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Scilab Textbook Companion for
Solid State Electronic Devices
by B. G. Streetman And S. K. Banerjee
Created by
Priyanka Jain
B.Tech + M.Tech Dual Degree
Electrical Engineering
IIT Bombay
College Teacher
Nil
Cross-Checked by
May 20, 2016
(^1) Funded by a grant from the National Mission on Education through ICT,
http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the โTextbook Companion Projectโ section at the website http://scilab.in
Book Description
Title: Solid State Electronic Devices
Author: B. G. Streetman And S. K. Banerjee
Publisher: PHI Learning Pvt. Ltd., New Delhi
Edition: 6
Year: 2006
ISBN: 978-81-203-3020-
Contents
List of Figures
3.1 E k Rleationship........................ 11
4.1 decay of excess population for a carrier recombination.... 17 4.2 decay of excess population for a carrier recombination.... 18
Chapter 1
Crystal Properties and Growth
of Semiconductors
Scilab code Exa 1.1 Maximum packing fraction
1 a = 5; // l a t t i c e c o n s t a n t 2 b = 0.5* sqrt ( a ^2 + a ^2 + a ^2) ; // s e p a r a t i o n b e t w e e n n e a r e s t atoms 3 r = 0.5* b ; // r a d i u s o f e a c h atom 4 V = 4/3* %pi * r * r * r ; // Volume o f e a c h atom 5 n = 1+8*0.125; // number o f atoms p e r c u b e 6 pf = V *n /( a * a * a ) ; // p a c k i n g f r a c t i o n 7 disp ( โ 1 ) โ ) 8 disp (a , โ l a t t i c e c o n s t a n t ( i n a r m s t r o n g )=โ ) 9 disp (r , โ r a d i u s o f atoms ( i n a r m s t r o n g ) =โ ) 10 disp ( pf , โmaximum p a c k i n g f r a c t i o n =โ )
Scilab code Exa 1.2 planes and directions
1 disp ( โ The p l a n e i l l u s t r a t e d i n F i g. 1 โ 5 h a s i n t e r c e p t s a t 2 a , 4b and l c a l o n g t h e t h r e e
2 k = 0.35; 3 l = 5000; // i n i t i a l l o a d o f S i i n grams 4 w =31; // a t o m i c w e i g h t o f P 5 d = 2.33; // d e n s i t y o f S i 6 i = n / k; // i n i t i a l c o n c e n t r a t i o n o f P i n melt , a s s u m i n g C( S )=kC ( L ) 7 V = l / d; // volume o f S i 8 N = i * V; // number o f P atoms 9 W = N * w /(6.02*10^23) 10 disp ( โ 4. a ) โ ) 11 disp (n , โ d e s i r e d d e n s i t y o f P atoms ( p e r c u b i c c e n t i m e t e r )=โ ) 12 disp (i , โ i n i t i a l c o n c e n t r a t i o n o f P i n m e l t ( i n p e r c u b i c cm )=โ ) 13 disp ( โ 4. b ) โ ) 14 disp (V , โ Volume o f S i ( i n c u b i c cm ) =โ ) 15 disp (N , โ number o f P atoms =โ ) 16 disp (W , โ w e i g h t o f p h o s p h o r u s t o be added ( i n grams ) = โ )
Chapter 2
Atoms and Electrons
Scilab code Exa 2.1 expectation of momentum
1 // j=complex ( 0 , 1 ) ; 2 // p s i = Aโ exp ( j โ k โ x ) ; 3 disp ( โ px = h c r o s s โ k ( x ) โ ) ; 4 disp ( โ I f we t r y t o e v a l u a t e t h e s e i n t e g r a l s d i r e c t l y , we run i n t o t h e p r o b l e m t h a t b o t h n u m e r a t o r and d e n o m i n a t o r t e n d t o i n f i n i t y , b e c a u s e an i d e a l p l a n e wave i s s t r i c t l y n o t a n o r m a l i z a b l e wave f u n c t i o n. The t r i c k t o u s e i s t o c h o o s e t h e l i m i t s o f i n t e g r a t i o n from , say , โL/2 t o +L/2 i n a r e g i o n o f l e n g t h L. The f a c t o r L c a n c e l s o u t i n t h e n u m e r a t o r and d e n o m i n a t o r. Then we can c o n s i d e r L a p p r o a c h e s i n f i n i t y. For wave f u n c t i o n s t h a t a r e n o r m a l i z a b l e , s u c h a m a t h e m a t i c a l t r i c k d o e s n o t have t o be u s e d. โ )
Figure 3.1: E k Rleationship
1 // p = mโ v 2 // p = hโ k ; // e l e c t r o n momentum , where h i s c o n s t a n t 3 //E = 0. 5 โ pโp/m 4 //E = 0. 5 โ hโ k โ k /m; // e l e c t r o n e n e r g y 5 k = -10:0.01:10; // l i m i t s on wave v e c t o r k 6 E = k ^2; // E i s p r o p o r t i o n a l t o s q u a r e o f wave v e c t o r 7 plot (k ,E )
Scilab code Exa 3.3 radius of electron orbit
1 n = 1; 2 epsilonr = 11.8; // r e l a t i v e d i e l e c t r i c c o n s t a n t f o r s i l i c o n 3 epsilon = 8.8510^ -12; // d i e l e c t r i c c o n s t a n t 4 m = 9.1110^ -31; // mass o f e l e c t r o n 5 mn = 0.26* m ; // f o r s i l i c o n 6 h = 6.6310^ -34; 7 q = 1.610^ -19; // e l e c t r o n i c c h a r g e 8 r = 10^10*( epsilonr * epsilon * h * h ) /( mn * q * q * %pi ) ; // r a d i u s i n a r m s t r o n g 9 disp (r , โ r a d i u s o f e l e c t r o n o r b i t a r o un d d o n o r ( i n a r m s t r o n g ) =โ ) 10 disp ( โ T h i s i s more t h a n 4 l a t t i c e s p a c i n g s a = 5. 4 3 a r m s t r o n g. โ )
Scilab code Exa 3.4 density of states effective mass
1 m = 9.1110^ -31; // mass o f e l e c t r o n 2 ml = 0.98 m ; 3 ms = 0.19* m ; 4 mn = 6^(2/3) *( ml * ms * ms ) ^(1/3) ; // d e n s i t y o f s t a t e s e f f e c t i v e mass c a l c u l a t i o n
Scilab code Exa 3.7 current and resistance in a Si bar
1 un = 700; 2 q = 1.6*10^ -19; 3 n0 = 10^17; 4 L = 0.1; 5 A = 10^ -6; 6 V = 10; 7 sigma = q * un * n0 ; 8 rho = 1/ sigma ; 9 R = rho *L / A ; 10 I = V / R ; 11 disp ( sigma , โ C o n d u c t i v i t y ( i n p e r ohmโcm )=โ ) 12 disp ( rho , โ r e s i s t i v i t y ( i n ohmโcm )=โ ) 13 disp (R , โ r e s i s t a n c e ( i n ohm )=โ ) 14 disp (I , โ c u r r e n t ( i n ampere )=โ )
Scilab code Exa 3.8 concentration and mobility of majority carrier
1 w = 0.01; 2 w1 = w 10^ - 3 t = 10^ -3; 4 L = 0.5; 5 B = 1010^ -5; 6 I = 10^ -3; 7 Vab = -2 10^ -3; 8 Vcd = 0.1; 9 q = 1.610^ -19; 10 q1 = q *10^ - 11 n0 = I *B /( q1 * - Vab ) ; 12 rho = ( Vcd /I ) /( L / w1 ) ; 13 u = 1/( rho * q * n0 ) ; 14 disp ( n0 , โ e l e c t r o n c o n c e n t r a t i o n ( i n p e r c u b i c c e n t i m e t e r )=โ ) 15 disp ( rho , โ r e s i s i t i v i t y ( i n ohmโcm )=โ )
16 disp (u , โ m o b i l i t y ( i n s q u a r e cm p e r v o l t โs e c )=โ )
Figure 4.1: decay of excess population for a carrier recombination
Scilab code Exa 4.2 decay of excess population for a carrier recombination
1 p0 = 10^15; 2 ni = 10^6; 3 n0 = ni ^2/ p0 ; 4 disp ( n0 , โ M i n o r i t y e l e c t r o n c o n c e n t r a t i o n ( i n p e r c u b i c c e n t i m e t e r )=โ ) 5 dn = 10^14; 6 dp = 10^14; 7 tn = 10; // i n n a n o s e c o n d s 8 tp = tn ; 9 t = 0:10:50; 10 del_n = dn * exp (- t / tn ) ; 11 del_p = dp * exp (- t / tp ) ; 12 p = p0 + del_p ; 13 n = del_n ; // s i n c e n0 i s n e g l i g i b l e 14 subplot (121) ; 15 plot (t , log ( p ) ) ; 16 plot (t , log ( n ) ) ; 17 subplot (122) ;
Figure 4.2: decay of excess population for a carrier recombination
18 plot (t ,p ) ; 19 plot (t ,n ) ;
Scilab code Exa 4.3 steady state carrier generation
1 n0 = 10^14; 2 ni = 1.5*10^10; 3 Tn = 2 *10^ -6; 4 Tp = 2 10^ -6; 5 p = 210^13; 6 p0 = ni ^2/ n0 ; 7 disp ( p0 , โ h o l e c o n c e n t r a t i o n ( p e r c u b i c c e n t i m e t e r )=โ )
Scilab code Exa 4.4 electron quasi fermi level position and carrier concen- tration
