Mechanism of the Formation of Donor States in Heat-Treated Silicon

A mechanism for the donor formation during heat treatment of silicon crystals is presented which accounts quantitatively for the complex kinetic phenomena and which is consistent with the known extra-kinetic information concerning this system. Atomically dissolved oxygen introduced during the growth of the silicon crystal reacts, in the course of heat treatment, to form a sequence of kinetically linked aggregates till finally a polymeric silica (Si${\mathrm{O}}_{2}$) is formed. Only those aggregates which possess fewer than five bound oxygen atoms appear to act intensively as donors at room temperature, and in particular donor states produced around 450\ifmmode^\circ\else\textdegree\fi{}C appear to consist principally of a donor [Si${\mathrm{O}}_{4}$] complex. The kinetic equations are integrated using a general-purpose analog computer for a variety of initial concentrations of oxygen, temperature, etc., and the results compare favorably with existing experimental observations.