## 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