We report on investigations into the fundamental surface emission parameters, the geometric field enhancement factor ($ensuremath{eta}$) and the work function ($ensuremath{phi}$), by making both field emission and Schottky-enabled photoemission measurements. The measurements were performed on a copper surface in the Tsinghua University $S$-band RF gun in two separate experiments. Fitting our data to the models for each experiment indicate that the traditionally assumed high value of $ensuremath{eta}(ensuremath{pprox}50--500)$ does not provide a plausible explanation of the data, but incorporating a low value of $ensuremath{phi}$ at some sites does. In addition, direct measurements of the surface conducted after the experiment show that $ensuremath{eta}$ is on the order of a few, consistent with our understanding of the electron emission measurements. Thus we conclude that the dominant source of electron emission in high gradient RF cavities is due to low $ensuremath{phi}$ sites, as opposed to the conventionally assumed high $ensuremath{eta}$ sites. The origin of low $ensuremath{phi}$ at these sites is unclear and should be the subject of further investigation.
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