<P> In this case, the electron motion is no longer directly comparable to a free electron; the speed of an electron will depend on its direction, and it will accelerate to a different degree depending on the direction of the force . Still, in crystals such as silicon the overall properties such as conductivity appear to be isotropic . This is because there are multiple valleys (conduction - band minima), each with effective masses rearranged along different axes . The valleys collectively act together to give an isotropic conductivity . It is possible to average the different axes' effective masses together in some way, to regain the free electron picture . However, the averaging method turns out to depend on the purpose: </P> <Ul> <Li> For calculation of the total density of states and the total carrier density, via the geometric mean combined with a degeneracy factor g which counts the number of valleys (in silicon g = 6): <Dl> <Dd> m density ∗ = g 2 m x m y m z 3 (\ displaystyle m_ (\ text (density)) ^ (*) = (\ sqrt ((3)) (g ^ (2) m_ (x) m_ (y) m_ (z)))) </Dd> </Dl> <P> (This effective mass corresponds to the density of states effective mass, described later .) </P> For the per - valley density of states and per - valley carrier density, the degeneracy factor is left out . </Li> <Li> For the purposes of calculating conductivity as in the Drude model, via the harmonic mean <Dl> <Dd> m conductivity ∗ = 3 (1 m x ∗ + 1 m y ∗ + 1 m z ∗) − 1 (\ displaystyle m_ (\ text (conductivity)) ^ (*) = 3 \ left ((\ frac (1) (m_ (x) ^ (*))) + (\ frac (1) (m_ (y) ^ (*))) + (\ frac (1) (m_ (z) ^ (*))) \ right) ^ (- 1)) </Dd> </Dl> Since the Drude law also depends on scattering time, which varies greatly, this effective mass is rarely used; conductivity is instead usually expressed in terms of carrier density and an empirically measured parameter, carrier mobility . </Li> </Ul> <Li> For calculation of the total density of states and the total carrier density, via the geometric mean combined with a degeneracy factor g which counts the number of valleys (in silicon g = 6): <Dl> <Dd> m density ∗ = g 2 m x m y m z 3 (\ displaystyle m_ (\ text (density)) ^ (*) = (\ sqrt ((3)) (g ^ (2) m_ (x) m_ (y) m_ (z)))) </Dd> </Dl> <P> (This effective mass corresponds to the density of states effective mass, described later .) </P> For the per - valley density of states and per - valley carrier density, the degeneracy factor is left out . </Li> <Dl> <Dd> m density ∗ = g 2 m x m y m z 3 (\ displaystyle m_ (\ text (density)) ^ (*) = (\ sqrt ((3)) (g ^ (2) m_ (x) m_ (y) m_ (z)))) </Dd> </Dl>

What is the effective mass of an electron in silicon