How does vacancies in crystal lattice increases electrical conductance?
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1. Introduction:
Because of their abundance in the Earth’s crust and their unique optical, electrical, magnetic, and catalytic properties, silicon- (Si-)based semiconductor materials have been employed for an increasingly wide range of applications. Additionally, with innovative developments in the electronics and microelectromechanical industries as well as light energy conversion devices, Si-related materials have been continually investigated in recent years, and Si-based materials have become the most critical materials for optoelectronic products. As the size of electronic components is continually reduced, the effects of size and surface confinement not only lead to changes in thermal conductivity and electron transport properties, but also produce significant variations regarding optical and mechanical properties. The effects of carrier confinement become especially critical when the size of materials reaches the nanoscale.
Perfect crystal materials do not exist in nature, and defects comprising vacancies and interstices occur in various natural materials. Some of these defects are innate, but others are created during the material manufacturing or processing stages. Microscopic structural defects can cause localized electron density changes and redistribution, induce scattering during the carrier (i.e., electron and phonon) transport processes, and result in changes in thermal conductivity. These effects reduce the mechanical reliability of the material structure and efficiency of electronic circuits, even shortening the lifecycles of system components. Particularly, more significant effects are induced when microscopic defects occur in nanoscale materials, mainly because carriers in the mesoscopic range possess elastic scattering, whereas those in the macroscopic range demonstrate inelastic scattering. When materials are reduced from a macroscopic three-dimensional structure to a smaller dimensional structure (e.g., zero-dimensional nanoparticles and one-dimensional nanowires), changes in the band structure and the density of states (DOS) near the Fermi energy level occur, and the correlation between the phonon dispersion and phonon group velocity is affected. This generates an energy filtering effect, increases the interface scattering of phonons, and causes alterations in the thermal conductivity coefficients of materials.
Recently, various theoretical, numerical, and experimental methods have been employed to investigate the physical properties of Si materials. Dai et al. adopted the lattice kinetic Monte Carlo method to examine the morphological evolution of voids and defects during high-temperature Si crystal growth. Lee et al. combined the Metropolis Monte Carlo method, tight-binding molecular dynamics, and density functional theory (DFT) to investigate interstitial defect growth in crystalline Si. Lysenko and Volz used the scanning probe experimental method to measure the thermal conductivity of porous Si and determined that the thermal conductivity coefficient was significantly smaller than that of bulk single-crystal Si and isotopically pure Si crystals (measured using a steady-state heat flux method). Poter et al. conducted simulations of the phonon dispersion curve and relevant thermal properties of silicon using the Stillinger-Weber, Tersoff, and hybrid potential energy functions. They confirmed that the thermal expansion coefficient, elasticity coefficient, and yield strength values derived from the Stillinger-Weber potential energy function were consistent with experimental values and that the simulated phonon dispersion curve and specific heat approximated those obtained during experiments. Currently, the majority of numerical studies have focused on exploring the properties of perfect Si crystals and nanostructures. However, numerous issues regarding the effects of vacancy cluster (VC) defects on the electrical and thermal properties of Si semiconductor materials require further clarification. Therefore, this study employed first-principle calculations to investigate differences in the electrical and thermodynamic properties between perfect Si crystals and crystals with VC defects. In addition, changes in band structures and DOS were explored, and corresponding relationships between defects and various thermal properties, such as heat capacity (), enthalpy, and free energy, were analyzed.
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