Fermi level analysis considering the case of n type

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Unformatted text preview: integral, which is available in tabulated form (look- up table) 19 Back to Non- Degenerate Case: Concentra`on Product and Intrinsic Concentra`on ni pi = N c e − ( Ec − Ei )/ kT no po = N c e • N ve − ( Ec − E f )/ kT − ( Ei − Ev )/ kT • N ve − ( E f − Ev )/ kT therefore no po = ni pi = ni2 and n (T ) = N c N v • e 2 i ni (T ) = N c N v • e − ( Eg )/ kT − ( Eg )/2 kT = N c N ve − ( Ec − Ev )/ kT = N c N ve = N c N ve − ( Ec − Ev )/ kT − Eg / kT = N c N ve − Eg / kT EC Ei EF EV •  The intrinsic carrier concentra`on depends upon –  Bandgap, temperature, electron effec`ve mass (through Nc), and hole effec`ve mass (through Nv) •  Ei is only at midgap if Nc = Nv (equal electron and hole effec`ve masses) 20 Minority Carrier Concentra`on in Equilibrium •  Why is the minority carrier concentra`on smaller than ni? •  In an intrinsic material, recall that no(K)=Nd, majority carrier n=p=ni •  These values are determined by the eee e ee genera`on and recombina`on Ec rates, which must be equal in e e Ed equilibrium 0.03 to •  Genera`on is set by the Eg(Si)=1.1eV temperature 0.06eV gi •  When the semiconductor is doped, ri there is an abundance of majority Ev carriers, the minority carrier...
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