Dr. Mohamed gave some links about the subject of the question. However, there is a basic answer to your question. There is a concept telling that you calculate and measure the quantities as you define them. Accordingly:
The small signal capacitance is defined as C= dQ/dV at a specified operating DC operating point.
So you simulate the device at the required operating point say VGS and VDS for a MOS transistor. And then you super pose an alternating small signal ac voltage Vgs for example on VGS and calculate the ac current flowing in the gate say Igs.
The admittance will be= Igs/Vgs= g+i wC, where g is the small signal conductance and C is the capacitance. Igs will contain a real part and an imaginary part. and w is the frequency of the applied small signal.
I am aware of the method you mentioned. I had tried it before and implemented that in my device simulator (MATLAB). There was an issue in calculating the phase difference with respect to the input voltage. When I applied input voltage as a sinusoid, I was not getting perfect sinusoidal output to estimate the phase difference and the magnitude.
I don't know anything about silicon controlled rectifier in particular, but the small signal analysis is the general method followed for capacitance extraction irrespective of the type of the device.
Sorry for not taking care of your questions. You get a distorted current sine wave form because you have to reduce your ac voltage till you obtain as pure sine wave as possible. In this case you can evaluate the phase difference between the current and the voltage. You may also vary the frequency to get an easy observable phase difference.
While doing the small-signal ac analysis in Silvaco, what is the exact equation via which capacitance is calculated between the two electrodes in case of a pn-junction diode?
Silvaco doesn't use a closed-form and well-defined equation for capacitance calculation.
Instead, it highly depends on the small-signal analysis.
Silvaco solves drift-diffusion equations from them it estimates the current from the obtained charge and the potential profiles.
In the variation case of small-signal analysis, ingeneral they apply a sinusoidal varaition in voltage and they measure the current. From the magnitude of the current and phase difference, impedance is calculated which eventually gives the admittance and the capacitance.