Band Gap Calculator
Calculate band gap energy and absorption edge wavelength for semiconductors
About Band Gap
The band gap is the energy difference between the valence band and conduction band in a semiconductor. It determines the minimum photon energy required to excite an electron from the valence band to the conduction band.
Key Formulas:
- Eg = hc/λ (photon energy)
- Eg(T) = Eg(0) - αT²/(T+β) (Varshni equation)
- 1240/λ(nm) ≈ Eg(eV) (quick conversion)
Spectral Regions:
- UV: λ < 400 nm → Eg > 3.1 eV
- Visible: 400-700 nm → Eg: 1.8-3.1 eV
- Near IR: 700-1500 nm → Eg: 0.8-1.8 eV
- Mid IR: > 1500 nm → Eg < 0.8 eV
What Is a Band Gap?
The band gap (Eg) is the energy difference between the top of the valence band and the bottom of the conduction band in a solid. Electrons in the valence band are bound to atoms, while electrons in the conduction band are free to move and conduct electricity. The band gap determines a material's electrical and optical properties — whether it's a conductor (no gap), semiconductor (moderate gap 0.5-3 eV), or insulator (large gap > 3 eV).
When a photon with energy greater than the band gap strikes a semiconductor, it can excite an electron from the valence band into the conduction band, creating an electron-hole pair. This process is the foundation of photovoltaics (solar cells), photodetectors, LEDs, and laser diodes. The wavelength of light absorbed or emitted is directly related to the band gap by the equation E = hc/λ.
Band Gap Energy Relations
Where:
- Eg= Band gap energy (eV)
- h= Planck constant = 6.626 × 10⁻³⁴ J·s
- c= Speed of light = 2.998 × 10⁸ m/s
- λ= Wavelength of absorbed/emitted photon (m)
- T= Temperature in Kelvin
- Eg(0)= Band gap at 0 K
- α, β= Varshni parameters (material-specific)
Semiconductor Classification by Band Gap
The band gap value classifies semiconductors into distinct categories:
| Category | Band Gap | Materials | Applications |
|---|---|---|---|
| Very Narrow / Semimetal | < 0.5 eV | InAs (0.415 eV), InSb (0.17 eV) | IR detectors, thermoelectrics |
| Narrow Bandgap | 0.5-1.5 eV | Si (1.12 eV), Ge (0.67 eV) | Transistors, solar cells, ICs |
| Standard Semiconductor | 1.5-3.0 eV | GaAs (1.42 eV), CdTe (1.5 eV) | Optoelectronics, RF, solar |
| Wide Bandgap | > 3.0 eV | GaN (3.47 eV), SiC (3.26 eV) | Power electronics, UV LEDs, 5G |
Temperature Dependence — Varshni Equation
Semiconductor band gaps shrink as temperature increases, following the empirical Varshni equation: Eg(T) = Eg(0) − αT²/(T+β). The parameters α and β are material-specific constants determined experimentally. This temperature dependence is crucial for device design — a transistor that works at room temperature may leak excessive current at 85°C (typical operating temperature for automotive electronics) because the band gap has narrowed, increasing intrinsic carrier concentration.
Silicon's band gap decreases by about 44 meV from 0K to 300K (from 1.166 eV to ~1.12 eV). Wide-bandgap semiconductors like GaN show smaller relative shifts, which is one reason they excel in high-temperature applications. The calculator uses Varshni parameters for seven common semiconductors and lets you compute the band gap at any temperature.
How to Use This Calculator
Choose from three calculation modes:
- From Wavelength: Enter the absorption edge wavelength in nanometers (the longest wavelength that can excite an electron across the band gap). The calculator computes Eg = hc/λ, frequency, and classifies the semiconductor type.
- From Energy: Enter the band gap energy directly in eV. The calculator computes the corresponding wavelength, frequency, and classification. This mode is ideal when you already know the band gap value.
- From Material (Temperature Dependent): Select a semiconductor material from the dropdown (Si, Ge, GaAs, InP, GaN, InAs, AlAs) and enter the temperature in Kelvin. The calculator applies the Varshni equation to compute the temperature-adjusted band gap, wavelength, frequency, and the energy shift from 0K.
Real-World Applications
Band gap engineering is the cornerstone of modern electronics. Silicon's band gap of 1.12 eV is nearly ideal for room-temperature logic circuits — low enough to conduct with modest voltage but high enough to prevent excessive leakage. The entire $500 billion semiconductor industry is built around controlling and exploiting silicon's band gap through doping, strain, and heterostructure design.
In optoelectronics, band gap determines emission color. Red LEDs use GaAs (1.42 eV → 873 nm, near-IR) with phosphor conversion, while blue LEDs required the development of GaN (3.47 eV → 357 nm, UV) — a breakthrough that earned the 2014 Nobel Prize in Physics. Solar cell efficiency depends critically on matching the band gap to the solar spectrum: the theoretical maximum efficiency for a single-junction cell occurs around 1.34 eV (Shockley-Queisser limit).
Worked Examples
Silicon Absorption Edge
Problem:
Silicon has a band gap of 1.12 eV at room temperature. What wavelength of light does this correspond to, and what part of the spectrum?
Solution Steps:
- 1Use conversion: λ = hc/Eg
- 2Convert Eg to joules: 1.12 × 1.602 × 10⁻¹⁹ = 1.794 × 10⁻¹⁹ J
- 3λ = (6.626 × 10⁻³⁴ × 2.998 × 10⁸) / 1.794 × 10⁻¹⁹ = 1.107 × 10⁻⁶ m = 1107 nm
- 4Quick check with approximation: 1240/1.12 ≈ 1107 nm ✓
- 51107 nm is in the near-infrared — silicon is transparent to IR beyond this wavelength
Result:
Absorption edge at 1107 nm (near-infrared). Silicon absorbs visible light strongly (explaining its metallic gray appearance) but is transparent to telecom wavelengths (1310 and 1550 nm), which is why fiber optics use those wavelengths.
GaN at Operating Temperature
Problem:
Calculate the band gap of GaN at 400 K (127°C). GaN parameters: Eg(0) = 3.47 eV, α = 7.7×10⁻⁴ eV/K, β = 600 K.
Solution Steps:
- 1Apply Varshni: Eg(T) = 3.47 - (7.7×10⁻⁴ × 400²) / (400 + 600)
- 2Compute numerator: 7.7×10⁻⁴ × 160,000 = 123.2
- 3Denominator: 400 + 600 = 1000
- 4Eg(400K) = 3.47 - 123.2/1000 = 3.47 - 0.1232 = 3.347 eV
- 5Shift from 0K: 3.47 - 3.347 = 0.123 eV (123 meV)
- 6Wavelength: λ = 1240/3.347 = 370.5 nm → UV-A
Result:
Band gap at 400 K = 3.347 eV (wavelength 370.5 nm, UV-A). Even at high temperature, GaN remains a wide-bandgap semiconductor, making it excellent for high-temperature power electronics.
Blue LED Material
Problem:
A blue LED emits at 450 nm. What approximate band gap does the semiconductor need?
Solution Steps:
- 1Use approximation: Eg ≈ 1240/λ
- 2Eg ≈ 1240/450 = 2.756 eV
- 3This falls between GaN (3.47 eV) and ZnSe (2.7 eV)
- 4Modern blue LEDs use InGaN — indium incorporation narrows GaN's band gap to reach visible wavelengths
- 5The exact InGaN composition can be tuned to produce any visible color from UV to green
Result:
Required band gap ≈ 2.76 eV. InGaN quantum wells in commercial blue LEDs achieve this through precise control of indium concentration, typically In₀.₂Ga₀.₈N.
Tips & Best Practices
- ✓1240/λ(nm) = Eg(eV) is an excellent quick approximation for converting between band gap and wavelength
- ✓Band gaps always decrease with temperature — devices designed for room temperature will have slightly higher band gap than spec sheets list at 300K
- ✓Direct semiconductors (GaAs, GaN, InP) are good for LEDs/lasers; indirect (Si, Ge) are good for transistors and solar cells
- ✓The Varshni parameters are material-specific — don't use Si parameters for GaAs or vice versa
- ✓A band gap of 0 eV means the material is a metal/conductor; > 3 eV means it's an insulator at room temperature
Frequently Asked Questions
Sources & References
Last updated: 2026-06-06
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: University Physics
by Young & Freedman