Studying Semiconductors: Recombination Mechanisms
When semiconductors absorb light, electrons are excited from the valence band into the conduction band. After the electrons are excited into the conduction band, they leave behind empty (positive) states in the valence band, which we call holes. Since both of these species carry charge, we refer to them collectively as charge carriers. Over time, the excited electrons will recombine with the holes, releasing energy in the process either in the form of light or lattice vibrations. The rate of these recombination processes dictates the amount of time over which you can use the excited carriers you have produced in devices, such as solar cells. These processes can also inform the efficiency of emitters, like LEDs.
As we increase the power of the incoming light, we excite more and more carriers. This often speeds up the recombination rate due to carrier-carrier interactions. We can therefore classify the various recombination processes by how they scale with the excited carrier concentration. This is often referred to as the ABC model: An + (B+B’+B’’)n^2 + Cn^3.
There are five major recombination processes (1 first order, 3 second order, 1 third order). Each process is referred to by multiple names in the literature and I have attempted to aggregate them here:
Shockley-Reed Hall Recombination (Trap-Assisted Recombination)
A is the recombination coefficient of trap-assisted recombination, also known as Shockley-Read-Hall (SRH) recombination, which scales linearly with the carrier concentration. It results from the collision of an excited carrier with a trap (a defect in the material). This defect traps the carrier in a lower energy, localized state where the carrier recombines. Excess momentum and energy are then released as phonons (lattice vibrations). This process primarily occurs at low carrier concentrations or in materials with high defect densities.
B is the recombination coefficient of bimolecular recombination. This encompasses three different processes. The first is radiative recombination of an electron and hole, which produces a photon. The other two are Auger (pronounced OJ, like the juice) processes which create new, high energy carriers. The first of these is defect-assisted Auger in which two carriers scatter with a defect. One carrier is trapped and recombines at the defect while another carrier scatters away with increased energy. The other type of Auger process involves excitons. Excitons are coulombically bound electron-hole pairs. Two excitons can scatter, causing one exciton to recombine and the other to break apart into a high energy exciton or a free electron and hole. This process is known as exciton-exciton annihilation.
Defect Assisted Auger Recombination
Exciton-Exciton Annihilation (EEA)
C is the recombination coefficient of three-body Auger recombination (usually just referred to as Auger). This involves the scattering of three carriers (an electron and two holes or two holes and an electron) in which an electron and hole recombine, while and the third carrier is scattered away with higher energy. This process can result in what is termed ‘efficiency droop’ in LEDs high currents. This is because at high carrier concentrations, the carriers will recombine via Auger recombination, generating heat, rather than emitting light. This effectively caps the efficiency of LEDs at high currents.
Three-Body Auger Recombination
Using these recombination mechanisms, researchers can fit experimental data and determine what the dominant mechanisms at play are. These recombination processes can be either beneficial or detrimental to a device depending on the desired functionality. For instance, devices with fast switching speeds may require fast recombination times, while devices that convert photoexcited carriers into current (like a photovoltaic) require longer recombination times. By better understanding what mechanisms are at play in a material, researchers can systematically optimize the performance of a device.