Results are presented of an investigation into electron-beam-induced conduction (EBIC) in films of SiO₂ thermally grown on a silicon substrate. A strong dependence on the polarity of the voltage applied during irradiation is observed. For negative applied voltages which correspond to an electron flow to the silicon substrate, the EBIC grain curves follow the predictions of a recent theory. For positive voltages an electron emission analogous to internal photoemission occurs from the silicon substrate as soon as the beam begins to penetrate into the silicon. In some samples this emission current was sufficiently low that an EBIC gain curve due to hole flow to the substrate was observed. However, only by taking into account the dispersive nature of hole transport could agreement between experiment and theory be obtained. Effects due to previous irradiation are observed and interpreted as the generation of traps and/or a space charge build-up during the initial irradiation.