Germanium's conduction-band minima lie along directions at the points

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Solid State Physics, Ch The Fermi surface: semiclassical dynamics and its measurement

Problem

Germanium's conduction-band minima lie along ⟨111⟩\langle111\rangle directions at the LL points. Near one such minimum the effective-mass tensor is diagonal along the valley axis and perpendicular to it, with longitudinal mass ml=1.59 mem_l=1.59\,m_e (along the axis) and transverse mass mt=0.082 mem_t=0.082\,m_e (perpendicular to it). A uniform force F\mathbf{F} is applied to an electron at the bottom of this valley, at 30∘30^\circ to the valley axis. ((a)) Find the angle between the resulting acceleration and the valley axis. ((b)) Find the angle between the force and the acceleration.

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