Lecture6(3)

e ec kt 3 2 e ef 1 2 x 1 2mn n kt 3

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Unformatted text preview: =∫ E − Ec exp( )dE 2 3 Ec kT 2π let x = ( E − Ec ) / kT ∞ * 3/ 2 E − EF ∞ 1/ 2 − x 1 ( 2mn ) n= ( kT )3 / 2 exp( − c ) ∫ x e dx 2 3 0 kT 2π ∞ Integration ∫ x 1/ 2e − x dx = 0 π 2 * 3/ 2 E − EF π 1 ( 2mn ) n= ( kT )3 / 2 exp( − c ) 2 3 kT 2 2π 3/ 2 3/ 2 ! m* kT $ ! m* kT $ E − EF = 2 # n 2 & exp( − c ) where Nc = 2 # n 2 & # 2π & # 2π & kT " % " % EE 332 Spring 2013 Equilibrium Hole Concentration Equilibrium Hole Concentration EE 332 Spring 2013 Effective Density Effective Density of Stateof States Eqn. 3-16a and 3-20 in Streetman’s book EE 332 Spring 2013 Example At room temperature (T=300 K), calculate equilibrium electron and hole concentrations in silicon when EF is 0.26 eV below Ec. For silicon Nc = 2.8 × 1019 cm −3 n0 = Nc e = Nc e −( Ec −EF ) / kT = 1.3 × 10 cm p0 = Nv e −( EF −Ev ) / KT = Nv e −0.86 / KT −0.26 / kT 15 Nv = 1.1× 1019 cm −3 −3 = 4.7 × 104 cm −3 Note: Fermi energy is shifted due to doping. Changing Ef only 0.26 eV (Eg/4) results in the carrier conc...
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This document was uploaded on 02/18/2014.

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