Energy Band Structure And Properties Calculation Of Two-dimensional Materials Based On K·p Method

As an emerging material for nanoelectronics,two-dimensional materials have great application prospects in many areas,such as optoelectronic devices,field effect transistors,and energy sources because of their excellent physical and chemical properties.And they have become the focus of research at home and abroad.Phosphorene is a two-dimensional semiconductor material with suitable band gap and high carrier mobility.It has attracted extensive attention because phosphorene makes up for the lack of zero band gap of graphene and low mobility of two-dimensional transition metal dichalcogenides.The research on the energy band structure of phosphorene is conducive to in-depth exploration and understanding of its optoelectronic properties and the modification of its performance by different methods.The k·p method,as a semi-empirical method for the calculation of energy band structure,extrapolates the energy band structure in the Brillouin zone from the perturbation theory based on some known parameters.It is very suitable for the calculation of energy band dispersion relationship and effective mass near the extreme point.The use of k·p method to calculate the energy band structure of two-dimensional materials is of great significance on expanding its application field.Based on the symmetry of phosphorene space-group,six?eigenstates in the center of Brillouin Zone are selected.According to the perturbation theory and invariant method,non-zero momentum matrix elements are determined,and finally a 6-band k·p matrix model is established.Under the second-order perturbation approximation,the energy band dispersion relationship and effective mass along the armchair and zigzag directions are given.Based on the k·p matrix model parameter values which obtained from first-principle calculations,the energy band structure and electrical properties of the monolayer phosphene are calculated through k·p method,including the constant-energy surface,effective mass and mobility.The results show that the monolayer phosphene is a quasi-direct band gap semiconductor,the bottom of conduction band is located at?point,and top of the valence band is located at the zigzag direction close to?point.In addition,we also reveal the reason for the offset of the top of valence band.The transport characteristics of monolayer phosphene are hole-dominated and exhibit strong anisotropy.The hole mobility in the zigzag direction is as high as 17260 cm²V^-1s^-1.Based on the L?wdin matrix partitioning and Pikus-Bir strain Hamiltonian,a 2-band k·p matrix model which only contains the conduction band and valence band levels and the perturbation matrix induced by strain are established respectively.Based on the uniaxial strain tensor model,the energy band structure of monolayer phosphene under the uniaxial tensile stress along the armchair and zigzag directions is calculated.According to the energy band structure,the energy level offset,band gap width,effective mass and mobility change with uniaxial tensile stress are analyzed.The results show that the uniaxial tensile stress in the armchair direction is more effective against the regulation of the energy band characteristics and can be used in the modification of monolayer phosphene.Furthemore,based on the 2-band k·p matrix model,the energy band structure,effective mass and mobility of few-layer phosphenes are also calculated,and the influence of the number of layers on the energy band properties of phosphene is analyzed.The few-layer phosphenes are direct band gap semiconductors,and not only the band gap width but also the effective mass and mobility show a strong layer dependence.