In this paper, we analytically study the relationship between the coercive field, remnant polarization and the thickness of a ferroelectric material, required for the minimum subthreshold swing in a negative capacitance capacitor. The interdependence of the ferroelectric material properties shown in this study is defined by the capacitance matching conditions in the subthreshold region in an NC capacitor. In this paper, we propose an analytical model to find the optimal ferroelectric thickness and channel doping to achieve a minimum subthreshold swing, due to a particular ferroelectric material. Our results have been validated against the numerical and experimental results already available in the literature. Furthermore, we obtain the minimum possible subthreshold swing for different ferroelectric materials used in the gate stack of an NC-FET in the context of a manufacturable semiconductor technology. Our results are presented in the form of a table, which shows the calculated channel doping, ferroelectric thickness and minimum subthreshold for five different ferroelectric materials.