Modern applicaiton of sub-micrometer-period gratings often requires the grating profile to be rectangular with steep sidewalls. By comparing cross sections of gratings made by reactive ion-beam etching in two etchers equipped with different types of ion-beam sources, we find that the divergence of ion-beam strongly influences the sidewall steepness of sub-micrometer-period gratings fabricated by using reactive ion-beam etching. All conditions being equal, a smaller divergence angle renderes higher sidewall steepness. The divergence angle of the two-grid Kaufman ion-beam source that is widely used in China at present is typically larger than 13°, limiting the attainable sidewall angle of gratings in etched fused silica to be only 77°, unless a special measure is taken. Using such an ion-beam source, we experimented with three etching methods (rotation-tilt method, alternate-tilt method and metallic-mask recoating method), and increased the sidewall angle of sub-micrometer-period fused silica gratings to 86°, 86° and 82°, respectively. Two mechanisms by which the ion-beam divergence affects the sidewall steepness are considered: the shrinkage rate of the mask's sidewalls and the difference between the ion fluxes at the bottom and the top of the grooves. The roles of these two mechanisms in the three etching methods are also explained.