ECE340_L15_S14_Distribution

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Unformatted text preview: l” What Happens to the Fermi Level? Equilibrium With Excess Carriers no(K) no(K)+δn Ÿ༉ Ei Ef Ÿ༉ Ÿ༉ Ÿ༉ po(K) Ÿ༉ Ÿ༉ Fn Ei Fp Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K)+δp The Fermi level in the presence of excess carriers is called the “quasi-Fermi level” n0 = ni e( EF − Ei )/kT p0 = ni e( Ei − EF )/kT n = ni e( Fn − Ei )/kT ( Ei − Fp )/kT p=ne i 10 Quasi Fermi Levels •  Electron Quasi- Fermi Level: n = ni e( Fn − Ei )/kT = ni e = ni e δ n = n − no = no (e = no e ( Fn − E f )/ kT ( Fn − E f )/ kT − 1) = gopτ n •  Hole Quasi- Fermi Level: p = po e ( E f − Fp )/ kT δ p = p − po = po (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 ( E f − Fp )/ kT − 1) = gopτ p Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Fn Ei Fp Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K)+δp δ n = δ p = gopτ n 11 Quasi- Fermi Levels in p- type Material Equilibrium With Excess Carriers no(K) no(K)+δn Ÿ༉ Ÿ༉ Fn Ei Ef Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K) Ÿ༉ Ÿ༉ Ÿ༉ Ei Fp Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K)+δp n = ni e( Fn − Ei )/kT ⎛ n⎞ Fn − Ei = kT ln ⎜ ⎟ ⎝ ni ⎠ 12 Quasi- Fermi Levels in n- type Material Equilibrium With Excess Carriers no(K) no(K)+δn Ÿ༉ Fn Ef Ÿ༉ Ÿ༉ Ei Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K) Ÿ༉ Ÿ༉ Ei Fp Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ po(K)+δp ( Ei − Fp )/kT p = ni e ⎛ p⎞ Ei − Fp = kT ln ⎜ ⎟ ⎝ ni ⎠ 13 Example: Steady- State Genera\on in Si 1) 1013 EHP/cm 3 optically created per microsecond 1013 EHP/cm 3 Therefore, gopt = = 1019 EHP/cm 3s −6 10 s 14 −3 2) n o = 10 cm in equilibrium (no illumination) Ef n 2.25 × 10 = cm −3 = 2.25 × 10 6 0.228 eV 14 no 10 3) The equilibrium Fermi level (no illumination) is calculated: Therefore, po...
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This note was uploaded on 03/06/2014 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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