Lithium fluoride is a wide-gap ionic insulator with

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

Lithium fluoride is a wide-gap ionic insulator with Eg=14.2 eVE_g=14.2\,\mathrm{eV}, static permittivity εs=9.0\varepsilon_s=9.0, rock-salt lattice constant a=4.03 A˚a=4.03\,\mathrm{\AA}, and, as is typical of an alkali halide's anion-derived valence band, an electron effective mass me∗≈1.0 mem_e^*\approx1.0\,m_e and a hole effective mass mh∗≈1.0 mem_h^*\approx1.0\,m_e. ((a)) Apply the hydrogenic (Wannier) exciton formula to compute μX\mu_X, the predicted binding energy EbE_b and the predicted radius aXa_X. ((b)) The lowest exciton absorption peak in LiF is observed at 12.6 eV12.6\,\mathrm{eV}, well below the gap. Find the measured binding energy and compare it with the value from part (a). ((c)) Using aXa_X from part (a) and the criterion for the validity of the effective-mass hydrogenic treatment, decide whether the LiF exciton is better described as Wannier or Frenkel, and explain in one or two sentences why the calculation of part (a) is not expected to be reliable here.

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