Surface Evolution During Semiconductor Processing

We discuss our approach to using the Riemann problem to compute surface profile evolutionduring the simulation of deposition, etch and reflow processes. Each pair of segments whichrepresents the surface is processed sequentially. For cases in which both segments are thesame material, the Riemann problem is solved. For cases in which the two segments are differentmaterials, two Riemann problems are solved. The material boundary is treated as theright segment for the left material and as the left segment for the right material. The criticalequations for the analyses are the characteristics of the Riemann problem and the ‘jump conditions’which represent continuity of the surface. Examples are presented to demonstrateselected situations. One limitation of the approach is that the velocity of the surface is notknown as a function of the surface angle. Rather, it is known for the angles of the left andright segments. The rate as a function of angle must be assumed for the explicit integrationprocedure used. Numerical implementation is briefly discussed