ECE340_L14_S14_Distribution

# 5 1010 e ei fp kt therefore e i fp 00259 ln13

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Unformatted text preview: r = α r np = α r (no + δ n )( po + δ p ) = α r [ nopo + noδ p + poδ n + δ nδ p ] no(K)+δn ༉ r = α r [ nopo + ( no + po )δ n + δ n 2 ] = g(T ) + gopt Recall: g(T ) = α r ni2 = α r n0 p0 so δn gop = α r ( n0 + p0 )δ n = τn and δ n = δ p = gopτ n gopt g(T) ༉ po(K)+δp What Happens to the Fermi Level? 27 What Happens to the Fermi Level? Equilibrium With Excess Carriers no(K) no(K)+δn ༉ ༉ ༉ ༉ ༉ ༉ ༉ ༉ Fn Ef ༉ ༉ ༉ po(K) Fp ༉ po(K)+δp The Fermi level in the presence of excess carriers is called the “quasi-Fermi level” 28 Quasi- Fermi Level •  A variety of mechanisms can create excess carriers (electrons and holes) •  The carriers may or may not be created in equal numbers –  This depends upon the mechanism that created them •  Regardless of how they were created, the quan_ty of excess carriers can be described by integra_ng the density of states _mes the probability of occupancy •  The probability of occupancy is s_ll a Fermi distribu_on, but with a modiﬁed Fermi energy, the “Quasi- Fermi Energy” or “Quasi- Fermi Level” Quasi Fermi Levels •  Electron Quasi- Fermi Level: n = ni e( Fn − Ei )/kT = ni e = ni e δ n = n − no = no (e no(K)+δn ( Fn − Ei + E f − E f )/ kT ( E f − Ei )/ kT ( Fn − E f )/ kT e Band Diagram, Fn and Fp = no e ( Fn − E f )/ kT ༉ ( Fn − E f )/ kT Fp ( E f − Fp )/ kT δ p = p − po = po (e δ n = δ p = gopτ n ( E f − Fp )/ kT ༉ ༉ ༉ ༉ ༉ ༉ Fn − 1) = gopτ n •  Hole Quasi- Fermi Level: p = po e ༉ − 1) = gopτ p n = ni e( Fn − Ei )/kT E − F / kT p = n e( i p ) i po(K)+δp 30 Quasi- Fermi Leve...
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