29 Jun 2025

Zener Breakdown and Voltage Regulation

Zener and avalanche mechanisms, reverse characteristic, and the shunt voltage-regulator operating limits.

bsc semester-iv mj-7 semiconductor-devices zener-diode voltage-regulator

A Zener diode is designed to operate safely in reverse breakdown. Let $V_Z>0$ denote the magnitude of its specified reverse voltage. Below the knee the reverse current is small; near $V_R=V_Z$, current rises sharply while the terminal voltage changes only slightly. The external circuit must limit current because breakdown itself does not.

Zener and avalanche mechanisms

In a heavily doped junction the depletion layer is narrow and the electric field can become large at a relatively low reverse voltage. Electrons then tunnel quantum mechanically between valence- and conduction-band states. This is Zener breakdown and normally has a negative temperature coefficient of $V_Z$.

In a more lightly doped, wider junction, carriers gain kinetic energy from the field and create new electron-hole pairs by impact ionization. Repeated multiplication produces avalanche breakdown, normally with a positive temperature coefficient. Both mechanisms can contribute near approximately $5$–$6\,\mathrm V$; the distinction is physical, not a different circuit symbol.

The incremental resistance in breakdown is

\[\boxed{r_Z=\frac{dV_Z}{dI_Z}},\]

measured in ohms. It is small but not zero, so a real Zener voltage varies with current and temperature.

Shunt regulator

The diode is reverse connected across the load and fed through a series resistance $R_s$.

In regulation, the output is approximately $V_Z$ and the source current divides between the Zener diode and load.

The editable source is zener-regulator.tex.

With $V_o\simeq V_Z$, Kirchhoff’s laws give

\[I_s=\frac{V_s-V_Z}{R_s}, \qquad I_L=\frac{V_Z}{R_L}, \qquad \boxed{I_Z=I_s-I_L}.\]

Regulation requires

\[I_{Z,\min}\le I_Z\le I_{Z,\max},\]

where the lower bound keeps the diode beyond its knee and the upper bound satisfies both current and power ratings:

\[P_Z=V_ZI_Z\le P_{Z,\max}.\]

The worst-case input limits are therefore

\[V_{s,\min}\ge V_Z+R_s(I_{L,\max}+I_{Z,\min}),\] \[V_{s,\max}\le V_Z+R_s(I_{L,\min}+I_{Z,\max}).\]

If either inequality is violated, the diode leaves regulation or overheats. In the small-signal model the Zener is $r_Z$, so

\[\frac{\Delta V_o}{\Delta V_s} =\frac{r_Z\parallel R_L}{R_s+(r_Z\parallel R_L)}.\]

Good line regulation requires $r_Z\parallel R_L\ll R_s$, while load regulation also requires enough current margin for the change in $I_L$.