Band structure and carrier concentration of Indium Phosphide (InP)
Band structure and carrier concentration
Basic ParametersTemperature 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 (E_{ΓL}) between Γ and L valleys | 0.59 eV |
Energy separation (E_{ΓX}) between Γ and X valleys | 0.85 eV |
Energy spin-orbital splitting | 0.11 eV |
Intrinsic carrier concentration | 1.3·10^{7} cm^{-3} |
Intrinsic resistivity | 8.6·10^{7}Ω·cm |
Effective conduction band density of states | 5.7·10^{17} cm^{-3} |
Effective valence band density of states | 1.1·10^{19} cm^{-3} |
Band structure and carrier concentration of InP. Important minima of the conduction band and maxima of the valence band. 300 K. E_{g} = 1.34eV; E_{L} = 1.93 eV; E_{X} = 2.19 eV; E_{so} = 0.11 eV |
Temperature Dependences
Temperature Dependences Temperature dependence of the energy gap
E_{g} = 1.421 - 4.9·10^{-4}·T^{2}/(T+327) (eV),where T is temperature in degrees K (0 < T < 800).
Temperature dependence of the energy separation between Γ and X valleys
E_{ΓX} = 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
N_{c}≈1.1·10^{14}·T^{3/2} (cm^{-3}).Effective density of states in the valence band
N_{v}≈2.2·10^{15}·T^{3/2} (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
E_{g} = E_{g}(0) + 8.4·10^{-3}P - 1.8·10^{-5}P^{2} (eV)E_{L} = E_{L}(0) + 4.6·10^{-3}P (eV),
E_{X} = E_{X}(0) + 2·10^{-3}P (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:
ΔE_{g}≈22.5·10^{-9}·N_{d}^{1/3} (eV)(Bugajski and Lewandowski [1985])
For p-type InP
ΔE_{g}≈10.3·10^{-9}·N_{a}^{1/3} + 4.43·10^{-7}·N_{a}^{1/4} + 3.38·10^{-12}·N_{a}^{1/2} (eV)(Jain et al. [1990]).
Effective Masses
Electrons: | |
For Γ-valley | m_{Γ} = 0.08m_{o} |
The are 4 equivalent L-valleys in the conduction band: | |
in one L-valley | m_{L} = 0.25m_{o} |
for all L-valley | m_{Ld} = 0.63m_{o} |
The are 3 equivalent X-valleys in the conduction band: | |
in one X-valley | m_{X} = 0.32m_{o} |
for all X-valley | m_{Xd} = 0.66m_{o} |
Holes: | |
Heavy | m_{h} = 0.6m_{o} |
Light | m_{lp} = 0.089m_{o} |
Split-off band | m_{so} = 0.17m_{o} |
Effective mass of density of states | m_{v} = 0.6m_{o} |
Donors and Acceptors
Ionization energies of shallow donors (eV) ~0.0057:
S, Si, Sn, GeIonization 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 |