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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.