Calculator Inputs
Use the physics model for semiconductor parameters or the datasheet model for vendor capacitance curves.
Example Data Table
These sample scenarios help compare how geometry, doping, and bias influence capacitance.
| Case | Method | Profile | Area | Bias | Key Inputs | Estimated Capacitance |
|---|---|---|---|---|---|---|
| 1 | Physics | Abrupt | 1.00 mm² | 5.0 V | εr 11.7, Vbi 0.72 V, Na 1e16 cm⁻³, Nd 5e15 cm⁻³ | About 79.0 pF |
| 2 | Physics | Abrupt | 0.50 mm² | 12.0 V | εr 11.7, Vbi 0.75 V, Na 2e16 cm⁻³, Nd 1e16 cm⁻³ | About 28.6 pF |
| 3 | Physics | Graded | 1.20 mm² | 3.0 V | εr 11.7, Vbi 0.70 V, a 1e20 cm⁻⁴ | About 64.1 pF |
| 4 | Datasheet | Bias model | 0.80 mm² | 8.0 V | Cj0 100 pF, m 0.50, Vj 0.75 V | About 29.3 pF |
Formula Used
For an abrupt junction, depletion width and capacitance follow the standard depletion approximation.
W = sqrt((2 ε / q) × (1/Na + 1/Nd) × (Vbi + Vr))
C = εA / W
Cj0 = εA / W0
For a linearly graded junction, the depletion width changes with the cube root of the effective reverse potential.
W = ((12 ε (Vbi + Vr)) / (q a))^(1/3)
C = εA / W
For a datasheet-style bias model, capacitance is scaled from a zero-bias reference using a grading coefficient.
C = Cj0 / (1 + Vr / Vj)^m
Where ε is semiconductor permittivity, A is junction area, q is electronic charge, Na and Nd are doping concentrations, a is doping gradient, Vbi is built-in potential, Vr is reverse bias, and m is the grading exponent.
How to Use This Calculator
- Select the calculation method that matches your available data.
- Choose a material preset or enter a custom relative permittivity.
- Enter the junction area and select the correct area unit.
- Provide reverse bias and temperature for the operating condition.
- For the physics model, choose abrupt or graded behavior.
- Enter Na and Nd for abrupt junctions, or the gradient for graded junctions.
- Use manual built-in potential, or let the abrupt model estimate it automatically.
- Press the calculate button to show the result above the form.
- Download the result in CSV or PDF format for documentation.
8 FAQs
1. What does junction capacitance represent?
It is the capacitance formed by charge separation across the depletion region of a semiconductor junction. It changes with area, doping profile, material permittivity, and reverse bias.
2. Why does capacitance decrease with higher reverse bias?
Higher reverse bias widens the depletion region. Since capacitance is proportional to permittivity times area divided by depletion width, a wider depletion region lowers capacitance.
3. When should I use the abrupt profile?
Use it when the transition between p and n regions is relatively sharp. Many textbook pn junctions, step junction approximations, and quick device estimates use this model.
4. When is the graded profile more suitable?
Choose it when the dopant concentration changes gradually through the junction. Diffused junctions often behave more like graded structures than abrupt ones.
5. What is the datasheet model useful for?
It is useful when a vendor provides zero-bias capacitance, grading coefficient, and junction potential. That lets you estimate capacitance quickly without detailed doping data.
6. Does this calculator include package parasitics?
No. It estimates depletion-region junction capacitance only. Lead, pad, package, interconnect, and frequency-dependent parasitics should be added separately in a full design model.
7. Can I use automatic built-in potential for every case?
Automatic estimation is provided for the abrupt physics model using doping and temperature. For graded and datasheet approaches, enter the potential manually or use vendor data.
8. Which units are used internally?
The physics equations use permittivity in F/cm, area in cm², doping in cm⁻³, gradient in cm⁻⁴, and depletion width in cm, then display user-friendly outputs.