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Currently, I have to put two different materials together to form a heterostructure. I've already transformed the unit cell of material A from trigonal to cubic. Now the unit cell has a rectangular shape in a,b plane, and the other one has a square dimension. I've try my best to find the size such that to minimize the mismatch of the unit cell. For example, now one unit cell has a $13.614 \times 13.614$ angstrom unit and the other one has a $13.326 \times 15.388$ dimension. Can I take an average on the lattice constant in b dimension and stretch the first lattice a little bit and compress another a little bit so that I can create a heterostructure? Is it acceptable? How large will it affect the result of the DFT calculation?

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I would like to add to Jack's answer that beyond the raw numbers of what an acceptable amount of strain may be, it can also be important to consider the physical situation of interest when matching two different compounds in a heterostructure. This is particularly relevant for your point about "taking the average" of the lattice parameters of the two compounds that you are matching. Situations that may occur in which you don't want to take the average include:

  1. Epitaxial strain. When you are looking into experiments that grow a thin film on a substrate, in the experiment the lattice parameter of the substrate is not affected because the material is almost in its bulk configuration while it is mostly the thin film that completely adapts to the substrate lattice parameter. When simulating such a situation, you typically want to only change the lattice parameter of the thin film part of the heterostructure, not take the average of the two.
  2. Bulk modulus. Even when the experimental situation you are trying to model is one in which there is no clear substrate-film distinction, different materials respond differently to compression/extension, as characterized by the bulk modulus. Rather than averaging the lattice parameters, a better approach may be to take the respective bulk moduli into account, to decide which material may be amenable to a larger compression/extension.
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There are lots of papers about the strain engineering of two-dimensional materials. For example:

The tensile strain even up to $10\%$ is considered.

Can I take an average on the lattice constant in b dimension and stretch the first lattice a little bit and compress another a little bit so that I can create a heterostructure? Is it acceptable?

  • The answer is OK. You can take that as your initial structure and relax to find the optimized lattice constant.

How large will it affect the result of the DFT calculation?

There are many things affected by strain, such as the band-gap, carrier mobility, and band alignment. Of course, how large the influence depends on the range of applied strain.

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