I still haven't decided whether it's possible to make an unpumped oscillator based on "negative capacitance" C:V behavior. It's probably impossible since I don't think anyone has done it. I can maybe use conservation of energy to prove it can't be done. Pumped parametric amps and oscillators (using varicap diodes) are old hat; they were more popular around 1960, when transistors were still slow.
I did manage to sumulate a frequency divider of sorts, really a subcycle parametric oscillator, based on the C:V curve of a diode. It should work with a ceramic cap, too. But it's still pumped, not self-oscillating.
This is a classic diode frequency multiplier, but it halves the frequency instead of doubling it. Conversion efficiency is impressively bad.