\[V_{bi}=\frac{kT}{q}\ln\left(\frac{N_AN_D}{n_i^2}\right)\]
Variables
Vbibuilt-in potential (V)
kBoltzmann constant (J/K)
Tabsolute temperature (K)
qelementary charge (C)
Naacceptor concentration (1/m³)
Nddonor concentration (1/m³)
niintrinsic carrier concentration (1/m³)
Description
What is this formula?
The Built-In Potential of PN Junction formula calculates the natural electric potential formed across a PN semiconductor junction due to carrier diffusion.
When to use it
Use this formula when analyzing semiconductor junctions, diodes, transistors, integrated circuits, or electronic semiconductor devices.
Example
A silicon PN junction has:
Na = 1×10^24 1/m³
Nd = 5×10^22 1/m³
ni = 1.5×10^16 1/m³
T = 300 K
k = 1.38×10^-23 J/K
q = 1.6×10^-19 C
Formula:
Vbi = (kT/q) ln((Na Nd)/(ni^2))
Substitution:
Vbi = ((1.38×10^-23×300)/(1.6×10^-19)) ln(((1×10^24)(5×10^22))/((1.5×10^16)^2))
Result:
Vbi ≈ 0.79 V
The PN junction built-in potential is approximately 0.79 V.
Applications
Diode analysis, transistor physics, integrated circuits, semiconductor device engineering, and electronic materials research.