AlGaAs - Aluminium Gallium Arsenide

Band structure and carrier concentration

Basic Parameters
Temperature Dependences
Dependence on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Band Discontinuities at AlxGa1-xAs/GaAs Heterointerface

Basic Parameters

Energy gap x<0.45      1.424+1.247x eV
x>0.45      1.9+0.125x+0.143x2
Energy separation (EΓL) between Γ and L valleys 0.29 eV
Energy separation (EΓ) between Γ and top of valence band 1.424+1.155x+0.37x2 eV
Energy separation (EX) between X-valley and top of valence band 1.9+0.124x+0.144x2 eV
Energy separation (EL) between L-valley and top of valence band 1.71+0.69x eV
Energy spin-orbital splitting 0.34-0.04x eV
Intrinsic carrier concentration x=0.1      2.1·105 cm-3
x=0.3      2.1·103 cm-3
x=0.5      2.5·102 cm-3
x=0.8      4.3·101 cm-3
Intrinsic resistivity x=0.1      4·109 Ω·cm
x=0.3      1·1012 Ω·cm
x=0.5      1·1014 Ω·cm
x=0.8      5·1014 Ω·cm
Effective conduction band density of states x<0.41      2.5·1019·(0.063+0.083x)3/2 cm-3
x>0.45      2.5·1019·(0.85-0.14x)3/2 cm-3
Effective valence band density of states 2.5·1019·(0.51+0.25x)3/2 cm-3


Band structure AlxGa1-x for x<0.41-0.45. Important minima of the condition band and maxima of the valence band
Band structure AlxGa1-x 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:
xc(L-X) = 0.35 eVEL=EX = 1.95 eV
xc(Γ-X) = 0.41 eVEΓ=EX = 1.97 eV
xc(Γ-L) = 0.47 eVEΓ=EL = 2.04 eV
(Saxena [1980]).
Ratio of the total carrier concentration to the carrier concentration in Γ-valley 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 EΓ, EX and EL one can use the data for GaAs (Aspnes [1976]).

EΓ=EΓ(0)-5.41·10-4·T2/(T+204) (eV)
      where EΓ(0)=1.519+1.155x+0.37x2 (eV)

EX=EX(0)-4.6·10-4·T2/(T+204) (eV)

      where EX(0)=1.981+0.124x+0.144x2 (eV)

EL=EL(0)-6.05·10-4·T2/(T+204) (eV)

      where EL(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 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)



Effective density of states in the conduction band Nc

X<0.41    Nc=4.82·1015·(mΓ/mo)3/2·T3/2 = 4.82·1015·T3/2·(0.063+0.083x)3/2 (cm-3)

X>0.41    Nc=4.82·1015·(mcd/mo)3/2·T3/2 = 4.82·1015·T3/2·(0.85-0.14x)3/2 (cm-3)

       where mcd 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 Nv

Nv = 4.82·1015·T3/2·(0.51+0.25x)3/2 (cm-3) X>0.41    Nc=4.82·1015·(mcd/mo)3/2·T3/2 = 4.82·1015·T3/2·(0.85-0.14x)3/2 (cm-3)

Effective density of states in the conduction band versus x.
(Calculated)

Intrinsic Carrier Concentration

ni = (Nc·Nv)1/2exp[-Eg/(2kbT)]

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

EΓ = (11.5 - 1.3 x)·10-3·P (eV)
EX = -0.8·10-3·P (eV)
EL = 2.8·10-3·P (eV)
where P is pressure in kbar. (Adachi [1985])
Pressure dependence of the Γ-X 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 p-GaAs 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 AlxGa1-xAs/GaAs Heterointerface

Valence band discontinuity:

ΔEv = - 0.46x (eV)

Conduction band discontinuity:

x<0.41       ΔEc = 0.79x (eV)
x>0.41       ΔEc = 0.475-0.335x+0.143x2 (eV)
Energy gap narrowing versus donor(curve 1) and acceptor (curve 2) doping density for GaAs (x=0).
Experimental points for p-GaAs are taken from four different papers
(Jain and Roulston [1991])