b gb g L N b gb gb g Chapter 13 Problem Solutions Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter

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1 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios Chpter rolem Solutios Sketch Sketch p-chel JE Silico 9 4 e ( ) ow l so / + h e (i), 0 h h h 05 µ m (ii), 5 h 0065 µ m / / (iii), 5 h 0045 µ m which implies o ueplete reio 4 p-chel JE GAs ( ) ow l so h + e (i), 0 h / h which yiels h 0 µ m / (ii), 5 h 00 µ m (iii), 5 h 0096 µ m which implies o ueplete reio / 99

2 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 5 e ( ) / h e so ( ) which yiels 556 ow l GAs: e h / e 4 / ( ) which c e writte s ow l e ( ) l (i) / + h e h ( ) ( ) / / 00

3 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios which yiels h cm (ii) h which yiels 4 ( ) 8850 ( 5 + ) h cm which implies o ueplete reio 8 -chel JE Silico / 9 4 e ( ) ow l h h / + e c h c hc h h (i) 0,, h 00 µ m (ii),, h 0044 µ m / / (iii),, h 0005 µ m which implies o ueplete reio ( 0059 ) l / + h e D h / 4 ( ) We wt h cm, , we i 5, we i 0 KJ 05 µ e W e ma / 0

4 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios Also ( 0059) l ow ( ) ( ) (i) 0 ( ) 06 (ii) ( ) 0795 (iii) 05 ( ) 05 (iv) ( ) 065 ( ) K J H G K J H 9 K KJ (i) 0 058mA (ii) 065 ( ) 040 ma (iii) 05 ( ) 006 ma (iv) 0795 ( ) 0045 ma / K J G where 0 0 G G 0 / chel JE GAs e W G µ ( 8000) G 690 S ( ) e

5 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios We i ( 0059 ) l We the oti ( ) ( ) ( ) 075 ( ) where K J H G K J µ e W ma H K mA 00mA KJ ( ma ) 0 ma, 9, 0874 he mimum trscouctce occurs whe 0 H G ( m) W 400 µ m, 054 ( m) cm / cm / mm KJ 4 he mimum trscouctce occurs 0, so we hve ( m) H G KJ KJ G We ou G 69, 4, 9 ( m) H G 4 69 K J 9 ( m ) 095 his is chel leth o 0 µ m the chel leth is reuce to µ m, the H K m KJ 48 m 0

6 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 5 -chel ESE GAs e ( ) ow φ B φ where 4 7 C φ t K J 47 0 H G l 0059 l K J 5 0 φ < 0 -chel evice, the evice is epletio moe ESE -chel ESE GAs We wt +00 φ φ B so e C l t K J which c e writte s ( 0059 ) l H G K J ( 0059 ) l H G K J By tril err cm At 400 K, 400 ( 400) ( 00) C C H 00 K ( 54 ) / cm C Also 400 t 0059 H K l which ecomes +005 H G K J / + h e where φ B φ ow 7 φ 47 0 H G 0059 l K J , h h / / 04

7 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios ( ) h ( µ m) φ φ We wt 0 φ + φ B B Device : 0 cm 7 φ 47 0 H G 0059 l K J ow / e e 099 µ m Device : 0 7 cm 7 φ 47 0 H G 0059 l K J ow / e µ m 9 φ φ We wt 05, so B / / φ ow φ 470 H G l K J e ( ) ( 0 059) l H G K J By tril err, we i cm chel ESE silico ol cotct, φ B 08 We i 9 φ 8 0 H G 0059 l K J φ φ B With 0, 05 We i h / e ( 7 ) ( ) µ m ow e 064 / 05

8 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios ( ) 8850 We oti 009 ( ) ow ( ) ( ) 058 -chel ESE - silico φ B φ 9 φ 8 0 H G 0059 l K J so ow e We i ( 0 6 ( ) ) ( ) , itiol o toms must e e e e ( 45 ) cm which mes tht cm Dos must e e 9 φ 8 0 H G 0059 l K J We i Also k 45 ( 0 68 ( ) ) ( ) 87 µ W k ma/ ( ) So r ( ) ( ) 0 k 06

9 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios r ( ) 904 µ A 5 0 ( ) 6 µ A k m 75 0 k ( ) which ives µ W k 5 0 A/ We oti 5 0 () W 4 ( 8000)( ) W 6 4 µ m 4 4 k 04, D , ( ) 78 8 µ A Computer plot 5 Computer plot ( ) 056 ma 6 r 090 / e 0, ( ) We i e ( ) l ( ) ( 7 ) ( ) µ m ow so ( ) 00 ( ) 54 µ m / 07

10 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 7 tht Assumi tht we re i the urtio reio, the ( ) ( ) We c write ( ) ( ) <<, the + tht / ( ) e / ( ) K J e ( ) e K J / ( ) K J e which c e writte s we write ( ) ( ) + λ the y compri equtios, we hve λ he prmeter is ot iepeet o Deie H K K J / cosier the uctio which is irectly proptiol to λ We i tht () So tht λ is erly costt Sturtio occurs whe Ε 0 4 / cm As irst pproimtio, let Ε Ε 0 0 tht h h ( 0059) 4 4 / + e l 089 0, we oti h ( ) 8850 ( ) h 006 µ m We the i ( ) e v h W ( ) 7 ma / () 0, we hve ow µ e W H G K J H G K J 08

11 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios Also e ma ( ) H 77 KH G 77 ( ) 908 ma KJ H K ma velocity urtio occurs, the the reltio ( ) oes ot pply 0 7 v µ Ε ( 8000) cm s / 4 t v t 5 ps Assume v 0 7 cm/ s 4 0 t 7 v 0 t 0 ps 9 µ m, the urtio will occur whe 4 4 Ε 0 0 We i / + h h e 089 0, we oti 4 / 7 ( ) ( + ) h h 047 µ m ( ) e v h W ( ) 486 ma velocity urtio i ot occur, the rom the previous prolem, we woul hve v µ Ε / 4 t v 0 0 t 0 ps 7 v 0 7 cm/ s, 4 0 t t ps 7 v 0 0 cm s he reverse-s curret is omite y the eertio curret We i l e 09

12 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios ( ) ow + e 4 / ( ) ( ) / / 0, 00 µ m, 065 µ m µ m he epletio reio volume is ol W + W () H K K J ol + 0 ol 0 cm ol 74 0 cm 5 ol 080 cm he eertio curret is i e ol ol DG K J 8 τ ol DG 0 pa DG pa DG pa DG he iel trscouctce 0 is G where e W G µ G 504 We i KJ 9 0 ( 4500) e ( ) φ 47 0 H G 0059 l K J φ φ B KJ 8 With source resistce m m m + r + r m s m m s m r m + s 0

13 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios which yiels r s 88 7 Ω ρ r s A σ A eµ so µ m 4 m π CG where W C G C 90 5 G We must use m, so we oti 8 0 ( 0 80) GHz 4 5 π9 0 τ C πτ 40 9 C τ C 8 0 s he chel trsit time is t 5 0 s t 7 0 he totl time costt is τ s πτ π GHz π π 5 costt molity eµ π 0 ( 5500) π( ) GHz Sturtio velocity moel: v π Assumi v 0 7 cm/ s, we i π0 5 9 GHz 6 where o EC φ B e e ( ) o o S o e ( + ) 0, we hve 4 ( ) S 0 ( ) cm S ( 07)

14 Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 7 W ( ) v D ( + ) We i v D s W W + H K 4 7 o s S cm 50 W mm At 0, we oti ( ) D v o S W ( + ) 4 ( ) ( 07 ) 0 8 ( ) 0 ( ) D 57 A/ cm 57 ma/ mm W 8 EC φ o B e We wt 0, so o e 09 We c the write e ( 0 9 ) We the oti cm 5 A

Topic 4 Fourier Series. Today

Topic 4 Fourier Series. Today Topic 4 Fourier Series Toy Wves with repetig uctios Sigl geertor Clssicl guitr Pio Ech istrumet is plyig sigle ote mile C 6Hz) st hrmoic hrmoic 3 r hrmoic 4 th hrmoic 6Hz 5Hz 783Hz 44Hz A sigle ote will