Depletion Width Abrupt Junction Calculator
Compute the total depletion width of an abrupt pn junction from built-in and applied reverse bias. Assumes silicon permittivity 11.7·ε0.
Description
Calculate total silicon depletion width for an abrupt pn junction from acceptor doping, donor doping, built-in voltage, and reverse bias.
An abrupt-junction depletion region extends into both sides of a pn junction, with more width on the more lightly doped side. This calculator returns the total width using both acceptor and donor concentrations.
When to use Abrupt PN Junction Depletion Width Calculator
- Estimate total depletion width of an abrupt silicon pn junction
- Study the square-root increase with reverse bias
- Compare a two-sided abrupt junction with a one-sided capacitance approximation
How the calculation works
The depletion approximation gives width proportional to the square root of total junction potential and of 1/NA + 1/ND. Silicon permittivity is modeled as 11.7·ε0.1
W = √[(2εSi/q)(Vbi + VR)(1/NA + 1/ND)] Interpreting the result
When one side is much more heavily doped, its reciprocal concentration contributes little and most depletion width lies in the lightly doped side.
Assumptions and limitations
- The junction is abrupt, one-dimensional, uniformly doped on each side, and treated with the depletion approximation.
- Built-in voltage is supplied rather than derived from doping and intrinsic concentration.
- Forward bias, breakdown, edge curvature, graded profiles, and field-dependent permittivity are not modeled.
References
-
Semiconductor Materials and pn Junction Fundamentals — University of Michigan