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The complex dance of dopant atoms in silicon

Pure silicon is not very useful.  Its usefulness typically comes only by the introduction of impurities, called dopants, that allow engineers to tune this ubiquitous material to the desired degree of semiconductivity.  However, once these dopants are implanted in the material they don't stay where they are placed.  Silicon, like most materials, constantly evolves under the influence of temperature, chemistry and stress.  This evolution happens by a process known as diffusion.  Studying diffusion in silicon is like playing a penny puzzle, the type consisting of a scrambled grid of numbers with one left out so you can slide them around.  One common way for a dopant atom to move in silicon is with the assistance of a vacancy (think of the gap in the puzzle).  It is, however, not enough for the vacancy to exchange places with the impurity.  If it does that the next most likely move is simply to exchange back, accomplishing nothing.  To actually get the impurity to move the vacancy must make a transit around the impurity like a partner in a square dance.  The computational problem is that you end up simulating many exchanges and few transits.  When we refer to many and few in this context, we typically mean a factor in excess of a million to one.  In the Materials Science and Engineering Department at Johns Hopkins we are working on ways to eliminate the million and simulate only the one without resorting to approximation.

    The techniques we are developing to do this (derived from the mathematics of absorbing state Markov chains) automate the work needed to precisely identify, for a given material, which moves are naturally coordinated in the physics of diffusion.  This is critical since it provides a means for the computer to provide insights into the precise atomic dance that dominates in a given material, hence providing a boon to materials theory.