🧗‍♀️Semiconductor Physics Unit 4 – Excess Carriers & Recombination-Generation

Excess carriers and recombination-generation processes are crucial in semiconductor physics. These phenomena involve electrons and holes beyond equilibrium concentrations, introduced by external stimuli like light or electrical injection. Understanding these processes is key to optimizing semiconductor device performance. Carrier lifetime and diffusion length are important parameters in this field. They determine how long excess carriers exist before recombination and how far they travel. These factors significantly impact the efficiency of devices like solar cells, photodetectors, and LEDs, influencing their overall performance and applications.

Study Guides for Unit 4

4.1

Optical absorption and emission

7 min read

4.2

Shockley-Read-Hall recombination

9 min read

4.3

Auger recombination

7 min read

4.4

Surface recombination

10 min read

4.5

Carrier lifetime and diffusion length

7 min read

Key Concepts

Excess carriers are electrons and holes present in a semiconductor beyond the equilibrium concentration
Generation mechanisms introduce excess carriers into the semiconductor (optical absorption, impact ionization, forward-biased p-n junctions)
Recombination processes remove excess carriers from the semiconductor (radiative recombination, Shockley-Read-Hall recombination, Auger recombination)
Carrier lifetime ( $\tau$ ) represents the average time an excess carrier exists before recombination occurs
Diffusion length ( $L$ $L$ ) is the average distance an excess carrier travels before recombination
- Determined by the carrier lifetime and diffusion coefficient ( $D$ ) as $L = \sqrt{D\tau}$
Steady-state conditions occur when the generation rate equals the recombination rate, resulting in a constant excess carrier concentration
Transient conditions involve time-dependent changes in the excess carrier concentration due to variations in generation or recombination rates
Measurement techniques (photoconductivity, photoluminescence, time-resolved spectroscopy) enable the characterization of excess carrier dynamics and properties

Excess Carriers in Semiconductors

Excess carriers are electrons and holes that exceed the equilibrium carrier concentration in a semiconductor
Generated by external stimuli (light absorption, electrical injection, thermal excitation)
Concentration of excess carriers depends on the generation rate and recombination rate
Excess electron concentration ( $\Delta n$ $Δ n$ ) and excess hole concentration ( $\Delta p$ $Δ p$ ) are equal in an intrinsic semiconductor
- In extrinsic semiconductors, $\Delta n \neq \Delta p$ due to the presence of majority and minority carriers
Excess carriers alter the electrical and optical properties of the semiconductor
- Increased conductivity due to higher carrier concentration
- Enhanced optical absorption and emission
Spatial distribution of excess carriers is influenced by diffusion and drift processes
Recombination mechanisms reduce the excess carrier concentration over time

Generation Mechanisms

Optical absorption generates electron-hole pairs when a semiconductor absorbs photons with energy greater than the bandgap
- Photon energy is transferred to an electron, exciting it from the valence band to the conduction band
- The absorbed photon leaves behind a hole in the valence band
Impact ionization occurs when a high-energy carrier (electron or hole) collides with a lattice atom, creating an additional electron-hole pair
- Requires carriers to gain sufficient energy from an applied electric field
Forward-biased p-n junctions inject excess carriers into the semiconductor
- Majority carriers (electrons in n-region, holes in p-region) diffuse across the junction
- Minority carrier concentration increases in the vicinity of the junction
Thermal generation creates electron-hole pairs through lattice vibrations (phonons) at elevated temperatures
- Probability of thermal generation increases with temperature according to the Fermi-Dirac distribution
Surface generation occurs at semiconductor surfaces and interfaces due to the presence of defects and dangling bonds
- Surface states can act as generation centers, creating excess carriers near the surface

Recombination Processes

Radiative recombination involves the annihilation of an electron-hole pair, releasing energy in the form of a photon
- Dominant recombination mechanism in direct bandgap semiconductors (GaAs, InP)
- Photon energy equals the bandgap energy of the semiconductor
- Radiative recombination rate depends on the excess carrier concentrations and the radiative recombination coefficient
Shockley-Read-Hall (SRH) recombination occurs through defect levels within the bandgap, acting as recombination centers
- Defects can capture electrons from the conduction band and holes from the valence band
- SRH recombination is a two-step process: carrier capture followed by recombination
- Dominant recombination mechanism in indirect bandgap semiconductors (Si, Ge) and at low injection levels
Auger recombination is a three-particle process involving the interaction of an electron-hole pair with a third carrier
- Energy released from the recombination is transferred to the third carrier, which then relaxes through phonon emission
- Auger recombination becomes significant at high injection levels or in heavily doped semiconductors
Surface recombination occurs at semiconductor surfaces and interfaces due to the presence of defects and dangling bonds
- Surface states act as recombination centers, reducing the excess carrier concentration near the surface
- Surface recombination velocity quantifies the rate of surface recombination
Carrier lifetime is influenced by the dominant recombination mechanism and the defect concentration in the semiconductor

Carrier Lifetime and Diffusion Length

Carrier lifetime ( $\tau$ $τ$ ) is the average time an excess carrier exists before recombination occurs
- Depends on the dominant recombination mechanism and the defect concentration
- Minority carrier lifetime is of particular importance in semiconductor devices
Recombination lifetime ( $\tau_r$ $τ_{r}$ ) is related to the recombination rate ( $R$ $R$ ) as $\tau_r = \Delta n / R$ $τ_{r} = Δ n / R$
- $\Delta n$ is the excess carrier concentration
Diffusion length ( $L$ $L$ ) is the average distance an excess carrier travels before recombination
- Determined by the carrier lifetime and diffusion coefficient ( $D$ ) as $L = \sqrt{D\tau}$
- Diffusion coefficient depends on the carrier mobility and temperature
Longer carrier lifetimes and diffusion lengths are desirable for efficient carrier collection in solar cells and photodetectors
Carrier lifetime and diffusion length can be measured using techniques such as photoconductivity decay and surface photovoltage
Effective carrier lifetime ( $\tau_{eff}$ $τ_{e ff}$ ) considers the combined effect of bulk and surface recombination
- $1/\tau_{eff} = 1/\tau_{bulk} + 1/\tau_{surface}$
- Surface recombination becomes dominant in thin semiconductor layers or nanostructures

Steady-State and Transient Conditions

Steady-state conditions occur when the generation rate ( $G$ $G$ ) equals the recombination rate ( $R$ $R$ )
- Excess carrier concentration remains constant over time
- Achieved by continuous illumination or electrical injection
Under steady-state conditions, the excess carrier concentration is given by $\Delta n = G\tau$ $Δ n = G τ$
- $\tau$ is the carrier lifetime
Transient conditions involve time-dependent changes in the excess carrier concentration
- Occur when the generation rate or recombination rate changes abruptly
- Examples include pulsed laser excitation or switching of electrical bias
Transient behavior is described by the continuity equation, which includes generation, recombination, and transport terms
Time-resolved measurements (photoluminescence, photoconductivity) can capture the transient dynamics of excess carriers
- Provide information about carrier lifetime, recombination rates, and transport properties
Transient analysis is important for understanding the response time and bandwidth of semiconductor devices (photodetectors, solar cells, transistors)

Measurement Techniques

Photoconductivity measures the change in conductivity of a semiconductor under illumination
- Excess carriers generated by light absorption increase the conductivity
- Time-resolved photoconductivity can determine the carrier lifetime and mobility
Photoluminescence (PL) detects the light emitted by a semiconductor due to radiative recombination of excess carriers
- PL spectrum provides information about the bandgap, defect levels, and material quality
- Time-resolved PL measures the decay of the PL signal, yielding the carrier lifetime
Surface photovoltage (SPV) measures the change in surface potential of a semiconductor under illumination
- Reflects the separation and accumulation of excess carriers near the surface
- SPV can determine the surface recombination velocity and minority carrier diffusion length
Electron beam induced current (EBIC) uses a focused electron beam to generate excess carriers in a semiconductor device
- Measures the collected current as a function of beam position, providing spatial information about carrier transport and recombination
Capacitance-voltage (C-V) measurements probe the charge storage and emission in semiconductor devices
- Provides information about the carrier concentration, depletion width, and interface states
Deep level transient spectroscopy (DLTS) characterizes the energy levels and capture cross-sections of defects in semiconductors
- Measures the capacitance transients associated with carrier emission from defect states

Applications and Device Implications

Solar cells rely on the generation and collection of excess carriers to convert light into electrical energy
- Carrier lifetime and diffusion length determine the efficiency of carrier collection and solar cell performance
- Surface passivation techniques are used to reduce surface recombination and improve carrier lifetime
Photodetectors detect light by generating excess carriers through optical absorption
- Responsivity and speed of photodetectors depend on the carrier lifetime and transit time
- Avalanche photodetectors utilize impact ionization to achieve high gain and sensitivity
Light-emitting diodes (LEDs) produce light through radiative recombination of injected excess carriers
- Efficiency of LEDs depends on the ratio of radiative to non-radiative recombination rates
- Carrier confinement and surface passivation techniques enhance the radiative recombination efficiency
Bipolar junction transistors (BJTs) and solar cells operate under minority carrier injection and rely on the diffusion of excess carriers
- Minority carrier lifetime and diffusion length affect the gain, switching speed, and efficiency of these devices
Recombination processes contribute to the dark current and noise in optoelectronic devices (photodetectors, solar cells)
- Minimizing non-radiative recombination is crucial for improving the signal-to-noise ratio and detectivity
Carrier lifetime engineering involves controlling the defect concentration and distribution to optimize device performance
- Techniques include gettering, passivation, and controlled doping to reduce recombination centers
Understanding excess carrier dynamics is essential for designing and optimizing semiconductor devices for various applications (renewable energy, optical communication, imaging)