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A number of possible near and long term semiconductor device technologies rely on abrupt metal-semiconductor interfaces with nm-dimensions, and with internal nm-scale inhomogeneity. It is therefore very important to be able probe the electronic properties of these buried interfaces with sub-10 nm resolution and to find out the impact of small-size effects on their transport properties. In our study we used Ballistic Electron Emission Microscopy (BEEM) and finite-element electrostatic modeling to quantify how small-size effects modify the energy barrier at metal/semiconductor quantum wells (QWs), formed by making Schottky contacts to cleaved edges of GaAs quantum wells. Our model semiconductor heterostructure is formed as a sequence of AlGaAs/GaAs/AlGaAs layers and contains a sequence of GaAs QWs with thickness between 1 and 15 nm. The Schottky barrier height (SBH) measurements as a function of QW thickness showed that the SBH value increases as the QW thickness is decreased, by up to 140 meV for a 1 nm thick QW. This is mostly due to a large quantum-confinement increase (200 meV for a 1nm QW), modified by smaller decreases due to environmental electric field effects. Our modeling gave excellent quantitative agreement with measurements for a wide range of QW thickness when both these effects are considered. In a separate study, the cleaved QW were used as nm-apertures to estimate the resolution of BEEM as a function of metal film thickness. We found that BEEM resolution degrades as the top metal film layer is made thicker, from 12 nm for a 4 nm thick Au layer, up to 22 nm for a 15 nm thick Au layer. Also presented is modeling of the electrostatic potential profile around charged threading dislocations (TD) in GaN, close to a metal-semiconductor interface, and its dependence on the energy of acceptor sites along the dislocation. We found that for energy values higher than 1.13 eV the near interface TD acceptors are completely filled right up to the interface. This results in a very large negative space charge and an increase in the local barrier height close to the TD core that should be observable by techniques such as BEEM.