Thermomechanical modelling for phonon transport and damping analysis of silicon nano-structure.

摘要

With the technology advancement in fabrication and processing over the past decades, the miniaturization of structures down to nano-scale has been successfully applied in many fields such as high strength automotive parts, ultra-high frequency electromechanical resonators, ultra-light sensors, high efficiency energy harvesting devices and etc. For these applications, the concept of energy efficiency is of particular significance to designing high performance and stability nanoscale electromechanical and thermomechanical systems. Similar to traditional engineering fields, effective computational tools can be extremely useful to investigate the properties and behavior, and to expedite the design process of nano-sized materials and structures. However, the development of these computational tools relies on physical models that accurately describe the fundamental physics of nano-scale systems, for which many classical continuum models of mechanics, transport and thermodynamics are no longer valid. Due to the lack of effective computational tools for nano-scale systems, atom based simulation tools are often adopted. However, atomistic simulations are computationally costly and become infeasible for systems larger than a few tens of nanometers. To tackle these challenges, in this research, we aim to develop thermomechanical models based on phonon theories and study the thermal transport and damping behavior of silicon nano-structures.;In the first part of this research, a computational approach is developed for the calculation of thermoelectric properties of nanoporous silicon. The approach employs a phonon Boltzmann transport equation (BTE) for phonon thermal transport analysis and a non-equilibrium Green's function (NEGF) for electronic transport analysis. The effects of doping density, porosity, temperature and nanopore size on thermoelectric properties of nanoporous silicon are investigated. It is confirmed that nanoporous silicon has significantly higher thermoelectric energy conversion efficiency than its nonporous counterpart. Specifically, this study shows that, with a n-type doping density of 1020 cm-3, a porosity of 36% and nanopore size of 3 nm x 3 nm, the thermoelectric figure of merit of nanoporous silicon can reach 0.32 at 600 K. The results also show that the degradation of electrical conductivity of nanoporous silicon due to the inclusion of nanopores is compensated by the large reduction in the phonon thermal conductivity and increase of absolute value of the Seebeck coefficient, resulting in a significantly improved figure of merit.;In the second part of this research, we study phonon-mediated intrinsic damping in single crystal silicon nano-resonators. In such nano-resonators, phonons are modulated by mechanical strain in both spatial and frequency domains when the strain field varies at ultra-high frequency level and phonon thermal transport is of partial ballistic and partial diffusive nature. The phonon modulation theory explains that the spatial inhomogeneity in the strain field induced by vibration results in internal phonon transport and relaxation, leading to thermoelastic energy dissipation. It also describes the intra-mode phonon scattering due to modulation of phonon frequency by the strain field, hence the Akhiezer dissipation. To account for both, a quasi-continuum thermomechanical (QCTM) model is developed. In the proposed model, the frequency-dependent phonon BTE is adopted and coupled with elasticity via phonon modulation theory. The mathematical model is implemented numerically by using the finite element method (FEM) and finite volume method (FVM). The quality factor of silicon nano-resonators under forced vibration is obtained from the numerical solution of the quasi-continuum model. The quasi-continuum model is validated by comparing the numerical results with those from molecular dynamics (MD) simulations.;In the third part of thesis, the intrinsic damping of silicon resonators is further investigated with focus on the dominant damping mechanisms and applicability of different thermomechanical models at different length scales. At micro-scale, thermoelastic damping is the primary intrinsic damping source and can be effectively described by the continuum thermoelasticity (TE) model which captures strain-induced thermal energy perturbation and re-equilibration through heat transfer along the temperature gradient. At nano-scale, however, the intrinsic damping is caused simultaneously by multiple energy dissipation mechanisms, namely the Akhiezer, thermoelastic and surface damping mechanisms. Acknowledging these, the quasi-continuum thermomechanical model proposed in the second part is adopted to study damping behavior of nano-resonators. Although the QCTM model reduces theoretically and computationally to the continuum TE model when the resonator size increases from nanometers to micrometers, the size limit of the QCTM model is a few hundred nanometers due to its high computational cost. At submicron-scale, transition of the dominant damping mechanisms takes place. The Akhiezer and surface scattering effects diminish in strength when the vibrational frequency reduces and surface-to-volume ratio decreases. For such cases, a gray QCTM model that treats phonon dispersion, transport and relaxation holistically is developed to account for these damping characteristics and at meantime reduce computational cost. The three thermomechanical models are used to perform a scaling analysis and the damping ratio of resonators at various length scales is calculated and compared. The results show that while the QCTM accurately captures the physical behavior, it becomes very time consuming when the resonator length is beyond 100 nm. However, the gray QCTM model, although much more efficient, is shown to be inadequate in the size range of 100 nm to 1 micron, suggesting the details of phonon dispersion and scattering should still be accounted for in this size range. When the size is larger than 1 micron, the gray QCTM and classical TE models give consistent results, indicating that the gray QCTM reduces theoretically and computationally to the classical TE model at this length scale.