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.

Description

Varshni Bandgap Calculator is a focused tool for the following task. 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. It reports Bandgap from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.

When to use Varshni Bandgap

Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.

Temperature (K): Required number in K. Lattice temperature. Must be a finite number greater than 0 K.
Bandgap at 0 K (eV): Optional number in eV. Bandgap at 0 K. Must be a finite number greater than 0 eV; silicon default 1.17 eV.
Varshni alpha (eV/K): Optional number in eV/K. Varshni alpha coefficient. Must be a finite number at least 0 eV/K; silicon default 4.73e-4 eV/K.
Varshni beta (K): Optional number in K. Varshni beta coefficient. Must be a finite number greater than 0 K; silicon default 636 K.

The cited overview of Band gap supplies background for the terminology and domain context used by this tool.^[1]

How Varshni Bandgap works

Bandgap (eV): Returned number in eV. Bandgap at temperature T (eV). Finite; may be negative if T far outside fitted range.

Limitations and assumptions

Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
Temperature must be at least 5e-324.
Bandgap at 0 K must be at least 5e-324.
Varshni alpha must be at least 0.
Varshni beta 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

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.
Heterojunction Band Offset Calculator
Partition a heterojunction bandgap difference into conduction- and valence-band offsets using a material-specific empirical fraction.
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.