Avalanche Diode

1. Theory

• Definition: An avalanche diode is a PN junction designed to break down by impact ionization and to operate safely and repeatably in reverse breakdown.
• Moderate doping: Lighter doping than a Zener diode gives a wider depletion region, so carriers gain enough energy between collisions to ionize the lattice instead of tunnelling.
• Impact ionization: A carrier accelerated by the high field knocks a valence electron into the conduction band, creating a new electron-hole pair; the rate per unit length is the ionization coefficient.
• Avalanche breakdown: When each carrier crossing the depletion region generates on average one more ionizing carrier (ionization integral ${\int }_0^W{\alpha }_{n}dx=1$), multiplication runs away and current rises sharply.
• Ionization ratio: Electrons and holes ionize at different rates; the ratio $k={\alpha }_p/{\alpha }_n$ decides both the breakdown condition and the multiplication noise.
• Uniform breakdown: The junction is shaped (guard rings, bevelled edges) so breakdown occurs evenly across the whole area rather than at hot spots on the edges.

2. Working Principle

• Forward bias: Conducts like an ordinary PN junction diode.
• Reverse bias below breakdown: Only a small leakage current flows, multiplied by a factor $M$ that grows as the voltage approaches breakdown.
• Avalanche breakdown: At the breakdown voltage, multiplication diverges and the diode clamps the voltage while carrying large reverse current.
• Positive temperature coefficient: Higher temperature increases phonon scattering, so more field is needed to ionize; breakdown voltage rises with temperature, which spreads current evenly and prevents thermal runaway.
• Multiplication noise: Each carrier produces a random number of secondaries, adding excess noise above shot noise (McIntyre’s factor $F(M)$).
• Energy absorption: Uniform breakdown over a large area lets the diode absorb short, high-energy transients without damage.

3. Applications

• Transient voltage suppression (TVS): Clamps fast surges such as ESD and lightning-induced spikes on power and data lines.
• Higher-voltage references: Above about 6 V in Si, stable “Zener” references are actually avalanche diodes.
• Controlled-avalanche rectifiers: Rectifiers rated to survive repeated reverse-voltage transients.
• Noise sources: Avalanche noise provides calibrated broadband RF noise generators.

Name	Formula	Related Formulae	Variables/Constants
Impact ionization coefficients (Chynoweth’s law)	${\alpha }_n(E)=A_n\exp \left(-\frac{b_n}{E}\right)$ ${\alpha }_p(E)=A_p\exp \left(-\frac{b_p}{E}\right)$		$\begin{array}{r}{\alpha }_n,{\alpha }_p:electronandhole\\ ionizationcoefficients(ionizing\\ collisionsperunitlength)\end{array}$ $\begin{array}{r}{A}_n,A_p,b_n,b_p:empirical,\\ material-dependentconstants\end{array}$ $E:localelectricfield$
Ionization rate ratio	$k=\frac{{\alpha }_p}{{\alpha }_n}$		$\begin{array}{r}k:ratioofholetoelectronionization\\ coefficients(material-and\\ field-dependent)\end{array}$
Avalanche breakdown condition (ionization integral)	${\int }_0^W{\alpha }_{n}dx=1$	${\int }_0^W{\alpha }_n\exp \left[-{\int }_0^x({\alpha }_n-{\alpha }_p)d{x}^{\prime }\right]dx=1\text{(general,}{\alpha }_n\ne {\alpha }_p\text{)}$	$W:depletion(avalanche)regionwidth$
Avalanche multiplication factor	$M=\frac{1}{1-(V/V_B{)}^n}$		$\begin{array}{r}M:avalanchemultiplicationfactor,\\ divergesasV\to V_B\end{array}$ $n:empiricalexponent(\approx 3\text{–}6)$
Breakdown voltage (one-sided junction)	$V_B\approx \frac{{\epsilon }_s{E}_{crit}^2}{2q{N}_B}$	$\begin{array}{r}\text{(see}\text{PN}\text{Junction}\text{Diode}\text{/}\\ \text{Metal-Semiconductor}\text{Contacts}\text{pages)}\end{array}$	$V_B:avalanchebreakdownvoltage$ $\begin{array}{r}{E}_{crit}:criticalfieldatwhichthe\\ ionizationintegralreachesunity\end{array}$
Temperature dependence of breakdown voltage	$V_B(T)=V_B(T_0)\left[1+{\alpha }_T(T-T_0)\right]$	$TC={\alpha }_T>0$	$\begin{array}{r}{\alpha }_T:positiveempiricaltemperature\\ coefficient(\sim 5\times 10^{-4}\text{ to }10^{-3}{\mathrm{K}}^{-1}\\ forSi)\end{array}$ $T_0:referencetemperature$
Excess noise factor (McIntyre’s formula)	$F(M)=kM+(1-k)\left(2-\frac{1}{M}\right)$		$\begin{array}{r}F(M):excessnoisefactormultipliesthe\\ shotnoisespectraldensityabovethe\\ ideal2qIlevel\end{array}$ $\begin{array}{r}\text{(pure}\text{electron}\text{injection,}\text{with}\\ k={\alpha }_p/{\alpha }_n\text{;}\text{for}\text{hole}\text{injection}\\ \text{replace}k\text{by}1/k\text{)}\end{array}$

Important Questions

Ques: What does the ionization integral physically represent, and why does reaching unity define breakdown?

As a carrier crosses the high-field avalanche region, it has some probability per unit distance of generating a new electron-hole pair through impact ionization, given by ${\alpha }_n$ (or ${\alpha }_p$). The ionization integral sums up the expected number of secondary carriers generated by a single primary carrier traversing the entire region; when this integral equals 1, each initiating carrier produces on average exactly one additional carrier capable of itself triggering further ionization, creating a self-sustaining chain reaction — a runaway multiplication process that is the formal definition of avalanche breakdown. Below this threshold, carrier multiplication is finite ($M$ stays bounded); at and above it, multiplication diverges, which is why the simplified multiplication-factor formula shows $M\to \infty$ as $V\to V_B$. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why do electrons and holes have different ionization coefficients, and why does the ratio $k$ matter beyond the breakdown condition itself?

Electrons and holes have different effective masses and different scattering behavior (band structure, phonon coupling) within a given semiconductor, so they require different amounts of accumulated kinetic energy between collisions to trigger an ionizing collision, giving genuinely different ${\alpha }_n$ and ${\alpha }_p$ values and material-dependent empirical constants. Beyond setting the exact breakdown condition, $k={\alpha }_p/{\alpha }_n$ directly controls the excess noise factor $F(M)$: a material where one carrier type ionizes far more readily than the other ($k\to 0$ when the injected carrier is the more strongly ionizing one, or $k\to \infty$ in the inverse convention; $k=1$, equal ionization rates, is the noisiest case) produces a more deterministic, lower-noise multiplication process, which is why avalanche photodiode materials are often chosen specifically to maximize this asymmetry rather than for breakdown voltage alone. Reference: R.J. McIntyre, “Multiplication noise in uniform avalanche diodes,” IEEE Trans. Electron Devices 13, 164 (1966).

Ques: Why does avalanche multiplication add noise beyond the shot noise already present in the unmultiplied current?

Avalanche multiplication is a statistical, not deterministic, process — every carrier that enters the high-field region produces a random number of secondary carriers rather than exactly $M$ every time, and this randomness in the multiplication process itself adds variance on top of the shot noise already inherent in the primary (unmultiplied) current. McIntyre’s excess noise factor $F(M)$ quantifies exactly how much extra variance this randomness contributes as a function of the average multiplication $M$ and the ionization ratio $k$; it is the reason avalanche photodiodes trade signal gain against a real, quantifiable noise penalty rather than offering “free” amplification, and it is the central design tradeoff in choosing an operating multiplication level for any avalanche-based detector or diode. Reference: R.J. McIntyre, “Multiplication noise in uniform avalanche diodes,” IEEE Trans. Electron Devices 13, 164 (1966); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: Zener Diode, Avalanche Photodiode (APD), Impact Ionization Avalanche Transit Time (IMPATT) Diode, PN Junction, Trapped Plasma Avalanche Triggered Transit (TRAPATT) Diode, Single-Photon Avalanche Diode and Silicon Photomultiplier (SPAD, SiPM), Diodes (PN, PIN, Schottky, Zener), Diode Compact Models, On-Chip ESD Protection Devices.