Semiconductor workpiece topography prediction method

A method of predicting the topography of a semiconductor workpiece after a plurality of manufacturing processes, each process changing the topography of the workpiece, are carried out on the workpiece comprising:

• establishing a desired topography for a semiconductor workpiece after sequential performance of a plurality of processes changing the topography of the workpiece are carried out on the workpiece;
• specifying, for each process, conditions for performing the respective process;
• establishing a plurality of points in a grid in a space including the workpiece;
• identifying the materials comprising the workpiece and the concentration of virtual particles representing the topography of the workpiece at each of the points before a first process on the workpiece;
• using the modified diffusion model equation to predict the material and concentration of virtual particles at each of the points after the completion of the first process in the sequence of processes;
• recording the material and virtual particle concentration for at least some of the points at the completion of the first process as a decimal number including an integer part representing the material and a decimal part representing the concentration of virtual particles;
• using the modified diffusion model to predict the materials and concentrations of virtual particles at each point after a second process beginning with the materials and virtual particle concentrations for each point from the prediction of the first process;
• repeating the topography prediction for each of the plurality of processes to predict a final topography, each prediction employing as the initial materials and virtual particle concentrations the materials and virtual particle concentrations predicted at the completion of the immediately preceding process;
• graphically displaying the final topography and comparing the final topography to the desired topography;
• and
• altering the conditions of at least one of the processes and repeating the topography prediction and graphical display steps until the desired topography is obtained for the sequence of processes.