InP is a direct-gap semiconductor with electron effective mass

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Dielectric and optical properties of solids · Dielectric and optical properties of solids

Solid State Physics, Ch Optical properties: interband absorption, excitons and luminescence

Problem

InP is a direct-gap semiconductor with electron effective mass me∗=0.077 mem_e^*=0.077\,m_e, heavy-hole effective mass mhh∗=0.60 mem_{hh}^*=0.60\,m_e, static relative permittivity εs=12.5\varepsilon_s=12.5 and conventional lattice constant a=5.87 A˚a=5.87\,\mathrm{\AA}. Treat the electron-hole pair as a hydrogenic Wannier exciton. ((a)) Find the reduced effective mass μX\mu_X. ((b)) Find the exciton binding energy EbE_b. ((c)) Find the exciton radius aXa_X, and check whether aX≫aa_X\gg a, the condition needed for the effective-mass treatment to be trusted.

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