Over the last three decades, molecular dynamics (MD) has become a powerful tool for understanding phonon transport, yet the number and fidelity of comparisons between MD and experiments has been stifled by the lack of availability of empirical interatomic potentials (EIPs) that accurately describe phonons. As a result, the Holy Grail for the MD community has become the development of a methodology that can enable fast, easy and accurate parameterizations of EIPs, to enable direct comparisons to experiments with high fidelity and deeper insights. My colleague Andrew Rohskopf recently developed such a methodology based on genetic algorithm (GA) that uses ab initio inputs. The method is basically based on fitting the EIP to DFT forces on each individual atom in the system, force constants, energy of configuration, and stress on the supercell. An example of an EIP with 50%, 10% and 3% error in forces is shown in the figure 1.
In this work, I collaborated with him to apply the method to different semiconductor materials in order to develop accurate EIP for thermal transport applications. I applied and tested the method to various solids including crystalline Si, Ge, InAs, GaAs, and GaN. The results for Si and Ge are shown in figure 2-5. As seen, excellent agreement between DFT and our developed EIPs are obtained for vibrational properties/phonons and thermal conductivity. The functional forms used here are “Tersoff + Born + Coulomb” (TBC) and “Morse + harmonic 3body + Born + Coulomb” (M3BC). The method can also be applied to disordered solids such as random alloys and amorphous materials to quickly and efficiently create EIPs that can accurately reproduce ab initio forces, energies, and stresses. This new method and its associated insights will close the gap between theory and experiment for phonons and have impacts far beyond, reaching other fields such as the study of defects, chemical reactions, interfaces, surfaces, mechanical properties and many others.
Figure 1| visual representation of different errors in forces. DFT forces (red vectors) are shown on lattice sites and compared to EIP forces (blue vectors) for 50%, 10% and 3% errors in forces from left to right.
Figure 2 | TBC, DFT, and experimental thermal conductivity vs. temperature. (a) Thermal conductivity as a function of temperature for c-Si with DFT, experimental, and TBC POPs. (b), Thermal conductivity as a function of temperature for c-Ge with DFT, experimental, and TBC POPs. The TBC POPs were able to consistently obtain thermal conductivities within 10% of DFT values.
Figure 3 | M3BC, DFT, and experimental8 thermal conductivity vs. temperature. (a) Thermal conductivity as a function of temperature for c-Si with DFT, experimental, and M3BC POPs. (b) Thermal conductivity as a function of temperature for c-Ge with DFT, experimental, and M3BC POPs. While M3BC-3 is within 10% of the DFT thermal conductivity for c-Si, other M3BC potentials were not able to reach this mark. DFT thermal conductivity ± 15% is therefore displayed to show the performance of the M3BC potential for c- Si.
Figure 4 | DFT, and experimental60 phonon dispersion for Ge, along with different POPs. a, DFT (black), M3BC-1 (red), M3BC-2 (blue), M3BC-3 (grey) and experiments (squares) are shown. These EIPs are shown to demonstrate the importance of 2nd order force constants in reproducing correct phonon dispersion. From best to worst agreement in 2nd order force constant error, M3BC-2 ( 5.1×10e-4 Ry/Bohr2 mean absolute error in 2nd order IFCs), M3BC-3 ( 9.7 × 10e-4 Ry/Bohr2 mean absolute error in 2nd order IFCs), and M3BC-1 ( 7.4 × 10e-4 Ry/Bohr2 mean absolute error in 2nd order IFCs) exhibit expected qualitative trends in phonon frequency error, especially at the zone boundaries where flattening is unable to occur. b, DFT (black), TBC-1 (red), TBC-2 (blue), TBC-3 (grey) and experiments (squares) are shown.
Figure 5 | DFT and experimental40 phonon dispersion for Si, along with various POPs. The original Tersoff and Stillinger-Weber potentials are shown as blue and red dotted lines, respectively. (a), DFT (black), TBC-1 (red), TBC-2 (blue), TBC-3 (grey) and experiments(squares) are shown. (b), DFT (black), M3BC-1 (red), M3BC-2 (blue), M3BC-3 (grey) and experiments (squares) are shown.