Last updated 01.01.98

The characteristics of the deposition of energy in matter by swift, massive particles is of interest in areas ranging from design of inertial confinement fusion devices to radiation therapy. The understanding and prediction of the processes involved in such energy deposition provide the unifying theme of my research. The research program has three distinct but interrelated parts dealing with:

- stopping in atoms and molecules, with especial emphasis on aggregation effects such as deviations from the Bragg rule, solid/gas sample phase effects, and stopping in large molecules
- stopping in ultra-thin (several atomic layers) films as models for imbedded layers, overlayers and interfaces and as intermediates between gas and solid targets
- trajectory dependent stopping if swift ions under channeling conditions in bulk targets, with emphasis on implantation profiles and exit energy/angle distributions.

Each of these areas is summarized below.

It is the aim of this project to develop a scheme for calculation o"f the energy deposition of swift ions in molecules. The attack is two pronged. One prong, direct calculation and integration of the appropriate generalized oscillator strengths (GOS's) using the polarization propagator formalism, is presently feasible only for small molecules, but in principle provides an accurate method to calculate stopping. This scheme will be developed for study of small molecules, such as water, to provide a normative comparison for the large molecule scheme, and to gain insight on how the large molecule scheme can be improved. The second prong, a scheme based on the additivity and transferability of properties of chemical bonds, is not as accurate, but is not limited by the size of target molecules, and thus admits calculation of stopping properties for target molecules of a size big enough to be biologically significant. The large molecule part of this work will initially be done in the context of the kinetic theory of stopping, but it is hoped that experience in the small molecule regime will lead to a GOS based large molecule scheme as well. Thus with the two, eventually related methods, stopping by molecules of all sizes can be considered.

Among the problems currently under study are:

- calculation of isotropic and anisotropic molecular mean excitation energies
- calculation of generalized oscillator strength distributions and their directional characteristics
- calculation of molecular dipole oscillator strength distributions and their energy weighted moments
- studies of deviations from the Bragg Rule
- development of additive fragment stopping functions for use in a cores and bonds generalization of the Bragg Rule
- study of target phase and allotrope effects

One field of advanced materials research that becomes critically important in the context of endeavors such as the fabrication of microelectronic components and their deployment in space, is the interaction of these materials with penetrating radiation. In particular, swift, massive particles impinging on materials can both create impurity distributions in materials which are essential to device function, yet destroy the devices themselves, depending on the incident particles, their energies, and the target systems. It thus is essential to understand the energy deposition process so that damage can be prevented in extant devices, and proper dopants can be introduced in fabrication. We have embarked on a theoretical research program to attack this problem.

The research has several facets. First, we must understand the materials which will be the targets for the radiation. This understanding must relate structure and electronic properties in a reliable, predictive, computationally tractable way for real materials systems. Simultaneously, we must understand the energy deposition process in terms of a systematic theoretical treatment which is computationally implementable. The two bodies of theory must be mutually compatible, not rooted in fundamentally irreconcilable models.

Because forefront microelectronics devices depend upon the detailed quantum mechanical behavior of the electrons, the electronic structure of the materials systems is fundamental. The problem becomes more acute as the systems grow thinner, which is precisely the limit toward which the drive for speed in microelectronics is driving the multiple layers in devices. Thus, we use full potential, all-electron, local-spin density methods which do not impose any arbitrary symmetries on the system (e.g., supercells such as are sometimes used to mimic laminar interfaces and/or surfaces). The object here is to model the thin films structures encountered in microelectronics at a high enough level to describe the effects energy deposition without encountering artifacts introduced by the description of the material.

The problem that concerns us is to understand the energy deposition process of swift particles in ultra-thin films. The two standard approaches to the problem of energy deposition are those associated with Lindhard, which is based on a dielectric description of the weakly inhomogeneous electron gas, and with Bethe, which is an atomic description. Neither of these is sufficient in the regime which we wish to characterize, namely thin material films. The atomic interactions make the Bethe description inappropriate, while the atomic structure of a film and its two dimensional periodicity makes the Lindhard description prohibitively formidable (no truly first principles calculation of the frequency and wave vector-dependent dielectric function of a real material has ever been performed). Consequently an intermediate way must be found that admits a proper description of thin layered targets. Our generalization of the Kinetic Theory of Stopping (KTS ) in connection with Lindhard's Local Plasma Approximation (LPA) provides such a description. The description, although involving several approximations, is internally consistent as all phases of the calculation are based on the target density.

Among current problems under study are:

- Stopping in H n-layers as a function of layer habit and number. Comparison of atomic-like to molecular habits gives information on the effect of chemical binding on stopping.
- Stopping in hexagonal Li n-layers. These are the delamination limit of the bulk solid, and provide information on the target phase effect.
- Study of stopping by the LiF monolayer: a archetypical ionic target system and its behavior under high pressure (metallization).
- Study of stopping at the GaAs interface.
- Study of structure and stopping in ultra thin layers of carbon allotropes.

Recent advances in technology have made experiments possible that depend on the details of the trajectories of swift ions under axial channeling conditions. Such experiments probe, for example, the location of interstitial impurities in solids. Recently we have implemented a semiclassical treatment of channeling, where we time step integrate the classical force law for the particle trajectory. The force consists of the gradient of the electrostatic potential plus a dissipation part, the electronic stopping power. The first of these comes from an all electron, full potential density functional theory (LAPW) calculation, while we use the stopping function of Echenique et al. for the low velocity stopping. It should be noted that this procedure uses a proper, quantum mechanical potential with all atoms explicitly considered, and does not assume charge strings, statistical equilibrium, nor makes any of the other assumption usual to this sort of calculation. (That is not to say assumptions are not made!)

So far, the only test case that has been run is for a 0.15 keV proton along the (1,1,0) channel in Ge, but the results look very encouraging.

We intend to study:

- implantation profiles of various ions in materials under channeling conditions
- energy/angle scans of ions transmitted through thin targets

- E.K. Dalskov, J. Oddershede, and J.R. Sabin, "Generalized Oscillator Strengths for Calculation of Molecular Stopping Properties, Some Preliminary Results: CO," AIP Proceedings CP392, 1373 (1997).
- S.P. Apell, J.R. Sabin, and S.B. Trickey, "Simple Physical Model for Layer-Number Dependences of Proton Stopping in Ultra-This Films," AIP Proceedings CP392, 1369 (1997).
- R. Cabrera-Trujillo, S.A. Cruz, J. Oddershede, and J.R. Sabin, "A
Bethe Theory of Stopping Incorporating Electronic Excitation of Partially
Stripped Projectiles," Phys. Rev. A
**55**, 2864 (1997). - J.R. Sabin, "Energy Deposition of Swift Alpha's in Neon: An Electron
Nuclear Dynamics Study," Adv. Quantum Chem.
**28**, 107 (1997). - J.R. Sabin and J. Oddershede, "Directional Characteristics of the
Generalized Oscillator Strengths for some Low Lying Transitions in H
_{2}," Nucl. Inst. and Meth.**B115**, 79 (1996). - S.P. Apell, J.R. Sabin and S.B. Trickey, "Approach to Bulk Behavior
from Ultrathin Layered Systems Probed by Energy Deposition," Int. J.
Quantum Chem.
**S29**, 153 (1995). - G.A. Aucar, J. Oddershede and J.R. Sabin, "Relativistic Extension of
the Bethe Sum Rule," Phys. Rev. A
**52**1054 (1995). - S.P.A. Sauer, J.R. Sabin and J. Oddershede, "Calculated Molecular Mean
Excitation Energies for Stopping and Straggling," Nucl. Inst. and Meth.
**B100**, 458 (1995). - H.H. Mikkelsen, J. Oddershede, J.R. Sabin and E. Bonderup, "Bethe
Theory for Directional Dependence of Stopping in Molecules," Nucl. Inst.
and Meth.
**B100**, 451 (1995). - J.A. Nobel, J.R. Sabin and S.B. Trickey, "Simulation of Ion
Implantation in Si for 0.25 keV H+ under Channeling Conditions," Nucl.
Inst. and Meth.
**B99**, 632 (1995). - A.C. Diz, Y. Ohrn and J.R. Sabin, "Dynamic Charge States and Energy
Deposition of Swift Helium Ions in Neon," Nucl. Inst. and Meth.
**B96**, 633 (1995). - J.Z. Wu, S.B. Trickey, J.R. Sabin and J.C. Boettger, "Calculated
Properties of a Prototypical Ionic Monolayer," Phys. Rev. B
**51**, 14576 (1995). - S.B. Trickey and J.R. Sabin, "Reply to: Note on Stopping Power and
Statistics of Particle Penetration," Nucl. Inst. and Meth.
**B95**, 480 (1995). - J.R. Sabin, I. Paidarova and J. Oddershede, "On the Relative
Importance of Temperature and Isotope Effects on the Dipole Oscillator Strength
Distribution of H2," Theoret. Chim. Acta
**89**, 375 (1994). - H.H. Andersen and J.R. Sabin, "Introduction" to the Topical Issue
of Nucl. Inst. and Meth. on Target Aggregation and Projectile Charge States,
Nucl. Inst. and Meth.
**B93**,*v*(1994). - J.Z. Wu, S.B. Trickey, J.R. Sabin and J.A. Nobel, "Energy Deposition
of Protons in Allotropic Carbon Ultra-Thin Layers," Int. J. Quantum Chem.
**QC28**, 299 (1994). - J.A. Nobel, J.R. Sabin and S.B. Trickey, "Theoretical Ion Implantation
Profiles for Low Energy Protons under Channeling Conditions," Int. J.
Quantum Chem.
**QC28**, 283 (1994). - S.B. Trickey, J.Z. Wu and J.R. Sabin, "Materials Specificity, Quantum
Length Scales, and Stopping Powers," Nucl. Inst. and Meth.
**B93**, 186 (1994). - J.R. Sabin, J. Oddershede and I. Paidarova, "An Estimate of the
Temperature Dependence of the Stopping Cross Section in Molecular Targets,"
Nucl. Inst. and Meth.
**B93**, 161 (1994). - J.Z. Wu, S.B. Trickey and J.R. Sabin, "Electronic Stopping Power for
Protons in an LiF Monolayer," Int. J. Quantum Chem.
**QC27**, 219 (1993). - D.E. Meltzer, J.R. Sabin, S.B. Trickey and J.Z. Wu, "Density
Decomposition Options in the Orbital Local Plasma Approximation," Nucl.
Inst. and Meth.
**B82**, 493 (1993). - J.Z. Wu, S.B. Trickey and J.R. Sabin, "Proton Stopping in Ultrathin
Lithium Films," Nucl. Inst. and Meth.
**B79**, 206 (1993). - S.P.A. Sauer, J.R. Sabin and J. Oddershede, "Directional
Characteristics of the Moments of the Dipole Oscillator Strength Distribution of
Molecules: H2 and H2O," Phys. Rev. B
**47**, 1123 (1993). - E.H. Mortensen, J. Oddershede and J.R. Sabin, "Polarization Propagator
Calculations of Generalized Oscillator Strengths and Stopping Cross Sections of
He," Nucl. Inst. and Meth.
**B69**, 24 (1992). - J.R. Sabin and J. Oddershede, "Status of the Calculation of the Energy
Loss of Swift Ions in Molecules," Nucl. Inst. and Meth.
**B64**, 678 (1992). - J.Z. Wu, S.B. Trickey, J.R. Sabin and D.E. Meltzer, "Stopping of Swift
Projectiles in Material Thin Films: Hydrogen," Nucl. Inst. and Meth.
**B56/57**, 340 (1991). - G.H.F. Diercksen, J. Oddershede, I. Paidarova and J.R. Sabin, "Calculation
of the Isotropic and Anisotropic Spectral Moments of the Dipole Oscillator
Strength Distribution of N2," Int. J. Quantum Chem.
**39**, 755 (1991). - P. Jensen, J. Oddershede and J.R. Sabin, "Geometric Dependence of the
Mean Excitation Energy and Spectral Moments of Water," Phys. Rev. A
**43**, 4040 (1991). - J. Oddershede and J.R. Sabin, "Polarization Propagator Calculations of
Spectroscopic Properties of Molecules," Int. J. Quantum Chem.
**39**, 371 (1991). - J.R. Sabin, J. Oddershede and G.H.F. Diercksen, "Moments of the Dipole
Oscillator Strength Distribution and Mean Excitation Energies of Helium,"
Phys. Rev. A
**42**, 1302 (1990). - J. Oddershede and J.R. Sabin, "Mean Excitation Energy and Moments of
the Dipole Oscillator Strength Distribution of Closed Shell Aluminum Ions,"
Nucl. Inst. and Meth.
**B48**, 34 (1990). - D.E. Meltzer, J.R. Sabin and S.B. Trickey, "Calculation of Mean
Excitation Energies and Stopping Cross Sections in the Orbital Local Plasma
Approximation," Phys. Rev. A 41, 220 (1990); Erratum,
**42**, 666 (1990). - J.R. Sabin and J. Oddershede, "A Comment on the Abstraction of Mean
Excitation Energies from Experimental Reduced Stopping Powers," Nucl. Inst.
and Meth.
**B44**, 253 (1990).

Please send email to request reprints.