The absorption coefficient of a semiconductor labelled is measured near its edge at…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Dielectric and optical properties of solids

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

Problem

The absorption coefficient of a semiconductor labelled

M

is measured near its edge at low temperature:

\alpha=25

49

81

121

169

and

225\,\mathrm{cm^{-1}}

\hbar\omega=2.10

2.14

2.18

2.22

2.26

and

2.30\,\mathrm{eV}

respectively. Band-structure calculations for

M

place the conduction-band minimum at the

L

point and the valence-band maximum at

\Gamma

. ((a)) Decide, by testing the two linearised plots taught for the direct and the indirect edge, which describes this data, and hence say whether the edge is direct or indirect. ((b)) The transition is assisted by the LA phonon at

L

, of energy

15\,\mathrm{meV}

. At this temperature the phonon-absorption branch is frozen out, so the intercept of the straight-line plot gives the threshold for phonon-emission-assisted transitions,

\hbar\omega_0 = E_g + \hbar\omega_{\rm LA}

. Find

E_g

. ((c)) State where the valence and conduction extrema lie, and give the crystal momentum the assisting phonon must supply, up to a reciprocal lattice vector.

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