The space dependence of charge carriers trapped in &agr;‐quartz under electron‐beam bombardment is investigated using a Monte Carlo algorithm. The average energy of the electron after being detrapped from a trap site is first calculated by considering both the polar and nonpolar phonon scatterings. Later, the detrapping and trapping rates are also included in the model to obtain a stable trapped charge distribution, which is found to be dependent on the size as well as the temperature of the sample. Comparisons with experimental results of the size effect on the dielectric strength obtained from a scanning electron microscope are also made.