Carrier lifetime

In practical applications, the electronic band structure of a semiconductor is typically found in a non-equilibrium state. Therefore, processes that tend towards thermal equilibrium, namely mechanisms of carrier recombination, always play a role.

Additionally, semiconductors used in devices are very rarely pure semiconductors. Oftentimes, a dopant is used, giving an excess of electrons (in so-called n-type doping) or holes (in so-called p-type doping) within the band structure. This introduces a majority carrier and a minority carrier. As a result of this, the carrier lifetime plays a vital role in many semiconductor devices that have dopants.

There are several mechanisms by which minority carriers can recombine, each of which subtract from the carrier lifetime. The main mechanisms that play a role in modern devices are band-to-band recombination and stimulated emission, which are forms of radiative recombination, and Shockley-Read-Hall (SRH), Auger, Langevin, and surface recombination, which are forms of non-radiative recombination.

Depending on the system, certain mechanisms may play a greater role than others.[2] For example, surface recombination plays a significant role in solar cells, where much of the effort goes into passivating surfaces to minimize non-radiative recombination.[3] As opposed to this, Langevin recombination plays a major role in organic solar cells, where the semiconductors are characterized by low mobility.[4] In these systems, maximizing the carrier lifetime is synonymous to maximizing the efficiency of the device.[5]

Because the efficiency of a semiconductor device generally depends on its carrier lifetime, it is important to be able to measure this quantity. The method by which this is done depends on the device, but is usually dependent on measuring the current and voltage.

In solar cells, the carrier lifetime can be calculated by illuminating the surface of the cell, which induces carrier generation and increases the voltage until it reaches an equilibrium, and subsequently turning off the light source. This causes the voltage to decay at a consistent rate. The rate at which the voltage decays is determined by the amount of minority carriers that recombine per unit time, with a higher amount of recombining carriers resulting in a faster decay. Subsequently, a lower carrier lifetime will result in a faster decay of the voltage. This means that the carrier lifetime of a solar cell can be calculated by studying its voltage decay rate.[10] This carrier lifetime is generally expressed as:[11]

${\displaystyle \tau =-{\frac {k_{B}T}{q}}\left({\frac {dV_{oc}}{dt}}\right)^{-1}}$

where ${\displaystyle k_{B}}$ is the Boltzmann constant, q is the elementary charge, T is the temperature, and ${\displaystyle {\frac {dV_{oc}}{dt}}}$ is the time derivative of the open-circuit voltage.

In bipolar junction transistors (BJTs), determining the carrier lifetime is rather more complicated. Namely, one must measure the output conductance and reverse transconductance, both of which are variables that depend on the voltage and flow of current through the BJT, and calculate the minority carrier transit time, which is determined by the width of the quasi-neutral base (QNB) of the BJT, and the diffusion coefficient; a constant that quantifies the atomic migration within the BJT.[12] This carrier lifetime is expressed as:[13]

${\displaystyle \tau _{BF}=-{\frac {W_{B}^{2}}{2D_{n}}}\cdot {\frac {G_{o}}{G_{r}}}}$

where ${\displaystyle G_{o},G_{r},W_{B}}$ and ${\displaystyle D_{n}}$ are the output conductance, reverse transconductance, width of the QNB and diffusion coefficient, respectively.

Because a longer carrier lifetime is often synonymous to a more efficient device, research tends to focus on minimizing processes that contribute to the recombination of minority carriers. In practice, this generally implies reducing structural defects within the semiconductors, or introducing novel methods that do not suffer from the same recombination mechanisms.

In crystalline silicon solar cells, which are particularly common, an important limiting factor is the structural damage done to the cell when the transparent conducting film is applied. This is done with reactive plasma deposition, a form of sputter deposition. In the process of applying this film, defects appear on the silicon layer, which degrades the carrier lifetime.[14] Reducing the amount of damage done during this process is therefore important to increase the efficiency of the solar cell, and a focus of current research.[15]

In addition to research that seeks to optimize currently favoured technologies, there is a great deal of research surrounding other, less-utilized technologies, like the Perovskite solar cell (PSC). This solar cell is preferable due to its comparatively cheap and simple manufacturing process. Modern advancements suggest that there is still ample room to improve on the carrier lifetime of this solar cell, with most of the issues surrounding it being construction-related.[16]

In addition to solar cells, perovskites can be utilized to manufacture LEDs, lasers, and transistors. As a result of this, lead and halide perovskites are of particular interest in modern research. Current problems include the structural defects that appear when semiconductor devices are manufactured with the material, as the dislocation density associated with the crystals is a detriment to their carrier lifetime.[17]

• Carrier Lifetime