A pure semiconductor's carrier density is read off a plot at two temperatures: and

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Semiconductor physics and devices

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

Problem

A pure semiconductor's carrier density is read off a plot at two temperatures:

n(320\ \mathrm{K}) = 5.00\times10^{14}\ \mathrm{cm^{-3}}

and

n(250\ \mathrm{K}) = 2.15\times10^{12}\ \mathrm{cm^{-3}}

. Using the same half-gap method as germanium's own data (correcting for the slowly varying

T^{3/2}

prefactor before comparing the two readings), estimate the gap extrapolated to

0\ \mathrm{K}

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