F i l e ; D l , U l , L i n e l $ , U n i t l $ 2570 OUTPUT eFile;D2,U2,Line2$,Unit2$ 2580 ! REDIM Stresszx<Ndeta2.Ndatal ) 2590 OUTPUT 8File;Datastore(* ) 2600 OUTPUT 8File;Logx,Logy 2610 ASSI6N BF i l e TO • 2620 GOTO F i n 2630 Err2:SELECT ERRN 2640 CASE 53 2B50 PRINT "Improper f i l e name.";CHR$<129>&Fil$&CHR$(128) 2660 BEEP 2670 CASE 54 2680 PRINT " F i l e already e x i s t . " 2690 BEEP 2700 CASE 83 2710 PRINT CHR$(129>&"The storage unit i s write protected"&CHR$(128) 2720 BEEP 2730 CASE ELSE 2740 DISP "ERROR *,ERRN 2750 BEEP 2760 WAIT 4 2770 END SELECT 2780 60T0 Save_data 2790 Fi n : PRINT " f i l e stored." 2800 DISP "Program Completed!" 2810 END 105 10 REM -20 REM 30 REM program name = plotconA 40 REM 50 REM This program read in a matrix and plots the contour lines 60 REM for the datavalues i n the matrix. The f i r s t row contains • 70 REM X values and the f i r s t column contain the Y values. 80 REM matrix dimension 9P REM j Ndatal —>X 100 REM I 110 REM I 120 REM NdataZ 130 REM U 140 REM 2 150 REM The p l o t t i n g routine was written for Hewlett-Packard. 160 REM It i s one of th e i r demonstration program. The program 170 REM was modified to plot matrix data. 180 REM 190 REM -200 OPTION BASE 1 210 COM REAL Datavalue(150,150>.Conmin.Conmax,Constep,INTEGER Ndatal,Ndata2 220 COM Linel$[50],Unitl$[30],Line2S[50],Unit2$[303 230 COM TitleS[80],Sample$t80],Xtitle*t50],YtitleS[50],Xunit$[30],Yunit$t30 ] 240 COM DSC11],U1,U2,D1,D2 250 REAL Xmax,Xmin,Ymax,Ymin,Logx,Logy,Zdata(110,110),Zmin,Zmax 260 REAL Xcord(110),Ycord(110) 270 INTEGER Xauto.Yauto 280 DIM Msus$(2>[113 290 Msus$<1 )-•:HP9133,702" 300 Msus$(2)-"--HP9133,700" 310 6et..data: ! Routine to get the data from a f i l e 320 INPUT "Input data f i l e name",Fil$ 330 INPUT "Which device (1) F l e x i b l e , (2) Winchester",D 340 DISP " r e t r i e v i n g data" 350 ON ERROR GOTO Err_hendle 360 ASSIGN e i n f i l e TO "6"&Fil$&Msus$(D) 370 T i t l e * - " " 380 Samples-"" 390 Y t i t l e S - " " 400 X t i t l e S - " " 410 XunitS-"" 420 YunitS-"" 430 Linel$="" 440 Line2$«=*" 450 Un i t l S - " " 460 Unit2$-"" 470 ENTER B l n f i l e ; T i t l e S , D S 480 ENTER Blnfile;SampleS 490 ENTER GI n f i l e ; X t i t l e $ , X u n i t $ 500 ENTER 8 I n f i l e : Y t i t l e S , Y u n i t S 510 ENTER Blnfile;Xauto,Xmin,Xmax,Yauto,Ymin,Ymax,Ndatal,Ndata2 520 ENTER 9Infile;Dl,U1,Linel$,UnitlS 106 530 ENTER BInfile;D2,U2,Line28,Unit2$ Z ' Z REDIM Detavalue<Ndata2,Ndatal) 550 ENTER §Infile;Datavalue(*> 5G0 ENTER 8Infile;Logx,Logy 570 ASSI6N e i n f i l e TO « 580 GOTO Fin 590 ! Routine to handle f i l e input/output error 600 Err_handle> SELECT ERRN 610 CASE 53 620 PRINT "Improper f i l e name.";CHR$(129)&Fi1S&CHR$<128) 630 BEEP 640 CASE 56 650 PRINT " F i l e name i s undefined in the storage unit." 660 BEEP 670 CASE 83 680 PRINT CHRS(129>&"The storage unit i s write protected*&CHR$(128) 690 BEEP 700 CASE ELSE 710 DISP "Error ";ERRN 720 BEEP 730 WAIT 2 740 END SELECT 750 GOTO Get_data 760 Fin; DISP "update matrix" 770 REDIM Xcord(Ndatal-l>,Ycord(Ndata2-1) 780 REDIM Zdata(Ndata2-l,Ndatal-l> 790 FOR Irow-2 TO Ndata2 800 FOR Jcol=2 TO Ndatal 810 Zdata<Irow-1,Jcol-1 )-Datavalue<Irow,Jcol) 820 NEXT Jcol 830 Ycord(Irow-1)«Datavalue(Irow,1) ! put y coordinate value in Ycord 840 NEXT Irow 858 FOR Jcol-2 TO Ndatal 860 Xcord(Jcol-1 )"Datavalue<1,Jcol> ! put x corodinate value in Xcord 870 NEXT Jcol 880 Zmin-MIN<Zdata<«)) 890 Zmax-MAX(Zdata<»)) 900 Conmin—2.5640E+8 910 Conmex-2.5640E+8»4 920 Constep-2.564E+7«2 930 Wtlp: DISP "Contour Conmin-",Conmin," Conmax-".Conmax," Constep-".Constep 940 ON KEY 7 LABEL * " GOTO Wtlp 950 ON KEY 5 LABEL " " GOTO Wtlp 960 ON KEY 2 LABEL "NEW FILE " GOTO Get_data 970 ON KEY 0 LABEL "EXIT* 60T0 Pend 980 ON KEY 9 LABEL "PLOTTER" GOSUB Pl o t t e r _ p l o t 990 ON KEY 8 LABEL "DUMP" GOSUB Dump_plot 1000 ON KEY 6 LABEL "SCREEN PLOT" GOSUB Crt_plot 1010 GOTO Wtlp 1020 P l o t t e r _ p l o t : ! send plot to p l o t t e r 1030 Crt_plotter-0 1040 GOSUB Call_cont 1050 RETURN 1060 Dump_plot:! 107 1(270 DUMP DEUICE IS 701,EXPANDED 1030 DUMP GRAPHICS 10SS RETURN 1100 C r i _ p l o t : ! 1110 Crt _plctter«l 1120 eOSUS Cell_cent 1130 RETURN 1140 C e l l _ c c n t : ! 1150 CALL Contour? Zdate( • ), Ccnmin.Conmax , Constep ,0,0, Crt_plot ter,Xcord< * ),Y cord(*)) 11E0 BEEP 500,1 1170 RETURN 1190 Pend^DISP "Program Completed" 1190 END 1200 Contour: SUB Contour?Sfc(«),Min,Max,Interval.Extremes,Stats,Crt,Xval(*),Yv e K O ) 1210 ! ! 1220 ! This subprogram p l o t s a contour nap of the array Sfc<«), and I 1230 I opt i o n a l l y plots l o c a l minima, maxima, and s t a t i s t i c s . ! 1240 I The program was o r i g i n a l l y a Hewlett Packard demo program I 1250 ! c a l l e d "Contour". It was modified for t h i s a p p l i c a t i o n . I 12S0 I Sfc(«): This i s the two-dimensional reel array containing the I 1270 I data to be plotte d . It need not be square. ! 1280 ! Min & Max: These ore the lowest and highest l e v e l s , respectively, ! 1290 I of the contour l i n e s . These allow you to specify the t 1300 I exact range within which ycu want contours. Every ! 1310 ! contour l i n e outside of th i s range w i l l not be plotted. ! 1320 ! Interval- This s p e c i f i e s hou fer apart the contour l i n e s have to I 1330 I be ( i n value, not in distance). The smeller the inte.— I 1340 ! v e l , the denser the contour p l o t . I 1350 ! Extremes-- This i s a l o g i c a l variable which s p e c i f i e s whether or I 13E0 ! not to label l o c a l maxims and minima. A loc a l maximum I 1370 I i s a point whose value i s lerger that i t s eight ! 13B0 ! neighbors immediately to the west, northwest, north, I 1390 1 northeast, east, southeast, south, and southwest. A ! 1400 I l o c e l minimum has a corresponding d e f i n i t i o n . I 1410 I Stats: This i s a l o g i c a l variable which s p e c i f i e s whether or I 1420 I not to print the "stats" ( s t a t i s t i c s ) of the date I 1430 I array. Stats include: 1) array si z e , rows and columns; ! 1410 I 2) Minimum and maximum contour l e v e l s , and 3) contour I 1450 I i n t e r v a l . I 14E0 I Crt: Logical variable specifying whether the plot i s going I 1470 I to a CRT or a p l o t t e r . I 1480 I • ! 1490 REAL Xshift,Ispace,-'space 1500 INTE6ER I,J,Imex,Jmex,Linecount 1510 IF Crt THEN 1520 6INIT 1530 GRAPHICS ON 1540 SOSUB Plot_cont 1550 60T0 End I5S0 ELSE 1570 GINIT 1580 PLOTTER IS 705,'HPGL" 108 1590 GRAPHICS ON 1600 60SUB Plot_cont 1610 PLOTTER IS 3, "INTERNAL" 1620 60T0 End 1630 END IF 1640 Plot_cont= PEN 1 1650 Imax-SIZE(Sfc,l) 1660 Jmax-SIZE(Sfc,2) 1670 Yshift-0 1683 Xshift=0 1690 X_gdu_max-.75 !MAX( XvaK * > >+0 1700 Y_gdu_max-0 !MAX<Yval(» ) )+0 1710 X_gdu_min—.25 !MIN(Xval(•))-0 1720 Y_gdu_min«.5 ! MIN( YvaK • > >-0 1730 Xspace-.l 1740 Yspace=.l 1750 Xorg»X_gdu_min 1760 Yorg-0 1770 Xmaj=l 1780 Ymaj-1 1790 Majsize-3 1800 CALL Plotpara 1810 ! 1820! INPUT "Window parameters,X_gdu_min,X_gdu_max,Y_gdu_min,Y_gdu_max 1830 WINDOW X_gdu_min,X_gdu_max,Y_gdu_min,Y_gdu_max 1840 !INPUT "AXES parameters",Xspace,Yspace,Xorg,Yorg,XmaJ,Ymej,Majsize 1850 AXES Xspace,Yspace,Xorg,Yorg,Xmaj,Ymaj,Majsize 1860 FRAME 1870 Northeast-0 ! \ 1880 Northwest«0 ! > Figure what to do for case 4. 1890 Cross»l I / 1900 FOR 1-1 TO Imax-1 19)0 FOR J=l TO Jmax-1 1920 Big-MAX(Sfc(I,J),Sfc(I,J+l ),Sfc(1 + 1,J),Sfc<1 + 1,J + l ) ) 1930 Small-MIN(Sfc(I,J ),Sfc(I,J+l ),Sfc(1 + 1,J ),Sfc(1+1,J+l )) 1940 Linecount-1 1950 FOR Cont-Min TO Max STEP Interval 1960 IF Cont>Small AND Cont<Big THEN 1970 LINE TYPE 1 1980 IF ABStCont Xl.E-3 THEN 1990 PEN 3 2000 ELSE 2010 PEN 1 2020 END IF 2030 Linecount"Linecount+l 2040 Top-Cont>MIN(Sfc(I,J ),Sfc<I,J+l)) AND Cont<MAX(Sfc(I,J>,Sfc(I,J+l) ) 2050 Bottom-Cont>MIN(Sfc(I + l , J ) , S f c ( I + l,J+ l ) ) AND Cont<MAX(Sfc(1 + 1,J>,S fc(I+l,J+l)) 2060 Left-Cont>MIN(Sfc(I,J),Sfc(I + l , J ) ) AND Cont<MAX(Sfc(I,J ),Sfc(1 + 1,J )) 2070 Right-Cont>MIN(Sfc(I,J+l ),Sfc<I + 1,J + 1 ) > AND Cont<MAX<Sfc(I,J+l),Sf c(I + l,J+l )> 2080 Ispace-ABS( YvaK I )-YvaK 1 + 1 )) 109 2090 Jspace-ABS(Xval( J >-Xval( J+l ) > 2100 SELECT Top+Bottom+Left+Right 2110 CASE 0 « Do nothing 2120 CASE 2 ! Two intersections, so draw one l i n e 2130 DISP " P l o t t i n g contour l i n e ",Cont 2140 IF Top THEN 2150 Jtop-XvaKJ )+<Cont-Sfc(I,J ))/(Sfc(I,J+l )-Sfc(I,J > >•Jspace 21B0 IF Bottom THEN I Top and Bottom 2170 Jbottom-XvaKJ >+(Cont-Sfc(1 + 1,J ))/(Sfc<1 + 1,J+l )-Sfc(1 + 1,J) )•Jspace 2180 MOVE Jtop+Xshift,Yvel(I> 2190 DRAW Jbottom+Xshi ft,Yval(1 + 1 ) 2200 ELSE ! <not Bottom) 2210 IF Left THEN ! Top and Left 2220 I l e f t - Y v a K I )+(Cont-Sfc(I,J ) )/(Sfc(1 + 1,J )-SfctI,J)>*Ispa ce 2230 MOVE Jtop+Xshift,YvaKI> 2240 DRAW Xval(J >+Xshift,Ileft 2250 ELSE • Not l e f t , therefore Top end Right 2280 Iright-YvaK I)+(Cont-Sfc(I,J + l ) ) / ( S f c ( 1 + 1,J+l )-Sfc(I,J+l ) )*Ispace 2270 MOVE Jtop+Xshift,YvaKI) 2280 DRAW XvaKJ+l>+Xshift,Iright 2290 END IF ! < i f l e f t ) 2300 END IF ! <if bottom) 2310 ELSE ! (not Top) 2320 IF Bottom THEN 2330 Jbottom-XvaKJ >+(Cont-Sfc(1 + 1,J ) )/(Sfc(1 + 1,J+l )-Sfc(1 + 1,J) )•Jspace 2340 IF Left THEN ! Bottom and Left 2350 Ileft-YvaKI>+(Cont-Sfc(I,J > )/<Sfc(1+1,J )-Sfc<I,J ) )«Ispa ce 2360 MOVE XvaK J >+Xshif t, I l e f t 2370 DRAW Jbottom+Xshift,Yval(1+1 ) 2380 ELSE ! Not l e f t , therefore Bottom end Right 2390 Iright-YvaKI )+<Cont-Sfc(I,J+l))/(Sfc<1 + 1,J+l )-Sfc(I,J+l ) >*Ispace 2400 MOVE Jbottom+Xshift,YvaK1+1> 2410 DRAW XvaKJ+l>+Xshift,Iright 2420 END IF ! ( i f l e f t ) 2430 ELSE ! Not Bottom, therefore Left and Right 2440 I l e f t - Y v a K I )+(Cont-Sfc(I,J )>/(Sfc(1+1, J )-Sfc(I,J >)*Ispace 2450 Iright-YvaKI)+(Cont-Sfc<I,J+l ) )/(Sfc(I+l.J+l )-Sfc(I,J + l ) ) •Ispace 2460 MOVE XvaK J )+Xsh j f t, I lef t 2470 DRAW XvaKJ + l )+Xshift,Iright 2480 END IF ! ( i f bottom) 2490 END IF • ( i f top) 2500 CASE 4 ! Four intersections 2510 DISP "P l o t t i n g contour l i n e ".Cont 2520 Jtop-XvaK J )+(Cont-Sfc(I,J > )/<Sfc(I,J+l>-Sfc(I,J))•Jspace 2530 Jbottom-XvaKJ>+(Cont-Sfc(1 + 1,J ))/(Sfc(I + l.J+l )-Sfc(1 + 1,J > >*Js pace 2540 Ileft-YvaKI)+(Cont-Sfc(I,J ))/(Sfc(1+1,J )-Sfc(I,J >)•!space n o Iright-YvaKI H(Cont-Sfc<I,J+l >>/<Sfc<1+1,J+l >-Sfc(I,J+l >HIsp ace 2560 2570 2560 2590 2600 2610 2620 2630 2640 2650 2660 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 IF Northeast THEN MOVE XvaK J H X s h i f t , I l e f t DRAW Jtop+Xshift,YvaKI) MOVE Jbottom+Xshift,YvaK1+1) DRAW XvaKJ + l )+Xshift,Iright END IF ! < i f northeast) IF Northwest THEN MOVE XvaK J HXshi f t , I l e f t DRAW Jbottom+Xshift,YvaKI + 1 ) MOVE Jtop+Xshift,YvaKI) DRAW XvaK J+l HXshi f t , Ir ight END IF ! ( i f northwest) IF Cross THEN MOVE XvaK J HXshi f t , I l e f t DRAW XvaK J+l HXshif t, Iright MOVE Jtop+Xshift,YvaKI) DRAW Jbottom+Xshift,YvaK1+1> END IF ! ( i f cross) END SELECT END IF NEXT Cont 2770 NEXT J 2780 NEXT I 2790 End: !CALL Pauset1> 2800 SUBEND 2810 SUB Plotpara 2820 OPTION BASE 1 2830 COM REAL Datavalue?150,150>.Conmin.Conmax.Constep,INTEGER Ndatal,Ndata2 2840 COM Lineltf50),Unitl$[30],Line2St501,Unit2$[301 2850 COM Title$C80],Sample$[80],Xtitle$[50J,Ytitle$[S0],Xunit$[30],Yunit$[30 2860 COM D$[11],U1,U2,D1,D2 2870 PEN 1 2880 P-RATI0/(25/18) 2890 S-15 2900 VIEWPORT 0,100»RATIO,100»(1-P),100 I SET UP THE SCREEN FOR OUTPUT 2910 WINDOW 0,25,0,18 I ASSUME 180mm X 250mm PAPER 2920 LORG 1 2930 LDIR 0 2940 MOVE 2,17 2950 CSIZE 4 2960 LABEL USING "*,K";Title$ ! OUTPUT TITLE 2970 CSIZE 3 2980 MOVE 2,16.25 2990 LABEL " 16 16 15 3" 3000 MOVE 2,16 3010 IMAGE "Contour: Min- -4x10 , Max- 10 •, Step- 2x10 charges/cm" 3020 LABEL USING 3010 3030 MOVE 2,15.25 3040 LABEL " 8 . 2 " 3050 MOVE 2,15 3060 ! LABEL Samples ! OUTPUT THE DATE 111 3070 ! LABEL "GaAs Substrate. Gate length - 1.0 um. S - 5x10 Neutons/m " 3080 LABEL "6aAs Substrate. 6ate length - 0.5 um. S - 5x10 Neuitons/m " 30SC ! LABEL "GaAs Substrate. Gate length - 0.2 um. S - 5x10 Neuitons/m * 3100 MOVE 2,14.75 3110 LABEL " o" 3120 IF Ul-1 THEN 3130 ! LABEL LinelS&" "&UAL$(D1>&" "&UnitlS,IOUTPUT LINE1 IF ANY 3140 ! LABEL "Film type i s SiO . Film thickness - 1.0 um" 3150 ! LABEL "Film type i s Si N . Film thickness - 1.0 um" 3160 LABEL "Film thickness - 0.2 um" 3170 MOVE 2,13.85 3180 ! LABEL " 2" 3190 ! LABEL " 3 4" 3200 END IF 3210 IF U2-1 THEN 3220 ! LABEL Line2$&" "&VAL$(D2>&" "&Unit2$ I OUTPUT LINE2 IF ANY 3230 END IF 3240 VIEWPORT 100»RATIO*l/25,100»RATIO»23/25,100*P*3/18+100»<1-P >,100«P»13.5 /18+100*(1-P) 3250 SUBEND 112 10 REM 20 REM 30 REM program name : ECQen 40 REM 50 REM This program generates a matrix of p o l a r i z a t i o n charges 60 REM using the edge concentrated method and stores the data 70 REM in a user s p e c i f i e d f i l e . 80 REM 90 REM 100 OPTION BASE 1 110 COM REAL Datavalue(150,150>,Conmin,Conmax,Constep,INTEGER Ndatal,Ndata2 120 COM Linel$[50],Unitl*[301,Line2$[50],Unit2$[301 130 COM TitleS[801,Sample$[80],Xtitle$C50],Ytitle$[50],Xunit$[30],Yunit$[30] 140 COM D$[11I,U1,U2,D1,D2 150 REAL Xmax,Xmin,Ymax,Ymin,Logx,Logy,Zdata(150,150),Zmin,Zmax 160 INTE6ER Xauto.Yauto 170 DIM Msus$(2)Cll] 180 Msus$(l>«-=HP9133,702" 190 Msus$(2)-":HP9133,700" 200 Ti t l e $ = " P o l a r i z a t i o n Charge Density. (ECM)" 210 Sample$-"6aAs Substrate." 220 Y t i t l e S - " " 230 X t i t l e S - " " 240 Xunit$="" 250 YunitS-"" 260 Linel$="Film stress: 5.0 E+14 Newton/cm"2." 270 Line2$="" 280 U n i t l S - " " 290 Unit2$="" 300 Ul-1 310 Chanel_dep-.5 !( defaults to .5 um> 320 INPUT "Input gatelength in um ?",6atelength 330 INPUT "Input step size in um ?",Chanel_step 340 Mateen; ! using the eqation i n Asbeck's paper 350 DISP "GEN MAT" 360 U-.23 370 B-<2+U)/<4+U> 380 Row_count»l 390 FOR Zl-l.E-20 TO Chanel_dep STEP Chanel_step I Z s p e c i f i e d in um 400 Row_count-Row_count+l 410 Z-Z1M.E-4 ! change Z to cm 420 Column_count«l 430 FOR X-l.E-20 TO Gatelength STEP Chanel_step 440 Column_count»Column_count+l 450 X2=(-l»Gatelength+X>»1.E-4 ! specify X2 in cm 460 Xl»X«l.E-4 ! specify XI in cm 470 Rlsq-XK2+Z A2 480 R2sq=X2*2+Z"2 490 A1-DR0UND((X1»Z»(XI"2-B«Z"2> >/Rlsq"3,5 ) 500 A2«DR0UND((X2«Z»(X2*2-B»Z A2 ) )/R2sq'3,5 ) 510 Datavalue(Row_count,Column_count )-Al-A2 520 Datavalue(1,Column_count>-X ! f i l l i n row 1 with x values 530 NEXT X 540 Datavalue(Row_count,1 )«Z1 ! f i l l in column 1 with z values 550 Ndatal-Column_count 5B0 PRINT "z-",Z,"Ndata2,ndatal-",Row_count,Ndatal 570 NEXT Zl 580 Ndata2»Row_count 590 Sav: Iseve data in t i o f i l e B00 Filelength-INT(Ndata2*Ndatal«8.0/256.0>+6 610 INPUT "Save into which f i l e ( <-9 Characters)?" , F iIS 620 INPUT "onto which device (1) F l e x i b l e , (2) Winchester",D 630 DISP "Saving Data" 640 ON ERROR 60T0 Err_hand 650 CREATE BOAT "G"°.FilS&Msus$<D ),Filelength 660 ASSI6N PFile TO "6"8,Fil$&MsusS(D > 670 OUTPUT 8 F i l e ; T i t l e $ , D $ 680 OUTPUT BFile;Sample* 690 OUTPUT 8F i l e ; X t i t l e S , X u n i t S 700 OUTPUT SF i l e ; Y t i t l e S , Y u n i t S 710 OUTPUT BFile;Xauto,Xmin,Xmax,Yauto,Ymin,Ymax,Ndatal,Ndata2 720 OUTPUT e F i l e ; D l , U l , L i n e l $ , U n i t l S 730 OUTPUT eFile;D2,U2,Line2$,Unit2$ 740 REDIM Zdata(Ndata2,Ndatal) 750 FOR Irow-1 TO Ndata2 760 FOR Jcol-1 TO Ndatal 770 Zdata(Irow,Jcol)-Datevalue<Irow,Jcol) 780 NEXT Jcol 790 NEXT Irow 800 OUTPUT §File;Zdata(«) 810 OUTPUT eFile;Logx,Logy 820 ASSIGN GFile TO • 830 GOTO F i n 840 Err_hand= ! error handling 850 SELECT ERRN 860 CASE 53 870 PRINT "Improper f i l e name.";CHR$(129)&Fi1$&CHR$<128> 880 BEEP 890 CASE 54 900 PRINT " f i l e already e x i s t s . " 910 BEEP 920 CASE 83 930 PRINT CHRS( 129 )"."Storage unit i s write protected"8.CHR$( 128 ) 940 BEEP 950 CASE ELSE 960 PRINT "error--",ERRN 970 BEEP 980 END SELECT 990 GOTO Sav 1000 Fin:DISP "program completed" 1010 END 

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