Optimal Summation of Gaussians for Ion Implantation Profile Control.
Abstract
The fact that the number of implanted ions can be accurately determined and controlled is used in the processing of numerous semiconductor devices. By contrast, there is very little fabrication of solid state devices which effectively uses the spatial impurity distribution of implanted ions. To a large degree, this is because the distribution of a particular implant is Gaussian, which is not a particularly useful profile. However, by using multiple implants the individual Gaussians may be effectively summed to approximate a wide range of desired impurity distributions. The summation of Gaussian distributions to achieve arbitrary functions is a mathematical problem of general interest, and the usefulness of solving the problem extends far beyond the desire to approximate impurity distributions in semiconductors. Unfortunately, the solution here is complicated by the physics of the situation which limits the available Gaussian expansion functions. Under this condition it will be shown that the analytical solution of the problem is not feasible. A numerical solution is presented for a number of profiles, indicating that many desirable impurity distributions may be satisfactorily approximated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1975
- Accession Number
- ADA019422
Entities
People
- Andrew Joseph Zaremba
Organizations
- University of Illinois Urbana–Champaign