Zener diode noise power
There are really two different things going on in a Zener diode, the Zener effect and avalanche breakdown. See What is the difference between an avalanche breakdown and a Zener breakdown?.

The avalanche process is much noisier than the Zener process, so you'll want to pick a diode that has a breakdown voltage significantly higher than 6V, where the avalanche process dominates.

Frequently, people use the reverse-biased B-E junction of a small-signal transistor as their noise source, because it shows a strong avalanche effect, and the parasitic capacitance is low, giving more bandwidth.