How does the veractor diode work?

They are usually used as voltage variable capacitors,not as diodes. The diode is made in such a way that when reverse biased (where the voltage across the diode is in the polarity where very little current flows) the capacitance varies considerably with the voltage across it. This action is usually used to make resonant Inductor-capacitor circuits have their resonant frequency dependent upon the "DC" voltage across them. For instance: A low frequncy signal, like Audio, is impressed across a veractor tuned resonant circuit to make a much higher frequency oscillator (at say an FM station frequency) vary its frequency in proportion to the amplitude of the "instantaneous" Audio signal. (at 100 MHz nominal oscillation frequency, the audio is like slowly moving "DC"). One can make a frequency modulated radio this way. (rather distorted; veractor characteristics of V across to C across are pretty non-linear).

These diodes are made by having one side of the "P-N" junction that forms the diode be very lightly doped. What this does is make the depletion region; the region where conductive carriers are pulled out by the reverse bias across the diode (where it doesn't conduct) change its width considerably more than usual. (all diodes have some of this voltage variability) This depletion width is non-conducting and acts like the dielectric of a capacitor. As the voltage across changes the width of the dielectric changes thus the capacitance across the device changes.