INFLUENCE OF SIMULATION PARAMETERS ON THE SPEED AND ACCURACY OF MONTE CARLO CALCULATIONS USING PENEPMA

摘要

PENEPMA [1, 2] is a dedicated programme for the simulation of electron probe microanalysis (EPMA) measurements which uses the general-purpose Monte Carlo simulation subroutine package PENELOPE [3]. The operation of PENEPMA is completely controlled from an input data file, which is edited by the user to set up the characteristics of their experiment (e.g., the electron beam parameters, the sample material and geometry, photon detectors, X-ray lines, etc.). The user can also set a number of simulation parameters which define the particle tracking algorithm and the different variance reduction techniques implemented in PENELOPE. These parameters determine the speed and accuracy of the simulation; tuning these parameters adequately can greatly improve the efficiency of the simulation. In this communication we analyse and discuss the effect of using different simulation parameters on the simulation speed for typical cases of interest in EPMA. These include the simulation of the characteristic X-ray intensity emitted from bulk and thin film samples, and the simulation of secondary fluorescence across the vertical boundary of a material couple. The simulation parameters that can be optimised in PENELOPE can be divided into cut-off energies (the electron absorption energy E_(abs,el) and the photon absorption energy E_(abs,ph)), physics parameters of the simulation algorithm (the average angular deflection C_1 and the maximum average fractional energy loss C_2 in single steps, the cut-off energy loss for hard inelastic collisions W_(cc) and the cut-off energy loss for hard bremsstrahlung emission W_(cr)) and variance-reduction parameters (the forcing factors for characteristic X-rays and bremsstrahlung photons f_(ch) and f_b and the splitting factors for characteristic X-rays and bremsstrahlung photons S_(ch) and S_b). Note that for samples consisting of different materials, all these parameters can be specified for each material. Also, the interaction forcing factors can be optimised independently for each interaction mechanism. Table 1 shows the CPU time T required to achieve a precision of 1% (at 3 σ level) in the intensity I of the Fe K-L2 X-ray line emitted from a bulk Fe sample bombarded with an electron beam of 20 kV, for different combinations (gradually varying) of the simulation parameters 2_(abs,el), E_(abs,ph), C_1, C_2, W_(cc), W_(cr), as well as forcing factors f_(ch) and f_b and splitting factors S_(ch) and sb. The tests were performed on an Intel Core i7 2.93 GHz processor with a RAM size of 8 GB. Table 1 also lists the efficiency ε of a simulation run, defined as ε=(I/3σ)~2 (1/7). We can see that a precision of 1 % can be achieved in about one minute (case 8) by setting C_1 and C_2 to their maximum allowed values, adjusting the absorption energies E_(abs,el) and E_(abs,ph) to values slightly lower than the ionisation energy of the Fe K-shell, and setting W_(cc), and W_(cr) to about 1 keV, and by using moderately large forcing factors and splitting factors. The selection of these simulation parameters, which does not alter practically the accuracy of results, represents an increase in simulation speed of ~11,000 times relatively to a detailed simulation with non-optimised cutoffs of 50 eV (case 1).