I am not sure I understand your question right but maybe I can explain few things in basic terms that might help you somewhat. Dark current is the current measurement made when there is no light to illuminate the sample. When you turn on the light then the current you are measuring is light current. Let say you are measuring dark current and suddenly you turned on the light and turn of the light. Assuming you are doing this measurement at constant voltage first you will see constant current which is your dark current then your current will jump a higher current straightly which is you photocurrent and then it will decay exponentially. This decay will depend on life time of your carriers and the recombination rate.