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SPECIAL SECTION ON NANOMATERIALS AND NANOMECHANICS

Atomistic Determination of Continuum Mechanical Properties of Ion-Bombarded Silicon

[+] Author and Article Information
N. Kalyanasundaram, H. T. Johnson

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign

J. B. Freund

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign

J. Eng. Mater. Technol 127(4), 457-461 (Jul 12, 2005) (5 pages) doi:10.1115/1.2020014 History: Received February 04, 2005; Revised July 12, 2005

Abstract

Highly disordered, ion-processed silicon is studied using a molecular dynamics simulation with empirical interatomic potentials. The surface free energy density, stress-strain relations, and continuum surface features of silicon, bombarded in the simulations to relatively high fluence by medium energy argon ions, are computed statistically by preparing multiple randomized ion-bombarded specimens. The surface-free energy per unit area for the ion-bombarded silicon is about $1.76J∕m2$, much lower than the $2.35J∕m2$ corresponding to a (001) unrelaxed, crystalline silicon surface. A stress-strain curve is obtained computationally by performing a constant strain test on the ion-bombarded specimens and by calculating stresses from the interatomic forces acting across different cross sections in the sample. The resulting tensile elastic modulus of the material, while slightly elevated due to the prominence of the free surface in the thin layer, is in good agreement with available experimental data. The surface is characterized using an interatomic potential-based $C2$ continuous sampling method.

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Figures

Figure 6

(a) Near surface atomic positions of highly damaged silicon are shown after a fluence of 3.39×1014ions∕cm2. The reconstructed continuum surface is shown in (b). The variation in surface height is approximately 0.3 nm, while on a crystalline [100] silicon surface it is computed to be approximately 0.03 nm by the method used here.

Figure 5

Comparison of moduli (in GPa) computed over various depths from the surface. Nearest to the surface the apparent modulus is highest, while averaging over more of the “bulk” amorphous silicon leads to a lower modulus.

Figure 4

Stress-strain curve for the near-surface ion bombarded material. A stress-free state is observed at a strain of about 0.05. Linear behavior is observed near the stress-free state, with an average linear modulus of 159 GPa.

Figure 3

Schematic illustrating the simulated constant strain test performed to obtain the stress-strain relationship. A force balance approach is used to calculate the mechanical stress.

Figure 2

Variation of surface energy through the depth of the material is shown (right). The figure on the left shows the structure, with the red and blue circles denoting argon and silicon atoms, respectively, seen from a direction parallel to the y−z plane, after a steady implantation and sputtering rates are attained. The top, ion damaged portion of the material extends to a depth of about 2.2 nm from the surface. The transition from amorphous, predominantly damaged state to the almost crystalline state is clearly seen in the surface energy graph.

Figure 1

Schematic of the configuration used to create an ion-bombarded specimen. Molecular dynamics is used to obtain the structure. An argon ion beam at 500 eV beam energy is incident on the [001] surface of initially crystalline silicon. The damage induced after a fluence of 3.39×1014ions∕cm2, as seen in a plane parallel to the y−z axis is shown on the right. The red circles are argon atoms and the blue circles are silicon atoms.

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