# Direct-Bandgap & Indirect-Bandgap Semiconductors

Direct Semiconductors

When light reaches a semiconductor, the light is absorbed if the photon energy is greater than or equal to the band gap, creating electron-hole pairs. In a direct semiconductor, the minimum of the conduction band is aligned with the maximum of the valence band.

One example of a direct semiconductor is GaAs. The band diagram for GaAs is shown to

the right. As the gap between the valence band and conduction band is 1.42eV, if a

photon of same or greater energy is applied to the semiconductor, a hole-electron pair is created for each photon. This is termed the photo-excitation of semiconductors. The photon is thereby absorbed into the semiconductor.

Indirect Semiconductors and Phonons

For an indirect semiconductor to absorb a photon, the process must be mediated by phonons, which are quanta of sound and in this case refer to the acoustic vibration of crystal lattice. A phonon is also used to provide energy for radiative recombination. When understanding the essence of a phonon, one should recall that sound is not necessarily within hearing range (20 – 20kHz). In fact, the sound vibrations in a semiconductor may well be in the Terrahertz range. The diagram to the right shows how an indirect semiconductor band would appear and also the use of phonon energy to mediate the process of allowing the indirect semiconductor to behave as a semiconductor.

Excitons

Excitons are bound electron-hole pairs that are created in pure semiconductors when a photon with bandgap energy or larger is absorbed. In bulk semiconductors, these excitons will dissipate rapidly. In quantum wells however, the excitons may remain, even at room temperature. The effect of the quantum well is to force an electron and hole to be very close to each other. This allows for a strong bonding effect to take place and allows the quantum well the ability to generate light as a semiconductor laser.

# Quiz

The band structure of a semiconductor is given by:

Where mc = 0.2 * m0 and mv = 0.8 * m0 and Eg = 1.6 eV. Sketch the E-k Diagram.