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The interface between nano-scale films is of relevance in many critical applications. Specifically, recent technological advances in semiconductor industry that utilize Silicon-on-Insulator (SOI) devices have given urgency to understanding thermal transport across Si-SiO2 interface. Estimates of interfacial (Kapitza) resistance to thermal transport across Si-SiO2 films do not appear to exist at the present time. In this paper, we develop and carryout reverse non-equilibrium molecular dynamics (NEMD) simulations by imposing known heat flux to determine the Kapitza resistance between Si-SiO2 thin films. For the Si-SiO2 interface, the average Kapitza resistance for a ~8 Aring thick oxide layer system was 0.503 times 10-9 m K/W and for a ~11.5 Aring thick oxide layer system was 0.518 times 10-9 m K/W. These values were of the same order of magnitude as the Kapitza resistance values determined from the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) for the Si-SiO2 interface.