Why does a real world capacitor behave like an inductor at frequencies above its self-resonant frequency?

I've come across some graphs comparing the impedance of a capacitor over frequency and it understandably declines as frequency increases -- up until a certain point. Afterwhich, the impedance begins to increase, like an inductor.

What exactly is going on here? Why do larger capacitors have a more gradual shift from decreasing to increasing impedance while smaller caps have a sharper change?

I'm sure this is something basic but I'm having a hard time finding anything about it.

Answer

The behavior of a realistic multi-layer ceramic capacitor is determined by its construction. It is made of ceramic pieces with conducting surfaces, which are connected together at collector electrodes.

Unfortunately, every conductor posess some self-inductance, which begins to play dominant role at higher frequencies. One good article about equivalent models of MLCC is presented by Taiyo Yuden corporation, as illustrated below:

For larger-size (more layers) the equivalent circuit grows up (see the article), so the effective characteristics change accordingly.