Stress Analysis Of AlN Crystal Prepared By PVT Method

As a representative of the third generation semiconductor materials,aluminum nitride（AlN）has a huge application prospect in the field of microelectronics and optoelectronics with excellent characteristics such as wide band gap（6.2e V）,high thermal conductivity,high breakdown field strength,high temperature resistance,and chemical resistance.The physical vapor transport（PVT）method is considered as the most effective method for preparing large-sized AlN single crystals.At present,the size of AlN crystals prepared by the PVT method has reached two inches.The growth temperature of the AlN crystal prepared by the PVT method is very high（over 2400K）and the growth window is narrow,so high requirements are placed on the growth system,especially the substrate material.At present,available substrate materials are mainly high-temperature resistant tungsten,tantalum carbide,and silicon carbide and so on.There are some lattice mismatches and thermal expansion coefficient mismatches between AlN crystals and these substrates.Therefore,these mismatches will inevitably lead to certain stress in the crystal during the process of growing temperature cooling to room temperature,which will affect the crystal quality and even cause crystal cracking in severe cases.Analyzing and predicting the stress correctly is important for the optimization of the experimental process of AlN crystal,the breakthrough of high-quality,large-sized of AlN crystal,and the commercial application of it.In this paper,the finite element analysis and Raman scattering spectroscopy analysis are used to study the stress distribution of AlN crystal prepared by the PVT method in both theoretical simulation and experimental research,including the following two aspects:1.We set up a three-dimensional model and then use the finite element method to study the stress distribution of AlN crystals under different conditions.First,a three-dimensional finite element model of AlN crystal was constructed by using ABAQUS finite element analysis software.Then,the effects of these factors on the stress distribution of AlN crystals,such as tungsten substrate material,crystal growth thickness,adjacent crystal growth and its growth direction,and different temperatures in the cooling section were explored.The simulation results show that when the most commonly used tungsten substrate is used to prepare AlN crystal,the contact surface between the crystal and the substrate will show a tensile stress state,and the stress value in the edge region of the crystal will be greater than that in the center region.The stress value in the corner region of the edge will reach the maximum.When the stress value exceeds the yield strength of the crystal,it will cause plastic deformation of the crystal,which is likely to cause cracks.As the crystal growth thickness increases,the stress on the crystal growth surface will gradually decrease along the growth direction,showing a transition from tensile stress to compressive stress.Adjacent crystals are usually found around the crystal.When their growth orientation is the same and the growth distance between them decreases,the stress value at the interface between the crystal and the substrate will increase.When the crystal and adjacent crystals have different growth orientations,the stress value of the crystal is smaller than that when the crystal and the adjacent crystal grow in the same orientation.By analyzing the stress of AlN crystals at different temperatures in the cooling section,it is found that when the temperature is reduced uniformly,the crystal stress will increase first,and the crystal stress will reach the maximum when the temperature is around 1500K.And then the stress begins to decrease until the crystals cool to room temperature.The above analysis conclusions can provide theoretical guidance for experimental process optimization of AlN crystals.During the crystal growth process using tungsten substrate,the growth of adjacent crystals should be avoided,especially the co-growth of adjacent crystals.At present,the uniform rate cooling method is generally used in the cooling stage.According to the stress distribution characteristics of AlN crystal in different cooling sections and the stress change rate,a four-step cooling method is proposed.2.We can analyze the stress of AlN crystal by Raman scattering spectrum measurement.Based on the relationship between Raman shift and stress,combined with the finite element analysis conclusions,stress analysis was performed on AlN single crystal and single wafer prepared by PVT method.By calculation,the biaxial stress σ_⊥that perpendicular to the c-axis of the AlN single crystal is about 0.15 GPa,indicating that the crystal is in a tensile stress state on the growth surface,and the uniaxial stress σ₂₂along the c-axis direction is -0.615 GPa,indicating that the crystal appears compressive stress in the growth direction.At the same time,by characterizing Raman spectra of planes with different thicknesses of AlN single wafers,extracting the displacement corresponding to the E₂（high）Raman peak,combined with the Raman shift distribution chart,it can be shown that the stress value in the edge area of the wafer is greater than the center area of the wafer.The stress on the bottom surface of the wafer as a whole is greater than the stress on the upper surface of the wafer.The analysis results of Raman scattering spectra are also consistent with the conclusions of theoretical simulations.In this paper,combined with finite element analysis and Raman scattering spectroscopy,the theoretical simulation and measurement analysis of AlN crystals prepared by PVT method are carried out to reduce the residual stress of AlN crystals prepared by PVT method and provide a theoretical basis for the optimization of the experimental process of preparing AlN crystals.Thereby,the crystal quality of the large-sized AlN single crystal can be improved.