EE415/515 Fundamentals of Semiconductor Devices Fall 2012

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Kelly Jenkins
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1 3 EE4555 Fudmls of Smicoducor vics Fll cur 8: PN ucio iod hr 8 Forwrd & rvrs bis Moriy crrir diffusio Brrir lowrd blcd by iffusio rducd iffusio icrsd mioriy crrir drif rif hcd 3 EE E. Morris

2 3 3 3 Trmiologyoio No: oml ioizio ssumio 3 EE E. Morris 4

3 3 Buil-i oil crrir dsiis From bfor V i R rrg N N Assum coml ioizio d Hc d bi d N N d V l whr V i bi N bi N N d. N N d so so i N bi i N d bi 3 EE E. Morris 5 Forwrd bis V : V bi V bi -V Vbi V bi d 3 EE E. Morris 6 3

4 3 4 E 8. Si ucio 3 K dod wih N d = 6 cm 3 & N =5 6 cm 3 forwrd bisd wih V =.65V. rmi mioriy crir cocrios h sc chrg dgs. os low icio sill ly? 3 EE E. Morris 7 Mioriy crrir disribio 3 EE E. Morris 8 whr for d whr for h so d sdy s for h dlio rgio ousid g E Assumig whr y : hols i N - Mioriy crrir rsor quio g E

5 3 Mioriy crrir disribio Grl soluio for A. wih boudry codiios. d So A d. Grl soluio for wih boudry codiios B.. d So d. 3 EE E. Morris 9 Fwd bis PN: Qusi-Frmi lvls Ecss crrirs i o - quilibrium E EF δ i EF E δ i oil fucios of d of E Hc E F E F No h E d for lir fucios of E F F E E so so i F i E F i A E E F E F E V V i i EF E V V 3 EE E. Morris F 5

6 3 6 PN ucio curr 3 EE E. Morris vluig h ucio curr: Tol curr mus b cos - <<+ Hc c vlu s h sum of lcro d hol currs cross h dlio rgio. Assumio: Assum currs cos cross dlio rgio Evlu lcro d hol currs s mioriy crrir currs h sc chrg rgio dgs. Forwrd bis: Moriy crrirs icd io dlio rgio iffus cross bcom mioriy crrirs Evlu mioriy crrir currs dgs.g. moriy hols i -y diffus cross h sc chrg rgio d bcom mioriy hols i -y. Evlu = - d d = 3 EE E. Morris PN ucio curr. & -. givs & for & d d d d s

7 3 iod chrcrisic 3 EE E. Morris 3 E 8. d h idl rvrs surio curr dsiy for GAs ucio 3 K wih N d = 6 cm 3 N =8 5 cm 3 =cm s τ = -7 s & τ =5-8 s. 3 EE E. Morris 4 7

8 3 Forwrd bis roimio = s [ ]- s [ ] for >> l = 3 EE E. Morris 5 E 8.3 rmi h lcro d hol curr dsiis h sc chrg rgio dgs d drmi h ol curr dsiy i h diod for GAs ucio 3 K d forwrd bis.5v wih N d = 6 cm 3 N =8 5 cm 3 =cm s τ = -7 s & τ =5-8 s. 3 EE E. Morris 6 8

9 3 oml currs d d givs & for - for for 3 EE E. Morris 7 Moriy drif curr cio urrs Moriy drif curr Mioriy diffusio curr Mioriy diffusio curr gur 5 7 Elcro d hol comos of curr i forwrd-bisd - ucio. hy is hr diffrc bw h wo currs? 3 EE E. Morris c 4: ucios 8 9

10 3 3 9 E 8.4 rmi h lcric fild i h url rgio d url rgio for h GAs ucio 3 K d forwrd bis.5v wih N d = 6 cm 3 N =8 5 cm 3 =cm s τ = -7 s & τ =5-8 s. 3 EE E. Morris

3 E 8.5 osidr GAs ucio iiilly bisd V =.5V T=3 K d clcul h chg i bis volg rquird o mii h sm curr wh T icrss o 3 K. 3 EE 4555. E. Morris Shor diod mlici ssumio bov h ± 3 EE 4555.

11 3 E 8.5 osidr GAs ucio iiilly bisd V =.5V T=3 K d clcul h chg i bis volg rquird o mii h sm curr wh T icrss o 3 K. 3 EE E. Morris Shor diod mlici ssumio bov h ± 3 EE E. Morris Assum log -rgio d shor -y & hck : sih sih s bfor d bu wih boudry codiios.. rgio for - As bfor givig B A

12 3 Shor diod 3 EE E. Morris 3 is coss d h rgio N - imlis o hol rcombiio i h No h so cosh d so sih sih Now if sih cosh sih sih d d d d For Grio & Rcombiio urrs: Rvrs bis: Sc chrg rgio EHP grio 3 EE E. Morris 4 o sur wih rvrs bis dos d rvrscurr Th rs E if ssumig whr ri i h sc chrg rgio for i.. grio G Rcombiio r R R g s R s d i i g i i i i i V N N Gd N N G N N

13 3 E 8.6 osidr GAs ucio 3 K wih N d =8 6 cm 3 N = 5 cm 3 =9.8cm s τ =τ =τ =5-8 s. lcul h idl rvrs bis surio curr dsiy b d h rvrs bis curr dsiy V R =5V c rmi h rio of g o s 3 EE E. Morris 5 Grio & Rcombiio urrs: Forwrd bis: Sc chrg rgio rcombiio N i For rcombiio r R gi E E E F E F d i & i w fid h R ks h middl of h sc chrg rgio s show E E E E F F E E E E F F d h cr of h sc chrg rgio whr mimum rcombiio occurs 3 EE E. Morris 6 3

14 3 Rcombiio curr N i i Rcombiio r R i if rs E gi d h cr of h sc chrg rgio [ i i ] E E E E F F Usig i i & i i i i i Rm.. if V i i Th rc Rd r 3 EE E. Morris 7 Rcombiio dds curr 3 EE E. Morris 8 4

15 3 Tol forwrd curr rc ro s s owv diffusio domi l owv rcombiio domi rc l ro d l l so discoiuiy i l vs V s 3 EE E. Morris 9 High lvl icio A high forwrd V low icio roimio mioriy moriy or mioriy moriy so δ i. δ if δ δ Hc sic. δ. δ i d High icio curr css curr : - i d δ 3 EE E. Morris 3 5

16 3 Smll sigl: iffusio rsisc g s d dv V V Q s s r d Q 3 EE E. Morris 3 iffusio ccic 3 EE E. Morris 3 6

17 3 7 crml chrg chgs Q 3 EE E. Morris 33 iffusio ccic 3 EE E. Morris 34 dc dc dc K K V v v v v V v V wih grl soluio d whr i.. d clusrig im idd d im dd rms givs givs Subsiuig i. rgio For -. ˆ h d for i.. h V f

18 3 8 iffusio ccic 3 EE E. Morris 35 g V V A V A V V K K K K d d dc dc so Y so d for low frqucy ˆ Î Î Y ˆ Î d ˆ Î d hc ˆ ˆ so ˆ d rquir Boudry codiios For grl soluio d E 8.7 Si ucio 3 K wih N d =8 6 cm 3 N = 5 cm 3 =5cm s =cm s τ =5-7 s τ = - 7 s d cs r A= -3 cm. d h diffusio rsisc d diffusio ccic if h diod is forwrd bisd V =.55V d b V =.6V. 3 EE E. Morris 36

19 3 Equivl circui o r s ffc 3 EE E. Morris 37 Ovrll chrcrisic

20 3 Swichig rsi: O off iilly forwrd curr For R VR R R F VF V R if diod volg V d o h diod volg co chg isously du o uciodiffusio ccic i. diod sill forwrd bisd F R 3 EE E. Morris 39 O off 3 4

21 3 Swichig rsi: O off 3 EE E. Morris 4 F R R F R F F s rf rf Rcovry im : l - Sorg im : 3 4

22 Assigm # EE E. Morris 44

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =