- Mathematically speaking, charge transfer in semiconductor devices is due both to conduction driven by the electric field (drift) and by diffusion. For a P-type region, where holes conduct with electrical conductivity σ and diffuse with diffusion constant D, the net current density is given by
- with q the elementary charge (1.6×10−19 coulomb) and p the hole density (number per unit volume). Conduction forces the holes along the direction of the electric field. Diffusion moves the carriers in the direction of decreasing concentration, so for holes a negative current results for a positive density gradient. (If the carriers are electrons, we replace the hole density p by the negative of the electron density n; in some cases, both electrons and holes must be included.) When the two current components balance, as in the pn-junction depletion region at dynamic equilibrium, the current is zero due to the Einstein relation, which relates D to σ.
Formation of depletion region in an MOS capacitor
Depletion width describes the width of the depletion region in a semiconductor, particularly in geometries that are one-dimensional, like the pn-junction and MOS capacitor. The width of the depletion region is governed by the principle of charge neutrality. Two examples follow:
Depletion width in pn-junction
Depletion width in MOS capacitor
Electric field in depletion layer and band bending
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