Lecture17(1)

N xn p ni e e f kt kt ni e fn fp kt ni2 e f f kt 2 ni

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Unformatted text preview: P ni e E F kT - - kT ni e FN FP kT ni2 e F F kT 2 ni e qV A 2 qV kT n p (x x )N ne n p (x x pp) N AA ni2ie kT N P A A A n pn( x x ( p A 2 2 i i qV A nn qV xx ) ) e kT 1 p e kT 1 p NA N A Georgia Tech Georgia Tech no no A and similarly at x and similarly at xx x n n ni2 qV qVA kT n p np n ( x x n x n ) N e ekT 1 1 (x ) ND D 2 i A EE 332 Spring 2013 E 3080 - Dr. Dr. Doolittle ECE CE 3080 - AlanAlan Doolittle ExcessExcess Carrier Concentrations Carrier Concentrations EE 332 Spring 2013 Example: Injection Example: CarrierCarrier Injection EE 332 Spring 2013 InjectedMinority Carrier Injection Minority Carriers Quantitative p-n Diode Solution p-type Depletion Region E0 n-type E0 E0 -xp xn Application of the Minority Carrier Diffusion Equation n ni e FN Ei n p (x n p (x n p (x n p (x n p (x Georgia Tech Boundary Condition : Boundary Condition : np (x xp ) ? kT and x p ) p p (x x p ) p p (x xp ) p ni e x p ) ni2 e Ei FP - kT FN FP x p ) n p (x p n ( x xn ) ? kT x p )N A 2 i ne qV A kT ni2 qVA kT e NA xp ) ni2 qVA kT e NA xp ) ni2 qVA kT e 1 NA no and similarly at x xn pn ( x xn ) ni2 qVA kT e 1 ND ECE 3080 - Dr. Alan Doolittle EE 332 Spring 2013 Diffusion Current of Excess Minority Carriers Diffusion Current of Excess Minority Carriers Minority Carrier Injection Quantitative p-n Diode Solution p-type E Depletion Region 0 E n-type 0 E 0 -xp xn Application of the Minority Carrier Diffusion Equation n ni e n p (x n p (x n p (x n p (x n p (x Boundary Condition : Boundary Condition : np (x xp ) ? - FN Ei kT and x p ) p p (x x p ) p p (x xp ) 2 i n e NA p xp ) xp ) qV A ni e 2 i ne Ei FP - xn ) ? kT FN FP n p (x pn ( x kT x p )N A 2 i ne qV A kT J=JN(-Xp)+JP(Xn) kT xp ) ni2 qVA kT e NA xp ) ni2 qVA kT e NA no 1 and similarly at x xn pn ( x ni2 qVA kT xn ) e 1 EE 332 Spring 2013 ND Diffusion Current Diffusion Current EE 332 Spring 2013 E Carrier Distribution Excess xcess Carrier Distribution EE 332 Spring 2013 EE 332 Spring 2013 E 0 Quantitative p-n Diode Solution 0 Spatial Gradient of of p-n Diode Solution Carriers Quantitative Excess Spatialp-type 2 Depletion RegionMinority Carriers Gradient Excess Minority n-type x’=0 ( pn ) ( pn ) 0 E D Region2 E 0 E0 -type Depletion P 0 n-type x2' ( pn ) ( ppn ) 0 E 0 0 DP E0 2 x ' / LP x ' / LP x ' p x’’=0 Ae Be where Lx’=0 D p p P ' / LP xx’=0 x’’=0 x '/ LP x' ) Ae Be where LP Dp p Boundary Conditions : 2 Boundary Conditions : pn ( x ' pn ( x ' ) 0 0 )0 2 i n p2qVA kT) Ae nin ( x 'qV kT1 p n ( x ' 0) e p n ( x ' 0) 1 ND N e A pnBe ' ) (x x ' / LP 2 pn ( x ' i n 2 i n ) qV kT A x' ' ee 2 kT qV 1 0 B and and A pn ( pn ( x0) 0) 0 1 N N0D ni e kT pn ( x ' D ) qV A 0 A 2 i ( x' ) 2 qV qV A i A kT kT n pn n e e pn ( x ' ) ND ND 1 e1 p x ' / LP p ( wh Boundary Conditions : pn ( x ' 1 p n ( x ' 0) 0 0 andforxx ' 0n ( x' 0) for A' p pn ( x ' ) ( pn ) x '2 Aewhere LP Be D p x e'/ LxP'/ LP B DP x ' / LP A ND ( pn ) 0 ( pn ) x '2 Boundary Conditions : D B x ' / LP DP 2 B )0 ni2 q...
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This document was uploaded on 02/18/2014.

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