Device physicsMVP
Bandgap energy explorer
How a semiconductor's bandgap shrinks with temperature, via the empirical Varshni relation.
Inputs
Empirical Varshni fit
Uses Eg(T) = Eg(0) − αT²/(T+β) with standard published parameters. It is an empirical fit valid over a limited temperature range, not a first-principles calculation.
Silicon (Si) bandgap at 300 K
1.125 eV
Interpretation
A semiconductor’s bandgap narrows as temperature rises, because the lattice expands and electron–phonon interactions grow. The Varshni fit captures this with three material-specific constants. A smaller bandgap at higher temperature is part of why intrinsic carrier concentration — and leakage — climb with temperature.
Formula
Eg(T) = Eg(0) − α·T² / (T + β)
Empirical; α and β are material-specific.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Eg(T) | Bandgap at temperature T | eV |
| Eg(0) | Bandgap at 0 K | eV |
| α | Varshni α parameter | eV/K |
| β | Varshni β parameter | K |
| T | Temperature | K |
Assumptions & validity
This tool assumes:
- Empirical Varshni fit with standard published parameters.
- Valid over a limited temperature range; not a first-principles result.
Worked example
Silicon at 300 K (Eg0 = 1.17 eV, α = 4.73×10⁻⁴, β = 636).
Eg ≈ 1.17 − 4.73e-4·300²/(300+636) ≈ 1.12 eV