Controllable taper windows in thermally grown silicon dioxide layers are produced by depositing a thin layer of silicafilm on the thermal oxide layer before chemical etching. As the densification temperature of silicafilm is varied from 175°C to 1150°C, taper angles from 3° to 40° are obtained. Fermat' s principle of least time is employed to derive the expression for the etched profiles of the oxide layer.