Gallium arsenide crystallises in the zinc-blende structure: a face-centred cubic…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Semiconductor physics and devices

Condensed Matter Physics, Ch Tight binding, band filling and the three kinds of solid

Problem

Gallium arsenide crystallises in the zinc-blende structure: a face-centred cubic lattice with a two-atom primitive cell, one gallium atom (3 valence electrons) and one arsenic atom (5 valence electrons). Its measured band gap is

1.42\ \mathrm{eV}

. ((a)) Find the number of valence electrons per primitive cell, and say how many bands this fills exactly. ((b)) Compute

E_g/k_BT

300\ \mathrm{K}

, and compare it with germanium's (

26

), silicon's (

43

) and diamond's (

212

) to classify gallium arsenide as a metal, semiconductor or insulator.

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