Software and databases of stopping powers

2. STOPPING POWER — DATA, MODELS AND METHODS

2.3. Software and databases of stopping powers

The literature on experimental stopping power data, including the range of ions in matter, is vast. The literature starts in the 1910s, but the majority of work dates from the 1980s and later, when IBA techniques became established as standard analytical techniques. Many datasets were only published in graphical form, and some of them were published in papers whose main subject was not stopping power. It is difficult to find the stopping power of a given ion of a given material only by searching the literature.

Ziegler et al. (see Ref. [19] and references therein) has collected many datasets and included them in the SRIM database. The data are not given in numerical form, but plots are shown on the SRIM web site⁵ with references to the original publications.

Paul has also collected a large database of experimental stopping power values, first published in the work of Paul and Schinner [20, 21]. The database has fewer datasets than SRIM, particularly for protons and alpha particles, but all of the data are given numerically and can, therefore, be directly used by other researchers. The data are available from the web site of the IAEA Nuclear Data Section⁶, which started to maintain and develop the original database of Paul in 2015.

5 www.srim.org

2.3.2. Computer programs

Many computer programs calculate stopping powers in the energy range useful for IBA. Several of them are freely available (under specific conditions of usage) [7] and some of them are listed in Table 3. Some are based on first principles; others are semiempirical and rely on the experimental data to produce an interpolative scheme that can calculate the stopping power of any material for any ion, even for ion–target combinations for which no experimental data are available.

The most widely used software is SRIM. Its calculations and models have changed over time and are sometimes updated. Users are, thus, advised to download the latest version from the SRIM web site. SRIM is used by new generation data analysis codes such as SIMNRA [26] and NDF [18]. NDF can also use other software, such as MSTAR [20], or experimental tabulated data [27], including for elements and for compounds, avoiding the need to use the Bragg rule when a given compound is known to be present.

2.3.3. Accuracy of stopping power software

Paul and Schinner have extensively studied, using statistical methods, the reliability of stopping power tables and programs. This included protons and alpha particle beams, heavy ions, and elemental and compound materials (see Ref. [5] and the references therein). Their very careful and extensive published

TABLE 3. SOME AVAILABLE PROGRAMS FOR THE CALCULATION OF STOPPING POWER

Program Web site Main source

SRIM www.srim.org [11, 19]

ASTAR www.nist.gov/pml/data/star/index.cfm [14]

PSTAR www.nist.gov/pml/data/star/index.cfm [14]

MSTAR www-nds.iaea.org/stopping/ [20, 21]

ATIMA www-linux.gsi.de/~weick/atima/ [22]

CASP www.casp-program.org [23]

GEANT4 geant4.web.cern.ch/geant4/ [24, 25]

work also provides the reliability of the stopping power of a given material for a given ion in each energy range.

Their main conclusion has been that, on the whole, SRIM describes the experimental data as well as, or better than, any other software. For the ion–target combinations for which it is available, MSTAR is at least as good as SRIM and can even be better in some cases.

For protons and alpha beams, the average accuracy of SRIM was found to be around 6–7% for solids and 3–4% for gaseous targets. This was in the entire energy range for which measurements are available, including very low energies for which experiments are difficult. Considering only the typical energy range of interest for IBA, the average accuracy of SRIM was found to be better, for instance, 3% for ⁴He in the 1–10 MeV/nucleon range [5]. For heavier ions, the accuracy is somewhat worse. For instance, for ions with a Z₂ between 19 and 92 in solid compounds, the average accuracy was found to be 10.7% [5].

The SRIM web site includes stated accuracy values for the stopping power for hydrogen, helium, lithium and heavier ions. These values are shown in Table 4 for elemental solid targets. This is not the same analysis as conducted by Paul [5], as it is based on a different dataset and the numbers can vary slightly.

Furthermore, the accuracy values presented by Paul are calculated standard deviations, whereas the values presented by Ziegler [11, 19] are the average of individual absolute deviations.

In addition to the average accuracy values, the number of data points that match the SRIM calculation within 5% and within 10% are given. Considering, for example, the stopping power for hydrogen ions, the average accuracy is 4%, but 26% of all data deviate from SRIM by more than 5%, and 13% deviate by more than 10%. As a result, the actual accuracy of SRIM is, in some cases, much worse than the average accuracy stated.

For compounds, the accuracy is worse, also because the Bragg rule is often assumed, and large deviations (commonly 10–20%) near the stopping power maximum are often observed in insulating compounds, particularly in oxides and nitrides of heavy elements.

The SRIM database is very sparse for ions heavier than lithium. In fact, for the 89 ions from berylium to uranium, only about as many measurements exist altogether as do for hydrogen. For many ion–target combinations, no data are available, and the SRIM calculations are then a pure interpolation, informed only by data for other systems. This lack of experimental data is certainly one of the reasons for the poorer accuracy of the calculation of stopping powers for heavy ions.