Modeling The Anisotropic Heat Conduction

With the manufacture of electronic devices entering micro-nano scale,the energy density in these devices can be very high,which increases the requirement for heat dissipation.It becomes an urgent problem to be solved on how to improve the ability of heat transport of materials.The anisotropic heat-transport ability of anisotropic materials provides new strategies for heat management in chips.Based on the wide engineering applications of anisotropic materials,it is significant to study the thermal properties,especially the thermal transport properties,of anisotropic materials.For theoretical study on heat conduction of anisotropic materials,though first principle calculation is an accurate tool to compute the thermal properties,it cannot reveal the relation between thermal properties and more fundamental physical quantities directly.So the analytical expressions of thermal properties are given for anisotropic materials,which can connect the physical quantities directly.The anisotropic Debye model has been developed in our previous works to calculate the thermal properties of anisotropic layered materials or chainlike materials.Improvement and important extensions are made to those previous works in this research.Jacobian determinant is used to substitute the integral variables for determining the integral intervals conveniently.The single integral expressions and their analytical expressions in limiting conditions are given in this research for phonon irradiation along arbitrary direction in ab plane.These expressions are used to calculate the thermal boundary conductance when ab plane is perpendicular to the interface.Furthermore,the single integral expressions are given for phonon irradiation along arbitrary direction,which are expected to be applied to the calculation of thermal conductivity of polycrystalline.The anisotropic Debye model has not yet been developed for three-dimensional anisotropic materials with anisotropy in ab plane.Therefore,based on basic assumptions of ellipsoidal iso-energy surface and ellipsoidal first Brillouin zone proposed by previous researchers,the mathematical model is developed which can be used to calculate the thermal properties of three-dimensional anisotropic materials.The double integral expressions are given for the specific heat and thermal conductivity of three-dimensional anisotropic materials.And the single integral expressions are given for phonon irradiation of threedimensional anisotropic materials.The analytical expressions of these properties in limiting conditions are also derived for three-dimensional anisotropic materials in this research.Black phosphorus is a representative three-dimensional anisotropic material.Its thermal properties are calculated and compared with experiments,which verifies that the new model satisfies the requirement of reflecting the anisotropy.So this research provides a method to calculate some crystal-orientation-dependence thermal properties of anisotropic materials.The single or double integral expressions provided improve the speed and accuracy of numerical calculation.The analytical expressions provided reveal the relation between physical quantities directly,help to rediscover the phonon focusing effect in three-dimensional anisotropic materials and offer theoretical guidance for the improvement of heat management and heat control.