In this paper, we have built a numerical p-n Si/GaAs heterojunction model using a quantum-mechanical tunneling theory with various quantum tunneling interfacial materials including two-dimensional semiconductors such as hexagonal boron nitride (h-BN) and graphene and ALD-enabled oxide materials such as HfO2, Al2O3, and SiO2. Their tunneling efficiencies and tunneling current with different thicknesses were systematically calculated and compared. Multiphysics modeling was used with the aforementioned tunneling interfacial materials to analyze changes in strain under different temperature conditions. Considering the transport properties and thermal-induced strain analysis, Al2O3 among three oxide materials and graphene in 2D materials are favorable material choices that offer the highest heterojunction quality. Overall, our results offer the viable route to guide the selection of quantum tunneling materials for myriad possible combinations of new heterostructures that can be obtained via remote epitaxy and the UO method.