Calculator Inputs
Positive applied voltage models forward bias and lowers the barrier. Negative applied voltage models reverse bias and raises the barrier.
Formula Used
Thermal voltage
VT = kT / q
Built-in potential
Vbi = VT ln[(NaNd) / ni2]
Junction barrier under bias
Vj = Vbi - Va
Depletion width
W = √[(2εs/q) × ((Na + Nd) / (NaNd)) × Vj]
Peak electric field
Emax = 2Vj / W
Junction capacitance
Cj = εsA / W
This page uses the ideal abrupt pn-junction approximation. Real devices may differ because of high-level injection, series resistance, grading, temperature-dependent mobility, and fabrication effects.
How to Use This Calculator
- Select a material preset or choose a custom material.
- Enter temperature, acceptor doping, donor doping, and junction area.
- Set the applied voltage. Use positive values for forward bias and negative values for reverse bias.
- Optionally override intrinsic carrier concentration if you already know a measured or reference value.
- Click the calculate button to show the result section above the form.
- Review the result table, the depletion interpretation, and the Plotly graph.
- Use the CSV or PDF buttons to export the calculated output.
Example Data Table
| Material | T (K) | Na (cm-3) | Nd (cm-3) | ni (cm-3) | Va (V) | Vbi (V) | Effective Barrier (V) | W (µm) | Cj (pF) |
|---|---|---|---|---|---|---|---|---|---|
| Silicon | 300 | 1.00e17 | 5.00e16 | 1.00e10 | 0.20 | 0.815 | 0.615 | 0.155 | 674.0 |
| Germanium | 300 | 1.00e16 | 1.00e16 | 2.40e13 | 0.10 | 0.312 | 0.212 | 0.274 | 517.5 |
| Gallium Arsenide | 300 | 5.00e17 | 1.00e17 | 2.00e6 | -1.00 | 1.315 | 2.315 | 0.201 | 578.3 |
FAQs
1. What does this calculator mainly compute?
It computes built-in potential, biased barrier voltage, depletion widths, peak electric field, and junction capacitance for an ideal abrupt pn junction using the values you enter.
2. Why does forward bias reduce the barrier?
Forward bias opposes the built-in electric field. That lowers the energy barrier carriers must cross, so the effective junction barrier decreases and the depletion region becomes narrower.
3. Why does reverse bias increase depletion width?
Reverse bias adds to the junction field. That raises the effective barrier, expands the charge-separated region, increases depletion width, and usually lowers junction capacitance.
4. Which side gets the larger depletion width?
The more lightly doped side gets the wider depletion region. Lower carrier concentration means more distance is needed to balance the same junction charge.
5. Why is intrinsic concentration important?
Intrinsic concentration appears inside the logarithm for built-in potential. It changes strongly with temperature and material, so it has a major effect on barrier voltage estimates.
6. Are the results exact for real diodes?
No. The results are idealized. Real diodes also depend on series resistance, recombination, trap states, nonuniform doping, geometry, and measurement conditions.
7. When should I use the override for ni?
Use the override when you have a trusted experimental value, handbook reference, or a material model that differs from the built-in temperature approximation used here.
8. What happens if forward bias exceeds built-in potential?
This calculator clamps the ideal barrier and depletion width at zero for stability. In real devices, conduction rises strongly and simplified depletion formulas become less reliable.