Band structure and carrier concentration of Gallium Arsenide (GaAs)

Band structure and carrier concentration
Basic ParametersTemperature 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 |
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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)
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The temperature dependences of the relative populations of the Γ, L and X valleys. (Blakemore [1982]). |
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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)
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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
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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 |