Silicon's conduction-band density-of-states mass is

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

Solid State Physics, Ch Semiconductors: masses, statistics, defect levels and mobility

Problem

m_{\rm DOS}=1.08\,m_e

, giving

N_c=2.8\times10^{19}\,\mathrm{cm^{-3}}

300\,\mathrm{K}

; the Boltzmann (non-degenerate) approximation for

n

starts giving errors of order 10 per cent or more once the doping reaches roughly a third of

N_c

. GaAs has a single, isotropic conduction-band valley with electron effective mass

m^*=0.067\,m_e

. ((a)) Using the scaling

N_c\propto (m^*)^{3/2}

, estimate GaAs's effective density of states at

300\,\mathrm{K}

. ((b)) Estimate the doping density above which the non-degenerate approximation is no longer reliable for GaAs.

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