Electron States And Light Absorption In Prismatic Wurtzite Nitride Core Shell Nanowires Considering Build-in Electric Fields

Wurtzite nitride core-shell nanowires?CSNW?are important candidates of next generation of optoelectronic devices.Experimentally grown GaN/AlGaN CSNW is usually triangular or hexagonal prism,while there is strong piezoelectric and spontaneous polarization induced built-in electric field?BEF?in[0001]direction.In this paper,firstly,the feasibility of finite element difference method?FEDM?based on effective mass approximation to solve electronic eigen states and energy levels in prismatic CSNW are tested firstly.The results show that the numerical electronic states in GaN rectangular CSNW is well consistent with the analytical solutions in the permitted error range.Then,FEDM is extended to solve the electronic states in triangular and hexagonal GaN/Al_xGa_1-xN CSNW prism by triangular difference grid,and the influence from built-in electric field in triangular prism is also considered further.The results show that:1.Without taking BEF into account,electronic wave functions of ground and the first excited states in triangular GaN nanowire and GaN/Al_xGa_1-xN CSNW prisms have the same geometric symmetry with prism.And two degenerate states are found on the electronic first excited level.2.By taking BEF into account,the descended potential leads to an increased electronic potential energy of electron along the electric field direction in CSNW.It results in to a lower electronic ground state and wider level separation.At the same time,electronic wave packet with a higher peak moves along the opposite direction of BEF due to the enhanced confinement.Besides,a symmetry breaking induced by BEF leads to the elimination of degenerate states on the first excited state.3.In both cases with and without BEF,proportional increase of prism size or separate increase of shell thickness,or increase of Al component in Al_xGa_1-xN shell,all leads to a lower energy level and smaller peak value of corresponding wave functions on the ground and first excited states,as well as a reduction of level spacing.After obtaining the electronic states,light absorption coefficient?AC?of electronic transition from ground state to the first exited state in triangular prismatic CSNW with size and ternary mixed crystal effects are analyzed further,based on Fermi's golden rule.The main conclusions are as follows:4.In both cases with and without BEF,proportional increase of the prism size or separate increase of shell thickness leads to a reduction of electron transition matrix and level spacing.As a result,absolute value of first-order linear,third order nonlinear and the final total optical AC all goes down with a redshift of absorption peak.5.Without taking BEF into account,as Al component of shell increases with prime size fixed,level spacing gets smaller to result in a redshift of absorption peak,and the absolute value of first-order linear,third order nonlinear as well as the total optical AC all decreases.6.In consideration of BEF,as Al component of shell increases,the electronic transition matrix element increases,while the space of energy levels decreases.As a result,first-order linear and third-order nonlinear as well as the total light AC all increases with a redshift of absorption peak.The conclusions of this paper is expected to be helpful for the design of wurtzite nitride CSNW photoelectric devices.