Carrier generation and recombination are the creation and annihilation of electron-hole pairs in a semiconductor. Every recombination mechanism competes for excess carriers, and whichever mechanism is fastest ends up dominating the overall carrier lifetime. Knowing which mechanism wins in a given material or operating regime is essential for device design.

Radiative recombination

An electron in the conduction band drops directly into a hole in the valence band, releasing a photon with energy approximately equal to the bandgap. This is the dominant recombination path in direct bandgap semiconductors like GaAs and InP, where momentum conservation is easily satisfied.

The radiative recombination rate is proportional to the product of electron and hole concentrations ( $R_{rad} \propto np$ ). This matters for optoelectronic devices because radiative recombination is the useful process in LEDs and lasers.

Shockley-Read-Hall (SRH) recombination

SRH recombination (also called trap-assisted recombination) happens through energy levels sitting inside the bandgap, introduced by crystal defects or impurities. An electron gets captured by the trap, then a hole gets captured at the same trap, and the pair recombines non-radiatively. The released energy goes into phonons (lattice vibrations) rather than photons.

This is the dominant mechanism in indirect bandgap semiconductors (Si, Ge) and under low-injection conditions
The SRH rate depends on trap density ( $N_t$ ), capture cross-sections ( $\sigma_n$ , $\sigma_p$ ), and where the trap level sits in the bandgap
Traps near mid-gap are the most effective recombination centers because they can capture both electrons and holes with roughly equal probability

Auger recombination

Auger recombination is a three-particle process. An electron and hole recombine, but instead of emitting a photon, the released energy is transferred to a third carrier (either an electron or a hole). That third carrier gets kicked to a higher energy state, then thermalizes back down by emitting phonons.

The Auger rate scales as $R_{Auger} \propto n^2 p$ or $R_{Auger} \propto n p^2$ , depending on whether the third carrier is an electron or hole
Because of this strong dependence on carrier concentration, Auger recombination becomes significant at high injection levels and in heavily doped material
It's a key efficiency-limiting mechanism in high-performance solar cells and high-power LEDs

Surface recombination

Semiconductor surfaces have dangling bonds and surface states that act as recombination centers, similar to SRH traps but concentrated at the interface. The rate is characterized by the surface recombination velocity ( $S$ ), which quantifies how effectively the surface captures carriers.

Surface passivation with dielectric layers ( $SiO_2$ , $Si_3N_4$ ) reduces $S$ by satisfying dangling bonds
Electric fields near the surface (from doping profiles or fixed charges in the passivation layer) can also repel minority carriers away from the surface, reducing surface recombination

Carrier lifetime

Carrier lifetime ( $\tau$ ) is the average time an excess carrier survives before recombining. It directly controls how much time carriers have to be collected or to participate in transport, making it one of the most important parameters in device physics.

Definition of carrier lifetime

The carrier lifetime is the ratio of the excess carrier concentration to the recombination rate:

$\tau = \frac{\Delta n}{R}$

where $\Delta n$ is the excess carrier concentration and $R$ is the net recombination rate. An equivalent expression holds for holes ( $\tau = \Delta p / R$ ). A longer lifetime means carriers persist longer before recombining.

Minority carrier lifetime

In practice, you almost always care about the minority carrier lifetime: electrons in p-type material, holes in n-type material. That's because minority carriers are the ones whose supply is limited and whose transport governs the behavior of bipolar devices like solar cells, LEDs, and bipolar junction transistors.

Radiative recombination, Photon Energies and the Electromagnetic Spectrum | Physics

Bulk vs. surface lifetime

Bulk lifetime ( $\tau_{bulk}$ ): determined by recombination processes inside the material (radiative, SRH, Auger)
Surface lifetime ( $\tau_{surface}$ ): determined by recombination at the semiconductor surface

These combine in parallel to give the effective lifetime:

$\frac{1}{\tau_{eff}} = \frac{1}{\tau_{bulk}} + \frac{1}{\tau_{surface}}$

Because they add as reciprocals, the effective lifetime is always shorter than either individual lifetime. The fastest recombination channel wins.

Effective lifetime

The effective lifetime $\tau_{eff}$ is what you actually measure in a real sample, since both bulk and surface recombination are always present. Improving $\tau_{eff}$ requires addressing whichever mechanism is currently limiting it. A pristine bulk won't help if the surfaces are poorly passivated, and vice versa.

Lifetime in low vs. high injection

Low injection: $\Delta n \ll N_D$ (or $\Delta p \ll N_A$ ). The majority carrier concentration is essentially unchanged, and the lifetime is roughly constant, set mainly by SRH recombination in silicon.
High injection: $\Delta n \geq N_D$ (or $\Delta p \geq N_A$ ). Both carrier types have comparable concentrations. Auger recombination becomes increasingly important, and the lifetime decreases with rising injection level.

The transition between these regimes matters because the dominant recombination mechanism shifts, changing both the lifetime value and its dependence on carrier concentration.

Radiative lifetime

The radiative lifetime $\tau_{rad}$ is set by band-to-band radiative recombination. Under low injection in a p-type semiconductor, for example:

$\tau_{rad} = \frac{1}{B \cdot p_0}$

where $B$ is the radiative recombination coefficient and $p_0$ is the equilibrium majority carrier concentration. In direct bandgap materials, $B$ is large, so $\tau_{rad}$ can be quite short (nanoseconds in GaAs). In indirect bandgap materials like Si, $B$ is very small and radiative recombination is negligible.

SRH lifetime

The SRH lifetime $\tau_{SRH}$ depends on trap properties. For a single trap level at energy $E_t$ :

Higher trap density $N_t$ → shorter $\tau_{SRH}$
Larger capture cross-sections $\sigma_n$ , $\sigma_p$ → shorter $\tau_{SRH}$
Traps near mid-gap are most effective at reducing lifetime

Reducing $\tau_{SRH}$ losses requires growing cleaner crystals with fewer defects and impurities. This is why high-purity float-zone silicon has much longer lifetimes than Czochralski-grown silicon.

Auger lifetime

The Auger lifetime scales inversely with the square of the carrier concentration:

$\tau_{Auger} = \frac{1}{C_n \cdot n^2 + C_p \cdot p^2}$

where $C_n$ and $C_p$ are the Auger coefficients for electrons and holes. At moderate doping and injection levels, Auger recombination is negligible. But in heavily doped regions (like emitters in solar cells) or under very high injection, it becomes the dominant lifetime-limiting mechanism. You can't "fix" Auger recombination through better material quality; it's an intrinsic process.

Lifetime measurement techniques

Several techniques are commonly used to measure carrier lifetime:

Photoconductance decay (PCD): A light pulse generates excess carriers; you monitor the conductance decay after the pulse ends. The decay time constant gives $\tau_{eff}$ .
Quasi-steady-state photoconductance (QSSPC): The sample is illuminated with a slowly varying flash, and conductance is measured as a function of time. This yields $\tau_{eff}$ over a range of injection levels in a single measurement.
Microwave photoconductance decay (µ-PCD): Similar to PCD, but uses microwave reflectance to probe the conductance contactlessly.
Time-resolved photoluminescence (TRPL): A short laser pulse excites the sample, and you measure the photoluminescence decay. Particularly useful for direct bandgap materials where radiative recombination is strong.

Carrier diffusion

When excess carriers are generated non-uniformly (for example, by light absorbed near a surface), a concentration gradient forms. Carriers then spread out from high-concentration regions to low-concentration regions through random thermal motion. This transport process is diffusion.

Diffusion current

The diffusion current density is proportional to the concentration gradient:

$J_{diff,n} = qD_n\frac{dn}{dx}$

$J_{diff,p} = -qD_p\frac{dp}{dx}$

Here $D_n$ and $D_p$ are the electron and hole diffusion coefficients, and $q$ is the elementary charge. Notice the sign difference: electrons and holes diffuse in the same spatial direction (down the concentration gradient), but they carry opposite charge, so their current contributions have opposite sign conventions.

Einstein relation

The diffusion coefficient and mobility of a carrier are not independent. They're connected by the Einstein relation:

$\frac{D}{\mu} = \frac{k_BT}{q}$

At room temperature (300 K), $k_BT/q \approx 0.026$ V. This relation holds because both diffusion and drift arise from the same underlying thermal motion of carriers. If you know the mobility (from Hall measurements, for instance), you immediately know the diffusion coefficient.

Ambipolar diffusion

When both electrons and holes are present as excess carriers, they can't diffuse independently without violating charge neutrality. The faster species (usually electrons, since $D_n > D_p$ ) gets pulled back by the internal electric field created by the slower species. The result is that both carriers diffuse together at an intermediate rate described by the ambipolar diffusion coefficient:

$D_a = \frac{n+p}{\frac{n}{D_p} + \frac{p}{D_n}}$

Under low injection, $D_a$ approaches the minority carrier diffusion coefficient, which is why minority carrier diffusion dominates transport in most device analyses.

Diffusion length

The diffusion length ties together carrier transport and recombination into a single parameter: the average distance an excess carrier diffuses before it recombines.

Definition of diffusion length

$L = \sqrt{D\tau}$

This comes directly from solving the diffusion equation with recombination. The excess carrier concentration decays exponentially with distance from the generation point as $\Delta n(x) \propto e^{-x/L}$ , so $L$ is the characteristic decay length.

Because $L$ depends on both $D$ (how fast carriers move) and $\tau$ (how long they survive), improving either one increases the diffusion length.

Minority carrier diffusion length

For device applications, the minority carrier diffusion length is the critical quantity:

In p-type material: $L_n = \sqrt{D_n \tau_n}$
In n-type material: $L_p = \sqrt{D_p \tau_p}$

As a concrete example, in device-grade p-type silicon with $D_n \approx 30 \text{ cm}^2/\text{s}$ and $\tau_n \approx 100 \text{ µs}$ , you get $L_n = \sqrt{30 \times 10^{-4}} \approx 0.055 \text{ cm} = 550 \text{ µm}$ . For a solar cell, you want $L_n$ to be at least comparable to the wafer thickness so that photogenerated carriers can reach the junction before recombining.

Diffusion length vs. carrier lifetime

Since $L = \sqrt{D\tau}$ , the diffusion length scales with the square root of the lifetime. Doubling the lifetime only increases the diffusion length by a factor of $\sqrt{2} \approx 1.41$ . This square-root dependence means that large improvements in material quality are needed to significantly extend the diffusion length.

Conversely, if you measure the diffusion length and know the diffusion coefficient, you can extract the lifetime: $\tau = L^2 / D$ .

Measurement of diffusion length

Common techniques for measuring diffusion length include:

Electron beam induced current (EBIC): An electron beam scans across the sample near a collecting junction. The collected current decays exponentially with distance from the junction, and fitting this decay gives $L$ .
Surface photovoltage (SPV): Light of varying penetration depth illuminates the sample, and the resulting surface voltage is measured. The relationship between photovoltage and absorption depth yields $L$ .
Cathodoluminescence (CL): Similar geometry to EBIC, but luminescence intensity is measured as a function of distance from the excitation point.

All three techniques exploit the fact that carrier collection efficiency depends on how far carriers must diffuse relative to $L$ . By varying this distance experimentally, you can extract the diffusion length from the spatial dependence of the signal.

2,589 studying →