🧗‍♀️Semiconductor Physics Unit 10 – Optoelectronic Devices in Semiconductor Physics

Fundamentals of Semiconductor Physics

• Semiconductors are materials with electrical conductivity between insulators and conductors, enabling control of their electrical properties
• Intrinsic semiconductors have equal numbers of electrons and holes, while extrinsic semiconductors are doped with impurities to create excess carriers (electrons or holes)
• Band structure of semiconductors consists of the valence band, conduction band, and the bandgap energy ($E_g$) separating them
  • Electrons in the valence band can be excited to the conduction band by absorbing energy greater than the bandgap
  • The Fermi level ($E_F$) represents the energy level with a 50% probability of being occupied by an electron at thermal equilibrium
• Carrier concentration in semiconductors depends on temperature and doping levels
  • Intrinsic carrier concentration ($n_i$) increases exponentially with temperature: $n_i = \sqrt{N_c N_v} \exp(-E_g/2k_BT)$, where $N_c$ and $N_v$ are the effective densities of states in the conduction and valence bands, respectively
• Carrier transport in semiconductors occurs through drift (under an electric field) and diffusion (due to concentration gradients)
  • Drift current density: $J_{drift} = q(\mu_n n + \mu_p p)E$, where $\mu_n$ and $\mu_p$ are electron and hole mobilities, $n$ and $p$ are electron and hole concentrations, and $E$ is the electric field
  • Diffusion current density: $J_{diff} = qD_n \frac{dn}{dx} - qD_p \frac{dp}{dx}$, where $D_n$ and $D_p$ are electron and hole diffusion coefficients
• P-N junctions form the basis of many optoelectronic devices, created by joining p-type and n-type semiconductors
  • Built-in electric field develops at the junction due to diffusion of carriers, leading to a depletion region
  • Applied bias can control the width of the depletion region and the flow of current through the junction

Light-Matter Interactions in Semiconductors

• Absorption of photons in semiconductors occurs when the photon energy is greater than the bandgap energy
  • Electrons are excited from the valence band to the conduction band, creating electron-hole pairs
  • Absorption coefficient ($\alpha$) depends on the photon energy and the material properties
• Photoluminescence is the emission of light from a semiconductor after the absorption of photons
  • Electrons relax from the conduction band to the valence band, releasing energy in the form of photons
  • Photoluminescence spectroscopy is used to characterize the optical properties of semiconductors
• Excitons are bound electron-hole pairs that can form in semiconductors due to Coulomb attraction
  • Excitons have lower energy than unbound electron-hole pairs and can influence the optical properties of the material
• Nonlinear optical effects can occur in semiconductors at high light intensities
  • Second-harmonic generation (SHG) and third-harmonic generation (THG) involve the creation of photons with double or triple the frequency of the incident light
  • Two-photon absorption (TPA) occurs when two photons are simultaneously absorbed to excite an electron across the bandgap
• Surface and interface effects can modify the optical properties of semiconductors
  • Surface states and defects can introduce energy levels within the bandgap, affecting absorption and emission processes
  • Quantum confinement effects in nanostructures (quantum wells, wires, and dots) can alter the electronic structure and optical properties of the material

Photodetectors and Solar Cells

• Photodetectors convert optical signals into electrical signals by exploiting the photovoltaic effect in semiconductors
  • Incident photons generate electron-hole pairs, which are separated by an electric field to produce a photocurrent
  • Key performance parameters include responsivity (A/W), dark current, and response time
• P-N junction photodiodes are widely used photodetectors
  • Operate under reverse bias to enhance the depletion region and improve the collection of photogenerated carriers
  • Avalanche photodiodes (APDs) provide internal gain through impact ionization, enabling high sensitivity detection
• PIN photodiodes have an intrinsic (undoped) semiconductor layer between the p-type and n-type regions
  • The intrinsic layer increases the absorption volume and reduces the capacitance, improving the response time and bandwidth
• Solar cells convert sunlight into electrical energy using the photovoltaic effect
  • Photogenerated carriers are separated by the built-in electric field of a p-n junction or a heterojunction
  • Key performance parameters include power conversion efficiency (PCE), open-circuit voltage ($V_{oc}$), short-circuit current density ($J_{sc}$), and fill factor (FF)
• Multijunction solar cells stack multiple p-n junctions with different bandgaps to absorb a wider range of the solar spectrum
  • Each junction is optimized to absorb a specific portion of the spectrum, improving the overall efficiency
• Organic and perovskite solar cells are emerging technologies that offer the potential for low-cost, flexible, and large-area fabrication
  • Organic solar cells use conductive polymers or small molecules as the active layer
  • Perovskite solar cells employ a perovskite structured compound (e.g., methylammonium lead halide) as the light-absorbing material

Light-Emitting Diodes (LEDs)

• LEDs are p-n junction devices that emit light through electroluminescence
  • Electrons and holes are injected into the active region, where they recombine radiatively to produce photons
  • The emission wavelength depends on the bandgap energy of the semiconductor material
• Direct bandgap semiconductors (e.g., GaAs, InP) are more efficient for LED applications than indirect bandgap materials (e.g., Si, Ge)
  • Direct bandgap materials have a higher probability of radiative recombination, as the momentum of electrons and holes is conserved
• Heterojunction LEDs consist of multiple semiconductor layers with different bandgaps
  • The active region is sandwiched between wider bandgap layers to confine carriers and improve the radiative recombination efficiency
  • Quantum well structures can further enhance the carrier confinement and the emission properties
• LED efficiency is characterized by the external quantum efficiency (EQE), which is the product of the internal quantum efficiency (IQE) and the light extraction efficiency
  • IQE represents the ratio of radiative recombination events to the total number of injected carriers
  • Light extraction efficiency depends on the device geometry and the refractive index contrast between the semiconductor and the surrounding medium
• White LEDs can be achieved through various approaches
  • Phosphor conversion: A blue LED is coated with a yellow phosphor, which absorbs part of the blue light and emits a broad spectrum of yellow light, resulting in white light
  • RGB color mixing: Red, green, and blue LEDs are combined to produce white light by adjusting their relative intensities
  • Organic LEDs (OLEDs) use organic compounds as the emissive layer and can directly emit white light through the careful selection of materials

Semiconductor Lasers

• Semiconductor lasers are p-n junction devices that emit coherent light through stimulated emission
  • Population inversion is achieved by injecting a high density of carriers into the active region
  • Optical feedback is provided by a resonant cavity, typically formed by cleaved facets or distributed Bragg reflectors (DBRs)
• Edge-emitting lasers (EELs) have a waveguide structure that confines light in the plane of the active region
  • Light is emitted from the cleaved facets at the edges of the device
  • EELs typically have high output power and good beam quality
• Vertical-cavity surface-emitting lasers (VCSELs) emit light perpendicular to the plane of the active region
  • The resonant cavity is formed by DBRs on either side of the active region
  • VCSELs have lower output power than EELs but offer advantages such as low threshold current, single-mode operation, and easy array integration
• Quantum cascade lasers (QCLs) are unipolar devices that emit light through intersubband transitions in a repeated stack of quantum well heterostructures
  • Electrons cascade down a series of energy levels, emitting photons at each step
  • QCLs can operate in the mid-infrared and terahertz regions of the electromagnetic spectrum
• Distributed feedback (DFB) lasers incorporate a periodic structure within the active region to provide optical feedback and wavelength selectivity
  • The periodic structure acts as a Bragg grating, reflecting light at a specific wavelength back into the cavity
  • DFB lasers offer stable single-mode operation and narrow linewidth, making them suitable for optical communication applications

Emerging Optoelectronic Technologies

• Quantum dot (QD) optoelectronic devices exploit the unique properties of zero-dimensional nanostructures
  • QDs have discrete energy levels and size-dependent optical properties, enabling tunable emission and absorption
  • QD LEDs and lasers offer the potential for high efficiency, broad spectral coverage, and temperature-insensitive operation
• Nanowire (NW) optoelectronics leverage the high surface-to-volume ratio and the ability to grow heterostructures in the radial direction
  • NW LEDs and lasers can achieve efficient carrier injection and light extraction
  • NW photodetectors benefit from enhanced light absorption and fast carrier collection
• Two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDs), are being explored for optoelectronic applications
  • Graphene has high carrier mobility and broadband absorption, making it promising for high-speed photodetectors and modulators
  • TMDs (e.g., MoS2, WSe2) have direct bandgaps in the visible to near-infrared range and exhibit strong light-matter interactions, suitable for LEDs, lasers, and photodetectors
• Neuromorphic photonics aims to develop optical computing systems inspired by the human brain
  • Photonic neural networks can process information at high speeds and with low energy consumption
  • Optoelectronic devices, such as photonic synapses and neurons, are being developed to enable neuromorphic computing architectures
• Integrated photonics combines multiple optoelectronic components on a single chip, often using silicon or III-V semiconductor platforms
  • Photonic integrated circuits (PICs) can include lasers, modulators, photodetectors, and waveguides
  • PICs enable compact, low-cost, and high-performance optoelectronic systems for applications such as optical communication, sensing, and quantum information processing

Applications and Industry Impact

• Optical communication systems rely on optoelectronic devices for high-speed data transmission
  • Semiconductor lasers (e.g., DFB lasers, VCSELs) are used as optical sources
  • Photodetectors (e.g., PIN photodiodes, APDs) convert optical signals back into electrical signals
  • Optical modulators encode information onto the optical carrier by varying the amplitude, phase, or polarization of the light
• Solid-state lighting using LEDs has revolutionized the lighting industry
  • LEDs offer high efficiency, long lifetime, and versatile color options compared to traditional lighting sources
  • LED lighting finds applications in residential, commercial, and industrial settings, as well as in automotive and display technologies
• Solar energy harvesting using photovoltaic cells is crucial for renewable energy generation
  • Silicon-based solar cells dominate the market, with increasing adoption of high-efficiency technologies such as heterojunction and passivated emitter and rear contact (PERC) cells
  • Emerging solar cell technologies, such as perovskite and tandem cells, aim to further improve efficiency and reduce costs
• Optical sensors and imaging systems rely on optoelectronic devices for various applications
  • Image sensors (e.g., CCD, CMOS) in digital cameras and smartphones use photodetector arrays to capture images
  • Fiber optic sensors employ LEDs or lasers as light sources and photodetectors to measure physical quantities such as temperature, strain, and pressure
  • LiDAR (light detection and ranging) systems use pulsed lasers and photodetectors for 3D mapping and autonomous vehicle navigation
• Medical and life sciences applications benefit from optoelectronic technologies
  • Pulse oximetry uses LED-based optical sensors to non-invasively monitor blood oxygen saturation
  • Optical coherence tomography (OCT) employs interferometry with broadband light sources to generate high-resolution 3D images of biological tissues
  • Flow cytometry uses laser excitation and fluorescence detection to analyze and sort individual cells based on their optical properties

Key Equations and Formulas

• Bandgap energy: $E_g = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency of the photon
• Intrinsic carrier concentration: $n_i = \sqrt{N_c N_v} \exp(-E_g/2k_BT)$, where $N_c$ and $N_v$ are the effective densities of states in the conduction and valence bands, $k_B$ is Boltzmann's constant, and $T$ is the temperature
• Drift current density: $J_{drift} = q(\mu_n n + \mu_p p)E$, where $\mu_n$ and $\mu_p$ are electron and hole mobilities, $n$ and $p$ are electron and hole concentrations, and $E$ is the electric field
• Diffusion current density: $J_{diff} = qD_n \frac{dn}{dx} - qD_p \frac{dp}{dx}$, where $D_n$ and $D_p$ are electron and hole diffusion coefficients
• Absorption coefficient: $\alpha(\lambda) = A(\hbar\omega - E_g)^{1/2}$, where $A$ is a constant, $\hbar\omega$ is the photon energy, and $E_g$ is the bandgap energy
• Responsivity of a photodetector: $R = \frac{I_{ph}}{P_{opt}}$, where $I_{ph}$ is the photocurrent and $P_{opt}$ is the incident optical power
• External quantum efficiency of an LED: $EQE = \frac{P_{opt}}{I_{LED}} \frac{q}{h\nu}$, where $P_{opt}$ is the output optical power, $I_{LED}$ is the LED current, $q$ is the elementary charge, $h$ is Planck's constant, and $\nu$ is the frequency of the emitted light
• Threshold current density of a semiconductor laser: $J_{th} = \frac{q d}{\eta_i \tau}(N_{th} - N_0)$, where $d$ is the active layer thickness, $\eta_i$ is the internal quantum efficiency, $\tau$ is the carrier lifetime, $N_{th}$ is the threshold carrier density, and $N_0$ is the transparency carrier density
• Bragg condition for distributed feedback: $m\lambda = 2n_{eff}\Lambda$, where $m$ is an integer, $\lambda$ is the wavelength, $n_{eff}$ is the effective refractive index, and $\Lambda$ is the grating period
• Power conversion efficiency of a solar cell: $PCE = \frac{V_{oc} J_{sc} FF}{P_{in}}$, where $V_{oc}$ is the open-circuit voltage, $J_{sc}$ is the short-circuit current density, $FF$ is the fill factor, and $P_{in}$ is the input optical power