( ) L = D e. e e. Example:
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1 xapl: A Si p juctio diod av acoss sctioal aa of, a accpto coctatio of c -3 o t p-sid ad a doo coctatio of 0 6 c -3 o t -sid. T lif ti of ols i -gio is 47 s ad t lif ti of lctos i t p-gio is 5 s. T dift obilitis of lcto i p-gios ad ol i gio a 0 ad 440 c V - s -, spctivly. a.calculat t ioity diffusio lgts at 300K. b.wat is t cut w t is a fowad bias of 0.6V acoss diod at 300 K? a) L Dτ D D L L kt 0.06 V μ c s 0 ( ) kt 0.06V μ s ( 440 ).39 c ( )( c 5 0 ) 4 s. 0 c D τ s ( )( 9.39 c 47 0 ) 4 s.8 0 c D τ s 34
2 b) Wat is t cut w t is a fowad bias of 0.6V acoss diod at 300 K? J V J so xp kt J so AJ D L N d D L N a so i D A L N d D L N a i Fo V>>kT/, (V0.6 V, ad kt/0.06 V) so V xp kt so V xp kt 35
3 so D A L N D L N i d a 9.39c s 3.c s 0 3 ( 0.0c )(.6 0 C) ( 0 c ) (.8 0 c)( 0 c ) (. 0 c)( 5 0 c ) A so xp V kt V Axp 0.06V A 36
4 xapl: Cosid a pp Si BJT tat as t followig poptis. T dopig coctatios i itt, bas ad collcto a 0 8,0 6, 0 6 c -3. T itisic coctatio is 0 0 c -3 T widt of itt ad bas a μ ud t activ opatio. T ol dift obility i t bas is 400 c V - s - ad lcto dift obility i t itt is 00 c V - s -. T coss-sctiosctio of t dvic is 0.0, T ol lifti i t bas is 400s. Assu t itt as 00% itt fficicy. Calculat t CB cut tasf atio α ad cut gai β. Wat is t itt-basd voltag if t itt cut is A? D kt 0.06V μ s ( 400) 0.36 c T ioity cai tasit ti τ t acoss t bas. τ t W B /D 0 c/( 0.36 c s ).93 0 s T bas taspot facto is α τ t αtγ 9 τ s s
5 T cut gai β of t tasisto is β α α T itt cut is du to t ol diffusio sic t itt fficicy is, so p AD W o p 0 B V xp kt B so V xp kt 0 i ( 0 ) N d ( 0 ) p 0 (.6 0 C )( c )( 0.36 cs )( 0 c ) 4 ( 0 c ) c AD W.66 0 B 4 A B V kt l so B V 46
6 xapl A sola cll ud a illuiatio of 500W - as a sot cicuit cut sc of 50 A ad a op cicuit output voltag V oc of V, wat is t sot cicuit cut ad op cicuit voltag w t ligt itsity is doubld? Assu idality facto η.5. T -V caactistic ud illuiatio is giv V p o xp ηkt Fo op cicuit, 0 At RT, V >> ηkt V xp p o ηkt 0 V oc ηkt l p o 89
7 sc p K T sot cicuit cut is t potocut, so at doubl t itsity tis is sc sc 300 ( 50A)( ) A At giv tpatu, t cag i V oc is V oc ηktη p ηkt Voc l l p η.5, t w op cicuit is V oc ηkt V l oc (.5 )( ) l ( )
8 Capt 5: aolctoics- T quatu dots optical p poptyp Sigl lcto dvic 9
9 Picipl of t quatu dots O f lcto is i t disioal ifiit pottial box c b a ( ) a N a a b c ) ( Δ 8a Δ gy diffc is sall as a icass to acoscopic disios, a Δ 0 fo a copltly f lcto its gy is cotiuous a Δ 0, fo a copltly f lcto its gy is cotiuous
10 Diffc btw aopaticl ad quatu dots: Quatu dots: t siz of quatu is sall oug tat t gy diffc btw t coscutiv gy lvls ca b distiguisd, aly, t gy is disct ad ot cotiuous. Naopatilc: t siz of aopaticls is sall (aoscal) ad t gy diffc btw t coscutiv gy lvls caot b distiguisd, aly, t gy is cotiuous. Caactistic siz: Mtods fo calculatig t citical siz:.d Bogli wavlgt at Fi gy (tal).xcito adius (sicoducto)
11 a sould b copaabl to t D Bogli wavlgt of t lcto p p λ, F F λ 3 / 3 8 π F ( ) 3 / 3 π π λ F ( ) 3 π Fo Copp, , λ F 0.46, if t paticl siz is sall o copaabl to 0.46, it is calld quatu dots.
12 Si bulk sigl cystal, t ub of atos is vy lag, tfo t coductio bad ad valc bad a cotiuous Fo aoscal-siz, t ub of t atos is sigificatly ducd g T gis i coductio bad ad valc bad bco disct Dict-gap itbad tasitios i quatu dots fo t lvl valc bad to t lvl coductio bad ca occu fo icidt poto gis. ϖ g
13 g ϖ 8 R 8 8 R R g ϖ Fo ad Fo ad ϖ 8 8 g g R R ϖ, Rducd ass 96
14 xcito: tbad tasitio i sicoducto oally assud tat t pocss of absoptio (of a poto, tal gy, tc.)cat f lcto ad a f ol. ac of wic ca cotibut tib t to coductio. Aot kid of tasitio: aft t lcto tasitio, t tasitd lcto ad catd ol is boud togt by ti utual Coulob attactio, foig a quasi paticl (lcto ad ol as a wol) kow as a xcito. c Fi v CB VB 97
15 xcito is vy siila to t two-paticl ydog syst. T ass of ol is uc sall ta tat of poto. Tfo t xcito ca ov aoud t cystal. T ass ow is ducd ass: T pittivity is ε 0 ε istad of ε 0, Substitutig t ε 0 wit ε 0 ε ad wit, t bid gy of lcto to ol ad adius of goud stat a giv by 8ε ε ε 4 RY ε V 4 πε o 0ε ε ε a x a0 (0.53A) 4 98
16 quatu dots, xcito ffcts oft play a doiat ol i dtiig optical poptis sic t ol ad lcto a vy clos i quatu dots. T optical tasitio i quatu dots a usually associatd wit xcito ad a appoxiatio xpssio kow as t Bus quatio odl, t tasitio gy i spical dots:.8 g ϖ, g R R ε πε ϖ 99
17 bulk sicoductos, t xcito adius is giv by, 4πε o 0ε ε ε a x a0 (0.53A) 4 Fo quatu dots, t actual spaatio btw lcto ad ol is iflucd by t siz of t dot. tis cas, w will cosid a x to b t xcitatio Bo adius, wic is oft tak as t asu of quatu cofit i quatu dots. R>>a x, t t cofit ffcts will gally ot b vy ipotat R>a x, t t cofit is wak; R<a x, t t cofit gio is stog 00
18 xapl: Fo cadiu slid (CdS) paticl wit R.9. Giv g (bulk).74 V, 0.3 ad 0.45 ad ε 9.4, fo tasitio fo t coductio to valc baddg. a x 4πε 0 ε ε a ε o (0.53A) Stog cofit ffct Witout cosidig t xcito ffct, ϖ g 8R ϖ.09 V, λ 593 V, Yllow ligt 0
19 Wit cosidig t xcito ffct, Bus quatio π ϖ λ λ 580, g R.8 4πε ε R 8 0 Wll cosistt wit t xpital sults 0
20 Bull's-y. Rd quatu dots ijctd ito a liv ous ak t locatio of a tuo. X.H.Gao t.al. Scic, 300 (003)
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