# Algorithms for Three-Dimensional Simulation of Etching and Deposition Processes in Integrated Circuit Fabrication

### Edward W. Scheckler

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M91/99

1991

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/ERL-91-99.pdf

Algorithms for general surface advancement, three-dimensional visibility, and convolution over a surface have been developed and coupled with physical models for pattern transfer yielding efficient 3D topography simulation capability. The program, SAMPLE-3D, is compatible with engineering workstations and allows practical simulation of etch lag, deposition and etching with density variation, silylation, ion milling with a rotating source, and other 3D problems. The simulations require from 1 to 32 megabytes of memory and from 1 minute to a few hours of CPU time. A survey of other research provides direction for this and future work, as well as a comprehensive listing of the important literature.

An efficient cell-removal algorithm, requiring less than 10 megabytes and a few minutes for 100x100x100 cells, was implemented and found to be applicable to development. The cell algorithm is not suited to general simulation due to the difficulty in determining the surface orientation. A general surface advancement algorithm based on the motion of triangular facets was developed and tested for accuracy and efficiency. The method for calculating a new surface from the advance facets uses the average intersection of facets, the solid angle swept out at the point, and the etch rate extrema directions. The algorithm maintains accuracy if no point advances further than 20% of the minimum mesh segment length.

The advancement is coupled with an array of rectangular prismatic cells to implement efficient algorithms for shadow detection, solid angle visibility, and loop identification. After sweeping out the cells based on the surface motion, the volume representation allows rapid determination of material properties at any point in the simulation region. Visibility determination then requires CPU time proportional to the surface area. Reflection and surface convolution require time proportional to the square of the surface area. Algorithm and data structure analysis gives rules for estimating CPU and memory requirements for specific simulations.

SAMPLE-3D is organized as a platform for continued model and algorithm development. Through the use of function calls, the modular structure allows the combination of process models and geometric operations to yield new simulation capability. A graphical user interface provides access to the simulator.

**Advisor:** Andrew R. Neureuther

BibTeX citation:

@phdthesis{Scheckler:M91/99, Author = {Scheckler, Edward W.}, Title = {Algorithms for Three-Dimensional Simulation of Etching and Deposition Processes in Integrated Circuit Fabrication}, School = {EECS Department, University of California, Berkeley}, Year = {1991}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/1875.html}, Number = {UCB/ERL M91/99}, Abstract = {Algorithms for general surface advancement, three-dimensional visibility, and convolution over a surface have been developed and coupled with physical models for pattern transfer yielding efficient 3D topography simulation capability. The program, SAMPLE-3D, is compatible with engineering workstations and allows practical simulation of etch lag, deposition and etching with density variation, silylation, ion milling with a rotating source, and other 3D problems. The simulations require from 1 to 32 megabytes of memory and from 1 minute to a few hours of CPU time. A survey of other research provides direction for this and future work, as well as a comprehensive listing of the important literature. An efficient cell-removal algorithm, requiring less than 10 megabytes and a few minutes for 100x100x100 cells, was implemented and found to be applicable to development. The cell algorithm is not suited to general simulation due to the difficulty in determining the surface orientation. A general surface advancement algorithm based on the motion of triangular facets was developed and tested for accuracy and efficiency. The method for calculating a new surface from the advance facets uses the average intersection of facets, the solid angle swept out at the point, and the etch rate extrema directions. The algorithm maintains accuracy if no point advances further than 20% of the minimum mesh segment length. The advancement is coupled with an array of rectangular prismatic cells to implement efficient algorithms for shadow detection, solid angle visibility, and loop identification. After sweeping out the cells based on the surface motion, the volume representation allows rapid determination of material properties at any point in the simulation region. Visibility determination then requires CPU time proportional to the surface area. Reflection and surface convolution require time proportional to the square of the surface area. Algorithm and data structure analysis gives rules for estimating CPU and memory requirements for specific simulations. SAMPLE-3D is organized as a platform for continued model and algorithm development. Through the use of function calls, the modular structure allows the combination of process models and geometric operations to yield new simulation capability. A graphical user interface provides access to the simulator.} }

EndNote citation:

%0 Thesis %A Scheckler, Edward W. %T Algorithms for Three-Dimensional Simulation of Etching and Deposition Processes in Integrated Circuit Fabrication %I EECS Department, University of California, Berkeley %D 1991 %@ UCB/ERL M91/99 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/1875.html %F Scheckler:M91/99