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Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator

Easily calculate and compute abrupt pn junction built-in potential (v_bi), depletion width & peak e-field calculator with accurate equations, live formulas, and expert guidance.

P-region acceptor impurity doping density.

N-region donor impurity doping density.

1.5e10 for Silicon at 300 K.

Reverse bias voltage (enter 0 for zero-bias equilibrium, positive for reverse bias).

11.7 for Silicon.

Calculated Result
0.68 V

Built-in Potential (V_bi)

Built-in Potential (V_bi)

0.68 V

Built In Potential Vbi

0.675

Total Depletion Width Um

0.512

P Side Depletion Xp Um

0.171

N Side Depletion Xn Um

0.341

0.68 — V

Calculation Breakdown

  1. Applied FormulaDetermines the equilibrium built-in contact potential, depletion layer width, penetration depths into P/N regions, and maximum junction electric field for an abrupt PN diode.V_{bi} = \frac{k_B T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right), \quad E_{max} = \frac{2(V_{bi} + V_R)}{W}

PN Junction Depletion Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.50.81.0Built-in Potential (V_bi)

What Is the Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator?

This tool computes abrupt pn junction built-in potential (v_bi), depletion width & peak e-field calculator with high precision arithmetic.

How Does the Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator Work?

Determines the equilibrium built-in contact potential, depletion layer width, penetration depths into P/N regions, and maximum junction electric field for an abrupt PN diode.

Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator Formula & Variables

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

Vbi=kBTqln⁡(NANDni2),Emax=2(Vbi+VR)WV_{bi} = \frac{k_B T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right), \quad E_{max} = \frac{2(V_{bi} + V_R)}{W}

Determines the equilibrium built-in contact potential, depletion layer width, penetration depths into P/N regions, and maximum junction electric field for an abrupt PN diode.

How to Use the Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Abrupt PN Junction Built-in Potential (V_bi), Depletion Width & Peak E-Field Calculator Example

Input Values:

acceptorDopingNaPerCm3:10000000000000000
donorDopingNdPerCm3:5000000000000000
intrinsicCarrierNiPerCm3:15000000000
appliedVoltageVolts:0
relativeDielectricConstEr:11.7
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required V.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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