NSM Archive  Aluminium Gallium Arsenide (AlGaAs)  Band structure and carrier concentration
Band structure and carrier concentration
Basic ParametersTemperature Dependences
Dependence on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Band Discontinuities at Al_{x}Ga_{1x}As/GaAs Heterointerface
Basic Parameters
Energy gap 
x<0.451.424+1.247x eV x>0.451.9+0.125x+0.143x^{2} 
Energy separation (E_{ΓL}) between Γ and L valleys  0.29 eV 
Energy separation (E_{Γ}) between Γ and top of valence band  1.424+1.155x+0.37x^{2} eV 
Energy separation (E_{X}) between Xvalley and top of valence band  1.9+0.124x+0.144x^{2} eV 
Energy separation (E_{L}) between Lvalley and top of valence band  1.71+0.69x eV 
Energy spinorbital splitting  0.340.04x eV 
Intrinsic carrier concentration 
x=0.12.1·10^{5} cm^{3} x=0.32.1·10^{3} cm^{3} x=0.52.5·10^{2} cm^{3} x=0.84.3·10^{1} cm^{3} 
Intrinsic resistivity 
x=0.14·10^{9} Ω·cm x=0.31·10^{12} Ω·cm x=0.51·10^{14} Ω·cm x=0.85·10^{14} Ω·cm 
Effective conduction band density of states 
x<0.412.5·10^{19}·(0.063+0.083x)^{3/2} cm^{3} x>0.452.5·10^{19}·(0.850.14x)^{3/2} cm^{3} 
Effective valence band density of states  2.5·10^{19}·(0.51+0.25x)^{3/2} cm^{3} 
Band structure Al_{x}Ga_{1x} for x<0.410.45. Important minima of the condition band and maxima of the valence band 
Band structure Al_{x}Ga_{1x} for x>0.45. Important minima of the condition band and maxima of the valence band 
Energy separation between Γ, X, and L conduction band minima and top of the valence band versus composition. Crossover points:

Ratio of the total carrier concentration to the carrier concentration in Γvalley as a function of equilibrium carrier concentration at 300K (Zarem et al. [1989]). 
Temperature Dependences
To estimate the temperature dependences of energy difference between the top of the valence band and the bottom of the Γ, X, and L valleys of the conduction band E_{Γ}, E_{X} and E_{L} one can use the data for GaAs (Aspnes [1976]).E_{Γ}=E_{Γ}(0)5.41·10^{4}·T^{2}/(T+204) (eV)
where E_{Γ}(0)=1.519+1.155x+0.37x^{2} (eV)
E_{X}=E_{X}(0)4.6·10^{4}·T^{2}/(T+204) (eV)
where E_{X}(0)=1.981+0.124x+0.144x^{2} (eV)E_{L}=E_{L}(0)6.05·10^{4}·T^{2}/(T+204) (eV)
where E_{L}(0)=1.815+0.0.69x (eV)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)
Effective density of states in the conduction band N_{c}
X<0.41 N_{c}=4.82·10^{15}·(m_{Γ}/m_{o})^{3/2}·T^{3/2} = 4.82·10^{15}·T^{3/2}·(0.063+0.083x)^{3/2} (cm^{3})X>0.41 N_{c}=4.82·10^{15}·(m_{cd}/m_{o})^{3/2}·T^{3/2} = 4.82·10^{15}·T^{3/2}·(0.850.14x)^{3/2} (cm^{3})
where m_{cd} is effective mass of the density of states;
Effective density of states in the conduction band versus x. (Calculated) 
Effective density of states in the valence band N_{v}
N_{v} = 4.82·10^{15}·T^{3/2}·(0.51+0.25x)^{3/2} (cm^{3}) X>0.41 N_{c}=4.82·10^{15}·(m_{cd}/m_{o})^{3/2}·T^{3/2} = 4.82·10^{15}·T^{3/2}·(0.850.14x)^{3/2} (cm^{3})Effective density of states in the conduction band versus x. (Calculated) 
Intrinsic Carrier Concentration
n_{i} = (N_{c}·N_{v})^{1/2}exp[E_{g}/(2k_{b}T)]
The temperature dependences of the intrinsic carrier concentration. 1. x=0 2. x=0.3 3. x=0.6 4. x=1 
Dependences on Hydrostatic Pressure
E_{Γ} = (11.5  1.3 x)·10^{3}·P (eV)E_{X} = 0.8·10^{3}·P (eV)
E_{L} = 2.8·10^{3}·P (eV)
where P is pressure in kbar. (Adachi [1985])
Pressure dependence of the ΓX crossover. 300 K (Saxena [1980]) 
Energy Gap Narrowing at High Doping Levels
Energy gap narrowing versus donor(curve 1) and acceptor (curve 2) doping density for GaAs (x=0). Experimental points for pGaAs are taken from four different papers (Jain and Roulston [1991]) 
Energy gap narrowing versus donor (curve 1) and acceptor (curve 2)doping density for AlAs (x=1). The curvesare calculated according (Jain et al. [1990]) 
Band Discontinuities at Al_{x}Ga_{1x}As/GaAs Heterointerface
Valence band discontinuity:
ΔE_{v} =  0.46x (eV)Conduction band discontinuity:
x<0.41 ΔE_{c} = 0.79x (eV)x>0.41 ΔE_{c} = 0.4750.335x+0.143x^{2} (eV)
Energy gap narrowing versus donor(curve 1) and acceptor (curve 2) doping density for GaAs (x=0). Experimental points for pGaAs are taken from four different papers (Jain and Roulston [1991]) 