Research at The College of Charleston

Molecular Dynamics Simulations and Secondary Ion Mass Spectrometry

Molecular Dynamics Simulation Background

As modern computing power increases, the utility of molecular dynamics (MD) simulations increases as well. Those unacquainted with computer simulations often question the validity of there use as an experimental probe, but anyone that has employed them can testify that simulations are an indispensable tool in studying complex systems, often beyond our present mathematical abilities. You can think of molecular dynamics simulations like a highly controlled experiment. The power in MD simulations is in the ability to place each molecule where we like, giving them energies and trajectories that suit our needs. This degree of control does not exist in experimental science. The omnipotence offered in an MD simulation is the key to using it to generalize certain effects that arise when the controlled conditions are modified.

Usually in an MD simulation, chemical reactions are represented solely by the motion of their nuclei with no recourse to quantum mechanics for descriptions of electronic transitions. The validity of classical mechanics is best illustrated by the DeBroglie wavelength of the particle in question For example a 1eV hydrogen atom has a DeBroglie wavelength of ~0.3 Angstroms, and an electron of the same energy has a DeBroglie wavelength of ~12 Angstroms. In general, quantum behavior becomes important when the interaction distances considered are smaller than the DeBroglie wavelength. A moderately small atom like silicon (also with 1eV kinetic Energy) has a DeBroglie wavelength of 0.05 Angstroms. Silicon interacting among a solid substrate with interatomic spacing averaging around 1-3 Angstroms requires no recourse to quantum mechanics and can thus be treated classically as a point particle.

There are two major steps in performing MD simulations for solids. There is the matter of the numerical solutions of the classical equations of motion. These solutions provide final trajectories of ejected particles from the substrate, often in terms of angular distribution, due to impinging particles prescribed in the initial conditions as well as the re-distribution of particles in the solid substrate. There is also the matter of the interaction potential used to describe the forces among atoms. Interaction potentials are usually two-body interactions based on experimental observations. The first step involves stepping forward in time Newton's second law (F=ma). The second step adjusts the force due to the empirical interaction potentials. The interaction potential is related to the force through the usual gradient relation (F=-Grad U).

Once the initial conditions are prescribed, then the positions and velocities are determined by integrating these two differential equations. To do this numerically it must be assumed that the forces are constant over a time step ∆t. Time steps are usually on the order of a femtosecond and are determined by the interaction potential employed. The current speed of computers implements a limitation on the number of time steps that can be iterated through. Simulations of several thousand atoms can presently be simulated up to around a hundred nanoseconds or so.

Secondary Ion Mass Spectrometry Background

Mass spectrometry is used to investigate the properties of ions including identification. A beam of ions flows between the poles of a powerful magnet that acts to deflect the ions along a circular path. The degree to which the path of a particular ion is deflected is determined by its charge-to-mass ratio. Consequently, the amount of deflection is inversely proportional to an ion's mass and directly proportional to an ion's charge. By adjusting the strength of the magnetic field, ions with the desired charge-to-mass ratio can be focused on a detector. If the ion beam consists of a mixture of ions of different mass, but with the same charge, it is divided into a number of beams, each of which contains ions of the same mass. This separation of ions by mass produces a mass spectrum.

Secondary ion mass spectrometry is similar, but the ions in question are molecular species ejected from the surface of the sample being studied. Bombardment of a sample surface with a primary ion beam followed by mass spectrometry of the emitted secondary ions constitutes secondary ion mass spectrometry (SIMS). The surface composition may be determined by bombarding the surface with some atomic, polyatomic, or cluster species resulting in ejection of surface species which are identified by their mass spectrum. Today, SIMS is widely used for analysis of trace elements in solid materials, especially semiconductors and thin films.

The Problem

SIMS experiments have raised some interesting questions regarding energy deposition in the substrate by the bombarding particles and the resulting ion ejection. There have been cases documented in which a large increase in secondary ion yield has resulted with polyatomic projectiles as compared to monoatomic projectiles. What has been proposed is a nonlinear dependence of secondary ion yield with cluster size. A nonlinear enhancement occurs when an n particle cluster with energy E yields more than n times the secondary ion yield of a monoatomic projectile with energy E/n. Experiments have shown that the degree of the enhancement depends on the following: mass, size, kinetic energy, and composition of the primary cluster and characteristics of the target including any substrate combination. Also the largest enhancements have been attributed to molecular ions and molecular fragments and multi-layer targets rather than monolayer targets. It has also been shown that increasing cluster size may lead to increased damage of the solid target. We used MD simulations to explain how atomic clusters result in nonlinear enhancements for the yield of ejected secondary ions in secondary ion mass spectrometry (SIMS). Since the output of an MD simulation are the positions of all the atoms in the system at a given time, movies of the atomic motions can be constructed like those below, which illustrates the role of the substrate in the ejection of secondary ions.

References

Barbara J. Garrison, "Molecular Dynamics Simulations of Surface Chemical Reactions", Chem. Soc. Reviews, 121, 155-162 (1992).

Jennifer A. Townes, Anna K. White, Elizabeth N. Wiggins, Kristin D. Krantzman, Barbara J. Garrison, Nicholas Winograd, "Mechanism for Increased Yield with the SF5+ Projectile in Organic SIMS: The Substrate Effect", J. Phys. Chem. A, 24, 4587-4589 (1999).

T. C. Nguyen, D. W. Ward, J. A. Townes, White, A. K., Krantzman, K. D., Garrison, B.J., "A Theoretical Investigation of the Yield-to-Damage Enhancement with Polyatomic Projectiles in Organic SIMS," Journal of Physical Chemistry B 104 (34), 8221 (2000).

David W. Ward, T.C. Nguyen, Kristin D. Krantzman, and Barbara J. Garrison, "A Comparison of the Energy Density Distribution with Atomic and Polyatomic Projectiles in Organic SIMS," in the proceedings of the 12th International Conference on Secondary Ion Mass Spectrometry, A. Benninghoven, P. Bertrand, H.-N. Migeon, and H.W. Werner, eds. (Elsevier Science B.V., Belgium, 1999.)

David W. Ward, "Energy Density Distribution of the High Energy Bombardment of an Organic Monolayer with Xe+ and SF5+ Projectiles," Undergraduate Thesis, College of Charleston, 1999.