Pseudo-Hydrogen Passivation: A Novel Way to Calculate Absolute Surface Energy of Zinc Blende (111)/(͞1 ͞1 ͞1) Surface

Abstract

Determining accurate absolute surface energies for polar surfaces of semiconductors has been a great challenge in decades. Here, we propose pseudo-hydrogen passivation to calculate them, using density functional theory approaches. By calculating the energy contribution from pseudo-hydrogen using either a pseudo molecule method or a tetrahedral cluster method, we obtained (111)/(111) surfaces energies of Si, GaP, GaAs, and ZnS with high self-consistency. This method quantitatively confirms that surface energy is determined by the number and the energy of dangling bonds of surface atoms. Our findings may greatly enhance the basic understandings of different surfaces and lead to novel strategies in the crystal growth.Absolute surface energies are fundamental physical quantities of solid surfaces with broad implications [1][2][3][4][5] . Equilibrium shapes and morphologies 4,5 , equilibrium growth rates 6-8 , as well as device performance of semiconductors 9 , are directly related to them. The wetting conditions of thin films or super lattices are also determined by these quantities 10 . Novel controlling strategies of growth modes (e.g. by strain or surfactants) are also often determined by them [10][11][12][13][14][15][16][17][18] . Therefore, determining accurate absolute surface energy is essential in understanding growth processes and in improving the performance of thin-film devices 3,19 .Absolute surface energies of symmetric non-polar surfaces can be calculated with a standard slab method 3 . However, for asymmetric polar surfaces such as zinc blende (111) and ( ) 111 surfaces, it is extremely difficult to separate the anion and cation terminated surfaces, due to the asymmetric nature of slabs 3,19 . Although surface reconstructions and surface kinetic processes can be calculated by passivating the conjugate surfaces with pseudo-H atoms, the absolute surface energy can't be obtained unless the energy of the passivated surface is known 3,19 . Despite the standard treatment of pseudo H passivation in surface calculations, a detailed analysis of the bonding between the surface atom and the pseudo H is lacking and may serve as a key to solve the difficult absolute surface energy problem. Chetty and Martin 21 first proposed local energy density approach to determine the absolute surface energies of polar surfaces. However, this approach suffers from a non-trivial approximation of the local energy density 3 , which leads to a large disagreement among calculations using exactly the same method 20 . Another early approach to calculate the absolute surface energies of zinc blende (111) surfaces is to construct a wedge structure and then calculate one polar surface without involving its conjugate surfaces 3 . Based on surface energies calculated by this approach, a common dangling bond rule was also proposed, which states that energies of surface atoms with similar electronic environment are the same regardless of the different surface orientations 3 . Following this method, absolute surface energies of quite a few ...

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“…The bottom layer had to be passivated with a pseudohydrogen layer for subsequent DFT simulations. [ 57 ] To create the pseudo‐hydrogen atoms we defined Change Element as “H1.5” so that hydrogen atoms possess 1.5 electron charges each. After saving the file (ctrl + s), we opened it in a text editor and added a 15 Å vacuum along the [111] direction; we could then relax the system with VASP to find the optimal positions for the Cu, O, and pseudo‐H atoms.…”