💡Optoelectronics Unit 2 – Fundamentals of Semiconductor Physics

Key Concepts and Terminology

• Semiconductors materials with electrical conductivity between insulators and conductors, enabling control of current flow
• Band theory describes the energy levels and bands available for electrons in a solid, crucial for understanding semiconductor properties
• Valence band highest occupied energy band in a semiconductor at absolute zero temperature
• Conduction band lowest unoccupied energy band, where electrons can move freely and contribute to electrical conductivity
• Band gap energy difference between the top of the valence band and the bottom of the conduction band, determining electrical and optical properties
  • Direct band gap allows efficient absorption and emission of light (GaAs, InP)
  • Indirect band gap requires additional phonon interactions for optical transitions (Si, Ge)
• Fermi level energy level with a 50% probability of being occupied by an electron at thermal equilibrium
• Carrier concentration number of electrons in the conduction band or holes in the valence band per unit volume
• Mobility measure of how quickly charge carriers can move through a semiconductor under an applied electric field

Atomic Structure and Band Theory

• Semiconductors have a periodic crystal structure, with atoms arranged in a repeating lattice
• Covalent bonding between atoms leads to the formation of energy bands, separated by forbidden energy gaps
• The electronic configuration of the atoms determines the number of valence electrons available for bonding
  • Group IV elements (Si, Ge) have four valence electrons, forming a diamond cubic crystal structure
  • III-V compounds (GaAs, InP) have an average of four valence electrons per atom, forming a zincblende crystal structure
• The overlap of atomic orbitals leads to the formation of bonding and antibonding states, which give rise to the valence and conduction bands
• The periodicity of the crystal structure results in the formation of a reciprocal lattice and Brillouin zones, which describe the allowed wave vectors for electrons
• The band structure of a semiconductor can be calculated using various methods, such as the tight-binding approximation or the pseudopotential method
• The effective mass of charge carriers is determined by the curvature of the energy bands near the band edges

Types of Semiconductors

• Intrinsic semiconductors pure semiconductors without any intentional doping, with equal numbers of electrons and holes
  • Electron and hole concentrations are determined by the band gap and temperature
  • Examples include undoped Si and Ge
• Extrinsic semiconductors semiconductors with intentional doping to control the type and concentration of charge carriers
  • n-type semiconductors doped with donor impurities (group V elements), providing excess electrons in the conduction band
  • p-type semiconductors doped with acceptor impurities (group III elements), creating excess holes in the valence band
• Direct band gap semiconductors have the conduction band minimum and valence band maximum at the same wave vector (k-value)
  • Examples include GaAs, InP, and GaN
  • Efficient absorption and emission of light, suitable for optoelectronic devices (LEDs, lasers)
• Indirect band gap semiconductors have the conduction band minimum and valence band maximum at different wave vectors
  • Examples include Si and Ge
  • Optical transitions require phonon assistance, making them less efficient for light emission
• Compound semiconductors formed by combining elements from different groups of the periodic table
  • III-V compounds (GaAs, InP) widely used in optoelectronics due to their direct band gaps and high electron mobility
  • II-VI compounds (CdTe, ZnSe) used in solar cells and detectors

Carrier Transport and Mobility

• Carrier transport in semiconductors occurs through drift and diffusion mechanisms
• Drift current flow of charge carriers due to an applied electric field
  • Electrons move opposite to the electric field, while holes move in the same direction
  • Drift velocity proportional to the electric field strength and mobility
• Diffusion current flow of charge carriers due to a concentration gradient
  • Carriers move from regions of high concentration to regions of low concentration
  • Diffusion current density proportional to the concentration gradient and diffusion coefficient
• Mobility characterizes the ease with which charge carriers can move through a semiconductor under an applied electric field
  • Electron mobility generally higher than hole mobility due to their smaller effective mass
  • Mobility depends on various scattering mechanisms (lattice vibrations, ionized impurities, defects)
• Conductivity measure of a semiconductor's ability to conduct electrical current, determined by carrier concentrations and mobilities
• The Hall effect used to measure the carrier concentration, mobility, and conductivity type (n or p) of a semiconductor
• High-field effects, such as velocity saturation and impact ionization, can limit carrier transport at high electric fields

Doping and Impurities

• Doping intentional introduction of impurities into a semiconductor to control its electrical properties
• Donor impurities (group V elements) provide excess electrons to the conduction band, creating n-type semiconductors
  • Examples include phosphorus (P) and arsenic (As) in silicon
  • Donor energy levels located slightly below the conduction band edge
• Acceptor impurities (group III elements) create excess holes in the valence band, forming p-type semiconductors
  • Examples include boron (B) and gallium (Ga) in silicon
  • Acceptor energy levels located slightly above the valence band edge
• Doping concentration determines the carrier concentration and Fermi level position
  • Higher doping levels shift the Fermi level closer to the corresponding band edge
  • Heavily doped semiconductors have a high conductivity and exhibit metallic behavior
• Compensation occurs when both donor and acceptor impurities are present, reducing the net carrier concentration
• Unintentional impurities and defects can also affect the electrical properties of semiconductors
  • Deep-level traps introduce energy levels within the band gap, acting as recombination centers
  • Oxygen and carbon are common unintentional impurities in silicon
• Ion implantation and diffusion are common techniques for introducing dopants into semiconductors
• Selective doping allows the creation of regions with different conductivity types, essential for device fabrication

Semiconductor Junctions

• Semiconductor junctions formed by bringing together regions with different doping types or concentrations
• p-n junction created by joining p-type and n-type semiconductors
  • Diffusion of carriers across the junction creates a depletion region with a built-in electric field
  • The built-in potential barrier controls the flow of carriers across the junction
  • Forward bias reduces the potential barrier, allowing current to flow
  • Reverse bias increases the potential barrier, limiting current flow
• Heterojunctions formed by joining semiconductors with different band gaps
  • Band alignment (type I, II, or III) determines the energy barrier for carriers
  • Heterojunctions used in various optoelectronic devices (LEDs, lasers, solar cells)
• Schottky junction formed between a metal and a semiconductor
  • The difference in work functions creates a potential barrier, known as the Schottky barrier
  • Rectifying behavior allows current flow in one direction only
• Ohmic contacts provide low-resistance, non-rectifying connections to semiconductors
  • Formed by heavily doping the semiconductor near the metal-semiconductor interface
  • Essential for efficient current injection and extraction in semiconductor devices
• Junction capacitance arises from the charge storage in the depletion region
  • Varies with the applied voltage and doping concentrations
  • Plays a role in the high-frequency performance of semiconductor devices

Optical Properties of Semiconductors

• Semiconductors interact with light through absorption, emission, and refraction processes
• Absorption occurs when a photon excites an electron from the valence band to the conduction band
  • The absorption coefficient depends on the photon energy and the band structure
  • Direct band gap semiconductors have a higher absorption coefficient than indirect band gap materials
• Emission of light occurs through radiative recombination of electrons and holes
  • Photoluminescence emission of light due to optical excitation
  • Electroluminescence emission of light due to electrical injection of carriers
• Refractive index determines the speed of light in the semiconductor and the reflection at interfaces
  • Varies with the photon energy and can be described by the Kramers-Kronig relations
  • Refractive index contrast enables the confinement of light in optical waveguides and cavities
• Excitons bound electron-hole pairs that can form in semiconductors with strong Coulomb interaction
  • Excitons have a lower energy than unbound electron-hole pairs and can contribute to optical transitions
  • Quantum confinement effects enhance the exciton binding energy in low-dimensional structures
• Nonlinear optical effects, such as second-harmonic generation and two-photon absorption, can occur at high light intensities
  • Nonlinear susceptibility depends on the crystal symmetry and band structure
  • Nonlinear effects are exploited in various optoelectronic devices (modulators, switches, frequency converters)

Applications in Optoelectronics

• Light-emitting diodes (LEDs) convert electrical energy into light through electroluminescence
  • Based on forward-biased p-n junctions or heterojunctions
  • Efficiency depends on the material's internal quantum efficiency and light extraction efficiency
  • Used in displays, lighting, and optical communication
• Laser diodes generate coherent light through stimulated emission
  • Require a gain medium, optical feedback, and carrier confinement
  • Edge-emitting lasers and vertical-cavity surface-emitting lasers (VCSELs) are common configurations
  • Used in optical storage, fiber-optic communication, and material processing
• Photodetectors convert light into electrical signals through photogeneration of carriers
  • p-n photodiodes, PIN photodiodes, and avalanche photodiodes (APDs) are common types
  • Responsivity, dark current, and bandwidth are key performance parameters
  • Used in cameras, optical receivers, and spectroscopy
• Solar cells convert sunlight into electrical energy through the photovoltaic effect
  • Based on p-n junctions or heterojunctions with a large surface area
  • Efficiency depends on the absorption, carrier collection, and voltage generation
  • Single-junction and multi-junction solar cells are used in terrestrial and space applications
• Optical modulators control the amplitude, phase, or polarization of light using electrical signals
  • Electro-absorption modulators based on the quantum-confined Stark effect
  • Electro-optic modulators exploit the change in refractive index with an applied electric field
  • Used in optical communication and signal processing
• Integrated optoelectronic circuits combine multiple optoelectronic devices on a single chip
  • Photonic integrated circuits (PICs) enable complex optical functionalities
  • Silicon photonics leverages CMOS-compatible fabrication for cost-effective integration
  • Applications in data centers, telecommunications, and sensing