Nanoscale Polishing of Gallium Arsenide Surfaces

In comparison to the traditional nanoscale polishing model, the nanoscale polishing model employed in this study takes into account the microconvex structures present on the actual processed surface. The variables under investigation pertain to the crystallographic orientations of gallium arsenide (GaAs) surfaces during the nanoscale polishing process, specifically the $\left\{100\right\}$ , $\left\{110\right\}$ , and $\left\{111\right\}$ crystallographic orientations. The nanoscale polishing model for GaAs crystals, as illustrated in Figure 1, can be conceptually divided into two main components: the equivalent spherical representation of the diamond polishing tool and the GaAs surface with its microconvex structures.
As depicted in Figure 1a, the equivalent diamond polishing particle had a diameter of 12 Å, consisting of 159,486 atoms, and possessed a lattice constant of 3.57 Å. The equivalent GaAs surface was composed of two parts: a substrate with dimensions of 300 Å × 220 Å × 50 Å and microconvex structures comprising one-quarter spheres at both ends and a central half-cylinder, all with a radius of 7 Å. The centers of the spherical structures at the two ends were located at (110 Å, 110 Å, 50 Å) and (190 Å, 110 Å, 50 Å), respectively. The position of the diamond particle was (−60 Å, 110 Å, 120 Å). The total number of gallium atoms was 104,963, and the total number of arsenic atoms was 103,420. The crystallographic structure of the GaAs crystal is depicted in Figure 1b, with a lattice constant of 5.654 Å.
The equivalent model for the gallium arsenide (GaAs) surface was divided into three distinct layers, as shown in Figure 1a: the Newtonian atomic layer situated at the top, where atomic motion follows Newton’s second law and is calculated using the velocity Verlet algorithm [47 (link)]; the isothermal atomic layer in the middle, which regulates temperature changes based on the Berendsen thermostat [48 (link)]; and the fixed atomic layer at the bottom, where atomic positions and velocities are constrained to prevent atoms from escaping the boundary. In the multilayer structure, the thickness of the Newtonian layer was 100 Å (70 Å for the radius of the microconvex body and 30 Å for the basal portion), the thickness of the thermostatic layer was 10 Å, and the temperature of the boundary layer was 10 Å. In addition to the potential energy parameters, to ensure convergence, the model set boundary conditions as well as energy minimization constraints so that the model was in a steady state before nanopolishing. To enhance computational efficiency in the simulation, this work employed periodic boundary conditions for the nanoscale polishing process. Specifically, periodic boundary conditions were applied in the y-direction to exploit the system’s symmetric properties, while nonperiodic boundary conditions were imposed in the x-direction (processing direction) and the z-direction (normal to the surface) to ensure a realistic representation of the system.
This study utilized the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [49 (link)] for molecular dynamics simulations and employed the open visualization tool (OVITO) [50 (link)] for the visualization and postprocessing of the simulation results. The detailed parameters of the model are presented in Table 1. The simulation workflow included the prepolishing energy minimization process using the conjugate gradient method [51 (link)]. The model’s relaxation process was conducted under the NPT ensemble with a relaxation time of 100 ps. During this process, the model’s temperature gradually stabilized at room temperature (293 K) using the Nose–Hoover thermostat, and the potential energy converged to −5.30 × ${10}^{-5}$ eV. The temperature and potential energy changes during the relaxation process are illustrated in Figure 2. Following the relaxation of the model, the ensemble was switched to NVE, and the simulation of nanoscale polishing was performed. During the relaxation phase of the model, the temperature gradually stabilized at 293 K, and the total potential energy of the model gradually stabilized at −5.30 × ${10}^{-5}$ eV. In this process, the polishing speed of diamond abrasive particles was set at 100 m/s in the (0,1,0) direction, with a polishing distance of 30 nm. Before the calculations for stresses, RDF, and temperature and after the nanopolishing simulation, the model was subjected to a relaxation process, which resulted in a more stable surface structure after processing. To observe the stable structure of the surface after the nanoscale polishing process, a second relaxation process was conducted for the model, also with a relaxation time of 100 ps.
During the process of nanoscale machining, the selection of the interatomic potential energy is of paramount importance. In the case of polishing gallium arsenide (GaAs) workpieces, the interatomic potential energy functions in Ga-Ga, Ga-As, and As-As atoms are described by the Tersoff potential [52 (link)] and the parameters refers to [53 (link)]. The expression of the Tersoff potential function is shown in Equation (1). For the interatomic potential energy function in carbon–carbon (C-C) atoms in diamond polishing particles, the Tersoff potential was employed. The interatomic potential energy functions between carbon (C) atoms in diamond polishing particles and gallium (Ga) or arsenic (As) atoms in GaAs workpieces are governed by the Ziegler–Biersack–Littmark universal screening function (ZBL) potential [54 ]. The expression of the ZBL potential is presented in Equation (2), where the parameter $inner$ is the distance where the switching function begins, and $outer$ is the global cutoff for the ZBL interaction. The parameters $inner$ of Ga-C and As-C are 31.0 and 33.0, respectively. The parameters $outer$ of Ga-C and As-C are 12.0.
$$\left\{\begin{array}{c}E=\frac{1}{2}{\sum }_i{\sum }_{i\ne j}{V}_{ij}\hfill \\ V_{ij}=f_{\mathrm{c}}\left(r_{\mathrm{ij}}\right)[f_{\mathrm{R}}\left(r_{\mathrm{ij}}\right)+b_{ij}{f}_{\mathrm{A}}\left(r_{\mathrm{ij}}\right)]\hfill \end{array}\right.$$
where $V_{ij}$ is the Tersoff potential energy, $f_{\mathrm{R}}$ means the two-body term, $f_{\mathrm{A}}$ means the three-body term, $f_{\mathrm{C}}$ means the cutoff of the coefficient.
$$V_{\mathrm{ij}}=\frac{1}{4\pi {\epsilon }_0}\frac{Z_1{Z}_2{e}^2}{r_{\mathrm{ij}}}\varphi (r_{\mathrm{ij}}/a)$$
where $Z_1$ , $Z_1$ are the number of protons in the nucleus, e is the electron charge, ${\epsilon }_0$ is the permittivity of vacuum, and $\varphi (r_{\mathrm{ij}}/a)$ is the universal screening function of ZBL potential.
When evaluating surface residual stresses in polished gallium arsenide (GaAs) workpieces, the von Mises stress was calculated. It was determined based on the atomic stress tensor, taking into account the combined effects of six stress components, as expressed in Equation (3). When considering temperature variations during the nanoscale polishing process, the temperature change was represented using the average kinetic energy expression [48 (link)], as shown in Equation (4).
$${\sigma }_{\mathrm{vm}}\left(i\right)={\left\{\frac{1}{2}\left[\begin{array}{c}{({\sigma }_{xx}\left(i\right)-{\sigma }_{yy}\left(i\right))}^2+{({\sigma }_{yy}\left(i\right)-{\sigma }_{zz}\left(i\right))}^2\hfill \\ +{({\sigma }_{zz}\left(i\right)-{\sigma }_{xx}\left(i\right))}^2+6({\sigma }_{xy}^2\left(i\right)+{\sigma }_{yz}^2\left(i\right)+{\sigma }_{zx}^2\left(i\right))\hfill \end{array}\right]\right\}}^{1/2}$$
where ${\sigma }_{\mathrm{vm}}\left(i\right)$ denotes the von Mises stress, and $\sigma \left(i\right)$ denotes an atomic stress tensor.
$$E_{\mathrm{k}}=(3/2)kT$$
where $E_{\mathrm{k}}$ represents the average atomic kinetic energy, k denotes the Boltzmann constant which is $1.381\times {10}^{-23}\mathrm{J}/\mathrm{K}$ , and T denotes the temperature.