Anisotropy of the Hot-Electron Problem in Semiconductors with Spheroidal Energy Surfaces

Energy gain for electrons in many-valley semiconductors for any orientation of electric field is determined. The anisotropy of the hot electron problem is characterized for conditions appropriate at low temperatures where noncollective behavior of the spheroidal surfaces prevails; it is expected that germanium and silicon will not generally exhibit pronounced anisotropy. Electrons ought to accelerate most readily in the [110] and [211] directions of the former element and in the [100] and [110] of the latter. Anisotropy of the collision time in germanium is shown not to affect the optimal energy gain directions in the limit of $K^{\prime }\to \infty$ ($K^{\prime }=\mathrm{ratio}\mathrm{of}\mathrm{longitudinal}\mathrm{to}\mathrm{transverse}\mathrm{collision}\mathrm{frequencies}$), but $K^{\prime }\to 0$ might produce a shift. The possible observation of the individual drift of injected electron pulses in the Haynes-Shockley experiment is discussed.