where Ek, H, Hm are the electrical and magnetic field components and the a's represent single-energy-surface conductivity coefficients. The first coefficient in equation (2.8) is the zero-magnetic field electrical conductivity, and the second coefficient is associated with the nondirectional Hall effect. In the limit of weak fields the expansion can be limited to the first two terms. We use the electrical conductivity coefficient, aC, to define the conductivity effective mass m*i, by the relationship
e2
OCi lli Pi m (2.9)
and the Hall effect coefficient, aH5 to define the Hall mobility effective mass by means of [37]
e3
aHi ' 123i i (2.10)
To solve for m i, mi, and mi equations (2.6), (2.9) and (2.10) are equated to the following expressions for pi, Gjk' and jkZ:
1
Pi 3 f f0(k)d3k (2.11)
47
e2 fo 3E 3E 3k
ejk T 3 a d (2.12)
4jk T31 f4E fTj Dp q k pq