Zinc oxide is a wide-gap semiconductor of interest for ultraviolet light-emitting devices

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

Zinc oxide is a wide-gap semiconductor of interest for ultraviolet light-emitting devices, with a direct gap

E_g=3.37\,\mathrm{eV}

300\,\mathrm{K}

, electron effective mass

m_e^*=0.24\,m_e

, hole effective mass

m_h^*=0.78\,m_e

(heavy, as is typical of oxide valence bands) and static permittivity

\varepsilon_s=8.5

. The wurtzite lattice constant is

a=3.25\,\mathrm{\AA}

. ((a)) Using the hydrogenic exciton model, compute the reduced mass

\mu_X

, the binding energy

E_b

and the radius

a_X

. ((b)) Compare

a_X

with the lattice constant

a

and decide whether the exciton is of the Wannier or the Frenkel type. ((c)) The measured lowest exciton absorption line sits

60\,\mathrm{meV}

below the gap. Compare this with the calculated

E_b

and comment briefly on why a hydrogenic calculation using the bulk static permittivity is expected to underestimate the binding energy when the exciton orbit spans only a modest number of lattice spacings. ((d)) Given

k_BT=25.9\,\mathrm{meV}

300\,\mathrm{K}

, state whether the ZnO exciton line, unlike GaAs's, can be resolved at room temperature, using the measured binding energy.

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