We have used scanning tunneling microscopy to examine N-terminated Cu(111) surfaces. For substaturation N coverages, elongated rectangular islands are formed, the internal structures of which are in good agreement with a model proposed in a previous LEED study. These islands sufficiently perturb the surface so as to reflect surface state electrons in the adjacent clean surface regions. This results in the observation of electron standing wave patterns. We have simultaneously observed both the electron wave patterns and atomic resolution. We have also shown that under conditions of high electric fields, the N atoms at the surface can be forced down into the second layer with Cu atoms liberated from the first layer to form single layer high islands.