Calculation of Built-in Potential Barrier in a PN Junction Diode

Introduction
A PN junction diode is a semiconductor device that allows the flow of electric current in only one direction. It is formed by joining a p-type semiconductor and an n-type semiconductor. When the p-type and n-type materials are brought together, they form a depletion region, which acts as a barrier to the flow of electric current. The potential difference across the depletion region is called the built-in potential barrier.

Formula for Built-in Potential Barrier
The built-in potential barrier in a PN junction diode can be calculated using the following formula:

Vbi = (kT/q) * ln(Na*Nb/ni^2)

where Vbi is the built-in potential barrier, k is the Boltzmann constant (1.38 × 10^-23 J/K), T is the temperature in Kelvin (300 K in this case), q is the electron charge (1.6 × 10^-19 C), Na and Nb are the doping densities of the p-type and n-type semiconductors respectively, and ni is the intrinsic carrier concentration (1.5 × 10^10 for silicon at 300 K).

Calculation
Using the formula above, we can calculate the built-in potential barrier for a silicon PN junction diode at 300 K with Na = 1 × 10^18 /cm^3 and Nb = 1 × 10^15 /cm^3.

Vbi = (kT/q) * ln(Na*Nb/ni^2)
Vbi = (1.38 × 10^-23 × 300 / 1.6 × 10^-19) * ln(1 × 10^18 × 1 × 10^15 / (1.5 × 10^10)^2)
Vbi = 0.0259 V

Therefore, the built-in potential barrier in a silicon PN junction diode with Na = 1 × 10^18 /cm^3 and Nb = 1 × 10^15 /cm^3 is 0.0259 V.

Conclusion
The built-in potential barrier in a PN junction diode is an important parameter that determines the diode's behavior. It can be calculated using the formula above, which takes into account the doping densities of the p-type and n-type semiconductors, the intrinsic carrier concentration, and the temperature.