We report a method of phase-sensitive detection of desorption from surfaces bombarded by a properly modulated electron beam. Mass-spectrometer signals detected by this method assure a high sensitivity and selectivity of the results. This method is used here for studying surfaces of ZnO powders, and it found that CO2 is the only desorbed species during electron bombardment of such surfaces. Following the CO2 desorption kinetics simultaneously with the associated surface conductivity change, we find one-to-one correspondence between both quantitites. Furthermore, the rates of the electron-induced CO2 desportion and the surface conductivity are in a very good agreement with a theoretical model, previously developed for photodesorption. This model predicts a slowing of the desorption rate due to the buildup of an electron accumulation layer and a corresponding band bending which hinder irradiation-generated holes from reaching the surface and neutralizing CO-2 species chemisorbed on it. Our observations seem to support this model together with pointing out the similarities between electron- and photon-induced desorption in this case.