Zener Diode

1. Theory

• Definition: A Zener diode is a specially designed PN junction diode that operates in reverse breakdown for voltage regulation.
• Heavy doping: Both P and N regions are heavily doped, producing a very thin depletion region and a strong electric field under reverse bias.
• Zener breakdown: At relatively low breakdown voltages, the strong electric field enables electrons to tunnel quantum-mechanically from the valence band of the P-side to the conduction band of the N-side.
• Breakdown voltage: The reverse voltage at which current increases sharply while the voltage across the diode remains approximately constant.

2. Working Principle

• Forward bias: Behaves like a conventional PN junction diode, conducting through majority-carrier injection.
• Reverse bias below breakdown: A small leakage current flows, and the depletion region widens.
• Zener breakdown: A strong electric field enables band-to-band quantum tunnelling across the narrow depletion region.
• Voltage regulation: Once breakdown occurs, the diode maintains an approximately constant voltage over its specified operating-current range.
• Current limiting: A series resistor limits the reverse current and prevents excessive power dissipation.

3. Applications

• Voltage regulation: Maintains a stable DC output voltage.
• Voltage reference: Provides a reference voltage for electronic circuits.
• Overvoltage protection: Limits voltage rises to protect sensitive components.
• Signal clipping: Restricts signal voltage beyond a chosen threshold.
• Waveform shaping: Modifies signal amplitudes in clipping and limiting circuits.
• Circuit protection: Used in protection networks, provided the diode’s current and power ratings are respected.

Name	Formula	Related Formulae	Variables/Constants
Breakdown voltage (one-sided junction)	$V_Z\approx \frac{{\epsilon }_s{E}_{crit}^2}{2q{N}_B}$	$\begin{array}{r}\text{(see}\text{PN}\text{Junction}\text{Diode}\text{/}\\ \text{Metal-Semiconductor}\text{Contacts}\text{pages)}\end{array}$	$V_Z:Zener(breakdown)voltage$ $E_{crit}:criticalfield$ $N_B:dopingofthemorelightlydopedside$
Zener (band-to-band tunneling) current density	$J_Z=\frac{q^{3}EV}{4{\pi }^2{\hslash }^2}\sqrt{\frac{2m^{\ast }}{E_g}}\exp \left(-\frac{4\sqrt{2m^{\ast }}{E}_g^{3/2}}{3q\hslash E}\right)$		$J_Z:interbandtunnelingcurrentdensity$ $V:appliedreversevoltage$ $\text{(}{E}_g\text{in joules and}E\text{in V/m)}$ $E:electricfieldatthejunction$ $m^{\ast }:tunnelingeffectivemass$
Avalanche multiplication factor	$M=\frac{1}{1-(V/V_Z{)}^n}$		$\begin{array}{r}M:avalanchemultiplicationfactor\\ (divergesasV\to V_Z)\end{array}$ $\begin{array}{r}n:empiricalexponent(\approx 3\text{–}6,\\ materialandcarrier-typedependent)\end{array}$
Zener–avalanche breakdown-regime crossover	$V_Z\lesssim \frac{4E_g}{q}:\text{Zener (tunneling) dominated}$ $V_Z\gtrsim \frac{6E_g}{q}:\text{avalanche dominated}$	$\begin{array}{r}\text{crossover}\approx 5\text{–}6\mathrm{V}\text{for}\text{Si}\\ (E_g=1.12\mathrm{eV})\end{array}$	$\begin{array}{r}\text{(regime}\text{set}\text{primarily}\text{by}\text{doping,}\\ \text{through}\text{its}\text{effect}\text{on}W\text{and}{E}_{max}\text{)}\end{array}$
Temperature coefficient of breakdown voltage	$TC=\frac{1}{V_Z}\frac{d{V}_Z}{dT}$	$TC<0(\text{Zener-dominated},V_Z\lesssim 5\mathrm{V})$ $TC>0(\text{avalanche-dominated},V_Z\gtrsim 6\mathrm{V})$	$TC:fractionaltemperaturecoefficientof{V}_Z$
Dynamic (Zener) resistance	$r_z={\left(\frac{d{I}_Z}{d{V}_Z}\right)}^{-1}$		$\begin{array}{r}{r}_z:small-signalresistancein\\ breakdown,decreaseswithincreasing{I}_Z\end{array}$
Maximum Zener current (power-limited)	$I_{ZM}=\frac{P_{max}}{V_Z}$	$P=V_Z{I}_Z\le P_{max}$	$I_{ZM}:maximumratedZenercurrent$ $P_{max}:maximumratedpowerdissipation$
Load (voltage) regulation	$\Delta V_Z\approx r_z\Delta I_Z$		$\begin{array}{r}\Delta V_Z:outputvoltagevariationfor\\ agivencurrentswingthroughtheZener\end{array}$
Tunneling probability (WKB approximation)	$T\approx \exp \left(-\frac{4\sqrt{2m^{\ast }}{E}_g^{3/2}}{3q\hslash E}\right)$	$E\approx E_{max}\text{(see Metal-Semiconductor Contacts / PN Junction Diode pages)}$	$\begin{array}{r}T:probabilityofanelectrontunneling\\ directlyfromthevalencebandtothe\\ conductionbandthroughtheforbiddengap\end{array}$ $E:electricfieldatthejunction$ $m^{\ast }:tunnelingeffectivemass$

Important Questions

Ques: What is the actual difference between “Zener breakdown” and “avalanche breakdown,” and why do both get called “Zener diodes”?

Zener breakdown is inter-band (band-to-band) quantum tunneling of valence-band electrons directly through a very thin, heavily doped depletion region into the conduction band. It requires no impact ionization at all and occurs at low breakdown voltages because heavy doping is needed to make the depletion width thin enough for tunneling. Avalanche breakdown, by contrast, is the same impact-ionization multiplication process used throughout the rest of this vault’s breakdown formulas, and dominates at lower doping (wider depletion regions, higher breakdown voltages). The commercial name “Zener diode” predates the clear separation of these two mechanisms and has stuck as a generic term for any diode intentionally operated in reverse breakdown as a voltage reference, even though most diodes marketed above roughly 5–6 V (for silicon) are actually avalanche-dominated devices, not Zener-tunneling devices in the strict physical sense. Reference: C. Zener, “A Theory of the Electrical Breakdown of Solid Dielectrics,” Proc. R. Soc. Lond. A 145, 523 (1934); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why does the temperature coefficient of breakdown voltage change sign around 5–6 V, and why does this matter practically?

Zener tunneling current depends exponentially on the bandgap $E_g$, which shrinks with increasing temperature, making tunneling easier and causing $V_Z$ to decrease with temperature (negative TC) in the tunneling-dominated regime. Avalanche breakdown works the opposite way: higher temperature increases lattice phonon scattering, shortening the mean free path between collisions, so a higher field (and hence higher voltage) is needed to let carriers gain enough energy between collisions to trigger impact ionization, giving a positive TC. Near the crossover voltage, both mechanisms contribute comparably and their opposing temperature dependences largely cancel, which is exactly why diodes rated around 5–6 V are the standard choice for temperature-stable voltage references, and why some precision references pair a Zener diode in series with a forward-biased PN junction (which has its own well-known negative TC) to fine-tune the cancellation further. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why is dynamic resistance $r_z$ a practically important parameter rather than just a theoretical detail?

An ideal voltage reference would hold $V_Z$ perfectly constant regardless of current, but a real Zener diode’s breakdown I-V curve has a finite slope, so any change in current through the device (from a changing load, for instance) produces a small but nonzero change in $V_Z$ given by $\Delta V_Z\approx r_z\Delta I_Z$. Since $r_z$ is largest near the “knee” of the breakdown curve at low current and decreases as $I_Z$ increases, Zener voltage references are generally operated well above the knee current to minimize $r_z$ and achieve better voltage regulation, which is why datasheets specify a recommended test current alongside the rated breakdown voltage. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: PN Junction, Avalanche Diode, Backward Diode, Tunnel or Esaki Diode, Schottky Diode, Steep Slope FETs (Tunnel FET, Impact Ionization MOS, Negative Capacitance FET), Diodes (PN, PIN, Schottky, Zener), Diode Compact Models, On-Chip ESD Protection Devices.