Concentraon ni n c e ec ei kt noknd majority

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Unformatted text preview: thus e e ee e has a greater opportunity to be e ee ee e e e involved in a recombina`on event •  For recombina`on and genera`on to remain balanced, the minority po(K)=ni2/no, minority carrier carrier concentra`on must become smaller ri = α r n0 p0 = gi 21 Why is the Minority Carrier Concentra`on Smaller than ni in Extrinsic Material? •  Fermi level analysis: –  Considering the case of n- type material, the Fermi level is shited closer to the conduc`on band –  The probability of finding a hole in the valence band, given by 1- f(Ev), is therefore smaller since the value of the Fermi func`on is closer to unity no(K)=Nd, majority carrier Ec Ef eee e ee e e Ed Ei Ev e e ee e ee ee e e e e po(K)=ni2/no, minority carrier 22 Intrinsic Fermi Level: Not Quite Midgap ni (T ) = N c N v • e no(K)=Nd majority carrier Ec Ef Ei Eg/2 Ev eee e e Nc Ec-Ef ni (T ) = N c • e− ( Ec − Ei )/kT so ni e Eg ⎧ Nv ⎫ − ( Ec − Ei ) = Δ = kT ln ⎨ ⎬ 2 ⎩ Nc ⎭ 1/2 Ef-Ei Ef-Ev − ( Eg )/2 kT Δ e e ee e ee ee e e po(K)=ni2/no, minority carrier Nv e e 1/2 ⎧⎛ m * ⎞ 3/2 ⎫ ⎪p ⎪ Δ = kT ln ⎨⎜ * ⎟ ⎬ ⎪⎝ m n ⎠ ⎪ ⎩ ⎭ If Δ is positive, E i is closer to E c than midgap. If Δ is negative, E i is closer to E v than midgap. Δ is positive when m * > m * p n 23 Referencing no and po to the Intrinsic Level & Intrinsic Carrier Concentra`on no = N c • e no(K)=Nd, majority carrier Ec Ef Ei Ev eee e Ec-Ef ee Nc ni Ef-Ev Nv e e ee e ee ee e e po(K)=ni2/no, minority carrier e e = Nc • e − ( Ec − Ei + Ei − E f )/ kT = Nc • e − ⎡( Ec − Ei )−( Ei − E f ) ⎤ / kT ⎣ ⎦ = Nc • e Ef-Ei − ( Ec −...
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