Depletion Width Calculator

Calculator Inputs

Junction Model

Acceptor Concentration (N_A)

Donor Concentration (N_D)

Doping Unit

Applied Bias (V)

Temperature (K)

Intrinsic Carrier Concentration (n_i)

n_i Unit

Relative Permittivity (ε_r)

Junction Area

Area Unit

Graph Bias Start (V)

Graph Bias End (V)

Graph Points

Example Data Table

Material	N_A (cm⁻³)	N_D (cm⁻³)	Bias (V)	Temperature (K)	ε_r	n_i (cm⁻³)
Silicon Diode A	1.0 × 10¹⁶	5.0 × 10¹⁵	0.00	300	11.7	1.0 × 10¹⁰
Silicon Diode B	5.0 × 10¹⁶	1.0 × 10¹⁶	-2.00	300	11.7	1.0 × 10¹⁰
Germanium Junction	2.5 × 10¹⁵	1.2 × 10¹⁵	-1.00	300	16.0	2.4 × 10¹³

Use these values to test the calculator and compare material sensitivity, doping imbalance, and reverse-bias widening.

Formula Used

For an abrupt PN junction, the built-in voltage is:

V_bi = V_T ln[(N_AN_D)/(n_i²)]

The thermal voltage is:

V_T = (kT / q)

The effective depletion potential under applied bias is:

V_eff = V_bi - V_a

The total depletion width is:

W = √[(2ε_s/q)(1/N_A + 1/N_D)V_eff]

The region split on each side is:

x_n = W·N_A / (N_A + N_D)

x_p = W·N_D / (N_A + N_D)

The peak electric field is approximated by:

E_max = 2V_eff / W

The small-signal junction capacitance is:

C_j = ε_sA / W

Here, ε_s = ε_rε₀, q is electronic charge, A is junction area, and all concentrations must be in consistent units.

How to Use This Calculator

Enter acceptor and donor doping concentrations for the semiconductor junction.
Select the concentration unit used by your source data.
Provide applied bias. Use negative values for reverse bias.
Enter temperature, intrinsic carrier concentration, and relative permittivity.
Add junction area to estimate capacitance directly.
Set graph start, end, and point count for the bias sweep.
Press the calculate button to show results above the form.
Review width split, capacitance, electric field, and plotted trend.
Use CSV or PDF buttons to export the current result set.

Frequently Asked Questions

1) What does depletion width represent?

Depletion width is the charge-free region around a PN junction where mobile carriers are swept out. It affects capacitance, electric field, switching behavior, and breakdown response in semiconductor devices.

2) Why does reverse bias increase depletion width?

Reverse bias adds to the junction potential barrier. That larger effective potential widens the depleted region, reduces capacitance, and increases the electric field across the junction.

3) Why does heavy doping reduce total width?

Higher doping raises charge density, so less physical distance is needed to balance the same junction potential. As doping increases, the depletion region becomes narrower overall.

4) Why are x_n and x_p different?

The depletion region extends further into the more lightly doped side. This happens because charge neutrality must hold, so the lower-concentration side needs a larger distance.

5) Can forward bias make the formula invalid?

Yes. If forward bias approaches or exceeds the built-in potential, the depletion approximation weakens and the square-root term can become nonphysical. This calculator warns when effective potential becomes nonpositive.

6) Why is intrinsic carrier concentration important?

Intrinsic carrier concentration affects built-in voltage. Since built-in voltage influences depletion width, using an appropriate n_i value for the semiconductor material improves accuracy.

7) What materials can this calculator model?

It can approximate abrupt PN junctions in materials such as silicon or germanium, provided you enter suitable relative permittivity and intrinsic carrier concentration values.

8) What is the plotted graph showing?

The chart shows how depletion width changes as bias varies across your selected range. Reverse bias widens the region, while forward bias narrows it toward collapse.