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Strong scattering by adatoms positioned with the tip of a scanning tunneling microscope (STM) has recently been used to confine surface state electrons to nanoscale structures. We develop a model for confinement by a circular potential on a metal surface, including substrate band structure effects. Scattering into bulk states provides an important broadening mechanism for partially confined states. Contrary to experiment the level width vanishes as the energy approaches the surface state band edge, indicating an additional dominant broadening mechanism for laterally confined surface state levels seen in the STM.

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