An indirect band gap semiconductor is a type of semiconductor in which the maximum energy point of the valence band and the minimum energy point of the conduction band occur at different momentum values (wave vectors). This means that the transition of an electron from the valence band to the conduction band (or vice versa) requires a change in momentum. The most well-known indirect band gap semiconductor is silicon, which is widely used in the electronics industry.

Key Characteristics of Indirect Band Gap Semiconductors:
Momentum Change Requirement: Since the conduction band minimum and valence band maximum are at different points in momentum space, an electron transition between these bands requires a change in momentum. This is typically facilitated by the involvement of a phonon (a quantum of lattice vibration) to conserve momentum.

Optical Properties: Indirect band gap semiconductors are less efficient at absorbing and emitting light compared to direct band gap semiconductors. This is because the electron transitions that involve phonons are less probable than direct transitions.

Applications: Due to their optical properties, indirect band gap semiconductors are not typically used for light-emitting devices such as LEDs and laser diodes. However, they are extensively used in electronic devices like transistors, diodes, and integrated circuits.

Comparison with Direct Band Gap Semiconductors:
Direct Band Gap: In direct band gap semiconductors, the maximum of the valence band and the minimum of the conduction band occur at the same momentum value. Electron transitions between these bands do not require a change in momentum, making them highly efficient for optical applications.

Efficiency: Direct band gap semiconductors are more efficient at emitting light and are thus preferred for optoelectronic devices. Examples include gallium arsenide (GaAs) and indium phosphide (InP).

Examples of Indirect Band Gap Semiconductors:
Silicon (Si): The most common material used in semiconductor devices, particularly for electronic applications.
Germanium (Ge): Used in some high-speed and high-performance applications.
Silicon Carbide (SiC): Known for its high thermal conductivity and robustness, used in high-power and high-temperature applications.

In the energy-momentum (E-k) diagram:

Indirect Band Gap: The conduction band minimum is at a different k-value (momentum) than the valence band maximum.
Direct Band Gap: The conduction band minimum and the valence band maximum occur at the same k-value.