Đang chuẩn bị liên kết để tải về tài liệu:
Silicon Carbide Materials Processing and Applications in Electronic Devices Part 8

Tham khảo tài liệu 'silicon carbide materials processing and applications in electronic devices part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Creation of Ordered Layers on Semiconductorsurfaces An ab Initio Molecular Dynamics study of the SiC 001 -3x2 and SiC 100 -c 2x2 Surfaces 235 where we have introduced the nuclear-nuclear Coulomb repulsion NN R E jst-Rt w Within the framework of KS DFT the force expression becomes FI - Ịdr W0 r ViVext r R - Vi nn R 13 The equations of motion Eq. 10 are integrated numerically for a set of discrete times t 0 At 2At . N At subject to a set of initial coordinates R1 0 . Rn 0 and velocities R1 0 . RN 0 using a solver such as the velocity Verlet algorithm . At2 . RI At RI 0 AtR 0 A- Fi 0 2Mị R I At R I 0 Fi 0 Fi At 14 where FI 0 and FI At are the forces at t 0 and t At respectively. Iteration of Eq. 14 yields a full trajectory of N steps. Eqs. 13 and 14 suggest an algorithm for generating the finite-temperature dynamics of a system using forces generated from electronic structure calculations performed on the fly as the simulation proceeds Starting with the initial nuclear configuration one minimizes the KS energy functional to obtain the ground-state density and Eq. 13 is used to obtain the initial forces. These forces are then used to propagate the nuclear positions to the next time step using the first of Eqs. 14 . At this new nuclear configuration the KS functional is minimized again to obtain the new ground-state density and forces using Eq. 13 and these forces are used to propagate the velocities to time t At. These forces can also be used again to propagate the positions to time t 2At. The procedure is iterated until a full trajectory is generated. This approach is known as Born-Oppenheimer dynamics because it employs at each step an electronic configuration that is fully quenched to the ground-state Born-Oppenheimer surface. An alternative to Born-Oppenheimer dynamics is the Car-Parrinello CP method Car Parrinello 1985 Marx Hutter 2000 Tuckerman 2002 . In this approach an initially minimized electronic configuration is subsequently propagated from one nuclear .