ECE340_L8_S14_Distribution

# Kt therefore no po ni pi ni2 and n t n c n v e 2 i ni

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Unformatted text preview: of States (cm -3 ) N c ( Ec ) = Effective Density of States Located at Conduction Band Edge f ( Ec ) = f ( Ec ) = e –  In this case, e(Ec- Ef)/kT &gt; 20 Temperature kT - 40°C (233K) 0.0201 eV 27°C (300K) 0.0259 eV 127°C (400K) 0.0345 eV ∫ f ( E ) • N (E )dE 1 1+ e − ( Ec − E f ) / kT ( Ec − E f ) / kT if e ( Ec − E f ) / kT ⎛ 2π • m kT ⎞ ⎟ N c ( Ec ) = 2⎜ 2 ⎜ ⎟ h ⎝ ⎠ * n no = N c • e &gt;&gt; 1 3/ 2 − ( Ec − E f ) / kT 18 The Case of Degenerate Doping ∞ n= ∫D C ( E ) f ( E ) dE Ec DC ( E ) = 1 ⎛ 2m ⎞ 2π 2 ⎜ 2 ⎟ ⎝ ⎠ * e 3 2 E − EC so n= 1 ⎛ 2m ⎞ 2π 2 ⎜ 2 ⎟ ⎝ ⎠ * e 3 2∞ E − EC ∫ 1 + e[( E−EF )/kT ] dE Ec Defining η = ( EF − EC ) / kT and ξ = ( E − EC ) / kT n= 1 ⎛ 2 m kT ⎞ 2π 2 ⎜ ⎟ ⎝ ⎠ * e 2 3 2∞ ξ ∫ 1 + e(ξ −η ) dξ 0 Using the Fermi-Dirac Integral, this becomes 3 2 ⎛ 2π m kT ⎞ n = 2⎜ ⎟ F1/2 (η ) = N C F1/2 (η ) ⎝h ⎠ * e 2 F1/2 (η ) is a tabulated function •  The full expressions for the density of states and Fermi distribu`on need to be used in the case of degenerate doping •  The integral is simpliﬁed using the Fermi- Dirac...
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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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