Misconceptions impairing the validity of the stopping power tables in the SRIM library and suggestions for doing better in the future

Abstract

The popular SRIM library delivers data and simulation codes for describing the slowing down of energetic atoms in matter. This study explored the validity of the tables containing cross sections for electronic and nuclear stopping together with the respective range parameters. The electronic stopping cross sections Se were produced, much like in previous and subsequent attempts of other groups, by bringing together the limited number of available experimental results in the form of ratios, r(Z1,He,υ)=Se(Z1,Z2,υ)/Se(He,Z2,υ). Z1 and Z2 denote the atomic numbers of projectiles (velocity υ) and target atoms, respectively. Reference data for He impact are available in reasonable volume only for about 15% of all solid targets; missing information has to be derived by interpolation. The concept of data evaluation is based on the assumption that the Bethe–Bloch (BB) theory, developed for bare projectiles, can serve as a guide at all velocities. For the purpose in question, the theory features an indispensible property: Z1 and Z2 appear as straight pre-factors, not in coupled form, Se,BB(υ)∝Z12Z2L(Z2,υ), with L(Z2,υ) representing the stopping number. Therefore, Z2 and L(Z2,υ) cancel out when taking ratios for fixed Z1 so that data for arbitrary Z2 may be combined in one set of r-values to determine the best fit rfit(Z1,He,υ). The stopping cross sections of interest are then derived as Se(Z1,Z2,υ)=rfit(Z1,He,υ)Se(He,Z2,υ). At low energies these results were often refined, Se⇒Se,f, to account for experimental data that did not comply with the anticipated Z2-independent trend.Major findings and suggestions are as follows: (i) At high velocities, υ>4Z12/3υ0 (Bohr velocity υ0), the SRIM predictions (have to) rely primarily on BB theory. (ii) At intermediate velocities, i.e., around the Bragg peak, SRIM appears to produce reasonable results (ca. ±15%). (iii) Below the Bragg peak the tabulated data often deviate strongly and inconsistently from the predictions of Lindhard–Scharff (LS) theory; they also exhibit various forms of exotic velocity dependence. These deviations are primarily due to the fact that the range of validity of BB theory is artificially extended to velocities at which the ‘effective-charge’ concept is assumed to be applicable. Coupled Z1,2 scaling as in theories of LS or Firsov would be much more appropriate. Overall, the electronic stopping cross sections by SRIM are of unpredictable value and often strongly misleading below 1MeV/u. (iv) Another consequence of the tight link to the Z1,2 dependence of BB theory is that only 2×92 master sets of electronic stopping cross sections were required to generate all conceivable 89×92 tables from Se,f-ratios for elemental targets (the tables for H, He and Li projectiles are derived separately). The information contained in the SRIM library at large thus exhibits a highly redundant character. (v) The nuclear stopping cross sections Sn mirror the predictions of the universal potential due by Ziegler, Biersack and Littmark, which differ from alternative suggestions typically by less than 15%. With this uncertainty, range distributions may be calculated with the TRIM program of SRIM, but only at energies where Sn dominates so that uncertainties in Se play a minor role. (vi) As a side aspect, an example is presented illustrating the efforts required to identify incorrect experimental data, notably when respected authors are accountable. (vii) Other approaches to establish stopping power tables are shown to be subject to the same problems as SRIM. It is recommended to add a warning to all theses tables, informing users at which energies the data are likely to lack reliability. (viii) The currently unacceptable quality of Se,f-data below 1MeV/u could be improved significantly in the future if the user friendly TRIM(SRIM) code were modified to allow simulations with a free choice of nuclear and electronic stopping cross sections. Researchers would thus be enabled to identify optimum input parameters for reproducing measured range distributions at energies at which Sn and Se are often of similar magnitude so that their contribution to the total energy loss is difficult to quantify without simulations.