Calculator Inputs
Example Data Table
| Material | NA cm^-3 | ND cm^-3 | ni cm^-3 | Temperature | Approximate Vbi |
|---|---|---|---|---|---|
| Silicon | 1e16 | 1e15 | 1e10 | 300 K | 0.655 V |
| Silicon | 1e17 | 1e17 | 1e10 | 300 K | 0.833 V |
| Silicon | 5e15 | 2e16 | 1e10 | 300 K | 0.714 V |
Formula Used
Built in voltage: Vbi = Vt ln(NA ND / ni²)
Thermal voltage: Vt = kT / q
Effective barrier: Veff = Vbi - Va
Depletion width: W = √[(2εs / q)(1 / NA + 1 / ND)Veff]
Junction split: xn = W NA / (NA + ND), and xp = W ND / (NA + ND)
Peak electric field: Emax = q ND xn / εs = q NA xp / εs
How to Use This Calculator
- Select a semiconductor preset or choose custom.
- Enter acceptor and donor doping concentrations.
- Enter intrinsic carrier concentration for the material.
- Set temperature and choose the correct unit.
- Enter permittivity, bandgap, bias, and junction area.
- Enable temperature adjustment when you need a broader estimate.
- Press Calculate to view voltage and depletion results.
- Use CSV or PDF export for reports and records.
Understanding PN Junction Built In Voltage
The built in voltage is the natural barrier inside a pn junction. It forms when electrons and holes diffuse across the junction. Mobile carriers recombine near the interface. This leaves fixed ionized donors and acceptors behind. The uncovered charge creates an electric field. That field opposes more diffusion. At equilibrium, drift current and diffusion current balance.
Why Doping Matters
Donor and acceptor concentrations set the carrier gradient. Heavier doping raises the ratio used in the logarithm. So the barrier voltage rises. A lightly doped side spreads the depletion region farther. This calculator also estimates that split. It shows how much depletion lies in each side. This is useful for diode, sensor, and transistor work.
Temperature Effects
Thermal voltage is kT divided by q. It increases as temperature rises. Higher temperature can also increase intrinsic carrier concentration. That effect often lowers the built in voltage. The optional temperature adjusted intrinsic concentration helps compare lab conditions. Use the custom mode when your material data is measured.
Depletion Region Checks
The depletion width formula uses semiconductor permittivity and effective barrier voltage. Forward bias reduces the barrier. Reverse bias raises it. The calculator reports peak electric field, charge density, depletion capacitance, and potential split. These values help check whether a junction may face high fields or capacitance limits.
Practical Use
Start with consistent doping data. Enter donor, acceptor, and intrinsic concentration in the same style. The tool converts common units internally. Select a material preset for quick estimates. Change relative permittivity when using another semiconductor. Add junction area to estimate total depletion charge and capacitance. Download the table when you need a record for reports.
Design Meaning
Built in voltage is not an external battery. It appears across the depletion region. A voltmeter connects metal contacts and Fermi levels align. The internal barrier still controls carrier injection. This is why diode current changes strongly with applied voltage.
Good Input Practice
Use realistic doping ranges. Avoid values lower than intrinsic concentration unless you study weak junctions. Check the warning when the logarithm becomes small or negative. That result can indicate bad units or an unsuitable material preset. For advanced review, compare capacitance per area with measured C-V data.
FAQs
What is built in voltage?
Built in voltage is the internal potential barrier formed across a pn junction. It appears because electrons and holes diffuse, recombine, and leave fixed ionized dopants in the depletion region.
Can I measure built in voltage directly?
Not with a simple voltmeter across diode terminals at equilibrium. Contact potentials cancel in the external loop. The barrier still exists inside the junction and affects current flow.
Why does higher doping increase Vbi?
Higher doping increases the product NA ND. The logarithmic ratio becomes larger, so the calculated built in voltage rises when intrinsic concentration stays fixed.
What temperature should I enter?
Use the actual junction temperature. Room temperature is often entered as 300 K. Device self heating can make the junction warmer than ambient air.
What does positive bias mean here?
Positive bias is treated as forward bias. It reduces the effective depletion barrier by using Veff = Vbi - Va in the depletion calculation.
Why is depletion wider on one side?
The depletion region extends farther into the lighter doped side. Charge balance requires NA xp = ND xn, so the lower concentration side needs more width.
When should I adjust ni for temperature?
Use the adjustment when temperature differs greatly from 300 K. It gives a broader estimate using bandgap energy, but measured material data is better for precision.
Does this handle degenerate doping?
No. This calculator uses a standard nondegenerate abrupt junction model. Very heavy doping, graded junctions, and high injection conditions need more advanced device simulation.