Photodiode parallel to a capacitor

[arrenio]

Dear Forum Members, I am looking for someone who can help me to model the behavior of a photodiode in parallel with a capacitor. I want to model the behavior of a device that I have developed.
As you can see in my attached file, the photodiode shows a current-to voltage characteristic with a turn-on voltage Vto, and receives irradiation for a given time tirr. The photodiode is connected in parallel with an ideal capacitor Cp. Once the photodiode is irradiated, a photocurrent Ip flows and the capacitor starts charging. A positive voltage drop Vac arises on the capacitor, with a sign so that the photodiode is forwardly biased. At a certain irradiation dose (i.e., after a certain irradiation time) the accumulated charge on the capacitor will produce a voltage drop > Vto, and a forward current will flow on the photodiode, so that voltage drop Vac is limited by such a current. Once irradiation stops, given the photodiode has a zero leakage current, the device keeps the photogenerated charge on the capacitor, but the behavior is not linear vs. irradiation time, due to the discharge of photogenerated charge above Vto.
Can someone help me in modeling such a behavior?
thank you!

schematic and experimental IV curve of the photodiode

 

[Charles Link]

The diode (without illumination) does not follow the ideal diode behavior characterized by a turn-on voltage, but is more properly represented by the Schockley diode equation. The Schockley diode equation has a couple of parameters that can be input to adjust it for the particular diode at hand. Google "Schockley diode equation". Hopefully this is helpful. ..editing...I think you may already have the Schockley diode equation there. The diode equation looks very similar when there is light shining on it versus no light=the I-V curve shifts in the y-direction. There is no such thing as "no leakage current". The Schockley diode equation should provide you with a number for the "leakage current as a function of voltage...I think the origins of this leakage current are the result of thermally generated electrons in the "p" side of the photodiode, but you may want to research that further.