A pure semiconductor's carrier density

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, with the slowly varying

T^{3/2}

prefactor already divided out as the text does for germanium, gives the following values of

y=\ln(n/T^{3/2})

against

1/T

, in arbitrary consistent units. Data: at

T=250\,\mathrm{K}

1/T=0.004000\,\mathrm{K^{-1}}

and

y=-9.57

; at

T=300\,\mathrm{K}

1/T=0.003333\,\mathrm{K^{-1}}

and

y=-5.32

; at

T=350\,\mathrm{K}

1/T=0.002857\,\mathrm{K^{-1}}

and

y=-2.28

; at

T=400\,\mathrm{K}

1/T=0.002500\,\mathrm{K^{-1}}

and

y=0.00

. Using the two end points, find the slope of

y

against

1/T

, and hence estimate the gap

E_g

extrapolated to

0\,\mathrm{K}

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