Starting from charge neutrality and the law of mass action

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

Starting from charge neutrality n−p=Nd−Nan-p=N_d-N_a and the law of mass action np=ni2np=n_i^2, derive the exact expression for nn in an uncompensated crystal (Na=0N_a=0). Then apply it to germanium doped with Nd=5.0×1013 cm−3N_d=5.0\times10^{13}\,\mathrm{cm^{-3}}, using the chapter's own rounded value for germanium's intrinsic density, ni=2.0×1013 cm−3n_i=2.0\times10^{13}\,\mathrm{cm^{-3}}, and find nn and pp.

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