9. 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

10. 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

11. 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

12. 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

14. 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