PN and Zener I-V graphs; diode ac resistance

I–V characteristics

Ordinary PN junction diode: in forward bias almost no current flows until the cut-in voltage (about 0.7 V for Si, 0.3 V for Ge); after that the current rises exponentially. In reverse bias only a very small saturation current IS flows, up to the breakdown voltage. An ordinary diode is not designed to work in breakdown and is usually damaged there by the large current and power.

Zener diode: the forward part is the same as for a normal diode. In reverse bias it blocks until the Zener voltage VZ; then the current rises sharply while the voltage stays almost constant at VZ. The device is designed to work safely in this region.

                         ID (mA)
                          |            /
                          |           /   forward region
                          |          /    (same for both diodes)
                          |        _/
      -VZ (Zener)         |     _-'
  ------+-----------------+---''-------------- VD (V)
        |  -IS (µA)       0     0.7 V (Si)
        |  reverse leakage
        |
        |  breakdown: very sharp knee for the Zener;
        |  current rises steeply at almost constant VZ
        |
      -IZ

(The first quadrant is the same for both diodes; the Zener's special feature is the sharp reverse knee at -VZ. An ordinary diode breaks down at a much larger reverse voltage, -VBR.)

AC equivalent model

For a small signal around a forward bias point (VD, ID), the diode behaves like a resistor rd:

  o----/\/\/----o
        rd

(In a more complete model, a cut-in voltage battery and the diode capacitance are added.)

Derivation of ac resistance

iD = IS exp(vD/(η VT))                    (v ≫ η VT)
1/rd = diD/dvD at Q = IS exp(VD/(η VT))/(η VT) = ID/(η VT)

        rd = η VT / ID

At 300 K, VT = 25 mV, so for η = 1: rd = 25 mV / ID(mA) ohms. Example: ID = 2.5 mA gives rd = 10 Ω.

For a given diode and temperature, rd depends only on the dc current, and it is small at high currents.