Intrinsic Semiconductors CONCENTRATION OF ELECTRONS IN CB AND HOLES IN VB FERMI ENERGY FOR INTRINSIC SEMICONDUCTOR Intrinsic Semiconductors To find the equilibrium concentration of electrons in the CB and holes in the VB Use the FD distribution function to write down the electron/hole density of states at the VB and CB edges

fFD = [1 + exp(E - EF)/kT]-1 n ~ NC[exp(EF - EC)/kT] CONCENTRATION OF ELECTRONS IN CB AND HOLES IN VB FERMI ENERGY FOR INTRINSIC SEMICONDUCTOR n(E) = N(E)fFD(E)  fFD = [1 + exp(E - EF)/kT]-1 n ~ NC[exp(EF - EC)/kT] p ~ NV[exp(EV - EF)/kT]   Exponential term >>> 1

n = electron number density p = hole number density CONCENTRATION OF ELECTRONS IN CB AND HOLES IN VB FERMI ENERGY FOR INTRINSIC SEMICONDUCTOR n = electron number density p = hole number density NC = DOS at CB edge EC = energy at CB edge NV = DOS at VB edge EV = energy at VB edge EF = Fermi energy of level where there is an equal probability of e or h

FERMI ENERGY FOR A SEMICONDUCTOR Intrinsic semiconductors n = p NC[exp(EF - EC)/kT] = NV[exp(EV - EF)/kT] Thus EF = (EV + EC)/2 + 1/2(kT)In(NV/NC) When NV ~ NC Then EF = (EV + EC)/2 EF is a virtual level in the forbidden gap - the chemical/electrochemical potential of charge carriers

CONCEPT OF EFFECTIVE MASS OF ELECTRONS AND HOLES IN SOLIDS Electron and hole carriers move in the periodic potential of the crystal lattice and therefore experience different interactions compared to free carriers