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PN Junction Built-in Potential & Depletion Width Calculator

Carrier diffusion across a metallurgical PN junction leaves uncompensated ionized dopant cores, establishing an internal electric barrier and space-charge region.

Calculated Result
0.430 µm

Depletion Layer Width (W)

Built-in Potential (Vbi)

0.714 V

Peak Electric Field (Emax)

33.2 kV/cm

Total Junction Barrier (Vbi + Vr)

0.714 V

Calculation Breakdown

  1. Compute thermal built-in contact potential Vbi = Vt · ln(Na·Nd / ni²)Vbi = 0.0259 * ln((10000000000000000 * 10000000000000000) / 1e20) = 0.714 V
  2. Calculate total depletion space-charge width WW = √[(2·ε_si / q) · (Na + Nd)/(Na·Nd) · (Vbi + Vr)] = 0.430 µm

Depletion Width vs Reverse Bias (µm)

Interactive visualization based on your current inputs

µm
0.00.40.81.21.70 V2 V5 V10 VReverse Bias (V)Width (µm)

What Is the PN Junction Built-in Potential & Depletion Width Calculator?

Carrier diffusion across a metallurgical PN junction leaves uncompensated ionized dopant cores, establishing an internal electric barrier and space-charge region.

How Does the PN Junction Built-in Potential & Depletion Width Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

PN Junction Built-in Potential & Depletion Width Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

V_{bi} = \frac{k_B T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right), \quad W = \sqrt{\frac{2 \epsilon_{si}}{q} \left(\frac{N_A + N_D}{N_A N_D}\right) (V_{bi} + V_r)}

Depletion width expands with the square root of total junction barrier voltage (Vbi + Vr) and is inversely proportional to dopant density.

How to Use the PN Junction Built-in Potential & Depletion Width Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

Symmetric 10^16 cm^-3 PN Diode

Input Values:

acceptorDopingNaCm3:10000000000000000
donorDopingNdCm3:10000000000000000
reverseBiasVolts:0

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Uses relative permittivity 11.7 for crystalline silicon.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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