Using , derive a formula for how far shifts, relative to its position in the pure…

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

Using n=Nce−(Ec−μ)/kBTn=N_ce^{-(E_c-\mu)/k_BT}, derive a formula for how far μ\mu shifts, relative to its position in the pure crystal, when a crystal's electron density is raised from the intrinsic value nin_i to a doped value nn. Then use it to find that shift for silicon doped so that n=1.0×1015 cm−3n=1.0\times10^{15}\,\mathrm{cm^{-3}}, with ni=1.0×1010 cm−3n_i=1.0\times10^{10}\,\mathrm{cm^{-3}} (the measured value), and check the result against the chapter's own doped worked example.

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