Understanding Band Gap Wavelength Relationship

In the field of solid-state physics and semiconductor electronics, the Band Gap (represented as E_g) is the energy range in a solid where no electronic states can exist. For semiconductors and insulators, the band gap represents the minimum energy required to excite an electron from the valence band to the conduction band.

The relationship between the band gap energy and the wavelength of light is fundamental to optoelectronics. When a semiconductor absorbs a photon, that photon must possess energy at least equal to the band gap for an electron to be promoted. Conversely, when an electron recombines with a hole, it emits a photon with energy approximately equal to the band gap. This calculation is vital for designing LEDs, solar cells, and laser diodes.

How to Use the Band Gap Calculator

This calculator allows for bidirectional conversion. Simply enter one value, and the tool will compute the other based on the fundamental constants of physics.

• To find Wavelength: Enter the Band Gap energy in electron-volts (eV). Click calculate to find the maximum wavelength (cut-off wavelength) the material can absorb or emit.
• To find Energy: Enter the wavelength in nanometers (nm) to determine the equivalent energy level in eV.

The Formula Behind the Calculation

The calculation is based on the Planck-Einstein relation: E = hc / λ

Where:

• E is the Energy (eV)
• h is Planck's constant (~4.1357 x 10⁻¹⁵ eV·s)
• c is the speed of light (~2.9979 x 10⁸ m/s)
• λ is the Wavelength (nm)

By combining the constants, we arrive at the simplified formula: λ (nm) ≈ 1239.84 / E (eV). This practical constant (1239.84) allows for quick conversion between the two units without dealing with scientific notation.

Common Semiconductor Band Gaps

Different materials have specific band gaps that determine their color and efficiency in electronics:

• Silicon (Si): 1.12 eV (~1107 nm - Infrared)
• Gallium Arsenide (GaAs): 1.42 eV (~873 nm - Near Infrared)
• Gallium Nitride (GaN): 3.4 eV (~365 nm - Ultraviolet)
• Indium Phosphide (InP): 1.34 eV (~925 nm)

Frequently Asked Questions

What is the cut-off wavelength?

The cut-off wavelength is the longest wavelength of light that a semiconductor can absorb. If the wavelength is longer than this value, the photon energy is lower than the band gap, and it will pass through the material without being absorbed.

Why is eV used instead of Joules?

The electron-volt (eV) is a more convenient unit of energy for atomic and subatomic scales, as the values in Joules are extremely small (1 eV ≈ 1.602 x 10⁻¹⁹ J).