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Mathematical Analysis

Minima of Conduction Band Valleys in [eV] at 300K:    AlxGa1-xAs                    [ref:1]

Eg(x) =     1.424 + 1.247x                              (0 < x < 0.45)
1.424 + 1.247 + 1.147(x-0.45)2     (0.45 < x < 1.0)

EL(x) = 1.708 + 0.642x

EX(x) = 1.900 + 0.125 + 0.143x2

E(k)  Diagram :  Effective Masses for AlxGa1-xAs   [ref:12]

A) Conduction Band Valleys
Eg(k) = h2k2/2mg*   where,
mg*/m0 = 0.067 + 0.083x (for Density of States); 0.067 + 0.083x (for Conductivity)
kg = 2p/a (0, 0, 0)

EL(k) = h2(k-kL)2/2mL*   where,
mL*/m0 = 0.56 + 0.1x (for DOS); 0.11 + 0.03x (for Conductivity)
kL = 2p/a (1/2, 1/2, 1/2)

EX(k) = h2(k-kX)2/2mX*   where,
mX*/m0 = 0.85 - 0.14x (for DOS); 0.32 - 0.06x (for Conductivity)
kX = 2p/a (0, 0, 1-D)

B) Valence Band Valleys
Ehh(k) = h2k2/2mhh*   where,
mhh*/m0 = 0.62 + 0.14x

Elh(k) = h2k2/2mlh*   where,
mlh*/m0 = 0.087 + 0.063x

Eso(k) = h2k2/2mso*  - Do    where,
mso*/m0 = 0.15 + 0.09x
Do = 0.34 - 0.04x

The Density of States effective mass for valence band, mvb, is found from
mvb = (mlh*3/2 + mhh*3/2)2/3
Eso(k)  is the split-off band and does not contribute to the DOS.