Ion scattering simulations of the $\mathrm{Si}(100)\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ interface

Ion scattering simulations of the $Si (100) − {SiO}_{2}$ interface

Angelo Bongiorno, Alfredo Pasquarello, Mark S. Hybertsen, and L. C. Feldman

Phys. Rev. B 74, 075316 – Published 15 August 2006

Abstract

We carry out ion scattering simulations to investigate the nature of the transition region at the $Si (100) − {SiO}_{2}$ interface. Ion scattering experiments performed in the channeling geometry provide us with a genuine interfacial property, the excess Si yield, resulting from distortions in the Si substrate and from Si atoms in intermediate oxidation states. To interpret the ion scattering data, we first generate a series of model structures for the interface by applying sequentially classical molecular dynamics and density-functional relaxation methods. These models reproduce atomic-scale features consistent with a variety of available experimental data. Then, we design a classical scheme to perform ion scattering simulations on these model interfaces. In our study, we separate the excess Si yield obtained from experiments in two distinct contributions. First, Si atoms in intermediate oxidation states account for $\sim 25 %$ of the excess Si yield, a contribution that is fully determined by the population of suboxide determined from photoemission data. The remaining $\sim 75 %$ of the excess Si yield characterizes the amount of lateral distortion of the substrate Si layers in the vicinity of the $Si (100) − {SiO}_{2}$ interface. The comparison between calculated and experimental excess Si yields indicates that the distortions propagating from the interface into the Si substrate are consistent with interfacial transition structures extending over more than two Si layers, eventually including a disordered bonding pattern. Nearly abrupt interfaces induce distortions in the upper layers of the Si substrate which are insufficient for reproducing the experimental excess Si yields.

Received 20 December 2005

DOI:https://doi.org/10.1103/PhysRevB.74.075316

Authors & Affiliations

Angelo Bongiorno^1,2,*, Alfredo Pasquarello^1,2, Mark S. Hybertsen³, and L. C. Feldman⁴

¹Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
²Institut Romand de Recherche Numérique en Physique des Matériaux (IRRMA), CH-1015 Lausanne, Switzerland
³Department of Applied Physics and Applied Mathematics & Center for Electron Transport in Molecular Nanostructures, Columbia University, New York, New York 10027, USA
⁴Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA

^*Present address: Georgia Institute of Technology, School of Physics, 837 State Street, Atlanta, GA 30332-0430, USA.

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Vol. 74, Iss. 7 — 15 August 2006

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Figure 1
Scheme of the two-atom model. Atoms are represented by black disks. The ions impinge parallel to the direction defined by the two atoms ( $z$ axis). Ion trajectories impinging with an impact parameter $b$ with respect to the top atom are deflected by an angle $θ$ . The ion beam interacts with the bottom atom when it is displaced from its original position by more than the critical distance $R_{m}$ (gray disk).Reuse & Permissions
Figure 2
Ion scattering yield for a two-atom model (depicted on the bottom, right side) vs displacement $(R)$ of the second atom in the direction perpendicular to the ion beam. Ions impinge with an energy of $0.1 MeV$ . When $R$ equals zero, the two atoms are aligned along the direction of the impinging ions. The yield is expressed in atoms per row. The angular aperture of the detector in the simulation is $20 °$ . The vertical dotted line indicates the location of the Molière radius, $R_{m} = 0.24086 Å$ .Reuse & Permissions
Figure 3
Fraction of the yield vs the depth of the atom participating in the backscattering collision, calculated for a $Si [100]$ column vibrating at $300 K$ . Simulations are carried out with an ion energy of $0.4 MeV$ (open circles) and $1 MeV$ (filled circles). The top atom of the column is located at the origin. Yields are calculated using an acceptance aperture of $20 °$ .Reuse & Permissions
Figure 4
Calculated excess Si yield for a distorted $Si [100]$ column vibrating at $300 K$ , for ion energies of 0.4 (dashed symbols) and $1 MeV$ (solid symbols). Distortions are introduced by displacing the top atom by $d$ with respect to the ideal position in the direction perpendicular to the ion flux. Lines correspond to excess yields derived by neglecting flux peaking and enhancement effects, and retaining only the yield contribution arising from the number of Si atoms exposed to the ion flux, for ion energies of 0.4 (dashed) and $1 MeV$ (solid). Circles refer to full yields, including both contributions. Vertical lines correspond to the location of the Molière radii for ion energies of $0.4 MeV$ $(0.14 Å)$ and $1 MeV$ $(0.088 Å)$ , respectively.Reuse & Permissions
Figure 5
Ion scattering yields vs ion energy from an ideally terminated Si crystal. Si yields are expressed in [100] monolayers $(1 ML = 6.8 \times 10^{14} atoms ∕ {cm}^{2})$ . Open symbols refer to the present calculations while full dots to values obtained with the stochastic model (Ref. 31). The solid line refers to the number of Si monolayers exposed to the ion flux. Reported data refer to ion energies ranging from 0.2 to $2 MeV$ .Reuse & Permissions
Figure 6
Top views of the transition structures in models $A^{'}$ , $B^{'}$ , and $C^{'}$ , obtained through minor variations of models $A$ , $B$ , and $C$ , respectively. Light (dark) spheres indicate $Si (O)$ atoms. On the right, in-plane displacements for the upper four Si layers. For each layer, a box is centered on the mean displacement with a vertical height giving the rms deviation. The first layer (dark box) contains partially oxidized Si atoms. The horizontal band indicates the sensitivity of ion scattering measurements to atomic displacements.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Ion scattering simulations of the $Si (100) − {SiO}_{2}$ interface

Angelo Bongiorno, Alfredo Pasquarello, Mark S. Hybertsen, and L. C. Feldman

Phys. Rev. B 74, 075316 – Published 15 August 2006

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Physical Review B

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Ion scattering simulations of the Si(100)−SiO2 interface

Angelo Bongiorno, Alfredo Pasquarello, Mark S. Hybertsen, and L. C. Feldman

Phys. Rev. B 74, 075316 – Published 15 August 2006

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Ion scattering simulations of the $Si (100) − {SiO}_{2}$ interface