What Is the PN Junction Built-in Potential & Depletion Width Calculator?
A PN junction is the elementary building block of semiconductor diodes, solar cells, and bipolar transistors.
How Does the PN Junction Built-in Potential & Depletion Width Calculator Work?
Diffusing electrons and holes uncover fixed ionized dopants, setting up an opposing built-in electric field.
PN Junction Built-in Potential & Depletion Width Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
V_{ ext{bi}} = rac{k_B T}{q} lnleft( rac{N_a N_d}{n_i^2}
ight), quad W = sqrt{ rac{2 epsilon_s}{q}left( rac{1}{N_a} + rac{1}{N_d}
ight)(V_{ ext{bi}} + V_R)}
One-dimensional step junction electrostatics and space charge layer width.
How to Use the PN Junction Built-in Potential & Depletion Width Calculator
- Enter acceptor and donor dopant densities, applied reverse bias, and absolute temperature.
Step-by-Step Example Calculation
Silicon Step Junction at Equilibrium
Input Values:
acceptorDopingNaCm3:10000000000000000
donorDopingNdCm3:100000000000000000
appliedReverseBiasVolts:0
temperatureKelvin:300
Worked Steps: Built-in potential V_bi = 0.754 V, depletion width W = 0.329 µm, capacitance C_j = 31.4 pF/cm².
Understanding Your Result
Shows depletion width in micrometers, junction capacitance, and peak field at the metallurgical interface.
Factors That Affect the Result
- Higher doping narrows the depletion region and increases junction capacitance.
When Should You Use This Calculator?
- Varactor diode tuning, photodiode active area sizing, and avalanche breakdown modeling.
Assumptions & Limitations
- Assumes abrupt step doping profile and complete ionization of dopants.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard depletion approximation in semiconductor physics.