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 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.
Bandgap Narrowing Calculator is a focused tool for the following task. 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. It reports Bandgap narrowing from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Bandgap Narrowing
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- Doping concentration (cm^-3)
- Required number in cm^-3. Doping concentration. Must be a finite number greater than 0 cm^-3 (reference 1e17 cm^-3; narrowing zero at/below reference).
The cited overview of Band gap supplies background for the terminology and domain context used by this tool.1
How Bandgap Narrowing works
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. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Bandgap narrowing (meV)
- Returned number in meV. Bandgap narrowing (magnitude). At least 0 meV.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- Doping concentration 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
-
Band gap — Wikipedia contributors
Similar or alternative tools
- Band-to-Band Tunneling Calculator
Estimate band-to-band tunneling current from the junction field through a field-driven exponential: I[nA]=coeff·E·exp(-E0/E) with E=electricFieldMVPerCm>0 MV/cm, E0=characteristicFieldMVPerCm>0 MV/cm, coeff=tunnelingCoefficient>=0 nA/(MV/cm). Defaults E0=40 MV/cm, coeff=1 nA/(MV/cm). Simplified Kane-like model; neglects barrier shape, temperature, and trap-assisted contributions; valid only for E comparable to E0 and for the fitted material.
- Varshni Bandgap Calculator
Evaluate the Varshni temperature dependence of a semiconductor bandgap: Eg(T)=Eg0 - alpha·T²/(T+beta), using a logarithmic evaluation that avoids overflowing T². The coefficients are material-specific empirical fit parameters; extrapolation beyond their fitted temperature range can produce nonphysical results.
- APD Breakdown Voltage Temperature Shift Calculator
Shift an APD breakdown voltage to operating temperature using the linear temperature coefficient model V(T)=Vref·[1+0.0011·(T-25 °C)]. Valid for reference breakdown Vref>0 V defined at 25 °C and junction temperature T in [-55, 175] °C inclusive; outside this range the 0.11%/°C linear approximation degrades. Vref is the breakdown magnitude (positive, not signed). Result is the breakdown magnitude at temperature. Device-specific tempco may vary.