Why is Zener avalanche noise saw tooth shaped?

Consider that you effectively have this:

^{simulate this circuit – Schematic created using CircuitLab}

where C is the junction capacitance, plus any external capacitance (leads, breadboard, etc). Some of the current from R1 leaks through D1, but the rest charges C. Once the voltage reaches a certain level, avalanche breakdown occurs and current flows from C until the avalanche stops. Then the current begins charging C again.

To calculate C you first need to know the leakage. Decrease V1 until the noise disappears. Then measure the current. Then increase V1 back to 30V. Measure the rising slope of the noise dV/dt. Measure the average value of V. The current through R1 is approximately constant at (30V - V)/100kohm. Subtract the leakage current from this, then use I=C dV/dt to calculate the capacitance.

The random discharges near breakdown are from random crystal dielectric charges breaking down under a high E field producing a pulse current that drops the voltage with an RC fall time. If you could measure how small the fall time was , you could estimate the size of the C in that charged particle.

If I guess each particle sees at least 50kV/mm or 50V/um or 50mV/nm so the charge size may be about 10 to 20 nm to get 500 to 1000 mV. This can be scaled according to the epixtaxial particle sizes in the Si crystal lattice.

Like a Unijunction oscillator except with random thresholds in a limited range, the C charges up and the Zener voltage collapses rapidly 1~5% just below the breakdown threshold at very low currents.

From looking at the waveform I expect the rise/fall time ratio to be ~ 100 or less in this sawtooth.