In this study, we used I-V spectroscopy, photoconductivity (PC) yield and internal photoemission (IPE) yield using IPE spectroscopy to characterize the Schottky barrier heights (SBH) at insulator-semiconductor interfaces of Pt/HfO2/p-type Si metal-insulator-semiconductor (MIS) capacitors. The leakage current characteristics of the MIS capacitor were analyzed according to the J-V and C-V curves. The leakage current behavior of the capacitors, which depends on the applied electric field, can be described using the Poole-Frenkel (P-F) emission, trap assisted tunneling (TAT), and direct tunneling (DT) models. The leakage current transport mechanism is controlled by the trap level energy depth of HfO2. In order to further study the SBH and the electronic tunneling mechanism, the internal photoemission (IPE) yield was measured and analyzed. We obtained the SBH values of the Pt/HfO2/p-type Si for use in Fowler plots in the square and cubic root IPE yield spectra curves. At the Pt/HfO2/p-type Si interface, the SBH difference, which depends on the electrical potential, is related to (1) the work function (WF) difference and between the Pt and p-type Si and (2) the sub-gap defect state features (density and energy) in the given dielectric.