Simulation of retarded diffusion of antimony and enhanced diffusion of phosphorus in silicon

The paper is concerned with the influence of point defects on dopant diffusion in silicon. This influence is analysed by means of comparing the experimental results of Mizuo and Higuchi with our simulation. The experiments deal with the oxidation retarded diffusion (ORD) of Sb and the oxidation enhanced diffusion (OED) ofP in FZ silicon at 1100°C. The simulation is carried out by using a physical model without simplifying assumptions. It is shown that simplifying assumptions are not admissible. A reasonable set of parameters is deduced from this analysis. As each parameter represents a physical effect, information about the importance of bulk and surface recombination of point defects and about the equilibrium concentration values and diffusion coefficients of diffusing species are obtained. It turns out that the influence of the surface is decisive for the distribution of point defects.Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Developing Prospective Elementary Teachers' Flexibility in the Domain of Proportional Reasoning

Flexibility in the use of mathematics procedures consists of the ability to employ multiple solution methods across a set of problems, solve the same problem using multiple methods, and choose strategically from among methods so as to reduce computational demands. The purpose of this study was to characterize prospective elementary teachers' (n = 148) flexibility in the domain of proportional reasoning before formal instruction and to test the effects of two versions of an intervention that engaged prospective teachers in comparing different solutions to proportion problems. Results indicate that (a) participants exhibited limited flexibility before formal instruction, (b) the intervention led to significant gains in participants' flexibility that were retained six months after instruction, and (c) varying the source of the problem solutions that participants compared had no discernible effects on their flexibility. Implications for mathematics teacher preparation and for research on flexibility development are provided.