What is a PN Junction Built-in Potential?

The built-in potential (V_bi) is a fundamental parameter of a PN junction diode. It represents the potential difference across the depletion region in thermal equilibrium. When a P-type and N-type semiconductor are brought into contact, diffusion of carriers (holes and electrons) occurs until an electric field is established that opposes further flow. This internal barrier is the built-in potential.

Formula for Calculation

The standard formula for calculating the built-in potential is:

V_bi = (kT / q) * ln(N_A * N_D / n_i²)

• k: Boltzmann constant (1.38 × 10^-23 J/K)
• T: Absolute Temperature (Kelvin)
• q: Elementary charge (1.602 × 10^-19 C)
• N_A: Acceptor doping concentration
• N_D: Donor doping concentration
• n_i: Intrinsic carrier concentration (typically 10¹⁰ for Silicon at 300K)

How to Use This Calculator

To use this tool, simply input your material parameters. For standard Silicon at room temperature, use N_A and N_D values between 10¹⁵ and 10¹⁸ cm^-3. The calculator will automatically determine the thermal voltage (V_T) and provide a step-by-step breakdown of the logarithmic calculation to help you verify your manual homework or engineering designs.

FAQs

Does temperature affect V_bi? Yes, as temperature increases, the thermal voltage (kT/q) increases, but the intrinsic carrier concentration (n_i) increases much more rapidly, typically causing the built-in potential to decrease as the material becomes more intrinsic.

What is the typical value for Silicon? For most standard Silicon diodes, the built-in potential ranges between 0.6V and 0.8V.