Origin of interfacial gap states in Ga$_{2}$O$_{3}$ layer grown on GaAs surface and interface passivation by F and Gd

III-V compound semiconductors are potential candidates to replace Si as the channel of future high performance n-MOSFETs. However, the poor III-V/dielectric interface quality leads to low performance of device operations. Prior to any high-k deposition on III-V, a passivated III-V surface could help to obtain a high quality high-k/III-V interface. We examine the native oxides of Ga$_{2}$O$_{3}$ on GaAs with density functional theory to determine the origin of gap states and propose possible ways to passivate the interface. Ga$_{2}$O$_{3}$ molecular species is gradually added in first principles molecular dynamics until one monolayer formed on the top of GaAs at 700 K within 3 ps. During the growth process, O atoms tend to diffuse into GaAs, and Ga-Ga dimer forms as well. The interface states originate from the Ga dangling bonds, Ga-Ga dimers and under-coordinated Ga suboxides Based on the understanding of the origin of the gap states, F and Gd are proposed to remove the gap states.