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Hybrid superconductor-semiconductor heterostructures are a promising platformfor quantum devices based on mesoscopic and topological superconductivity. Inthese structures, a semiconductor must be in close proximity to asuperconductor and form an ohmic contact. This can be accommodated in narrowband gap semiconductors such as InAs, where the surface Fermi level ispositioned close to the conduction band. In this work, we study the structuralproperties of near-surface InAs quantum wells and find that surface morphologyis closely connected to low-temperature transport, where electron mobility ishighly sensitive to the growth temperature of the underlying graded bufferlayer. By introducing an In$_{0.81}$Al$_{0.19}$As capping layer, we show thatwe can modify the surface Fermi level pinning within the first nanometer of theIn$_{0.81}$Al$_{0.19}$As thin film. Experimental measurements show a strongagreement with Schr\"odinger-Poisson calculations of the electron density,suggesting the conduction band energy of the In$_{0.81}$Ga$_{0.19}$As andIn$_{0.81}$Al$_{0.19}$As surface is pinned to \SI{40}{\milli eV} and\SI{309}{\milli eV} above the Fermi level respectively.

Controlling Fermi level pinning in near-surface InAs quantum wells