Lecture Notes #9: Class #11

Transcription

1 Chem 40a Lecture Note #9: Cla # ecombiatio uder differet light iteity - Low level ijectio v High level ijectio

2 <eview> We looed at recombiatio/geeratio : We uually wor away from the equilibrium. o we wat to udertad -G roce yically we add more carrier o that > i! ecombiatio i domiat e E cb E E vb d d d r = = + =! " " (! f ) " N + '" f " N dt dt dt d d d r = = + =! " " f " N + '" (! f ) " N dt dt dt 3 4 b b By alyig equilibrium coditio: Pricile of detailed balace r = r = 0 (! f ) N = ' f N b,0! ' = b,0 f f

3 <eview> he we calcaulated! = ex[!( E! E ) / ] F! f " ' = ( ) = ex[!( E! E ) / ]= N ex[!( E! E ) / ] f f b,0 b,0 F C C f (! =N ex[!( E! E ) / ]) b,0 C C F ' doe't deed o the Fermi level ad oly deed o the tra eergy level Let =N ex[!( E! E ) / ] C =N ex[!( E! E ) / ] he, V ' = ' = By luggig i ' ad ', C V d r = =! " " (! f ) " N + " " f " N dt b d r = =! " " f " N + " " (! f ) " N dt b

4 <eview> For teady tate aumed cae, bul d d =! =! = dt dt Plug i our value for r recombiatio rate & r " " (! f ) " N! " " f " N = " " f " N! " " (! f ) " N b b N f cacel ad olve for f =! f = b " b + " + " b + " " + " " + " b " + " + " + " b b Now that we have f ad - f we ca ue them to calculate.

5 <eview> bul =! " " (! f ) " N + " " f " N bul d d =! =! dt dt = b N " " ( " + " )! " " ( " + " ) b b b " ( + ) + " ( + ) b b " " ( b " b! " ) bul = N " ( + ) + " ( + ) b b " = NC ex[!( EC! E ) / ] " NV ex[!( E! EV ) / ] = N " N " ex[!( E! E ) / ] = C V C V i So the recombiatio rate i bul, " " ( b " b! i ) bul = N " ( + ) + " ( + ) b b

6 Surface ecombiatio It tur out we ca write the ame equatio for the urface, but by modifyig all term to be urface related oe,!,! (! " i ) urface = N, S,! +, +,! +, ( ) ( ) N, S - -3 : differet from the bul. it i [cm ], ot [cm ],,,S, i ad are differet from the bul E i differet from E (bul) # i differet from (bul) # i the oly term that i the ame

7 Surface v Bul ecombiatio it " " ( b " b! i ) bul = N " ( + ) + " ( + ) b b 3 3 cm cm cm! 6! 3 cm 3 3 "! 3 [ ][ ] [ ][ ][ ] article # bul : = [ ] cm cm cm, ", " ( "! i ) urface = N, S, " +, +, " +, # urface ( ) ( ) 3 3 cm cm cm! 6! = cm 3 "! 3 [ ][ ] [ ][ ][ ] article : flux=[ ] cm cm cm

8 Surface v Bul ecombiatio For the bul recombiatio, # # ( b # b " i ) bul = N # ( + ) + # ( + ) Divide by $ = # # N bul b b N cm cm b # b " i # ( + ) + N # N # # ( + ) b b " 3 3 # :[ ]#[ / ] = / $ =! N # Similarly, where! i the lifetime of carrier N # =! bul b # b " i =! # ( + ) +! # ( + ) b b

9 Surface v Bul ecombiatio For the bul recombiatio,! = /! = N % N % What i a good value for! or!? 3 ecall / / = cm = cm % cm = " V Aume atom radiu of 3 &, # r = 0! th cm $ 5 Good aroximatio to ay " = " For low tra deity i the bul, let' ay 0 cm V ' cm ( = % cm = cm th 7 $ $ / 0 0 / 0 / -3 (!,b = = = m (About right for bul Si) $ % 0 0 But for the urface recombiatio, thi doe't wor the ame way

10 Bul ecombiatio: uder Low Level Ijectio For -tye bul, Low-level ijectio N D b,0 b,0 ( LLI ) = N bul ( LLI ) = N bul = "! =! " N " "[( D +! ) " (! + b,0 ) # i )] " " ( N + ) + " ( + ) D N " $ =! +!! D i b,0 [ N D N D b,0 b,0 i ] " ( N ) + " ( + ) " " N D! bul ( LLI ) = N " ( N ) + " (! + + ) If $ "! +!! + +! # D i b,0 b,0 D b,0 D b,0 i b,0 ( = = N % So N ad are caceled each othe D, the whole term go away. ( LLI ) = N! bul

11 Bul ecombiatio: uder Low Level Ijectio ( LLI ) = N! bul emember, rate=(rate cotat) " (cocetratio) We ca geeralize ad defie # S! for -tye where S, the recombiatio velocity i a rate cotat For low-level ijectio i the bul, Sbul ( LLI ) = N = for -tye $ %! %! = S! & = & = & % t % t %! %! & = S! ' & = S% t % t!! = ex(- ) = ex(- / ) 0 St 0 t $

12 Bul ecombiatio: uder High Level Ijectio For -tye bul, High-level ijectio! =!! =N! b,0 D b,0 " "[( N D +! ) " ( b,0 +! ) # i )] bul ( HLI ) = N " ( N +! + ) + " ( +! + ) " "! "! bul ( HLI ) = N " (! ) + " (! ) But! =! " bul ( HLI ) = N! + " Now Sbul ( HLI ) = N = + S bul ( HLI ) = D b,0 $ + $ + N N % he carrier with the loger life time determie the recombiatio velocigy

13 Bul ecombiatio: uder High Level Ijectio Fially, if S S bul bul ", the! "! #! ( HLI ) = = =! +!!! ( LLI ) = bul! bul hi reult how that Sbul ( HLI ) = Sbul ( LLI ) der low level ijectio, we oly have to wait for the hotogeerated hole, $ to relax. hi i becaue = N + $ % N. D he erturbed electro cocetratio i eetially zero. D But for high level ijectio, we have to wait for both electro( $ ) ad hole( $ ) to relax. hi will tae twice a log if! "!. (or ele it will tae! +! )