🔬Condensed Matter Physics Unit 7 – Semiconductor physics

Key Concepts and Fundamentals

• Semiconductors materials with electrical conductivity between insulators and conductors, enabling control of current flow
• Intrinsic semiconductors pure semiconductor materials without added impurities (silicon, germanium)
• Extrinsic semiconductors semiconductors doped with impurities to modify their electrical properties (n-type, p-type)
• Band theory describes the energy levels and allowed states of electrons in a solid, crucial for understanding semiconductor behavior
  • Valence band highest occupied energy band at 0 K
  • Conduction band lowest unoccupied energy band, separated from valence band by the band gap
• Fermi level represents the energy level with a 50% probability of being occupied by an electron at thermodynamic equilibrium
• Charge carriers in semiconductors electrons in the conduction band (n-type) and holes in the valence band (p-type)
• Doping process of intentionally introducing impurities into a semiconductor to control its electrical properties (donor impurities for n-type, acceptor impurities for p-type)

Crystal Structure and Lattices

• Semiconductors have a regular, periodic arrangement of atoms in a crystal lattice, which influences their electronic properties
• Unit cell smallest repeating unit that defines the crystal structure (diamond cubic for silicon and germanium)
• Lattice constant distance between two adjacent atoms in the crystal lattice, affects band structure and electronic properties
• Reciprocal lattice mathematical construct representing the Fourier transform of the real-space lattice, used to describe electronic states and phonons
• Brillouin zone primitive cell in the reciprocal lattice, contains all unique wave vectors describing electronic states
  • High-symmetry points (Γ, X, L) used to characterize the band structure and electronic properties
• Lattice vibrations (phonons) collective excitations of atoms in the crystal lattice, influencing thermal and electrical properties
• Defects and impurities disrupt the perfect periodicity of the crystal lattice, affecting electronic properties and device performance (point defects, line defects, surface defects)

Energy Bands and Band Gaps

• Energy bands form due to the periodic potential of the crystal lattice, resulting in a range of allowed energy states for electrons
• Band gap energy difference between the top of the valence band and the bottom of the conduction band, determines the electrical and optical properties of the semiconductor
  • Direct band gap conduction band minimum and valence band maximum occur at the same wave vector (GaAs, InP)
  • Indirect band gap conduction band minimum and valence band maximum occur at different wave vectors (silicon, germanium)
• Effective mass tensor describes the response of an electron or hole to an applied electric field, influenced by the curvature of the energy bands
• Density of states (DOS) number of electronic states per unit energy and volume, determines the concentration of charge carriers and optical absorption
• Fermi-Dirac distribution probability of an electronic state being occupied at a given temperature and Fermi level, governs the concentration of electrons and holes
• Temperature dependence of the band gap decreases with increasing temperature due to lattice expansion and electron-phonon interactions, affecting device performance
• Strain and quantum confinement effects can modify the band structure and band gap of semiconductors, enabling band gap engineering for specific applications

Charge Carriers and Doping

• Electrons and holes serve as charge carriers in semiconductors, responsible for electrical conduction
• Intrinsic carrier concentration depends on the band gap and temperature, equal concentrations of electrons and holes in intrinsic semiconductors (ni)
• Extrinsic semiconductors are doped with impurities to control the type and concentration of charge carriers
  • n-type doping introduces donor impurities (phosphorus, arsenic) that provide extra electrons to the conduction band
  • p-type doping introduces acceptor impurities (boron, gallium) that create holes in the valence band
• Doping concentration determines the majority carrier type (electrons in n-type, holes in p-type) and influences the Fermi level position
• Mobility characterizes the ease with which charge carriers move through the semiconductor under an applied electric field, affected by scattering mechanisms (lattice vibrations, ionized impurities, defects)
• Drift current flow of charge carriers due to an applied electric field, proportional to the carrier concentration, mobility, and electric field strength
• Diffusion current flow of charge carriers due to a concentration gradient, driven by the random thermal motion of carriers
• Recombination and generation processes that balance the concentration of electrons and holes, influencing the carrier lifetime and device performance (radiative, Shockley-Read-Hall, Auger)

Electrical Properties and Conductivity

• Electrical conductivity measure of a material's ability to conduct electric current, determined by the concentration and mobility of charge carriers
  • Intrinsic conductivity depends on the intrinsic carrier concentration and mobility, relatively low in pure semiconductors
  • Extrinsic conductivity enhanced by doping, depends on the concentration and mobility of majority carriers (electrons in n-type, holes in p-type)
• Resistivity reciprocal of conductivity, characterizes the material's resistance to current flow, important for device design and performance
• Hall effect transverse voltage generated in a conductor or semiconductor when a magnetic field is applied perpendicular to the current flow, used to determine carrier type, concentration, and mobility
• Magnetoresistance change in electrical resistance due to an applied magnetic field, relevant for magnetic sensor applications and spintronics
• Temperature dependence of conductivity influenced by changes in carrier concentration and mobility with temperature, important for device operation and thermal management
• Ohmic contacts metal-semiconductor junctions with linear current-voltage characteristics, essential for efficient current injection and extraction in devices
• Schottky contacts metal-semiconductor junctions with rectifying current-voltage characteristics, used in diodes, solar cells, and transistors

Optical Properties of Semiconductors

• Absorption process by which a semiconductor absorbs photons, exciting electrons from the valence band to the conduction band
  • Direct absorption occurs in semiconductors with a direct band gap, enabling efficient light absorption and emission (GaAs, InP)
  • Indirect absorption requires the assistance of phonons to conserve momentum, resulting in weaker absorption and emission (silicon, germanium)
• Photoluminescence emission of light from a semiconductor due to the recombination of electrons and holes, used to study band structure, defects, and impurities
• Refractive index describes the speed of light in a material relative to vacuum, important for optical device design and light propagation
• Optical band gap energy threshold for photon absorption, determining the wavelength range of light-matter interaction
• Excitons bound electron-hole pairs formed by Coulomb attraction, influencing optical absorption and emission spectra, particularly at low temperatures
• Quantum confinement effects modification of optical properties in nanostructures (quantum wells, wires, dots) due to the confinement of charge carriers, enabling the tuning of absorption and emission wavelengths
• Nonlinear optical properties describe the response of a semiconductor to high-intensity light, relevant for applications in optical switching, frequency conversion, and signal processing

Semiconductor Devices and Applications

• p-n junction formed by joining p-type and n-type semiconductors, creating a built-in electric field and depletion region, fundamental building block of many semiconductor devices
  • Diodes allow current flow in one direction (forward bias) and block it in the reverse direction, used for rectification, voltage regulation, and light emission (LEDs)
  • Solar cells convert light into electrical energy by separating photogenerated electron-hole pairs across the p-n junction
• Bipolar junction transistors (BJTs) three-terminal devices consisting of two p-n junctions (npn or pnp), used for amplification and switching applications
• Field-effect transistors (FETs) three-terminal devices that control current flow using an electric field, essential for modern electronics (MOSFETs, JFETs, HEMTs)
  • Metal-oxide-semiconductor FETs (MOSFETs) utilize an insulated gate to control the conductivity of a channel between source and drain terminals, the backbone of digital logic and memory devices
• Optoelectronic devices convert between electrical and optical signals, enabling applications in telecommunications, displays, and sensing (LEDs, lasers, photodetectors)
• Power electronics devices handle high voltages and currents, used in power conversion, motor control, and renewable energy systems (power diodes, thyristors, IGBTs)
• Integrated circuits (ICs) miniaturized electronic circuits fabricated on a semiconductor substrate, enabling complex functionality and high-density packaging (microprocessors, memory chips, ASICs)

Advanced Topics and Current Research

• Wide bandgap semiconductors materials with bandgaps larger than 2 eV (GaN, SiC, diamond), offering advantages in high-power, high-frequency, and high-temperature applications
• Organic semiconductors carbon-based materials with semiconducting properties, enabling flexible, low-cost, and environmentally friendly electronics (OLEDs, OPVs, OFETs)
• Spintronics exploitation of electron spin for information processing and storage, promising for low-power and high-density devices (spin valves, magnetic tunnel junctions)
• Topological insulators materials with insulating bulk but conducting surface states protected by time-reversal symmetry, potential applications in quantum computing and spintronics
• 2D semiconductors atomically thin materials with unique electronic and optical properties (graphene, transition metal dichalcogenides), suitable for flexible and transparent electronics
• Perovskite semiconductors emerging class of materials with excellent optoelectronic properties, particularly promising for high-efficiency solar cells and light-emitting devices
• Neuromorphic computing hardware implementations inspired by biological neural networks, utilizing semiconductor devices to mimic brain-like functionality and efficiency (memristors, synaptic transistors)
• Quantum computing harnessing quantum phenomena (superposition, entanglement) for computation, with potential applications in cryptography, optimization, and simulation (superconducting qubits, spin qubits)