A calculation claims that a silicon sample is doped so heavily that sits only below at

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 calculation claims that a silicon sample is doped so heavily that μ\mu sits only Ec−μ=0.020 eVE_c-\mu=0.020\,\mathrm{eV} below EcE_c at 300 K300\,\mathrm{K}, then computes n=Nce−(Ec−μ)/kBT=2.8×1019×e−0.020/0.02585=1.29×1019 cm−3n=N_ce^{-(E_c-\mu)/k_BT}=2.8\times10^{19}\times e^{-0.020/0.02585}=1.29\times10^{19}\,\mathrm{cm^{-3}} and reports it as an accurate electron density. Find the error, and explain the direction in which the true density differs from the one computed.

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