4.2 Shockley-Read-Hall recombination

Shockley-Read-Hall recombination is a key process in semiconductors where electrons and holes recombine through defects in the crystal lattice. It significantly impacts device performance, affecting solar cells, LEDs, and transistors by limiting efficiency and increasing leakage current.

Understanding this mechanism is crucial for optimizing semiconductor devices. It involves carrier capture and emission at trap states, with recombination rates depending on factors like trap energy levels, carrier concentrations, and temperature. Minimizing Shockley-Read-Hall recombination is essential for improving device efficiency.

Shockley-Read-Hall recombination

• Fundamental recombination mechanism in semiconductors that involves defects or impurities in the crystal lattice
• Plays a crucial role in determining the performance and efficiency of various semiconductor devices (solar cells, LEDs, transistors)
• Understanding Shockley-Read-Hall recombination is essential for optimizing device design and minimizing losses

Recombination vs generation

• Recombination process where an electron in the conduction band transitions to the valence band, eliminating a hole
• Generation process where an electron is excited from the valence band to the conduction band, creating an electron-hole pair
• Recombination and generation processes are in dynamic equilibrium under steady-state conditions

Recombination through defect levels

• Defects or impurities in the semiconductor crystal introduce energy levels within the bandgap, known as trap states
• Trap states act as recombination centers, facilitating the capture and emission of carriers
• Carriers can be captured by the trap states and subsequently recombine with carriers of the opposite type

Carrier capture and emission

• Capture process where a carrier (electron or hole) is trapped by a defect state
• Emission process where a trapped carrier is released back into the corresponding band (conduction band for electrons, valence band for holes)
• Capture and emission rates depend on the carrier concentrations, trap energy level, and capture cross-sections

Electron and hole lifetimes

• Electron lifetime ($\tau_n$) represents the average time an electron spends in the conduction band before recombining
• Hole lifetime ($\tau_p$) represents the average time a hole spends in the valence band before recombining
• Lifetimes are influenced by the trap density, capture cross-sections, and thermal velocity of carriers

Steady state conditions

• Under steady-state conditions, the recombination rate equals the generation rate
• Carrier concentrations remain constant over time
• Steady-state conditions are often assumed in device modeling and analysis

Carrier concentrations and lifetimes

• Carrier concentrations (electrons and holes) are determined by the doping levels and injection conditions
• Lifetimes are inversely proportional to the trap density and capture cross-sections
• Higher trap densities or larger capture cross-sections lead to shorter carrier lifetimes

Temperature dependence

• Shockley-Read-Hall recombination exhibits temperature dependence
• Capture and emission rates are influenced by the thermal velocity of carriers, which increases with temperature
• Higher temperatures generally lead to increased recombination rates and reduced carrier lifetimes

Doping concentration effects

• Doping concentration affects the position of the Fermi level and the carrier concentrations
• Higher doping levels can increase the recombination rate by providing more majority carriers for recombination
• Doping can also introduce additional defects or impurities that act as recombination centers

Surface vs bulk recombination

• Surface recombination occurs at the surfaces or interfaces of the semiconductor
• Bulk recombination takes place within the bulk of the semiconductor material
• Surface recombination can be significant due to the presence of surface states and defects
• Passivation techniques are used to minimize surface recombination and improve device performance

Radiative vs non-radiative recombination

• Radiative recombination involves the emission of a photon when an electron-hole pair recombines
• Non-radiative recombination, such as Shockley-Read-Hall recombination, does not emit a photon
• Radiative recombination is dominant in direct bandgap semiconductors (GaAs)
• Non-radiative recombination is more prevalent in indirect bandgap semiconductors (Si)

Direct and indirect bandgap semiconductors

• Direct bandgap semiconductors have the conduction band minimum and valence band maximum at the same crystal momentum
• Indirect bandgap semiconductors have the conduction band minimum and valence band maximum at different crystal momenta
• Radiative recombination is more efficient in direct bandgap semiconductors due to the direct transition of electrons
• Indirect bandgap semiconductors rely more on non-radiative recombination processes, such as Shockley-Read-Hall recombination

Minority carrier lifetime

• Minority carrier lifetime refers to the average time minority carriers (electrons in p-type, holes in n-type) spend before recombining
• Minority carrier lifetime is a critical parameter in determining the performance of devices (solar cells, photodetectors)
• Longer minority carrier lifetimes allow for better collection of photogenerated carriers and improved device efficiency

Carrier diffusion length

• Diffusion length ($L$) represents the average distance a carrier can travel before recombining
• Diffusion length is related to the carrier lifetime ($\tau$) and diffusion coefficient ($D$) by $L = \sqrt{D\tau}$
• Longer diffusion lengths enable carriers to be collected more efficiently in devices like solar cells

Quasi-Fermi levels

• Under non-equilibrium conditions (illumination, bias), the electron and hole populations are described by separate quasi-Fermi levels
• Quasi-Fermi levels represent the energy levels at which the carrier populations are in equilibrium with their respective bands
• The separation of the quasi-Fermi levels determines the recombination and generation rates

Shockley-Read-Hall recombination rate

• The Shockley-Read-Hall recombination rate ($R_{SRH}$) depends on the carrier concentrations, trap density, and capture cross-sections
• $R_{SRH} = \frac{np - n_i^2}{\tau_p(n + n_1) + \tau_n(p + p_1)}$, where $n$ and $p$ are the electron and hole concentrations, $n_i$ is the intrinsic carrier concentration, $\tau_n$ and $\tau_p$ are the electron and hole lifetimes, and $n_1$ and $p_1$ are the electron and hole concentrations when the Fermi level coincides with the trap level
• The recombination rate is maximum when the trap level is close to the middle of the bandgap

Derivation of recombination rate

• The Shockley-Read-Hall recombination rate is derived by considering the capture and emission processes at the trap level
• The derivation involves solving the rate equations for the trap occupancy and carrier concentrations
• Detailed balance principle is applied to obtain the steady-state solution

Assumptions and limitations

• The Shockley-Read-Hall model assumes a single trap level with well-defined capture cross-sections
• The model assumes that the capture cross-sections are independent of the trap occupancy and the electric field
• The model does not account for the spatial distribution of traps and assumes a uniform trap density
• The model assumes that the capture and emission processes are independent and not influenced by other recombination mechanisms

Single level trap states

• The Shockley-Read-Hall model considers a single trap level within the bandgap
• The trap level acts as a recombination center, capturing and emitting carriers
• The energy position of the trap level relative to the band edges determines its effectiveness as a recombination center

Capture cross sections

• Capture cross-sections ($\sigma_n$ and $\sigma_p$) represent the probability of a carrier being captured by a trap
• Capture cross-sections have units of area and depend on the nature of the trap and the carrier type
• Larger capture cross-sections lead to higher recombination rates and shorter carrier lifetimes

Thermal velocity of carriers

• The thermal velocity ($v_{th}$) represents the average speed of carriers due to their thermal motion
• The thermal velocity is given by $v_{th} = \sqrt{\frac{3kT}{m^}}$, where $k$ is the Boltzmann constant, $T$ is the temperature, and $m^$ is the effective mass of the carrier
• Higher thermal velocities increase the probability of carriers being captured by traps

Trap energy level effects

• The energy level of the trap relative to the band edges influences its effectiveness as a recombination center
• Traps with energy levels near the middle of the bandgap are the most effective recombination centers
• Traps close to the band edges are less effective due to the lower probability of capturing both electrons and holes

Mid-gap vs shallow traps

• Mid-gap traps have energy levels close to the middle of the bandgap
• Shallow traps have energy levels close to the band edges (conduction band for electron traps, valence band for hole traps)
• Mid-gap traps are more efficient recombination centers compared to shallow traps
• Shallow traps can act as trapping centers, temporarily capturing carriers before releasing them back to the bands

Minority and majority carrier traps

• Minority carrier traps have a higher probability of capturing minority carriers (electrons in p-type, holes in n-type)
• Majority carrier traps have a higher probability of capturing majority carriers (electrons in n-type, holes in p-type)
• The impact of minority and majority carrier traps on the recombination rate depends on the injection level and the trap energy level

Injection level dependence

• Injection level refers to the concentration of excess carriers (electrons and holes) compared to the equilibrium concentrations
• Low injection conditions occur when the excess carrier concentration is much lower than the majority carrier concentration
• High injection conditions occur when the excess carrier concentration is comparable to or higher than the majority carrier concentration
• The Shockley-Read-Hall recombination rate exhibits different behavior under low and high injection conditions

Low and high injection conditions

• Under low injection, the recombination rate is limited by the minority carrier concentration and lifetime
• Under high injection, the recombination rate depends on both the electron and hole concentrations and lifetimes
• The transition from low to high injection occurs when the excess carrier concentration becomes comparable to the doping concentration

Auger recombination comparison

• Auger recombination is another non-radiative recombination mechanism that involves three carriers
• In Auger recombination, the energy released from an electron-hole recombination is transferred to a third carrier (electron or hole)
• Auger recombination becomes significant at high carrier concentrations and can compete with Shockley-Read-Hall recombination
• The relative importance of Shockley-Read-Hall and Auger recombination depends on the material, doping levels, and injection conditions

Device performance impact

• Shockley-Read-Hall recombination can have a significant impact on the performance of semiconductor devices
• In solar cells, Shockley-Read-Hall recombination reduces the collection efficiency of photogenerated carriers, limiting the power conversion efficiency
• In LEDs, Shockley-Read-Hall recombination competes with radiative recombination, reducing the internal quantum efficiency and brightness
• In bipolar transistors, Shockley-Read-Hall recombination in the base region can limit the current gain and switching speed

Leakage current and dark current

• Shockley-Read-Hall recombination contributes to the leakage current in reverse-biased junctions
• The leakage current, also known as the dark current, is the current that flows in the absence of light or applied bias
• Higher Shockley-Read-Hall recombination rates lead to increased leakage current and reduced device performance

Solar cell efficiency limitations

• Shockley-Read-Hall recombination is one of the main factors limiting the efficiency of solar cells
• Recombination of photogenerated carriers through trap states reduces the collection efficiency and short-circuit current
• Minimizing Shockley-Read-Hall recombination is crucial for achieving high-efficiency solar cells

LED efficiency droop

• Efficiency droop in LEDs refers to the decrease in quantum efficiency at high injection currents
• Shockley-Read-Hall recombination can contribute to efficiency droop by competing with radiative recombination
• At high current densities, Shockley-Read-Hall recombination becomes more significant, reducing the radiative efficiency of LEDs

Experimental characterization techniques

• Several experimental techniques are used to characterize Shockley-Read-Hall recombination in semiconductors
• Deep Level Transient Spectroscopy (DLTS) is a powerful technique for studying deep-level traps and their properties
• Photoluminescence (PL) measurements provide information about the radiative and non-radiative recombination processes
• Time-resolved spectroscopy techniques (time-resolved PL, transient absorption) can reveal the carrier dynamics and lifetimes

Deep level transient spectroscopy (DLTS)

• DLTS is a capacitance-based technique that measures the transient capacitance response of a semiconductor device
• It allows the identification and characterization of deep-level traps, including their energy levels, capture cross-sections, and densities
• DLTS provides valuable information about the nature and properties of the traps responsible for Shockley-Read-Hall recombination

Photoluminescence measurements

• PL measurements involve the excitation of a semiconductor with light and the detection of the emitted luminescence
• The PL spectrum and intensity provide information about the radiative recombination processes and the presence of non-radiative recombination centers
• Temperature-dependent PL measurements can help distinguish between different recombination mechanisms

Time-resolved spectroscopy

• Time-resolved spectroscopy techniques measure the temporal evolution of the carrier populations or the emitted light
• Time-resolved PL measures the decay of the PL intensity after pulsed excitation, providing information about the carrier lifetimes and recombination rates
• Transient absorption spectroscopy measures the change in absorption after pulsed excitation, revealing the carrier dynamics and recombination processes

Carrier lifetime extraction methods

• Various methods are used to extract the carrier lifetimes from experimental data
• The time-dependent PL intensity can be fitted with exponential decay functions to determine the carrier lifetimes
• The open-circuit voltage decay (OCVD) method measures the decay of the open-circuit voltage in a solar cell to extract the minority carrier lifetime
• The photoconductivity decay (PCD) method measures the decay of the photoconductivity to determine the carrier lifetimes