In this paper, for the ITO-SiOx (In, Sn)/n-Si photovoltaic device, the molecular coacervate of In–O–Si bonding and two kinds of quantum states for indium-grafted in amorphous silicon oxide a-SiOx (In, Sn) layers are predicted by molecular dynamics simulation and density function theory calculation, respectively. The results show that the SiOx layers are the result of the inter-diffusion of the In, Sn, O, Si element. Moreover, In–O–Si and Sn–O–Si bonding hybird structures existing in the SiOx layers are found. From the result of formation energy calculations, we show that the formation energies of such an In–O–Si configuration are 5.38 eV for Si-rich condition and 4.27 eV for In-rich condition respectively, which are both lower than the energy (10 eV) provided in our experiment environment. It means that In–O–Si configuration is energetically favorable. By the energy band calculations, In and Sn doping induced gap states (Ev+4.60 eV for In, Ev+4.0 eV for Sn) within a-SiO2 band gap are found, which are different from the results of doping of B, Al, Ga or other group-Ⅲ and V elements. The most interesting phenomena are that there is either a transition level at Ev+0.3 eV for p-type conductive conversion or an extra level at Ev+4.60 eV induced by In doping within the dielectric amorphous oxide (a-SiOx) model. These gap states (GSⅡ and GSIS) could lower the tunneling barrier height and increase the probability of tunneling, facilitate the transport of photo-generated holes, strengthen the short circuit current, and/or create negatively charged defects to repel electrons, thereby suppressing carrier recombination at the p-type inversion layer and promoting the establishment of the effective built-in-potential, increasing the open-circuit voltage and fill factor. Therefore, the multi-functions such as good passivation, built-in field, inversion layer and carriers tunneling are integrated into the a-SiOx (In, Sn) materials, which may be a good candidate for the selective contact of silicon-based high efficient heterojunction solar cells in the future. This work can help us to promote the explanations of the electronic structure and hole tunneling transport in ITO-SiOx/n-Si photovoltaic device and predict that In–O–Si compound could be as an excellent passivation tunneling selective material.