University of Twente Student Theses


Slater-Koster energy integrals of simple and face cubic crystals

Schopbarteld, A. (2022) Slater-Koster energy integrals of simple and face cubic crystals.

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Abstract:Electronic band structures are the primary component used to calculate electrical, optical and even magnetic properties of crystals. For this reason physicists, chemists, and material scientists want to develop methods to accurately compute these band structures. Accurate calculations will help directly in for example the development of more efficient solar cells. Several of these methods exist, for example Density Functional Theory (DFT) or the GW-approach. The downside of these methods are that although very accurate they are often too computationally expensive or require too much working memory. This thesis investigates an alternative method, first proposed by J.C. Slater and G.F. Koster in 1954, a variation on the method called the LCAO or tight binding method. Energy contributions of electrons beyond a certain distance from the origin are neglected by assuming these are sufficient tightly bound to their nucleus. We will derive the energy contributions or matrix elements for s, p and d orbitals on a simple cubic and FCC lattice. These formulas contain several integrals, which we cannot solve without reverting back to DFT or GW calculations. These formulas can still be used however, using the integrals as fitting parameters to fit to bandstructure data from DFT or GW calculations. The method proposed in this thesis, and by Slater \& Koster therefore functions as an interpolation method for more expensive and accurate calculations. This reduces the computational complexity of these algorithms.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:33 physics
Programme:Applied Mathematics BSc (56965)
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