Dispersion in accumulation is a widely observed phenomenon in technologically important InGaAs gate stacks. Two principal different interface defects were proposed as the physical origin of this phenomenon - disorder induced gap states and border traps. While the gap states are located at the semiconductor side of the interface, the border traps are related to the dielectric side. The study of Al2O3, HfO2, and an intermediate composition of HfxAlyO deposited on InGaAs enabled us to find a correlation between the dispersion and the dielectric/InGaAs band offset. At the same time, no change in the dispersion was observed after applying an effective pre-deposition treatment which results in significant reduction of the interface states. Both observations prove that border traps are the physical origin of the dispersion in accumulation in InGaAs based metal-oxide-semiconductor gate stacks.