Band structure and carrier concentration of Gallium Arsenide (GaAs)
Band structure and carrier concentration
Basic ParametersTemperature 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 (E_{ΓL}) between Γ and L valleys  0.29 eV 
Energy separation (E_{ΓX}) between Γ and X valleys  0.48 eV 
Energy spinorbital splitting  0.34 eV 
Intrinsic carrier concentration  2.1·10^{6} cm^{3} 
Intrinsic resistivity  3.3·10^{8} Ω·cm 
Effective conduction band density of states  4.7·10^{17} cm^{3} 
Effective valence band density of states  9.0·10^{18} cm^{3} 
Band structure and carrier concentration of GaAs. 300 K E_{g} = 1.42 eV E_{L} = 1.71 eV E_{X}= 1.90 eV E_{so} = 0.34 eV 
Temperature Dependences
Temperature dependence of the energy gap
E_{g}=1.5195.405·10^{4}·T^{2}/(T+204) (eV)
where T is temperatures in degrees K (0 < T < 10^{3}).
Temperature dependence of the energy difference between the top of the valence band and the bottom of the Lvalley of the conduction band
E_{L}=1.8156.05·10^{4}·T^{2}/(T+204) (eV)
Temperature dependence of the energy difference between the top of the valence band and the bottom of the Xvalley of the conduction band
E_{L}=1.9814.60·10^{4}·T^{2}/(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
n_{i} =(N_{c} ·N_{ν} )^{1/2}exp(E_{g}/(2k_{b}T))
Effective density of states in the conduction band taking into account the nonparabolicity of the Γvalley and contributions from the X and Lvalleys
N_{c}= 8.63·10^{13}·T^{3/2}[11.9310^{4}·T4.19·10^{8}·T^{2} +21·exp(E_{ΓL}/(2k_{b}T))
+44·exp(E_{ΓX}/(2k_{b}T)) (cm^{3})
Effective density of states in the valence band
N_{v}= 1.83·10^{15}·T^{3/2}(cm^{3})
Fermi level versus temperature for different concentrations of shallow donors and acceptors. 
Dependences on Hydrostatic Pressure
E_{g} = E_{g}(0) + 0.0126·P  3.77·10^{5}P^{2} (eV)E_{L} = E_{L}(0) + 5.5·10^{3}P (eV)
E_{X} = E_{X}(0) + 1.5·10^{3}P (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}·N_{a}^{1/2} (eV) (N_{a} in cm.^{3})
Effective Masses
Electrons:
For Γvalley  m_{Γ} = 0.063m_{o} 
In the Lvalley the surfaces of equal energy are ellipsoids  
m_{l}= 1.9m_{o}  
m_{t}= 0.075m_{o}  
Effective mass of density of states  
m_{L}=(16m_{l}m_{t}^{2})^{1/3}  m_{L}=0.85m_{o} 
In the Xvalley the surfaces of equal energy are ellipsoids  
m_{l}= 1.9m_{o}  
m_{t}= 0.19m_{o}  
Effective mass of density of states  
m_{X}=(9m_{l}m_{t}^{2})^{1/3}  m_{X}=0.85m_{o} 
Holes:
Heavy  m_{h} = 0.51m_{o} 
Light  m_{lp} = 0.082m_{o} 
Splitoff band  m_{so} = 0.15m_{o} 
Effective mass of density of states  m_{v} = 0.53m_{o} 
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 