Etching profiles and neutral shadowing in long trenches

The neutral flux in the plasma etching of semiconductor wafers or organosilicon planarizing layers has been derived analytically for a simple model for a long rectangular trench. The neutral molecules obey a Maxwellian distribution function and mutual collisions are neglected in the trench. Scattering of the neutrals with the sidewalls and trench bottom is ignored. The two-dimensional flux vector which is given at each point on the etching profile surface is a function of the local aspect ratio, the lateral ratio, the density (concentration) of the neutral molecules and their thermal speed. The flux vector reduces to the expression previously determined at the center of the trench. Etching profiles of the trench are displayed for a photoresist that is etched and one that is not by applying the method of characteristics to the evolution equation of the trench etch profile.