Computational Simulation in MEIS: The VEGAS Algorithm

Medium Energy Ion Scattering (MEIS), when used with the shadowing and blocking phenomena in crystalline materials, is a highly precise technique for determining the atomic structure of surfaces and interfaces. However, extracting exact quantitative geometric parameters - namely, the atomic positions - from experimental spectra requires a robust bridge between the laboratory and theory. This minicourse focuses precisely on the latter part of this transition, i.e. extracting three-dimensional crystallography via advanced computational simulation.

We will begin with a brief review of the MEIS experimental setup, connecting the instrumentation to the nature of the collected data. Next, we will delve into the mathematical problem of multiple scattering and the nuclear encounter probability, directly addressing the "complete-crystal" method solved via Monte Carlo simulations [1], in order to build the so-called blocking curves. Beyond geometric modeling, accurately reproducing the experimental data requires a rigorous treatment of the energy loss spectrum. To this end, we will discuss how the algorithm employs models, such as the Coupled Channels scheme [2], to simulate inelastic energy loss and quantitatively reproduce the MEIS energy spectrum, in particular, the so-called surface peak.

The core of the course will be dedicated to the architecture and operation of the VEGAS program, developed originally at the FOM Institute (today AMOLF) in Amsterdam [1]. We will detail the software's workflow, the configuration of input parameters (including three-dimensional geometry, relaxations, and the treatment of thermal vibrations), and the interpretation of the generated simulations.

Course Program

   An Experimental Overview of MEIS

•  Brief review of the experimental setup.
• The nature of energy spectra and the experimental detection of shadowing and blocking.
• The limitations of purely analytical analysis and the necessary transition to a computational environment.

   Mathematical Foundations of the Scattering Problem:

• Ion-atom scattering potentials and the calculation of trajectories.
• The theory of nuclear encounter probability.
• Monte Carlo modeling in the "complete-crystal" limit.

   The VEGAS Algorithm: Architecture and Practical Implementation

• General structure of the code.
• Inputs: Construction of the crystal lattice in the virtual environment plus setting up experimental parameters.
• Processing and Outputs: Execution of simulations and reading of the generated structural data and angular patterns.

    Spectra Simulation: The Treatment of Inelastic Energy Loss

• The physics of inelastic energy loss and its manifestation in MEIS spectra.
• The use of the Coupled Channels scheme in computational modeling.
• How the algorithm builds and simulates the profile of surface peaks.

   Practical Applications and Case Studies

• Simulation of relaxed surfaces.
• Treatment of reconstructed surfaces.
• Optimization and fitting strategies between the VEGAS simulated output and real experimental data.

References

[1] Ion beam crystallography. J.F. van der Veen. Surface Science Reports, v. 5 (1985) pp 199–288.

[2] Coupled-channel calculation of stopping powers for intermediate-energy light ions penetrating atomic H and He targets. G. Schiwietz.  Physical Review A, v. 42 (1990) pp 296-306.