lecture11

# lecture11 - Lecture 11 Friday February18 EE 332...

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Lecture 11 Friday February18 EE 332 Semiconductor Devices Problem Assignment Friday ! 3.23 and 3.26 Recombination Rate of EHP = np dt t dn r α = ) ( 0 0 2 0 0 2 of made was Use by m equilibriu at thermal p n n p n n G i r i r th = = = α α Spontaneous formation of electron hole pairs by thermal energy is independent of instantaneous concentrations. The G th rate is related to α r The rate is proportional to the n electrons waiting to decay and the p available states in the valance band. Steady State Solution ( )( ) ( ) [ ] 2 0 0 0 0 0 0 ) ( ) ( n n p n p n p p n n t p t n G G r r r r op th + + + = + + = = + α α α α ( Generation Rate = Recombination Rate) ) ( ) ( t p t n G G r op th α = + Write instantaneous concentration as the equilibrium concentration plus a small departure. G op =optical generation ) ( ) ( ) ( ) ( 0 0 t p p t p t n n t n + = + = Because we have EHP generation, n= p Steady State Solution ( ) [ ] 2 0 0 0 0 n n p n p n G G r r op th + + + = + α α 0 0 but p n G r th α = ( ) [ ] where 0 0 n r op n n p n G τ α = + = and for low excitation n>> n 2 . Thus n op G p n τ = = ( ) 0 0 1 p n r n + = α τ

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