Band Gap Calculator

Photon Energy and Wavelength

In semiconductor physics and optoelectronics, the Band Gap ($E_g$) of a material determines the amount of energy required to excite an electron from the valence band to the conduction band.

When an electron falls back across the band gap (recombination), it can emit a photon. The energy of this photon is closely related to its wavelength, which determines the color of light emitted by devices like LEDs and lasers.

The Equation

The energy ($E$) of a photon is related to its wavelength ($\lambda$) by the Planck-Einstein relation:

$E = \frac{hc}{\lambda}$

Where:

• $E$ is the energy of the photon (in Joules or Electron-volts)
• $h$ is Planck's constant ($6.626 \times 10^{-34}\ \text{J}\cdot\text{s}$)
• $c$ is the speed of light ($2.998 \times 10^8\ \text{m/s}$)
• $\lambda$ is the wavelength

The Electron-Volt Shortcut

In solid-state physics, it is much more convenient to measure energy in electron-volts (eV) and wavelength in nanometers (nm). By combining the physical constants ($hc = 1240\ \text{eV}\cdot\text{nm}$), the equation drastically simplifies to the commonly used "1240 rule":

$E\text{ (in eV)} \approx \frac{1240}{\lambda\text{ (in nm)}}$

Applications

• Solar Cells: A semiconductor must have a band gap smaller than the energy of incoming solar photons to absorb them.
• LEDs: The band gap of the emissive material directly dictates the color of light produced (e.g., Gallium Nitride $\approx 3.4$ eV $\rightarrow$ Ultraviolet/Blue light).