At room temperature (300 K) the effective density of states in the valence band is 
2.66 x 1019 cm-3
for Si and 7 x 1018 cm-3
for GaAs. Find the corresponding effective masses 
of holes? Compare these masses with the free-electron mass?

Working on my fermi level project. Interested in determining theintrinsic carrier concentration of gallium nitride (GaN).

T=300; % Temperature in Kelvin
k=8.617e-5; % Boltzmann constant (eV/K)
e0=8.85e-14; % permittivity of free space (F/cm)
q=1.602e-19; % charge on an electron (coul)
KS=8.9; % Dielectric constant of GaN
ni=X; % intrinsic carrier conc. in Galium Nitride at 300K
EG=3.44 ; % Galium Nitride band gap (eV)

Could you show steps on how you calculated X?

Honestly, just give me a value and show me how you got there. Cutthe gibberish.
Its couple hours before sunrise.

Intrinsic carrier concentration:
ni = (Nc·Nv)^(1/2)*exp(-Eg/(2kBT))

Effective density of states in the conduction band: Nc
Zinc Blende
Nc = 2.3*(1e14)*T^(3/2) (cm-3)

Effective density of states in the valence band: Nv
Zinc Blende BN
Nv = 8.0*(1e15)*T^(3/2) (cm-3)

Helpful Source: http://www.ioffe.ru/SVA/NSM/Semicond

Conceivably, an electron and a hole in germanium could form astable holeium state, in which they orbited around their commoncenter of mass in a manner similar to a Bohr hydrogen atom. Whatwould be the rough size of an "atom", and what would be itsionization energy? At what maximum temperature would be expected toobserve such a state?
The effective mass of electrons in Ge is: m*/mass(of electron) =0.12. The effective mass of holes in Ge is m*/m(of electron) =0.21. And the dielectric constant of Ge is k=16.0.

Pure silicon at room temperature has an electron number density ofabout 5 x 1015 m-3 and an equal density of holes in the valenceband. Suppose that one of every 106 silicon atoms is replaced by aphosphorus atom. (a) What charge carrier number density will thephosphorus add (in terms of nm-3)? (b) What is the ratio of thecharge carrier number density (electrons in the conduction band andholes in the valence band) in the doped silicon to that in puresilicon? The density of silicon is 2.33 g/cm3 and its molar mass is28.086 g/mol