Lattice Dynamics Simulation Of The Thermal Conductivity Of Silicon Crystals

Silicon crystal is a semiconductor material with good physical properties.Along with the advance of semiconductor device manufacturing technology,integration of semiconductor devices is higher and higher,its thermal effect more serious,it's thermal stability and the reliability of the semiconductor device put forward higher requirements.The thermal conductivity of silicon crystals determines the heat dissipation capacity of the device,so it is closely related to the reliability and thermal stability of semiconductor devices.It can be seen that t.he research on the heat conduction properties of silicon crystals is of great significance for the design and reliable use of semiconductor devices.It has always been used to study the thermal conductivity of materials based on Newton's classical mechanics method,boltzmann transmission equation and classical molecular dynamics simulation.But since the semiconductor devices to the nanometer scale development,make the effect of quantum effects on device performance is more and more obvious,the classic methods ignore the quantum effect,such as low temperature quantum effects obvious situation will bring certain error.Therefore,this paper studies the thermal conduction properties of silicon crystals by using lattice dynamics simulation method considering quantum effects.Based on the framework of lattice dynamics theory,the silicon crystal lattice dynamics matrix is deduced,the lattice dynamics equation is solved,get the silicon crystal lattice vibration eigenfrequency and eigenvectors,and on the basis of calculating the silicon crystal third-order not harmonious potential energy is calculated.In this paper,the third order non-harmonic potential energy is used as perturbation,and the phonon Green function of silicon crystal is deduced,and the iterative formula of phonon spectral line width is obtained by the imaginary part of the Green function pole.By using the iterative formula of the width of the spectral line,the width value of all phonon spectral lines can be obtained only by the iterative calculation of about 10 times.Flux formula is deduced in this article,through hardy energy formula of silicon crystal lattice vibration energy flux,and the use of Green Kubo formula the heat transfer coefficient formula of bulk silicon crystal was derived,based on this,the final S-W model,numerical calculation and correction force constant model,get the silicon crystal heat transfer coefficient changing with temperature,the relationship between numerical calculation and the result was compared with the experiment.al results,the results show that the calculated results based on fixed force constant model than S-W model calculation results more close to the experimental value.Therefore,the modified force constant model can describe the interaction between atoms more accurately than the s-w model.