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Characteristics and Properties

NSM Archive - Aluminium Gallium Arsenide (AlGaAs) - Band structure and carrier concentration

Band structure and carrier concentration

Basic Parameters
Temperature Dependences
Dependence on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Band Discontinuities at Al_xGa_1-xAs/GaAs Heterointerface

Basic Parameters

Energy gap	x<0.451.424+1.247x eV x>0.451.9+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=0.12.1·105 cm-3 x=0.32.1·103 cm-3 x=0.52.5·102 cm-3 x=0.84.3·101 cm-3
Intrinsic resistivity	x=0.14·109 Ω·cm x=0.31·1012 Ω·cm x=0.51·1014 Ω·cm x=0.85·1014 Ω·cm
Effective conduction band density of states	x<0.412.5·1019·(0.063+0.083x)3/2 cm-3 x>0.452.5·1019·(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 eV EL=EX = 1.95 eV xc(Γ-X) = 0.41 eV EΓ=EX = 1.97 eV xc(Γ-L) = 0.47 eV EΓ=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 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·T²/(T+204) (eV)
where E_Γ(0)=1.519+1.155x+0.37x² (eV)

E_X=E_X(0)-4.6·10^-4·T²/(T+204) (eV)

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

E_L=E_L(0)-6.05·10^-4·T²/(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 L-valley of the conduction band

E_L=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

E_L=1.981-4.60·10^-4·T²/(T+204) (eV)

Effective density of states in the conduction band N_c

X<0.41  N_c=4.82·10¹⁵·(m_Γ/m_o)^3/2·T^3/2 = 4.82·10¹⁵·T^3/2·(0.063+0.083x)^3/2 (cm^-3)

X>0.41  N_c=4.82·10¹⁵·(m_cd/m_o)^3/2·T^3/2 = 4.82·10¹⁵·T^3/2·(0.85-0.14x)^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 = 4.82·10¹⁵·T^3/2·(0.51+0.25x)^3/2 (cm^-3) X>0.41  N_c=4.82·10¹⁵·(m_cd/m_o)^3/2·T^3/2 = 4.82·10¹⁵·T^3/2·(0.85-0.14x)^3/2 (cm^-3)

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

Intrinsic Carrier Concentration

n_i = (N_c·N_v)^1/2exp[-E_g/(2k_bT)]

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 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 Al_xGa_1-xAs/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 = 0.475-0.335x+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])