Gallium arsenide has relative permittivity and a conduction electron effective mass of .

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Semiconductor physics and devices

Condensed Matter Physics, Ch Homogeneous semiconductors: counting carriers, doping and mobility

Problem

Gallium arsenide has relative permittivity

\epsilon_r=12.9

and a conduction electron effective mass of

0.067m

. ((a)) Estimate a donor's binding energy and orbit radius in gallium arsenide, using the same hydrogen-scaling model as for phosphorus in silicon. ((b)) Gallium arsenide holds

4.42\times10^{22}

atoms per

\mathrm{cm^3}

. Estimate how many atoms the donor orbit encloses, and say whether treating the crystal as a uniform dielectric is still reasonable at this size.

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