Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios Chpter rolem Solutios Sketch Sketch p-chel JE Silico 9 4 e 0 0 5 0 0 4 7 ( ) 8850 579 ow 8 500 0059 l 0 5 0 0884 so 579 0884 49 / + h e (i), 0 h 05 0 4 9 0 0 4 7 8850 0884 + h 05 0 4 0 40 884 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 4 050 0 4 ( ) 8850 58 ow 8 500 0059 l 6 8 0 5 so 58 5 8 h + e (i), 0 h 05 0 4 / 9 0 0 4 8850 5 + h 05 0 4 0 480 5 which yiels h 0 µ m / (ii), 5 h 00 µ m (iii), 5 h 0096 µ m which implies o ueplete reio / 99
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 5 e 9 4 0 0 50 80 4 7 ( ) 8850 55 / h e so 4 4 0 0 0 50 4 7 ( ) 8850 9 0 80 0 0 90 8 0 which yiels 556 ow 8 080 0059 l 0 5 0 0896 0897 556 466 6 GAs: e h 9 4 0 0 50 80 8850 8 / e 4 / 0 0 0 50 4 4 4 ( ) 8850 9 0 80 which c e writte s 0 0 90 80 497 ow 8 080 0059 l 6 8 0 6 497 6 497 6 7 e 9 4 0 0 0 0 4 ( ) 8850 86 8 500 0059 l 6 8 0 5 86 5 05 (i) / + h e h 0 0 4 4 ( ) ( ) 8850 5 9 0 0 / / 00
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios which yiels h 4450 6 cm (ii) h 0 0 4 which yiels 4 ( ) 8850 ( 5 + ) 9 0 0 h 7 0 6 cm which implies o ueplete reio 8 -chel JE Silico / 9 4 e 0 0 5 0 4 0 4 7 ( ) 8850 79 ow 8 5040 0059 l 0 5 0 089 089 79 90 h h 05 0 4 / + e 4 7 885 0 0 89 + 9 0 40 c h c hc h h 05 0 4 0 0 089 + (i) 0,, h 00 µ m (ii),, h 0044 µ m / / (iii),, h 0005 µ m which implies o ueplete reio 9 8 50 40 ( 0059 ) l 6 8 0 59 / + h e D h 05 0 4 / 4 ( ) + 8850 59 9 0 40 We wt h 005 0 4 cm, 4 4 0 050 0 50 60 0 59 + 0, we i 5, we i 0 KJ 05 µ e W 6 9 000 0 0 67 885 0 0 e 4 4 4 4000 0 50 4 00 ma / 0
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios Also 9 4 0 0 50 0 7 8850 9 ( 0059) l 4 9 0 0 0 5 0 0874 ow ( ) 9 0874 + ( ) 06 + 0874 9 06 (i) 0 ( ) 06 (ii) 065 4 ( ) 0795 (iii) 05 ( ) 05 (iv) 0795 4 ( ) 065 ( ) 0 0874 K J H G K J H 9 K KJ 0874 9 (i) 0 058mA (ii) 065 ( ) 040 ma (iii) 05 ( ) 006 ma (iv) 0795 ( ) 0045 ma / K J G where 0 0 G 0 0 9 G 0 / 0-065 -05-0795 -06 045 0590 077 0945 0 -chel JE GAs e W G µ 05 07 06 0 0 9 4 4 0 ( 8000) 0 0 0 0 5 0 00 G 690 S ( ) e 4 9 4 0 0 50 0 9 8850 4 0
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios We i 8 50 0 ( 0059 ) l 6 8 0 4 4 9 05 We the oti ( ) 9 4 0 5 + 0 ( ) 05 075 ( ) 075 ( ) where K J H G K J µ e W 6 9 4 6 885 0 4 4 00 0 50 4 00 8000 0 0 5 ma 5 4 9 H K 075 4 9 0 00504mA 00mA KJ ( ma ) 0 ma, 9, 0874 he mimum trscouctce occurs whe 0 H G 0 0874 ( m) 9 9 054 W 400 µ m, 054 ( m) 4000 4 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 095 0 KJ 48 m 0
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 5 -chel ESE GAs e 9 4 0 0 50 5 0 ( ) 8850 59 ow φ B φ where 4 7 C φ t K J 47 0 H G l 0059 l K J 5 0 φ 0089 0 90 0 089 0 8 0 8 59 78 < 0 -chel evice, the evice is epletio moe ESE -chel ESE GAs We wt +00 φ φ B so e C 00 089 l t K J which c e writte s 470 7 ( 0059 ) l H G K J 9 4 0 05 0 + 089 00 4 8850 7 470 7 ( 0059 ) l H G K J + 845 0 079 By tril err 8 0 5 cm At 400 K, 400 ( 400) ( 00) C C H 00 K 47 0 7 ( 54 ) / 400 7407 cm C Also 400 t 0059 H K 0 045 00 7 740 0 89 0 045 l 5 8 0 845 0 8 0 which ecomes +005 H G K J 7 5 7 / + h e where φ B φ ow 7 φ 47 0 H G 0059 l K J 0058 50 0 80 0 058 0 74 05, h 08 0 4 4 + 9 0 50 0 8980 0 4 + 8850 074 05 h 080 0 4 / / 04
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios ( ) h ( µ m) 0 5 8 φ φ We wt 0 φ + φ B B 07 060 0545 040 Device : 0 cm 7 φ 47 0 H G 0059 l K J 007 0 0 89 0 07 0 887 ow / 4 9 0 0 e e 099 µ m 8 85 0 0 887 Device : 0 7 cm 7 φ 47 0 H G 0059 l K J 00 7 0 0 89 0 0 0 8784 ow / 4 9 7 0 0 e 8 85 0 0 8784 0065 µ m 9 φ φ We wt 05, so B / / φ 0 5 0 85 ow φ 470 H G 7 0059 l K J e 9 4 0 05 0 4 ( ) 8850 4 0 7 470 7 0 5 0 85 ( 0 059) l H G K J By tril err, we i 545 0 5 cm 40 7 0 -chel ESE silico ol cotct, φ B 08 We i 9 φ 8 0 H G 0059 l K J 006 0 φ φ 0 8 0 06 0 64 B With 0, 05 We i h 0075 0 4 / e 0075 0 4 4 ( 7 ) 8 85 0 ( 0 64 0 5) + 9 0 0 06 µ m ow e 064 / 05
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 9 4 064 0 06 0 0 4 7 ( ) 8850 We oti 009 ( ) ow ( ) 05 009 ( ) 058 -chel ESE - silico φ B φ 9 φ 8 0 H G 0059 l K J 088 0 so 080 088 06 ow e 9 4 0 0 40 0 7 8850 We i 0 6 47 47 ( 0 6 ( ) ) ( ) 0858 4 45, itiol o toms must e e e e 4 7 8850 ( 45 ) 9 4 0 0 40 64 0 cm which mes tht 64 0 0 4 0 cm Dos must e e 9 φ 8 0 H G 0059 l K J 07 64 0 0 80 0 7 0 68 We i 068 45 87 Also k 45 ( 0 68 ( ) ) ( ) 87 µ W 7800 8 850 00 4 4 0 00 0 4 4 k ma/ ( ) So 5 05 0 r ( ) 006 0 ( ) 0 k 06
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 5 5 0 06 r ( ) 904 µ A 5 0 ( ) 6 µ A k m 75 0 k ( 0 50 0 5) which ives µ W k 5 0 A/ We oti 5 0 () 0 50 0 W 4 ( 8000)( ) 8 850 W 6 4 µ m 4 4 k 04, D 5 0 04 05 065, ( ) 78 8 µ A 5 0 0 65 0 5 4 Computer plot 5 Computer plot ( ) 056 ma 6 r 090 / e 0, ( ) We i e 9 4 0 0 40 0 4 7 ( ) 8850 7 9 0 0 0059 l 0 5 0 090 ( ) 7 090 8 4 ( 7 ) ( ) 8 85 0 5 8 9 0 0 007 µ m ow 090 09 00 so 4 007 0 00 ( ) 00 ( ) 54 µ m / 07
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 () 5 75 0 5 50 75 0 So tht λ is erly costt 0 045 050 047 040 0 0 8 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 8 5040 0 5 0 4 7 ( ) 8850 ( 089 + ) 9 0 40 h 006 µ m We the i ( ) e v h W 9 7 0 40 0 0 50 0 06 ( ) 7 ma / 0 0 0 () 0, we hve ow µ e W 6 4 4 H G K J H G K J 08
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 9 000 0 40 Also 4 4 4 00 0 50 4 0 67 885 0 4 e ma 9 4 0 0 50 40 4 7 ( ) 8850 77 4 089 089 H 77 KH G 77 ( ) 908 ma KJ H K 908 8 ma velocity urtio occurs, the the reltio ( ) oes ot pply 0 7 v µ Ε ( 8000) 50 40 cm s / 4 t v 0 40 7 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 8850 089 9 0 4 0 h 047 µ m ( ) e v h W 9 7 0 40 0 0 50 0 47 0 0 0 4 4 ( ) 486 ma velocity urtio i ot occur, the rom the previous prolem, we woul hve v µ Ε 000 0 0 4 7 / 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 8 500 0059 l 0 5 0 0884 e 09
Semicouct hysics Devices: Bsic riciples, r eitio Chpter Solutios ul rolem Solutios 9 4 0 0 0 0 7 ( ) 8850 09 0 884 09 ow + e 4 / ( ) ( ) 7 8 85 0 0 884 4 0 0 09 + / 4 + 9 0 0 / 0, 00 µ m, 065 µ m 5 055 µ m he epletio reio volume is ol W + W () H K 4 4 40 4 0 0 K J00 4 4 + 0 60 0 0 8 080 80 ol + 0 ol 0 cm ol 74 0 cm 5 ol 080 cm he eertio curret is 9 0 0 50 i e ol ol DG K J 8 τ 50 4 0 ol DG 0 pa DG 09 04 pa DG 5 050 pa DG he iel trscouctce 0 is G where e W G µ G 504 We i KJ 9 0 ( 4500) 70 4 5 0 50 4 00 4 e 9 4 0 0 0 70 4 ( ) 8850 45 7 φ 47 0 H G 0059 l K J 0049 7 0 φ φ 0 89 0 049 0 84 B 084 504 45 KJ 8 With source resistce m m m + r + r m s m m s m 080 8 r m + s 0
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 0 0 50 so 9 88 7 0 4500 70 4 4 4 4 0 0 50 067 µ m 4 m π CG where W C G 8 850 50 5 0 4 0 0 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 4 5 0 t 5 0 s t 7 0 he totl time costt is τ 5 0 + 8 0 0 s πτ π 0 976 GHz 4 4 4 π π 5 costt molity eµ π 0 ( 5500) 0 0 50 4 4 π( ) 885 00 755 GHz Sturtio velocity moel: v π Assumi v 0 7 cm/ s, we i 7 0 4 π0 5 9 GHz 6 where o 9 7 4 EC φ B e e 9 8 8 0 0 500 ( ) 8 850 7 o 0 89 0 4 7 07 o S o e ( + ) 0, we hve 4 ( ) 8 85 0 S 0 ( 50 + 80) 0 4 9 8 5 0 cm S ( 07)
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 8 850 0 S 50 8 50 + 80 0 cm 50 W mm At 0, we oti ( ) D v o S W ( + ) 4 ( ) 8 850 7 ( 07 ) 0 8 ( 50 + 80) 0 ( ) D 57 A/ cm 57 ma/ mm W 8 EC φ o B e We wt 0, so o 00 085 0 e 09 We c the write e 4 8 850 ( 0 9 ) We the oti 9 8 0 0 6 50 cm 5 A