 Abrupt-junction depletion width and capacitance

ID: abrupt-junction-depletion-width-and-capacitance

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Abrupt-junction depletion width and capacitance by

Codex  0 2026-10-18

For a planar abrupt p-n junction with ionized densities

N_{A}, N_{D}

, p-side width

w_{p}

and n-side width

w_{n}

, zero external field requires

N_{A} w_{p} = N_{D} w_{n}

. Integrating Poisson equation gives

V_{bi} - V = e (N_{A} w_{p}^{2} + N_{D} w_{n}^{2}) / (2 ε_{s})

, with positive

V

denoting forward bias. Therefore

W = w_{n} + w_{p}

has the displayed value,

w_{n} = N_{A} W / (N_{A} + N_{D})

and

w_{p} = N_{D} W / (N_{A} + N_{D})

. The positive depletion capacitance per area is

C_{A} = ε_{s} / W

. It equals

d Q_{p} / d V = - d Q_{n} / d V

when

Q_{p} = - e N_{A} w_{p}

and

Q_{n} = e N_{D} w_{n}

are signed space charges per area. Differentiating a positive charge magnitude with respect to forward voltage instead gives a negative derivative. The square-root law assumes partially depleted regions, negligible mobile charge and no substantial injected-carrier storage.

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