The interband of a direct-gap semiconductor is tabulated at five photon energies: : ; :

PHYSICS · Subjective · 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

The interband ε2(ℏω)\varepsilon_2(\hbar\omega) of a direct-gap semiconductor is tabulated at five photon energies: ℏω (eV)\hbar\omega\,(\mathrm{eV}): 2,3,4,5,62,3,4,5,6; ε2\varepsilon_2: 5.0, 20.0, 15.0, 8.0, 3.05.0,\ 20.0,\ 15.0,\ 8.0,\ 3.0. Assume ε2\varepsilon_2 is negligible outside 22 to 6 eV6\,\mathrm{eV}, so this range carries the whole static Kramers-Kronig sum. Using the static Kramers-Kronig relation ε1(0)−1=2π∫0∞ε2(ℏω)ℏω d(ℏω),\varepsilon_1(0)-1=\frac{2}{\pi}\int_0^{\infty}\frac{\varepsilon_2(\hbar\omega)}{\hbar\omega}\,d(\hbar\omega), estimate ε∞\varepsilon_\infty, the part of ε1(0)\varepsilon_1(0) that this interband absorption accounts for, by trapezoidal integration over the four 1 eV1\,\mathrm{eV} strips of the table.

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