Avalanche Breakdown: Impact Ionization Coefficient

What Is Avalanche Breakdown?

Definition and physical mechanism

Avalanche breakdown is the sudden, steep rise in reverse current through a p-n junction once the internal electric field becomes strong enough for free carriers to gain enough kinetic energy between collisions to knock bound electrons out of the crystal lattice. Each liberated electron-hole pair can itself be accelerated and produce further pairs, creating a multiplying chain reaction — the "avalanche." Unlike normal reverse leakage, which is governed by minority-carrier diffusion and generation currents, avalanche current is a field-triggered multiplication process layered on top of whatever leakage already exists. For a baseline understanding of that leakage floor before multiplication kicks in, see Reverse Bias: Leakage Current, Breakdown Mechanisms.

Difference from Zener breakdown

Zener breakdown is a quantum-mechanical tunneling effect: in heavily doped junctions the depletion region is thin enough (often under 10 nm) that electrons tunnel directly through the forbidden gap without needing extra kinetic energy. It dominates in junctions with breakdown voltages below roughly 5–6 V and has a negative temperature coefficient — breakdown voltage drops as temperature rises, because the bandgap narrows. Avalanche breakdown dominates in more lightly doped, wider depletion regions and shows a positive temperature coefficient — breakdown voltage rises with temperature, because increased phonon scattering shortens the mean free path and carriers need a higher field to reach ionization energy. Many commercial "Zener" diodes rated above about 5.5 V are actually operating in avalanche mode; the datasheet name is historical, not physical.

Role in reverse-biased junctions

Avalanche multiplication occurs inside the depletion region, where the field is highest and essentially free of equilibrium carrier recombination. The width and shape of that region — set by doping concentration and applied reverse bias — directly determine the peak field a carrier experiences. Reviewing Depletion Region: Width, Electric Field, Charge Distribution is the natural prerequisite, since everything in this article is a consequence of how that field is shaped and where it peaks.

Impact Ionization: The Cascade Effect

Carrier acceleration in high electric fields

Under reverse bias, the depletion region supports fields that can reach 2×10^5 to over 1×10^6 V/cm near breakdown, depending on doping. An electron or hole drifting through this field accelerates between lattice collisions, gaining kinetic energy proportional to field strength times mean free path. In silicon's diamond-cubic lattice — see Crystal Structure: Silicon Lattice and Covalent Bonds for the bonding picture — collisions are primarily with phonons (lattice vibrations) and occasionally with a bound valence electron.

Electron-hole pair generation by collision

When a carrier's kinetic energy exceeds a threshold tied to the bandgap energy (roughly 1.5–3.2× the bandgap, depending on band structure), a collision with a lattice atom can break a covalent bond, promoting a valence electron to the conduction band. This creates a new electron-hole pair. Both the original carrier and the two new carriers are then accelerated by the same field, each capable of triggering further ionization events. The result is exponential multiplication of carrier pairs across the depletion width — the defining signature of avalanche breakdown.

Threshold energy and mean free path

For impact ionization to occur, a carrier must accumulate energy above the threshold between collisions, meaning the mean free path and the field must jointly supply enough energy per unit distance. Shorter mean free paths (more frequent phonon scattering) require higher fields to reach the same threshold energy, which is why ionization coefficients are exponentially sensitive to field strength rather than linearly so.

Temperature dependence of ionization

Raising temperature increases phonon population density, which shortens the mean free path and increases the energy lost to non-ionizing collisions. Carriers need a higher field to reach ionization threshold energy at elevated temperature, which is the microscopic reason avalanche breakdown voltage increases with temperature — a trend every power-device datasheet characterizes and that directly affects margin calculations in high-temperature automotive or industrial designs.

Impact Ionization Coefficient: Definition and Significance

Alpha (α) and beta (β) coefficients explained

The ionization coefficient α (for electrons) and β (for holes) is defined as the number of electron-hole pairs generated by a carrier per unit distance traveled in the direction of the field, with units of cm⁻¹. These are strongly field-dependent, typically modeled as:

α(E) = a · exp(-b / E)

where a and b are material-specific constants and E is the local electric field. Because α and β differ (electrons and holes ionize at different rates in most materials), avalanche behavior is asymmetric — in silicon, α > β, so electron-initiated ionization dominates at a given field.

Multiplication factor and breakdown voltage relationship

The avalanche multiplication factor M describes how much a primary current is amplified:

M = 1 / (1 - ∫ α(x) dx)

integrated across the depletion width. Breakdown is defined as the bias at which this integral reaches unity — M formally goes to infinity, meaning a vanishingly small leakage current sustains an arbitrarily large multiplied current, which is the ionization integral criterion used in every TCAD breakdown voltage simulation.

Material dependence: Si, Ge, GaAs, SiC

Ionization coefficients and the resulting critical fields vary by nearly an order of magnitude across materials because they scale with bandgap energy. Wider-bandgap materials need stronger fields before carriers reach ionization threshold, which is why SiC devices sustain breakdown fields roughly 7–10× higher than silicon for comparable doping, enabling much thinner, lower-resistance high-voltage drift regions. Germanium, with its narrower bandgap, ionizes at lower fields than silicon, while GaAs sits between silicon and SiC with different α/β ratios that make it attractive for avalanche photodiodes. Exact coefficient values and their field-range validity should always be pulled from the specific process or material datasheet or a TCAD material library rather than assumed from general trends.

Empirical models and temperature scaling

The Chynoweth model (the exponential form above) is the standard starting point, with a and b extracted from measured breakdown data at a reference temperature, then scaled using empirical temperature coefficients that increase the effective b parameter (raising the field required for a given α) as temperature rises. Device simulators such as Synopsys TCAD and Silvaco Atlas implement these temperature-scaled models directly for breakdown voltage prediction across a device's rated operating range.

Electric Field Requirements for Avalanche

Critical field strength in depletion regions

The critical field E_crit is the peak field at which the ionization integral reaches unity for a given depletion width. It is not a fixed material constant — it depends on doping concentration, because lower doping produces a wider depletion region, allowing the same total multiplication to occur at a lower peak field.

Relationship to junction doping profiles

Lightly doped junctions (common in high-voltage power diodes and the drift region of power MOSFETs) spread the field over a wide depletion region, lowering the peak field and raising breakdown voltage at the cost of higher on-resistance. Heavily doped junctions concentrate the field over a narrow region, reaching critical field — and breakdown — at a much lower applied voltage.

Field distribution in abrupt vs. graded junctions

Abrupt junctions produce a triangular field profile peaking sharply at the metallurgical junction, while linearly graded junctions produce a smoother, lower-peak parabolic profile for the same voltage, generally pushing breakdown voltage higher for a given maximum doping gradient. This is why power device designers use graded or guard-ring junction terminations to suppress localized field crowding at junction edges.

Practical Impact on Device Design

Breakdown voltage prediction in diodes and transistors

Designers compute BV by solving the ionization integral across the simulated or measured field profile for a given doping and geometry, rather than relying on a single critical-field number, because real devices have curvature, edge termination, and non-uniform doping that reshape the field from the ideal planar-junction case.

Safe operating area (SOA) limits

SOA charts for power transistors incorporate avalanche margin: operating a device near but below its rated breakdown voltage under high current and temperature can still trigger localized avalanche multiplication at hot spots, long before the nominal bulk BV is reached.

Thermal runaway and second breakdown

Because avalanche current increases with temperature-dependent field redistribution and self-heating increases local current density, a positive feedback loop can form — this is the mechanism behind "second breakdown" in bipolar power devices, where a localized hot spot collapses voltage and concentrates current until the device fails.

Application in Zener diodes and avalanche photodiodes

Avalanche photodiodes deliberately exploit controlled multiplication (M in the range of 10–100) to amplify weak optical signals, while avalanche-mode Zener diodes use the positive temperature coefficient of avalanche breakdown for stable voltage references above ~5.5 V.

Measurement and Characterization

Extracting ionization coefficients from I-V curves

Ionization coefficients are typically extracted by measuring reverse I-V characteristics on test structures with known, simple field profiles (e.g., one-sided abrupt junctions), fitting the measured multiplication factor M(V) to the ionization integral, and solving for α(E) and β(E) parameters.

Temperature and field-dependent testing

Characterization sweeps breakdown voltage across a temperature range (often -40°C to 150°C or higher for automotive-grade parts) to extract the temperature coefficient needed for the empirical scaling model used in design margin calculations.

Simulation in SPICE and device modeling

Circuit-level SPICE models typically use empirical breakdown voltage and temperature coefficient parameters rather than solving the ionization integral directly, while device-level TCAD tools implement the full field-dependent α/β models for physical breakdown voltage prediction during process and layout design.

Key Takeaways

Impact ionization coefficient predicts breakdown voltage

The coefficients α and β, integrated across the depletion field profile, determine the exact bias at which multiplication becomes unbounded.

Critical for high-voltage and power device engineering

Doping profile, junction grading, and edge termination all exist to manage peak field relative to the critical field implied by these coefficients.

Temperature and material selection drive reliability

Wider-bandgap materials and accurate temperature scaling of ionization coefficients are what separate a reliable high-voltage design from one with hidden avalanche margin.