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Electron beams are commonly used to inspect wafers for defective contact plugs during the manufacturing of semiconductor integrated circuits. The plugs form a part of the overall electrical connection to the transistors. These plugs can fail to make adequate electrical contact to the underlying circuitry. They may also be connected to faulty circuits. As a result, the voltage from such defective plugs evolves differently upon irradiation by an electron beam. The paths of the secondary electrons emitted from a defective plug respond to this voltage, thereby modifying the fraction of the emitted current that reaches a detector as compared to the fraction obtained from a healthy contact plug. This paper analyzes the fundamental kinetics that ultimately produces this contrast in a scanning electron microscope designed for wafer inspection. In particular, the paper investigates the kinetics of secondary electron emission from an isolated, biased plug embedded in a charge-neutral dielectric. It presents analytic models for the dependence of the electron collection efficiency with the plug voltage and an applied vertical field at the wafer. The analytic results are compared with those from numerical simulations to test the assumptions that enter the models. The mathematical derivations may ultimately be used to estimate the signal that can be extracted from plugs at dissimilar potentials.