Negative capacitance (NC) phenomena is recently suggested as a breakthrough that can lead to the improved transistor by decreasing the subthreshold swing. To understand the NC phenomena, we investigated the effects of the ferroelectric properties such as the remnant polarization depending on the switching cycles in Si-doped HfO2 thin film capacitor. The ferroelectric properties were controlled by using the wake-up effect, in which the remnant polarization enhances as the number of switching cycles increase. The relation between the wake-up effect and the voltage drop region with the negative differential capacitance were elucidated. The dynamic hysteresis loops were fitted based on Landau-Khalatnikov equation, and the free energy as a function of polarization was obtained. The Landau coefficients showed that the double-well feature of the free energy becomes more apparent due to the wake-up. Based on the wake-up effect on NC phenomena, we show that the NC phenomena is well described by Landau-Ginzburg theory of ferroelectrics.