 ## 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 0.726 eV Energy separation (EΓL) between Γ and L valleys 0.084 eV Energy separation (EΓX) between Γ and X valleys 0.31 eV Energy spin-orbital splitting 0.80 eV Intrinsic carrier concentration 1.5·1012 cm-3 Intrinsic resistivity 103 Ω·cm Effective conduction band density of states 2.1·1017 cm-3 Effective valence band density of states 1.8·1019 cm-3 Band structure and carrier concentration of GaSb. 300 K Eg= 0.726 eV EL = 0.81 eV EX = 1.03 eV Eso = 0.8 eV

### Temperature Dependences

#### Temperature dependence of the energy gap(Wu and Chen )

Eg = 0.813 - 3.78·10-4·T2/(T+94) (eV),
where T is temperature in degrees K (0 < T < 300).

#### Temperature dependence of energy EL

EL = 0.902 - 3.97·10-4·T2/(T+94) (eV)

#### Temperature dependence of energy EX(Lee and Woolley )

EX = 1.142 - 4.75·10-4·T2/(T+94) (eV)

#### Effective density of states in the conduction band

Nc = 4.0·1013·T3/2 (cm-3)

#### Effective density of states in the conduction band

Nc = 4.0·1013·T3/2 (cm-3)

#### Effective density of states in the valence band

Nv = 3.5·1015·T3/2 (cm-3) The temperature dependences of the intrinsic carrier concentration.

### Dependences on Hydrostatic Pressure

Eg = Eg(0) + 14.5·10-3P (eV)
EL = EL(0) + 5.0·10-3P (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 versus acceptor acceptor doping density. Curve is calculated for p-GaSb according to Jain et al. . Points show experimental results (Titkov et al. ).

#### For n-type GaSb(Jain et al. ):

Eg = 13.6·10-9·Nd1/3 + 1.66·10-7·Nd1/4 + 119·10-12·Nd1/2 (eV)

#### For p-type GaSb(Jain et al. ):

Eg = 8.07·10-9·Na1/3 + 2.80·10-7·Na1/4+ 4.12·10-12·Na1/2 (eV)

### Effective Masses

#### Electrons:

 For Γ-valley mΓ = 0.041mo In the L- valley the surfaces of equal energy are ellipsoids ml= 0.95mo mt= 0.11mo Effective mass of density of states mL= 16(mlmt2)1/3= 0.57mo In the X- valley the surfaces of equal energy are ellipsoids ml= 1.51mo mt= 0.22mo Effective mass of density of states mX= 9(mlmt2)1/3= 0.87mo

#### Holes:

 Heavy mh = 0.4mo Light mlp = 0.05mo Split-off band mso = 0.14mo Effective mass of density of states mv = 0.8mo Effective mass of density of conductivity (Heller and Hamerly ) mvc = 0.3mo

### Donors and Acceptors The diagram of IV group donor states (Vul' et al. ).

#### Ionization energies of shallow donors (eV)

 Te(L) Te(X) Se(L) Se(X) S(L) S(X) ~0.02 ≤0.08 ~0.05 ~0.23 ~0.15 ~0.30
For typical donor concentrations Nd≥ 1017 cm-3 the shallow donor states connected with Γ-valley did not appear.

#### Ionization energies of shallow acceptors (eV):

The dominant acceptor of undoped GaSb seems to be a native defect.
This acceptor is doubly ionizable
 Ea1 Ea2 Si Ge Zn 0.03 0.1 ~0.01 ~0.009 ~0.037 