Impact ionization
Impact ionization is a fundamental carrier multiplication process in semiconductors, in which a high-energy electron or hole, accelerated by a strong electric field, gains sufficient kinetic energy to collide with a bound valence electron and excite it across the bandgap, thereby generating an additional electron-hole pair.[1] This threshold energy for ionization is typically approximately 1.5 times the semiconductor's bandgap energy, ensuring conservation of energy and momentum during the collision.[2] The mechanism involves non-equilibrium transport under high electric fields, often exceeding 10^5 V/cm, where carriers undergo inelastic scattering events that favor pair creation over phonon emission.[3] The probability of impact ionization is quantified by field-dependent coefficients, such as the electron ionization coefficient α_n, which follows empirical forms like α_n = A exp(-B/E) (where E is the electric field), reflecting the exponential rise in rate as carriers surpass the threshold.[4] In materials like silicon, α_n reaches values around 10^6 cm^{-1} at fields of several hundred kV/cm, while wide-bandgap semiconductors like GaN exhibit lower coefficients, enabling higher breakdown voltages.[4] This process is critical for device physics, underpinning avalanche breakdown in p-n junctions, where iterative ionization leads to rapid current amplification and potential device failure if uncontrolled.[5] Conversely, it is deliberately exploited in avalanche photodiodes (APDs) and single-photon detectors for internal gain, enhancing sensitivity in optical communications and particle detection.[1] In power electronics and high-speed transistors, impact ionization influences hot carrier effects and reliability, driving research into mitigation strategies like band-structure engineering.[6]Fundamentals
Definition
Impact ionization is the process by which an energetic charge carrier, either an electron or a hole, in a material with a band structure loses kinetic energy through a collision with a bound electron, thereby exciting that electron across the bandgap to create an additional electron-hole pair, resulting in carrier multiplication. This phenomenon occurs primarily in semiconductors and insulators, where the accelerated carrier, often termed a "hot" carrier, acquires sufficient kinetic energy from an applied electric field to enable the ionization event.[7] The process demands specific prerequisites: a material exhibiting a distinct valence and conduction band, such as in semiconductors, and a high electric field to impart the necessary kinetic energy to free carriers, typically on the order of those found in high-field device regions. Without these conditions, carriers lack the energy for such collisions, preventing ionization. Impact ionization differs fundamentally from thermal generation, which produces electron-hole pairs through random thermal excitations across the bandgap without requiring high-energy carrier collisions or external fields, relying instead on temperature-driven processes in equilibrium.[8] In contrast to photoionization, where photons directly supply the energy to excite electrons from the valence to the conduction band, impact ionization is induced solely by the kinetic energy transfer during carrier-carrier interactions under electric acceleration.[7] For example, in a semiconductor, a hot electron accelerated to an energy exceeding the bandgap can collide with a valence band electron, promoting it to the conduction band and generating a new electron-hole pair. This microscopic mechanism enables macroscopic effects, such as avalanche breakdown in semiconductor junctions.[7]Physical Mechanism
Impact ionization occurs when a primary charge carrier, typically an electron or hole, is accelerated by a strong electric field within a semiconductor, attaining kinetic energy greater than the threshold energy necessary to initiate the process. This acceleration happens through repeated scattering events with phonons and impurities, but in high fields, the carrier gains sufficient energy to become "hot." Once this kinetic energy surpasses the required threshold—roughly on the order of the bandgap energy—the carrier is capable of participating in an ionizing collision.[5] The core of the mechanism is an inelastic collision between the hot primary carrier and a bound valence electron in the semiconductor lattice, governed by the Coulomb interaction due to electron-electron repulsion. In the binary collision approximation, the primary electron transfers a portion of its kinetic energy to the valence electron, exciting it across the bandgap into the conduction band and thereby generating a secondary electron-hole pair. This energy transfer is inelastic, meaning the total kinetic energy of the system decreases by at least the bandgap energy, with conservation of both energy and momentum enforced during the two-body interaction; momentum conservation necessitates that the threshold kinetic energy of the primary carrier exceeds the bandgap to account for the kinematics of the three resulting particles. The excess energy beyond this threshold is distributed among the primary electron (now with reduced velocity), the secondary electron, and the newly created hole.[5][4] Following pair creation, all three carriers—the original primary carrier and the secondary pair—experience the electric field and can gain kinetic energy, potentially undergoing further collisions to produce additional pairs in a cascading manner. A representative energy band diagram illustrates this process: the initial hot carrier appears high above the conduction band minimum with substantial kinetic energy, while the post-collision states show the valence band with a hole, the conduction band populated by two electrons (one primary with diminished energy and one secondary near the band edge), highlighting the multiplication effect. This microscopic process underpins carrier multiplication but is distinct from macroscopic phenomena like avalanche breakdown.[5][3]Key Parameters
Threshold Energy
The threshold energy, denoted as E_{th}, represents the minimum kinetic energy a charge carrier must acquire to trigger impact ionization in a semiconductor, enabling the generation of an electron-hole pair through collision. This energy is generally greater than the material's bandgap energy E_g to account for momentum conservation and energy dissipation via phonon emission during the process. Typically, E_{th} \approx 1.5 \times E_g, as the impacting carrier loses a portion of its energy to lattice vibrations (phonons), ensuring the final states satisfy energy and momentum requirements.[9][10] The value of E_{th} varies significantly with the semiconductor material, primarily due to differences in bandgap and band structure. In silicon (Si), an indirect bandgap material with E_g \approx 1.12 eV, the threshold for electrons is approximately 1.8 eV, while for holes it is higher, around 2.3 eV. In gallium arsenide (GaAs), a direct bandgap semiconductor with E_g \approx 1.42 eV, the electron threshold is about 1.7 eV. Wider-bandgap materials like silicon carbide (SiC), with E_g \approx 3.2 eV for 4H-SiC, exhibit higher thresholds, typically approximately 1.5 times the bandgap (around 4.8 eV or more), reflecting the increased energy barrier for pair creation.[11][12][13] Several factors influence E_{th}, including the semiconductor's band structure, carrier effective masses, and scattering mechanisms. Direct bandgap materials like GaAs allow for lower thresholds compared to indirect ones like Si, as the former facilitate easier momentum matching without phonon assistance. Lighter effective masses enable carriers to reach higher energies under electric fields, potentially lowering the effective threshold, while frequent phonon scattering reduces the net kinetic energy available for ionization. These effects collectively determine the precise E_{th} and its anisotropy within the Brillouin zone.[14][15] Experimentally, E_{th} is determined by observing the onset of carrier multiplication in p-n junction diodes or similar structures under applied electric fields, where the multiplication gain begins to exceed unity. Measurements involve varying the field strength and analyzing the current amplification, often using photomultiplication techniques to isolate the ionization threshold.[11][16] A key concept in describing the threshold behavior is the Chynoweth condition, which models the ionization probability as rising sharply once the carrier energy exceeds E_{th}, transitioning from negligible to significant rates in high-field environments. This "soft" threshold reflects the probabilistic nature of the process, where the rate follows an exponential dependence on energy above E_{th}.Ionization Coefficients
Ionization coefficients, denoted as \alpha for electrons and \beta for holes, quantify the average number of electron-hole pairs generated per unit distance traveled by a carrier in the direction of the applied electric field, provided the carrier energy exceeds the threshold for impact ionization.[17] These coefficients become significant only above the threshold energy, where carriers gain sufficient kinetic energy from the field to initiate ionization.[17] An empirical expression for the field dependence of these coefficients, known as Chynoweth's law, is given by \alpha(E) = A \exp\left(-\frac{B}{E}\right), where E is the electric field strength, and A and B are material-dependent constants reflecting the probability of ionization events.[17] For silicon, representative parameters for electron-initiated ionization are A \approx 7 \times 10^5 cm^{-1} and B \approx 1.2 \times 10^6 V/cm, while hole-initiated parameters differ, typically with a higher B value around $2 \times 10^6 V/cm.[18] This form captures the exponential increase in ionization probability with field strength, as higher fields accelerate carriers more effectively between scattering events.[17] In silicon, the coefficients exhibit asymmetry, with \alpha > \beta across relevant field ranges, attributed to the valence and conduction band structures that favor electron-initiated processes due to differences in effective masses and density of states.[5] For instance, at fields of $3 \times 10^5 V/cm, \alpha can exceed \beta by an order of magnitude or more, influencing the directionality of avalanche multiplication in devices.[18] These coefficients are experimentally determined from measurements of the carrier multiplication factor M in reverse-biased p-n junctions, defined as M = I_\text{total} / I_\text{primary}, where I_\text{total} is the total current and I_\text{primary} is the primary generation current (e.g., from thermal or optical sources).[18] By varying the bias to achieve high fields in the depletion region and solving the ionization integral iteratively—accounting for junction profiles via capacitance measurements—the local \alpha and \beta are extracted as functions of E.[18] This approach ensures the coefficients reflect bulk material properties rather than edge effects.[18] The ionization coefficients display a pronounced temperature dependence, decreasing with rising temperature due to increased phonon scattering, which shortens carrier mean free paths and reduces the likelihood of reaching ionization thresholds.[19] Monte Carlo simulations confirm this effect, showing \alpha and \beta dropping by factors of 2–5 over 300–500 K in silicon at fixed fields around $4 \times 10^5 V/cm, as enhanced optical and acoustic phonon interactions dissipate carrier energy more efficiently.[19] At high electric fields exceeding $10^5 V/cm, typical in avalanche regimes, the coefficients reach $10^3–$10^4 cm^{-1}, resulting in exponential carrier multiplication over micrometer-scale distances and enabling gain factors of $10^2 or higher before breakdown.[5]Semiconductor Applications
Avalanche Breakdown
Avalanche breakdown in semiconductors arises from a chain reaction driven by impact ionization, where thermally generated or injected charge carriers are accelerated by a high electric field, gaining sufficient energy to create additional electron-hole pairs upon collision with lattice atoms. This process multiplies the number of carriers exponentially, resulting in a rapid increase in reverse current through the device. The multiplication factor M, which quantifies the gain as the ratio of the total carrier current to the initial current, is expressed as M = \frac{1}{1 - \int_0^W \alpha(x) \, dx} for pure electron-initiated multiplication across a depletion region of width W, where \alpha(x) is the position-dependent electron impact ionization coefficient. The ionization coefficients \alpha and \beta (for holes) serve as the key drivers in the multiplication integral. Runaway current occurs when \int_0^W (\alpha - \beta) \, dx \approx 1, at which point the denominator approaches zero and M diverges, leading to uncontrolled carrier generation.[5] The breakdown voltage is the critical reverse bias at which this infinite multiplication is achieved, corresponding to an electric field strength where impact ionization dominates. In silicon p-n junctions, this critical field is approximately $3 \times 10^5 V/cm, beyond which the device can no longer sustain the applied voltage without current surge. For a uniform field approximation in the depletion region, the multiplication factor simplifies to M = \frac{I}{I_0} = \frac{1}{1 - (\alpha - \beta)W}, where I is the multiplied current, I_0 is the initial current, and W is the depletion width; breakdown ensues as (\alpha - \beta)W nears unity.[20][21] Avalanche breakdown manifests in two primary types: local and non-local. Local breakdown assumes a uniform electric field across the multiplication region, well-described by the above models in longer-channel devices where carriers fully thermalize between collisions. In contrast, non-local breakdown predominates in short-channel structures, such as submicron transistors, where the channel length is comparable to the carrier mean free path, leading to "streaming" effects that alter the energy distribution and ionization rates without local equilibrium. Additionally, breakdown often localizes into microplasmas—tiny hotspots of high carrier density—due to field non-uniformities or defects, forming current filaments that pulse intermittently and contribute to noisy current characteristics.[22][23] The consequences of avalanche breakdown are severe, including thermal runaway from localized Joule heating generated by the high current density, which raises lattice temperature and further enhances ionization rates in a positive feedback loop, ultimately causing permanent device damage through melting or structural degradation. To mitigate premature or edge-related breakdown, design strategies such as guard rings—lightly doped annular regions surrounding the junction—and tailored doping profiles are implemented to smooth the electric field distribution, increasing the effective breakdown voltage by up to 50% in some silicon structures.[24][25] This phenomenon was first systematically observed in the early 1950s through studies of silicon p-n junctions, where K. G. McKay and colleagues demonstrated the avalanche mechanism via light emission and current multiplication in reverse-biased diodes. Avalanche breakdown is particularly relevant in distinguishing operating regimes from Zener (tunneling) breakdown, which prevails in heavily doped junctions at reverse voltages below approximately 6 V, while avalanche dominates above this threshold due to the field strength required for carrier multiplication.[26][27]Carrier Multiplication Devices
Avalanche photodiodes (APDs) are semiconductor devices that exploit impact ionization to achieve internal current gain for detecting low-light signals. These devices typically feature a p-i-n structure where the intrinsic (i) region serves as a high electric field multiplication zone, enabling carrier multiplication without reaching destructive breakdown. Photogenerated carriers in the absorption layer drift into the multiplication region, where the applied reverse bias accelerates them to energies sufficient for impact ionization, producing secondary electron-hole pairs and amplifying the photocurrent by a factor M, often ranging from 100 to 1000 for enhanced sensitivity in photon-starved environments.[28] The noise performance in APDs is characterized by the excess noise factor F, which quantifies the additional variance from the stochastic nature of impact ionization:F = kM + (2 - 1/M)(1 - k),
where M is the mean gain and k = β/α is the ratio of hole to electron ionization coefficients. This factor arises because random multiplication chains lead to fluctuations beyond Poisson statistics, limiting the effective gain in noisy conditions. In materials like InGaAs, electron-initiated multiplication is preferred as it yields k < 1, resulting in lower F and reduced noise compared to hole-initiated processes.[29] APDs, first invented in 1952 by Jun-ichi Nishizawa, underwent significant development in the 1970s for telecommunications, enabling high-speed optical receivers by providing gain to compensate for weak signals in fiber-optic systems. Another class of carrier multiplication devices is the impact ionization metal-oxide-semiconductor (I-MOS) transistor, which employs a gated p-i-n structure to modulate the high-field region for impact ionization. By controlling the gate voltage to tune the ionization probability, I-MOS devices achieve sub-60 mV/decade subthreshold swing, surpassing the Boltzmann limit of conventional MOSFETs while maintaining low off-state leakage.[30][31] A related technology is single-photon avalanche diodes (SPADs), which operate in Geiger mode where a single carrier triggers a self-sustaining avalanche, providing high internal gain for single-photon detection. SPADs are widely used in applications such as fluorescence lifetime imaging, quantum key distribution, and time-of-flight LIDAR, offering picosecond timing resolution and low dark count rates in modern silicon and InGaAs implementations as of 2025.[32] These devices find applications in optical receivers for telecom, where APDs boost signal-to-noise ratios in long-haul links, and in LIDAR systems for precise ranging in autonomous vehicles and environmental sensing. The primary advantages of carrier multiplication devices include high sensitivity for weak signal detection, enabling single-photon or low-flux measurements. However, they suffer from temperature sensitivity, as ionization coefficients vary with thermal energy, and timing jitter from multiplication delays, which can degrade performance in high-speed or pulsed applications.[33][34][35]