In a metal, due to the attraction of all the ions evenly distributed throughout the crystal, a conduction band electron is not subjected to any force on average, so the metal volume is equipotential and the electron free.
As an electron approaches the surface, the attractive forces are no longer perfectly balanced, and their resultant force tends to hold the electron inside the metal. Close to the surface, therefore, there's an electric field directed outwards, the effect of which is to keep the electrons inside. To cross this potential barrier, an electron must lose kinetic energy equal to the gain in potential energy:
Φ
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