Hybrid superconductor-semiconductor heterostructures are a promising platform for quantum devices based on mesoscopic and topological superconductivity. In these structures, a semiconductor must be in close proximity to a superconductor and form an ohmic contact. This can be accommodated in narrow band gap semiconductors such as InAs, where the surface Fermi level is positioned close to the conduction band. In this work, we study the structural properties of near-surface InAs quantum wells and find that surface morphology is closely connected to low-temperature transport, where electron mobility is highly sensitive to the growth temperature of the underlying graded buffer layer. By introducing an In0.81Al0.19As capping layer, we show that we can modify the surface Fermi level pinning within the first nanometer of the In0.81Al0.19As thin film. Experimental measurements show a strong agreement with Schrödinger-Poisson calculations of the electron density, suggesting the conduction band energy of the In0.81Ga0.19As and In0.81Al0.19As surface is pinned to 40 meV and 309 meV above the Fermi level respectively.