Calculate the built-in potential for a Silicon P-N junction with ND=10...
Calculation of Built-in Potential for a Silicon P-N Junction
Given Data
- ND = 10^16/cm3
- NA = 10^19/cm3
- Temperature T = 300 K
- Intrinsic Carrier Concentration ni = 10^10/cm3
Explanation
The built-in potential for a P-N junction is the potential difference that exists across the junction when the P-type and N-type regions are brought in contact with each other. This potential barrier is due to the diffusion of the majority carriers from one side to the other and the recombination of minority carriers in the junction region.
The built-in potential is given by the equation:
Vbi = (kT/q) * ln(NA * ND / ni^2)
Where k is the Boltzmann constant, T is the temperature, q is the electronic charge, NA and ND are the doping concentrations of the P-type and N-type regions, respectively, and ni is the intrinsic carrier concentration of silicon.
Calculation
Substituting the given values in the above equation:
Vbi = (1.38 * 10^-23 * 300 / 1.6 * 10^-19) * ln(10^19 * 10^16 / 10^20)
Vbi = 0.7 V
Conclusion
The built-in potential for a Silicon P-N junction with ND=10^16/cm3 and NA = 10^19/cm3 at 300 K is 0.7 V.