Ag pastes added to Bi-oxide frits have been applied to the electrode material of Si solar cells. It has been reported that frits induce contacts between the Ag electrodes and the Si wafer after firing. During firing, the control of interfaces among Ag, the glass layer, and Si is one of the key factors for improving cell performance. Specifically, the thermo-physical properties of frits considerably influence Ag-Si contact. Therefore, the thermal properties of frits should be carefully controlled to enhance the efficiency of cells. In this study, the interface structures among Ag electrodes, glass layers, and recrystallites on an $n^+$ emitter were carefully analyzed with the thermal properties of lead-free frits. First, a cross-section of the area between the Ag electrodes and the Si wafer was studied in order to understand the interface structures in light of the thermal properties of the frits. The depth and area of the pits formed in the Si wafer were quantitatively calculated with the thermal properties of frits. The area of the glass layers between the Ag electrodes and Si, and the distribution of recrystallites on the $n^+$ emitter, were measured from a macroscopic point of view with the characteristics of the frits. Our studies suggest that the thermophysical properties should be controlled for the optimal performance of Si solar cells; our studies also show why cell performance deteriorated due to the high viscosity of frits in Ag pastes.