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Amorphous Materials and Interfaces
Yuhai Tu
We are trying to understand the structure and properties of covalent amorphous material and their interfaces with crystalline substrate by using Monte Carlo methods.
Figure 1. The continuous random network structure
of amorphous silicon dioxide, notice that
each Si atom (gold shpere) has 4 bonds, and
each oxygen atom (red sphere) has 2 bonds.
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The structure of covalent amorphous material, such as a-Si and a-SiO2 can be best described as continuous random network: each atom in the amorphous solid has the same number of covalent bonds as in their crystalline phase, the amorphous nature of the structure is reflected by the random network made by the covalent bonds. An illustrative picture of an amorphous silicon dioxide structure is shown in figure 1 .We model the structure of such covalent amorphous material by a random graph (network), where the vertices of the graph represent the atoms, and the edges of the graph represent the chemical bonds. Locally, the graph is under the constraint that the number of edges from each vertex is fixed, e.g., in the case of a-SiO2, every Silicon vertex (gold) has 4 edges and every Oxygen (red) vertex has 2 egdes.
The energy of each individual graph is calculated by a simple Keating type model with energy contributions from bond length and bond angle constraints, the positional degrees of freedom can be further integrated out and we are left with a energy function depending only on the topology of the graph. Following [1], we explore the graph configuration space by local reconstruction of the graph which preserved the number of edges for each vertex (figure 2). We study the thermodynamic properties of such amorphous material by Monte Carlo simulation using the above mentioned energy function and graph switching moves, for example, we have studied the glass transition in such material [2].
More importantly, such method provide an unique way in looking at interfaces between amorphous material and crystalline substrate, in particular, we are interested in understanding the structure of the interface between a-SiO2 and c-Si, one of the most important, yet poorly understood interface in semiconductor industry. We have simulated the a-SiO2/c-Si (001) interface structure using the methods outlined above [3]. We find that the interface structure is dominated by Si-O-Si bridge bonds (figure 3a), the formation of oxygen bridge bonds relaxes most of the strain energy caused by the lattice mismatch between the two material. Furthermore, we find that the lowest interfacial strain energy state corresponds to the interface structure where oxygen bridge bonds form (2X1) striped pattern (figure 3b). This structure with bulk amorphous SiO2 and ordered interfacial oxygen bridge bonds seems to reconcile with many previously contradictory experiments. Currently, we are trying to understand the kinetics of the oxidation process using this approach.
Figure 2. Graphical illustration of Wooten-Winer-Weaire move
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Figure 3. (a) Side view of the a-SiO2/c-Si(001) interface structure, the arrows indicate the locations of the Si-O-Si bridges. (b)Top view of the stripe structure of the oxygen bridge bonds at the interface.
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- F. Wooten, K. Winer, and D. Wearie, Phys. Rev. Lett. 54, 1392 (1985).
- Y. Tu, J. Tersoff, G. Grinstein and D. Vanderbilt, Phys. Rev. Lett. 81, 4899 (1998).
- Y. Tu and J. Tersoff, Phys. Rev. Lett. 84, 4393 (2000).
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