GaAs - Gallium Arsenide

Band structure and carrier concentration

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

Basic Parameters

Energy gap 1.424 eV
Energy separation (EΓL) between Γ and L valleys 0.29 eV
Energy separation (EΓX) between Γ and X valleys 0.48 eV
Energy spin-orbital splitting 0.34 eV
Intrinsic carrier concentration 2.1·106 cm-3
Intrinsic resistivity 3.3·108 Ω·cm
Effective conduction band density of states 4.7·1017 cm-3
Effective valence band density of states 9.0·1018 cm-3


Band structure and carrier concentration of GaAs. 300 K
Eg = 1.42 eV
EL = 1.71 eV
EX= 1.90 eV
Eso = 0.34 eV

Temperature Dependences

Temperature dependence of the energy gap

Eg=1.519-5.405·10-4·T2/(T+204) (eV)
where T is temperatures in degrees K (0 < T < 103).

Temperature dependence of the energy difference between the top of the valence band and the bottom of the L-valley of the conduction band

EL=1.815-6.05·10-4·T2/(T+204) (eV)

Temperature dependence of the energy difference between the top of the valence band and the bottom of the X-valley of the conduction band

EL=1.981-4.60·10-4·T2/(T+204) (eV)

The temperature dependences of the relative populations of the Γ, L and X valleys.
(Blakemore [1982]).
The temperature dependences of the intrinsic carrier concentration.
(Shur [1990]).

Intrinsic Carrier Concentration

ni =(Nc ·Nν )1/2exp(-Eg/(2kbT))

Effective density of states in the conduction band taking into account the nonparabolicity of the Γ-valley and contributions from the X and L-valleys
Nc= 8.63·1013·T3/2[1-1.9310-4·T-4.19·10-8·T2 +21·exp(-EΓL/(2kbT)) +44·exp(-EΓX/(2kbT)) (cm-3)

Effective density of states in the valence band

Nv= 1.83·1015·T3/2(cm-3)

Fermi level versus temperature for different concentrations of shallow donors and acceptors.

Dependences on Hydrostatic Pressure

Eg = Eg(0) + 0.0126·P - 3.77·10-5P2 (eV)
EL = EL(0) + 5.5·10-3P (eV)
EX = EX(0) + 1.5·10-3P (eV)
where P is pressure in kbar.

Energy Gap Narrowing at High Doping Levels

Energy gap narrowing at high doping levels.
(Tiwari and Wright [1990])

ΔEg ≈ 2·10-11·Na-1/2 (eV) (Na- in cm.-3)

Effective Masses

Electrons:

For Γ-valley mΓ = 0.063mo
In the L-valley the surfaces of equal energy are ellipsoids
  ml= 1.9mo
  mt= 0.075mo
Effective mass of density of states
mL=(16mlmt2)1/3 mL=0.85mo
In the X-valley the surfaces of equal energy are ellipsoids
  ml= 1.9mo
  mt= 0.19mo
Effective mass of density of states
mX=(9mlmt2)1/3 mX=0.85mo

Holes:

Heavy mh = 0.51mo
Light mlp = 0.082mo
Split-off band mso = 0.15mo
Effective mass of density of states mv = 0.53mo

Donors and Acceptors

Ionization energies of shallow donors (eV)
(Milnes [1973])
S Se Si Ge Sn Te
~0.006 ~0.006 ~0.006 ~0.006 ~0.006 ~0.03

Ionization energies of shallow acceptors (eV)
(Milnes [1973])
C Si Ge Zn Sn
~0.02 ~0.03/0.1/0.22 ~0.03 ~0.025 ~0.2