Bandgap Narrowing Calculator
Estimate heavy-doping bandgap narrowing in silicon relative to a 1e17 cm^-3 reference: ΔEg[meV]=max(0,18·log10(N/1e17)) where N is dopingPerCm3>0 cm^-3. Clamped to >=0 meV below reference. Empirical log-decade model for silicon; neglects temperature, compensation, and degeneracy beyond the fitted decade slope; invalid for N<=0.
Description
Estimate silicon heavy-doping bandgap narrowing from dopant concentration with a clipped logarithmic decade model.
Estimate heavy-doping bandgap narrowing in silicon relative to a 1e17 cm^-3 reference: ΔEg[meV]=max(0,18·log10(N/1e17)) where N is dopingPerCm3>0 cm^-3. Clamped to >=0 meV below reference. Empirical log-decade model for silicon; neglects temperature, compensation, and degeneracy beyond the fitted decade slope; invalid for N<=0.
When to use Bandgap Narrowing Calculator
- Estimate silicon heavy-doping bandgap narrowing from dopant concentration with a clipped logarithmic decade model.
- Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
- Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.
How the calculation works
Each tenfold increase above 10^17 cm⁻³ adds 18 meV; concentrations at or below the reference return zero.
ΔEg = max[0, 18·log10(N/10^17)] meV Interpreting the result
Each tenfold increase above 10^17 cm⁻³ adds 18 meV; concentrations at or below the reference return zero.
Assumptions and limitations
- The empirical slope omits temperature, dopant species, compensation, carrier degeneracy, and many-body model choice.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.