Carrier generation and recombination
Because the valence band is so nearly full, its electrons are not mobile, and cannot flow as electric current.
As predicted by thermodynamics, a material at thermal equilibrium will have generation and recombination rates that are balanced so that the net charge carrier density remains constant.
[1] As the electron moves from one energy band to another, the energy and momentum that it has lost or gained must go to or come from the other particles involved in the process (e.g. photons, electron, or the system of vibrating lattice atoms).
When light interacts with a material, it can either be absorbed (generating a pair of free carriers or an exciton) or it can stimulate a recombination event.
Absorption is the active process in photodiodes, solar cells and other semiconductor photodetectors, while stimulated emission is the principle of operation in laser diodes.
Besides light excitation, carriers in semiconductors can also be generated by an external electric field, for example in light-emitting diodes and transistors.
When light with sufficient energy hits a semiconductor, it can excite electrons across the band gap.
This generates additional charge carriers, temporarily lowering the electrical resistance of materials.
The latter occurs when the excess energy is converted into heat by phonon emission after the mean lifetime
, whereas in the former at least part of the energy is released by light emission or luminescence after a radiative lifetime
Because the photon carries relatively little momentum, radiative recombination is significant only in direct bandgap materials.
This type of recombination depends on the density of electrons and holes in the excited state, denoted by
If the semiconductor is in thermal equilibrium, the rate at which electrons and holes recombine must be balanced by the rate at which they are generated by the spontaneous transition of an electron from the valence band to the conduction band.
disappear Solve this differential equation to get a standard exponential decay where pmax is the maximum excess hole concentration when t = 0.
Stimulated emission together with the principle of population inversion are at the heart of operation of lasers and masers.
It has been shown by Einstein at the beginning of the twentieth century that if the excited and the ground level are non degenerate then the absorption rate
Trap emission is a multistep process wherein a carrier falls into defect-related wave states in the middle of the bandgap.
The trap emission process recombines electrons with holes and emits photons to conserve energy.
Non-radiative recombination in optoelectronics and phosphors is an unwanted process, lowering the light generation efficiency and increasing heat losses.
Since traps can absorb differences in momentum between the carriers, SRH is the dominant recombination process in silicon and other indirect bandgap materials.
However, trap-assisted recombination can also dominate in direct bandgap materials under conditions of very low carrier densities (very low level injection) or in materials with high density of traps such as perovskites.
On the other hand, if their energy lies close to the valence band they become hole traps.
Alternatively, if the difference is larger than the thermal energy, it is called a deep trap.
This difference is useful because shallow traps can be emptied more easily and thus are often not as detrimental to the performance of optoelectronic devices.
In the SRH model, four things can happen involving trap levels:[11] When carrier recombination occurs through traps, we can replace the valence density of states by that of the intragap state.
are the electron and hole densities when the quasi Fermi level matches the trap energy.
Since this process is a three-particle interaction, it is normally only significant in non-equilibrium conditions when the carrier density is very high.
The mechanism causing LED efficiency droop was identified in 2007 as Auger recombination, which met with a mixed reaction.
[15] In 2013, an experimental study claimed to have identified Auger recombination as the cause of efficiency droop.
[16] However, it remains disputed whether the amount of Auger loss found in this study is sufficient to explain the droop.
