A silicon crystal doped with a single donor species (no acceptors) is measured over a…

PHYSICS · Subjective · 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

A silicon crystal doped with a single donor species (no acceptors) is measured over a wide temperature range, giving the electron densities below (ignore the slow

T^{3/2}

prefactor within each sloped region, as the chapter does). Data:

T=40\,\mathrm{K}

n=2.58\times10^{13}\,\mathrm{cm^{-3}}

;

T=50\,\mathrm{K}

n=1.23\times10^{14}\,\mathrm{cm^{-3}}

;

T=250\,\mathrm{K}

n=2.00\times10^{15}\,\mathrm{cm^{-3}}

;

T=750\,\mathrm{K}

n=5.52\times10^{15}\,\mathrm{cm^{-3}}

;

T=800\,\mathrm{K}

n=8.65\times10^{15}\,\mathrm{cm^{-3}}

. Identify which regime each row belongs to, and use the

40\,\mathrm{K}

and

50\,\mathrm{K}

points to find the donor energy

E_d

, and the

750\,\mathrm{K}

and

800\,\mathrm{K}

points to find the gap

E_g

(there

n

is only a few times its plateau value, so the doping cannot be ignored).

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