UNIVERSAL EXPRESSIONS FOR RANGE PARAMETERS OF IONS IN SOLIDS

The detailed parametric analysis of the Boltzmann equation of ion tran sport shows that there is an approximately one-to-one correspondence b etween ion transport quantities and a characteristic parameter named t he scaled transport cross section and defined earlier [Z. Luo, Nucl. I nstrum. Methods B 48, 444 (1990)]. To attest to a significant conclusi on, we have completed systematic calculations over numerous-ranges for ions implanted in solids. The systematic calculations include 3410 io n-target-energy combinations. The calculations show that range paramet ers present a good single-value dependence on the scaled transport cro ss section at low incident energies. Based on this result, universal e xpressions for range parameters have been obtained. To test the validi ty of the expressions, the range distributions of ions in solids have been calculated by universal expressions. The comparisons between the results of the universal expressions and experimental or Monte Carlo d ata show that the universal expressions given in the present article c an give good predictions to range distributions of low energy ions imp lanted in solids.