Depletion width, built-in potential and junction capacitance calculator
Device physics and crystals. Everything is calculated in your browser; nothing you enter is sent to a server.
KEY POINTS
For an abrupt junction, the depletion width is W = √(2ε(Vbi + VR)/q × (NA + ND)/(NA·ND)). It extends mostly into the lightly doped side and grows with the square root of reverse bias. Junction capacitance Cj = ε/W falls as reverse bias rises. A silicon p⁺n junction with 10¹⁶ cm⁻³ on the n side has a built-in potential of about 0.8 V and a zero-bias depletion width of about 0.3 µm.
Inputs
Calculated with full ionization, an abrupt junction and the depletion approximation. For graded junctions made by diffusion, W scales with the cube root of voltage and is slightly wider than this value.
Reverse bias, depletion width and junction capacitance
p⁺n junction reference table (NA = 1×10¹⁹ cm⁻³)
| ND (cm⁻³) | Vbi (V) | W (0 V, µm) | W (10 V, µm) | Cj (10 V, nF/cm²) |
|---|---|---|---|---|
| 1.0×10¹⁴ | 0.774 | 3.163 | 11.804 | 0.878 |
| 1.0×10¹⁵ | 0.833 | 1.038 | 3.743 | 2.77 |
| 1.0×10¹⁶ | 0.893 | 0.340 | 1.187 | 8.72 |
| 1.0×10¹⁷ | 0.952 | 0.112 | 0.378 | 27.4 |
| 1.0×10¹⁸ | 1.012 | 0.038 | 0.125 | 82.8 |
Which side the depletion region grows into
The depleted charge is equal on both sides of a pn junction (NA·xp = ND·xn), so the depletion region extends mostly into the lightly doped side. In a one-sided junction such as p⁺n, almost all of it lies on the n side, and width and capacitance depend only on the lightly doped side. That is why the drift layer of power devices, which must withstand high voltage, is lightly doped and thick.
Under reverse bias, the depletion region widens with the square root of voltage and junction capacitance falls with the inverse square root. Varactors (variable capacitance diodes) use this effect, and plotting 1/C² against voltage gives the doping of the lightly doped side from the slope (C-V doping profiling).
FAQ
Why does the depletion region extend into the lightly doped side?
The depleted charge must balance on both sides (NA·xp = ND·xn), so the side with fewer dopants must be depleted over a longer distance.
How is doping measured from capacitance?
Plotting 1/C² against reverse bias gives a line whose slope yields the doping of the lightly doped side (C-V profiling).
Related equipment and companies
More calculators
Device physics and crystals
- All semiconductor calculators
- MOSFET threshold voltage (Vth) calculator
- Miller index, d-spacing and plane angle calculator
- Sheet resistance and resistivity calculator (four-point probe, doping)
- Intrinsic carrier concentration and Fermi level calculator
- MOSFET drain current (I–V characteristics) calculator
- Diode I–V characteristics and forward voltage calculator
- Carrier mobility, diffusion coefficient and diffusion length calculator (silicon)
Last updated: October 23, 2026