Physical bombardment plays a dominant role in the O2 reactive ion etching (RIE) pattern transfer step in multilevel lithography. Statistical mechanical models of sheath collision processes relate the flux, energy, and angular distribution of particles bombarding the surface to the pressure, sheath thickness, and voltage drop across the sheath. The estimated flux of bombarding particles allows measured etching rates to be converted into yields. We find that the trends for the etching rate as a function of pressure, bias voltage, frequency and other system variables reflect a single trend for the yield as a function of the average bombardment energy. Organic polymer etching yields are proportional to bombardment energy while there is a threshold energy in organosilicon polymer etching; consequently the selectivity in bilevel lithography increases as the bombardment energy decreases. Etching profiles and process latitudes are determined by the yield weighted angular distribution, and by the etching rate relative to the mask erosion rate. The angular distributions are determined by the dimensionless sheath thickness in units of the mean free path for momentum transfer collisions. Mask erosion is not significant in trilevel lithography where the etching mask is Si02, however, depending on the selectivity and the wall angle, mask erosion may significantly affect profiles and latitudes in bilevel lithography. The etching rate at each point on the polymer interface is proportional to an energy flux vector that is calculated by performing a double integral of the energy weighted angular distribution function over the field of view accessible to that point on the interface. The resulting interface evolution equation is mathematically equivalent to a free surface evolution equation for a two phase hydro-dynamic system, where the energy flux vector plays the role of the fluid velocity vector in the hydrodynamic system. This convective partial differential equation is reduced to a coupled set of ordinary differential equations via the method of characteristics (or rays) and solved numerically. The predicted etching profiles are in good agreement with observed profiles over a wide range of etching conditions. Simulated process latitude trends in multilevel lithography are presented.