The band gap of a semiconductor is an important material parameter for optoelectronics, as it determines the peak emission wavelength and also the maximum wavelength at which absorption can occur. The band gap is commonly measured in electronvolts (a unit of energy), while when visible/infrared light is involved it is common to use nanometres or micrometres (units of wavelength).
The relationship between the two can be simply expressed by the Planck relation
where E is the photon energy, h is Planck’s constant and ν is the frequency of the light. The frequency can be expressed in terms of the speed of light, c, and the wavelength of the light, λ.
Thus, the photon energy is inversely proportional to the wavelength. Since h and c are both constants, the equation can be written as
when the wavelength is in micrometres and the energy is in electronvolts.
While the above situation is true for bulk material, it is more complex for quantum systems. In these systems the charge carriers are confined in one dimension (quantum wells), two dimensions (quantum wires) or all three dimensions (quantum dots). This is accomplished by surrounding a semiconductor with a semiconductor that has a larger band gap. e.g. a thin layer of GaAs sandwiched between two layers of AlGaAs, as shown in the diagram below.
The confinement leads to quantization of the energy levels within the system, that is, the electrons and holes can only have certain energy values. This means that emission can only occur at wavelengths corresponding to these values. The lowest quantized energy level is at an energy above the band edge: thus, the energy of the emitted photons increases compared to the bulk material, and the wavelength becomes shorter. The splitting between the energy levels is inversely proportional to the size of the system. This allows control of the emission wavelength by varying the size.