Gallium nitride (GaN) has

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

Gallium nitride (GaN) has, at a photon energy of

3.45\,\mathrm{eV}

just above its direct band edge at

300\,\mathrm{K}

, optical constants

n_{\rm opt}=2.4

and

\kappa_{\rm opt}=8\times10^{-3}

. Its free-exciton binding energy is

E_b=26\,\mathrm{meV}

. ((a)) Estimate the absorption coefficient and the absorption depth (

1/\alpha

) at

3.45\,\mathrm{eV}

. ((b)) Estimate the highest temperature at which GaN's free-exciton line could still be resolved, using the criterion that the line is resolvable while

E_b

exceeds the thermal energy

k_BT

. Comment on the result in the light of the room-temperature value

k_BT=26\,\mathrm{meV}

used elsewhere for GaAs.

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