We report dependence of the extreme ultraviolet quantum efficiency (QE) of a microchannel plate (MCP) detector upon the electric field strength above its input face. Using an uncoated plate, we measured increases up to 80% as the field was raised from 0 V/μ to between 0.01 and 0.1 V/μ. Further increases in electric field resulted in a monotonic decrease in QE. Detector spatial resolution was found to degrade for these small field values but could be recovered, while maintaining most of the QE increase, by operating with fields in excess of 0.3 V/μ. Other detector parameters such as modal gain and output charge pulse-height distribution were not significantly affected by the applied electric field. We explain the QE and resolution variations in terms of photoelectrons ejected from the interchannel web and subsequently returned to the input face of the MCP by the applied electric field. We present a model and a computer simulation which quantitatively reproduce our experimental results. Applying our model to MCPs coated with photocathode materials, we conclude that the maximum QE is obtained by optimizing the combined contributions from the web area and open area of the MCP, rather than by maximizing the open area alone. In this case, most of the QE can arise from the interchannel web rather than from the directly illuminated channels.