If your Zener have a good voltage, like 30-200V, you can see a funny effect.
Observe the (amplified) noise in the darkness. Provide light an access to the junction (saw...) and illuminate, at identical Zener current: the noise decreases sharply.
I did it to verify that the cause of noise is that charge carriers move in bunches created by avalanche multiplication. Light creates more avalanche "seeds" so each bunch gets smaller and this reduces the noise.
Consistently, heat reduces the noise, as well as a low Zener voltage. The noise sqrt(2*I*Q*B) makes also bunches of Q total charge roughly compatible with the Zener voltage.
For instance, a 5V Zener (which isn't a good Zener then, rather a Tunnel diode) has a very soft (=bad) I-V characteristic because 5V don't suffice to multiply the charge carriers much, but is very silent. Much more silent than a bandgap voltage reference. So if you want a silent voltage reference chip, say for an ADC, choose one that integrates a Zener (with the necessary compensations) and not a bandgap circuit.