Adsorption and Diffusion of In and Bi Adatoms on (0001) Surfaces of of β-Phase In₂Se₃ and Bi₂Se₃

This paper presents the results of first-principles calculations of the adsorption and diffusion of indium atoms on the (0001) surfaces of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex>-phase <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{In}_{2} \text{Se}_{3}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Bi}_{2} \text{Se}_{3}$</tex>. Using first principle method, it was found that the hole positions on both surfaces are the most favorable ones for indium adatoms. For bismuth adatoms, the most favorable positions are hollow sites, but hcp and brg positions have a negligible energy difference. Using a nudged elastic band method, we have calculated migration activation barriers for indium and bismuth adatoms on the (0001) surfaces of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\beta}$</tex>-phase <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{In}_{2} \text{Se}_{3}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Bi}_{2} \text{Se}_{3}$</tex>. The energy barriers for indium (bismuth) atom migration on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\beta}$</tex>-phase In <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{2 S e}_{3}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Bi}_{2} \text{Se}_{3}(0001)$</tex> surfaces are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.153(0.074)$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.158(0.156) \text{eV}$</tex>, respectively. Based on the obtained activation energy values, the dependence of the surface diffusion coefficient on the substrate temperature was calculated. At the room temperature, diffusion length for all adatoms under consideration significantly exceeds the width of terraces on both studied surfaces.