Germanium's conduction-band minimum lies at the point of the Brillouin zone

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Semiconductor physics and devices

Solid State Physics, Ch Semiconductors: masses, statistics, defect levels and mobility

Problem

Germanium's conduction-band minimum lies at the LL point of the Brillouin zone, giving four full ellipsoidal valleys (Mv=4M_v=4) with longitudinal mass ml=1.59 mem_l=1.59\,m_e and transverse mass mt=0.082 mem_t=0.082\,m_e. ((a)) Calculate the density-of-states mass of a single valley, md=(mlmt2)1/3m_d=(m_lm_t^2)^{1/3}. ((b)) Calculate the density-of-states mass for all four valleys together, mDOS=Mv2/3mdm_{\rm DOS}=M_v^{2/3}m_d. ((c)) Calculate the conductivity mass mc=3(1ml+2mt)−1m_c=3\left(\dfrac{1}{m_l}+\dfrac{2}{m_t}\right)^{-1}.

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