Research On Pmn2₁-BAlNP By First-principles And Machine Learning

The crystal structure of a compound determines its properties,so it is an important problem to build the mathematical model of the relationship between the crystal structure and the properties.In general,there are two basic methods to deal with this problem:the first-principle calculation and the machine learning method.The first-principle method and the machine learning method infiltrate each other,and some of the parameters needed by machine learning in this paper are derived from the preliminary results of the first principle calculation.The III-V compound semiconductors have very high thermal conductivity,low dielectric constant,low density,high melting point,large bulk modulus,good hardness,good corrosion resistance,and wide band gap.In this paper,the CASTEP program based on the first-principle and machine learning algorithm are used to study orthorhombic BAlNP(denoted as Pmn2₁-B_x Al_1-xN_yP_1-y).The mechanical stability,thermodynamic stability and lattice dynamics stability of several typical structures of Pmn2₁-B_x Al_1-xN_y P_1-y are estimated by CASTEP program.The results show that all the structures are stable.Pmn2₁-B_1-x-x Al_xN is taken as an example to analyze the thermodynamic properties of this series of compounds.In order to obtain the lattice constants of Pmn2₁-B_xAl_1-xN_yP_1-y,it is necessary to perform the structure optimization by the first-principle calculation.Sometimes researchers need to estimate the lattice constants of Pmn2₁-B_xAl_1-x-x N_yP_1-y quickly with only the information of components,the complicated calculation is a great obstacle to it,so it is necessary to find a way to calculate the lattice constants quickly.Similarly,it is sometimes necessary to quickly estimate the mechanical properties of Pmn2₁-B_x Al_1-xN_yP_1-y.In this paper,the data such as lattice constants and elastic properties of Pmn2₁-B_xAl_1-xN_yP_1-y are used as training sets of machine learning.Then,the average absolute percent error（MAPE）of each model is calculated by using7-fold cross-validation,and the lattice constant prediction model and several mechanical characteristic prediction models of Pmn2₁-B_x Al_1-xN_yP_1-y are selected respectively.In this paper,linear regression algorithm is used for modeling lattice constants,GBDT algorithm is used for modeling volume modulus,and Xgboost algorithm is used for modeling shear modulus.On the test sets,it is found that the error is within the acceptable range by comparing the data predicted by the models with the real data.Therefore,the machine learning prediction models of lattice constants,bulk modulus B and shear modulus G have strong generalization ability.The Young’s moduli and its anisotropy of Pmn2₁-B_xAl_1-x-x N_y P_1-y compounds are calculated.It is found that the greater the composition of B and N elements,the greater the Young’s modulus,the greater the hardness,and the more the composition of Al and P elements,and the smaller the Young’s modulus,the smaller the hardness.In addition,the anisotropy of Young’s modulus of AlN_0.25P_0.75 is the smallest and the anisotropy of BN_0.25P_0.75 is the largest.The optoelectronic properties of Pmn2₁-B_xAl_1-x-x N_y P_1-y are calculated by using hybrid PBE0 functional.The direct band gaps are found in AlN,BP,AlP,B_0.25Al_0.75N,B_0.75Al_0.25P,B_0.5Al_0.5P,B_0.25Al_0.75P,AlN_0.75P_0.25,AlN_0.5P_0.5 and AlN_0.25P_0.75.Then,Pmn2₁-B_1-x-x Al_xN is taken as an example to analyze the density of states and optical properties of this series of compounds.Pmn2₁-B_1-xAl_x N has strong B-N or Al-N covalent bonds,so Pmn2₁-B_1-x-x Al_xN is a typical covalent crystal.In addition,with the increase of Al composition,the B-N bond becomes weaker and the Al-N bond becomes stronger.The static dielectric constant along the[001]polarization direction is the highest,while that along the[100]polarization direction is the lowest.In addition,with the increase of x,the static dielectric constant decreases.With the increase of x,the dielectric function of Pmn2₁-B_1-x-x Al_xN decreases,absorption coefficient and Raman intensity are transferred from high frequency to low frequency.The machine learning algorithms and first-principle calculations are used to study Pmn2₁-B_x Al_1-xN_yP_1-y,which provides a theoretical basis for the experimental synthesis of Pmn2₁-B_x Al_1-xN_yP_1-y.It also provides the data of performance characteristics and quantization parameters for the design of wide band gap semiconductor optoelectronic devices based on Pmn2₁-B_x Al_1-xN_yP_1-y.These studies have important practical value for the development of wide band gap semiconductor materials and related devices.At the same time,the lattice constants and some mechanical properties of Pmn2₁-B_xAl_1-x-x N_y P_1-y can be predicted quickly by using the machine learning model built in this paper.