Band structure and carrier concentration of Germanium (Ge)

Band structure and carrier concentration
Basic ParametersTemperature Dependences
Dependences on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Effective Masses and Density of States
Donors and Acceptors
Basic Parameters
Energy gap | 0.661 eV |
Energy separation (EΓ1) | 0.8 eV |
Energy separation (ΔE>) | 0.85 eV |
Energy spin-orbital splitting | 0.29 eV |
Intrinsic carrier concentration | 2.0·1013 cm-3 |
Intrinsic resistivity | 46 Ω·cm |
Effective conduction band density of states | 1.0·1019 cm-3 |
Effective valence band density of states | 5.0·1018 cm-3 |
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Band structures of Ge.
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Temperature Dependences
Temperature dependences of the energy gap:
Eg = 0.742- 4.8·10-4·T2/(T+235) (eV),where T is temperature in degrees K.
Temperature dependence of the direct band gap EΓ1:
EΓ1 = 0.89 - 5.82·10-4·T2/(T+296) (eV),Effective density of states in the conduction band:
Nc = 4.82·1015·M·[mc/mo]3/2·T3/2 (cm-3), or Nc = 1.98·1015·T3/2 (cm-3)M = 4 is the number of equivalent valleys in the conduction band,
mc = 0.22mo is the effective mass of the density of states in one valley of the conduction band.
Effective density of states in the valence band:
Nν = 9.6·1014T3/2 (cm-3)Dependences on Hydrostatic Pressure
Eg = Eg(0) + 5.1·10-3P (eV)EΓ1 = EΓ1(0) + 1.53·10-2P (eV),
where P is pressure in kbar.
Energy Gap Narrowing at High Doping Levels
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Energy gap narrowing versus donor (curve 1) and acceptor (curve 2) doping density. Open curves are experimental values. (Jain and Roulston [1991]) |
For n-type Ge:
ΔEg = 8.67·(Nd·10-18)1/3 + 8.14·(Nd·10-18)1/4 + 4.31·(Nd·10-18)1/2 (eV)For p-type Ge:
ΔEg = 8.21·(Na·10-18)1/3 + 9.18·(Na·10-18)1/4 + 5.77·(Nd·10-18)1/2 (eV)(Jain and Roulston [1991]).
Effective Masses
Electrons: | |
The surfaces of equal energy are ellipsoids | |
ml = 1.59mo | |
mt = 0.0815mo | |
Effective mass of density of states | |
mc=(9mlmt2)1/3 | mc=0.22mo |
Effective mass of conductivity | mcc=0.12mo |
Holes: | |
Heavy | mh = 0.33mo |
Light | mlp = 0.043mo |
Split-off band | mso = 0.084mo |
Effective mass of density of states | mv = 0.34mo |
Donors and Acceptors
Ionization energies of shallow donors (eV):
As | P | Sb | Bi | Li |
0.014 | 0.013 | 0.010 | 0.013 | 0.093 |
Ionization energies of shallow acceptors (eV):
Al | B | Ga | In | Tl |
0.011 | 0.011 | 0.011 | 0.012 | 0.013 |