Band structure and carrier concentration of Indium Phosphide (InP)

InP - Indium Phosphide

Band structure and carrier concentration

Basic Parameters
Temperature Dependences
Dependences on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Effective Masses
Donors and Acceptors

Basic Parameters

Energy gap 1.344 eV
Energy separation (EΓL) between Γ and L valleys 0.59 eV
Energy separation (EΓX) between Γ and X valleys 0.85 eV
Energy spin-orbital splitting 0.11 eV
Intrinsic carrier concentration 1.3·107 cm-3
Intrinsic resistivity 8.6·107Ω·cm
Effective conduction band density of states 5.7·1017 cm-3
Effective valence band density of states 1.1·1019 cm-3


Band structure and carrier concentration of InP.
Important minima of the conduction band and maxima of the valence band. 300 K.
Eg = 1.34eV;
EL = 1.93 eV;
EX = 2.19 eV;
Eso = 0.11 eV

Temperature Dependences

Temperature Dependences Temperature dependence of the energy gap

Eg = 1.421 - 4.9·10-4·T2/(T+327) (eV),
where T is temperature in degrees K (0 < T < 800).

Temperature dependence of the energy separation between Γ and X valleys

EΓX = 0.96 - 3.7·10-4·T (eV),
where T is temperature in degrees K (0 < T < 300).

Effective density of states in the conduction band

Nc≈1.1·1014·T3/2 (cm-3).

Effective density of states in the valence band

Nv≈2.2·1015·T3/2 (cm-3).
The temperature dependence of the intrinsic carrier concentration.
Fermi level versus temperature for different concentrations of shallow donors and acceptors.

Dependences on Hydrostatic Pressure

Eg = Eg(0) + 8.4·10-3P - 1.8·10-5P2 (eV)
EL = EL(0) + 4.6·10-3P (eV),
EX = EX(0) + 2·10-3P (eV),
where P is pressure in kbar.

Energy Gap Narrowing at High Doping Levels

Energy gap narrowing versus donor (curve 1 and experimental points) and acceptor (curve 2) doping density, T = 300 K.
Curve 1 and experimental points (Bugajski and Lewandowski [1985]);
Curve 2 (Jain et al. [1990]).

For n-type InP:

ΔEg≈22.5·10-9·Nd1/3 (eV)
(Bugajski and Lewandowski [1985])

For p-type InP

ΔEg≈10.3·10-9·Na1/3 + 4.43·10-7·Na1/4 + 3.38·10-12·Na1/2 (eV)
(Jain et al. [1990]).

Effective Masses

Electrons:  
For Γ-valley mΓ = 0.08mo
The are 4 equivalent L-valleys in the conduction band:
in one L-valley mL = 0.25mo
for all L-valley mLd = 0.63mo
The are 3 equivalent X-valleys in the conduction band:
in one X-valley mX = 0.32mo
for all X-valley mXd = 0.66mo
Holes:  
Heavy mh = 0.6mo
Light mlp = 0.089mo
Split-off band mso = 0.17mo
Effective mass of density of states mv = 0.6mo

Donors and Acceptors

Ionization energies of shallow donors (eV) ~0.0057:

S, Si, Sn, Ge

Ionization energies of shallow acceptors (eV):

C Hg Zn Cd Si Cu Be Mg Ge Mn
0.04 0.098 0.035 0.057 0.03 0.06 0.03(MBE) 0.03(MBE) 0.021 0.27