kt 2m 2 2 32 1 e e f kt 2 m 2 2

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Unformatted text preview: `ple valleys due to symmetry and energy degeneracy –  This is included in the density of states effec2ve mass http://www.ioffe.rssi.ru/SVA/NSM/Semicond/Ge/Figs/221.gif 13 Carrier Concentra`on at Thermal Equilibrium The Fermi Function Multiplied by the Density of States ∞ n0 = ∫ f ( E ) N c ( E ) dE Ec p0 = ∫ ⎡1 − f ( E ) ⎤ N v ( E ) dE ⎦ −∞ ⎣ Ev DOS: Appendix IV 15 Electron Concentra`on no in a n- type Semiconductor at Equilibrium no(K)=Nd, majority carrier Ec Ef eee e ∞ no = ee e Ec e Ed Ei Ev e e ee e ee ee e e no = N c ( Ec ) • f ( Ec ) f ( E ) = Fermi Distribution Funtion N ( E ) = Density of States (cm -3 ) N c ( Ec ) = Effective Density of States (located at conduction band edge) e e f ( Ec ) = po(K)=ni2/no, minority carrier ∞ no = ∞ ∫ f ( E ) • N (E )dE = ∫ 1 + e Ec ∞ ∫e Ec Ec − ( E − E f )/ kT • 2⎛m ⎞ π 2 ⎜ 2 ⎟ ⎝⎠ * 3/2 1 ( E − E f )/ kT 2 ⎛ m* ⎞ • 2⎜ 2⎟ π ⎝ ⎠ 3/2 ⎛ 2π m kT ⎞ E 1/2 dE = 2 ⎜ ⎟ ⎝h ⎠ = N C (T ) e( EF − EC )/kT = N C (T ) e−( EC − EF )/kT * n 2 ∫ f ( E ) • N (E )dE 1/2 E dE 3/2 e( EF − EC )/kT f ( Ec ) = e 1 1+ e − ( Ec − E f )/ kT ( Ec − E f )/ kT if e ( Ec − E f )/ kT ⎛ 2π • m kT ⎞ N c ( Ec ) = 2 ⎜ ⎟ h2 ⎝ ⎠...
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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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