Can someone explain in terms of physics why a DC bias affects the capacitance value of certain capacitors? Is it because the electric field from the bias voltage does something to the dielectric?
I cannot tell you the exact details, but here is a rough explanation. If I get this wrong, please correct me.
Many common insulators like glass, plastics, mica have a dielectric constant of about 2 to 5 - ie 2 to 5 times better then a vacuum.
The best behaved ceramic capacitor - the NPO cap - has a dielectric constant of about 60. So you can get a over 20 times the capacitance then you could with a common insulator.
Y5U and Y5V can have dielectric constants over 10,000, so you get a massive increase of capacitance for a given size of capacitor. This happens because the particles in the ceramic have charges that can move slightly under an electrical field. If you apply enough electric field by increasing the DC bias, you start to saturate these particles - they have aligned their charge to the field as much as they can and they cannot do any more. At his point the dielectric constant plummets downward, and so the capacitance decreases proportionally.
In the dielectrics with a low dielectric constant, the material will fail from voltage breakdown long before this situation occurs.
Richard