Semiconductor Physics Unit 2 Review: Energy Bands & Carrier Transport in Semiconductors

Key Concepts and Definitions

• Semiconductors materials with electrical conductivity between insulators and conductors, enabling control of current flow
• Energy bands ranges of allowed energy states for electrons in a solid, formed by overlapping atomic orbitals
• Valence band highest occupied energy band at absolute zero temperature, where electrons are bound to atoms
• Conduction band lowest unoccupied energy band, where electrons can move freely and contribute to electrical conduction
  • Energy gap (bandgap) separates valence and conduction bands, determining electrical properties
• Fermi level energy level with 50% probability of being occupied by an electron at thermodynamic equilibrium
• Carriers charge carriers in semiconductors, including electrons (negative) and holes (positive)
• Doping intentional introduction of impurities to modify electrical properties by altering band structure and carrier concentrations
  • n-type doping introduces excess electrons (pentavalent impurities like phosphorus)
  • p-type doping introduces excess holes (trivalent impurities like boron)

Energy Band Formation in Solids

• Solid-state physics describes the formation of energy bands through the interaction of atomic orbitals
• Isolated atoms have discrete energy levels, but in solids, these levels split and form continuous energy bands due to the periodic potential of the crystal lattice
• Wave functions of electrons in neighboring atoms overlap, leading to the formation of bonding and antibonding orbitals
  • Bonding orbitals lower energy states occupied by valence electrons
  • Antibonding orbitals higher energy states that are usually unoccupied
• Energy bands are separated by forbidden energy gaps (bandgaps) where no electron states exist
• The width of energy bands and bandgaps depends on the strength of atomic interactions and the periodicity of the crystal structure
• The electronic structure of a solid determines its electrical, optical, and thermal properties
• The filling of energy bands follows the Pauli exclusion principle and Fermi-Dirac statistics

Types of Energy Bands in Semiconductors

• Direct bandgap semiconductors have the conduction band minimum and valence band maximum at the same crystal momentum (k-value)
  • Examples: GaAs, InP, and CdTe
  • Enable efficient optical transitions and are used in optoelectronic devices (LEDs, lasers)
• Indirect bandgap semiconductors have the conduction band minimum and valence band maximum at different crystal momenta
  • Examples: Si, Ge, and GaP
  • Optical transitions require phonon assistance, making them less efficient
• The bandgap energy determines the wavelength of absorbed or emitted light and the intrinsic carrier concentration
• Degenerate semiconductors have high doping levels, causing the Fermi level to lie within the conduction or valence band
  • Behave more like metals due to the high carrier concentration
• Amorphous semiconductors lack long-range periodic order, resulting in localized states and a distribution of bandgap energies
  • Example: amorphous silicon (a-Si) used in thin-film solar cells and displays

Carrier Generation and Recombination

• Carrier generation the process of creating electron-hole pairs in a semiconductor
  • Thermal generation dominates at room temperature, with electrons excited across the bandgap by absorbing thermal energy
  • Optical generation occurs when electrons absorb photons with energy greater than the bandgap
• Carrier recombination the process of eliminating electron-hole pairs, with electrons relaxing from the conduction band to the valence band
  • Radiative recombination releases energy as photons and is dominant in direct bandgap semiconductors
  • Non-radiative recombination releases energy as phonons (lattice vibrations) and is dominant in indirect bandgap semiconductors
    • Shockley-Read-Hall (SRH) recombination occurs through defect states within the bandgap
    • Auger recombination involves three-particle interactions, becoming significant at high carrier concentrations
• Generation and recombination rates determine the carrier lifetime and affect device performance
  • Minority carrier lifetime the average time before a minority carrier (electron in p-type, hole in n-type) recombines
  • Photovoltaic devices (solar cells) aim to maximize carrier lifetime for efficient charge collection
  • Light-emitting devices (LEDs) aim to maximize radiative recombination for high quantum efficiency

Carrier Transport Mechanisms

• Drift the movement of carriers under the influence of an electric field
  • Drift velocity ($v_d$) proportional to electric field ($E$) and carrier mobility ($\mu$): $v_d = \mu E$
  • Electron mobility typically higher than hole mobility due to lower effective mass
• Diffusion the movement of carriers from regions of high concentration to low concentration, driven by concentration gradients
  • Diffusion current density ($J$) proportional to the diffusion coefficient ($D$) and concentration gradient ($\nabla n$): $J = -qD\nabla n$
  • Einstein relation connects diffusion coefficient and mobility: $D/\mu = k_BT/q$
• Carrier mobility a measure of how easily carriers move through a semiconductor under an electric field
  • Affected by scattering mechanisms: lattice vibrations (phonons), ionized impurities, and defects
  • Temperature dependence: mobility decreases with increasing temperature due to enhanced phonon scattering
• Conductivity ($\sigma$) a measure of a material's ability to conduct electric current, determined by carrier concentrations ($n$, $p$) and mobilities ($\mu_n$, $\mu_p$): $\sigma = q(n\mu_n + p\mu_p)$
• Current-voltage (I-V) characteristics of semiconductor devices depend on carrier transport mechanisms and device structure
  • Ohmic contacts have linear I-V characteristics and low resistance
  • Rectifying contacts (p-n junctions) have nonlinear I-V characteristics and enable current flow in one direction

Doping and Its Effects on Band Structure

• Doping introduces impurities into a semiconductor to modify its electrical properties
  • n-type doping (donor impurities) adds electrons to the conduction band, increasing conductivity
    • Examples: phosphorus, arsenic, and antimony in silicon
  • p-type doping (acceptor impurities) adds holes to the valence band, increasing conductivity
    • Examples: boron, aluminum, and gallium in silicon
• Doping shifts the Fermi level towards the conduction band (n-type) or valence band (p-type)
  • Ionization energy the energy required to ionize dopant atoms and contribute carriers to the bands
  • Dopant activation the fraction of dopant atoms that are ionized at a given temperature
• Heavy doping can lead to the formation of impurity bands, narrow energy bands associated with dopant states
  • Impurity bands can overlap with the conduction or valence band, leading to metallic behavior
• Compensation the presence of both donor and acceptor impurities, reducing the effective doping concentration
• Modulation doping a technique to spatially separate dopants from the conducting channel, reducing ionized impurity scattering and enhancing mobility
  • Used in high-electron-mobility transistors (HEMTs) and quantum well structures

Semiconductor Device Applications

• p-n junctions the foundation of many semiconductor devices, formed by joining p-type and n-type regions
  • Diodes allow current flow in one direction (forward bias) and block it in the reverse direction
  • Solar cells convert light into electrical energy by separating photogenerated carriers
  • Light-emitting diodes (LEDs) emit light through electroluminescence when forward biased
• Bipolar junction transistors (BJTs) three-terminal devices with emitter, base, and collector regions
  • Amplify current and are used in analog circuits and high-power applications
• Field-effect transistors (FETs) three-terminal devices that use electric fields to control current flow
  • Metal-oxide-semiconductor FETs (MOSFETs) have an insulated gate and are the building blocks of modern electronics
  • Junction FETs (JFETs) have a reverse-biased p-n junction as the gate and are used in low-noise amplifiers
• Optoelectronic devices convert between electrical and optical signals
  • Photodetectors (photodiodes, phototransistors) convert light into electrical current
  • Laser diodes emit coherent light through stimulated emission in a resonant cavity
• Power devices handle high voltages and currents in power electronics applications
  • Thyristors (SCRs, TRIACs) are four-layer (pnpn) devices used for switching and power control
  • Power MOSFETs and IGBTs (insulated-gate bipolar transistors) are used in high-efficiency power converters

Advanced Topics and Current Research

• Quantum confinement effects arise when the size of a semiconductor structure approaches the de Broglie wavelength of carriers
  • Quantum wells, wires, and dots exhibit discrete energy levels and modified optical properties
  • Enables the development of quantum cascade lasers, quantum dot displays, and single-photon sources
• Spintronics exploits the spin degree of freedom of electrons in addition to their charge
  • Spin-based devices (spin valves, spin transistors) offer low power consumption and non-volatility
  • Topological insulators have conducting surface states protected by time-reversal symmetry, promising for spintronic applications
• Wide and ultrawide bandgap semiconductors (GaN, SiC, Ga2O3, diamond) have bandgaps larger than 3 eV
  • Enable high-power, high-frequency, and high-temperature electronics for power grids, electric vehicles, and 5G networks
• Organic and perovskite semiconductors offer low-cost, flexible, and solution-processable alternatives to inorganic semiconductors
  • Organic light-emitting diodes (OLEDs) are used in displays and solid-state lighting
  • Perovskite solar cells have achieved power conversion efficiencies over 25% in a short time
• Neuromorphic computing aims to emulate the energy efficiency and parallel processing of biological neural networks
  • Memristors and phase-change memory devices can act as artificial synapses and neurons
  • Enables brain-inspired computing for AI, machine learning, and edge computing applications