Built-In Potential Calculator
Compute the pn-junction built-in potential at 300 K as Vbi = (kT/q)·ln(NA·ND/ni²) where kT/q = 0.02585 V, NA and ND are acceptor and donor concentrations and ni is intrinsic concentration in cm⁻³.
Description
Compute the pn-junction built-in potential at 300 K as Vbi = (kT/q)·ln(NA·ND/ni²) where kT/q = 0.02585 V, NA and ND are acceptor and donor concentrations and ni is intrinsic concentration in cm⁻³.
Built-In Potential Calculator is a focused tool for the following task. Compute the pn-junction built-in potential at 300 K as Vbi = (kT/q)·ln(NA·ND/ni²) where kT/q = 0.02585 V, NA and ND are acceptor and donor concentrations and ni is intrinsic concentration in cm⁻³. It reports Vbi from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Built-In Potential
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- NA (cm^-3)
- Required number in cm^-3. Acceptor concentration on the p side. Must be greater than 0 cm⁻³.
- ND (cm^-3)
- Required number in cm^-3. Donor concentration on the n side. Must be greater than 0 cm⁻³.
- ni (cm^-3)
- Required number in cm^-3. Intrinsic carrier concentration at 300 K. Must be greater than 0 cm⁻³.
The cited overview of P–n junction supplies background for the terminology and domain context used by this tool.1
How Built-In Potential works
Compute the pn-junction built-in potential at 300 K as Vbi = (kT/q)·ln(NA·ND/ni²) where kT/q = 0.02585 V, NA and ND are acceptor and donor concentrations and ni is intrinsic concentration in cm⁻³. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Vbi (V)
- Returned number in V. Positive built-in potential across a nondegenerate pn junction at 300 K.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- NA must be at least 5e-324.
- ND must be at least 5e-324.
- ni must be at least 5e-324.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.
References
-
P–n junction — Wikipedia contributors
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