2.2 Carrier transport and recombination mechanisms

Carrier transport in semiconductors involves drift and diffusion currents, influenced by electric fields and concentration gradients. Understanding these mechanisms is crucial for designing efficient optoelectronic devices and optimizing their performance.

Recombination processes, both radiative and non-radiative, play a vital role in semiconductor physics. These mechanisms affect carrier lifetimes and device efficiency, impacting the functionality of solar cells, LEDs, and other optoelectronic components.

Carrier Transport

Drift Current and Mobility

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• Drift current occurs when an electric field is applied to a semiconductor, causing charge carriers (electrons and holes) to move in opposite directions
• The drift velocity $(v_d)$ of charge carriers is proportional to the applied electric field $(E)$: $v_d = \mu E$, where $\mu$ is the mobility
• Mobility $(\mu)$ is a measure of how easily charge carriers can move through a semiconductor material under the influence of an electric field
  • Electron mobility $(\mu_e)$ and hole mobility $(\mu_h)$ are typically different due to their respective effective masses
  • Higher mobility leads to higher drift current and better device performance (faster response times, lower resistance)
• The drift current density $(J_d)$ is given by: $J_d = q(n\mu_e + p\mu_h)E$, where $q$ is the elementary charge, $n$ and $p$ are the electron and hole concentrations, respectively

Diffusion Current and Conductivity

• Diffusion current arises from the concentration gradient of charge carriers in a semiconductor
  • Electrons diffuse from regions of high concentration to regions of low concentration
  • Holes diffuse from regions of low concentration to regions of high concentration
• The diffusion current density $(J_{diff})$ is proportional to the concentration gradient $(\frac{dn}{dx}$ for electrons and $\frac{dp}{dx}$ for holes$)$: $J_{diff,n} = qD_n\frac{dn}{dx}$ and $J_{diff,p} = -qD_p\frac{dp}{dx}$, where $D_n$ and $D_p$ are the diffusion coefficients for electrons and holes, respectively
• Conductivity $(\sigma)$ is a measure of how easily a semiconductor material conducts electric current
  • It depends on the carrier concentrations and their mobilities: $\sigma = q(n\mu_e + p\mu_h)$
  • Higher conductivity implies lower resistance and better current flow in semiconductor devices (solar cells, LEDs)

Recombination Mechanisms

Radiative and Non-Radiative Recombination

• Recombination is the process by which electrons and holes annihilate each other, releasing energy in the form of photons (radiative) or phonons (non-radiative)
• Radiative recombination involves the emission of a photon with energy equal to the bandgap of the semiconductor
  • This process is the basis for light emission in LEDs and lasers
  • The rate of radiative recombination depends on the concentrations of electrons and holes: $R_{rad} = B(np - n_i^2)$, where $B$ is the radiative recombination coefficient and $n_i$ is the intrinsic carrier concentration
• Non-radiative recombination occurs when electrons and holes recombine without emitting photons, instead releasing energy as phonons (lattice vibrations)
  • This process is detrimental to the efficiency of optoelectronic devices (solar cells, LEDs) as it reduces the number of available charge carriers without producing useful output (electricity or light)
  • Examples of non-radiative recombination include Shockley-Read-Hall (SRH) recombination and surface recombination

Auger Recombination and Carrier Lifetime

• Auger recombination is a three-particle process where an electron-hole pair recombines, transferring its energy to a third carrier (electron or hole), which then relaxes back to its original energy state by emitting phonons
  • This process becomes dominant at high carrier concentrations and limits the efficiency of high-power LEDs and lasers
  • The rate of Auger recombination is proportional to the cube of the carrier concentration: $R_{Auger} = C_nn^2p + C_pnp^2$, where $C_n$ and $C_p$ are the Auger coefficients for electrons and holes, respectively
• Carrier lifetime $(\tau)$ is the average time a charge carrier (electron or hole) survives before recombining
  • It is a crucial parameter in determining the performance of semiconductor devices (solar cells, LEDs, photodetectors)
  • The total carrier lifetime is influenced by all recombination mechanisms: $\frac{1}{\tau} = \frac{1}{\tau_{rad}} + \frac{1}{\tau_{SRH}} + \frac{1}{\tau_{Auger}}$, where $\tau_{rad}$, $\tau_{SRH}$, and $\tau_{Auger}$ are the lifetimes associated with radiative, SRH, and Auger recombination, respectively
  • Longer carrier lifetimes allow for better charge collection in solar cells and higher efficiency in LEDs and lasers