InGaAs gate stacks comprising the moderate dielectric constant (k) Al2O3 have a significantly lower dispersion in accumulation in comparison to stacks with the high-k HfO2 of the same physical thickness. As a result, a HfO2/Al2O3 bi-layer structure seems attractive in terms of both high effective dielectric constant and low dispersion in accumulation. The influence of Al2O3 thickness on the dispersion was investigated in metal/HfO2/Al2O3/InGaAs gate stacks with a fixed overall dielectric thickness. An effective suppression of the dispersion with the increase of the Al2O3 thickness was observed. However, the Al2O3 thickness required for passivation of the dispersion in accumulation was significantly higher in comparison to both the border traps related tunneling distance in Al2O3 and the minimal thickness required for the Al2O3/InGaAs band offset stabilization. The phenomenon can be explained by the lower dielectric constant of Al2O3 film (compared to the subsequently deposited HfO2 layer), where Al2O3 dielectric constant dependence on the film thickness enhances the dispersion intensity. As a result, the guidelines for the passivation layer engineering are: maximization of both majority carriers band offsets and of the dielectric constant of the passivation layer.