Quasi-confined And Propagating Optical Phonons In Cylindrical Wurtzite Core Multi-shell Nanowires And Their Ternary Mixed Crystal Effects

Wurtzite core multi-shell nanowires shows prospects in applications of optoelectronic devices due to their high level of integration and low subthreshold swing.The scattering of carriers from optical phonons is one of the major mechanisms to affect the device performance,and always plays a major role at room temperature.The carriers in nanowire heterostructures tend to be confined in a certain layer because of the two-dimensional quantum confinement.It strengths the interaction between confined optical phonons and electrons.When the material composition close to each other in layers of nanowire,there is scattering from propagating optical phonons to electrons in addition to that from confined phonons.There is no analytical expressions for the electrostatic potential of confined and propagating optical phonons in wurtzite core multi-shell nanowires,due to their complexity of structure and mixed crystal effect.Therefore,a general process of transfer matrix method for these two types of optical phonons is presented in consideration of the mixed crystal effects in this paper.Here is the process.Firstly,the analytical expressions with unknown coefficients for electrostatic potential of the confined and propagating optical phonons in each layer is deduced from Maxwell’s equations,on the ground of dielectric continuum and Loudon’s uniaxial crystal models.Then,according to the continuity conditions of the electrostatic potential and electric displacement along the normal direction at the interface,the relationship of the coefficients of phonon electrostatic potential in adjacent layers is given by transfer matrix.The dispersion relationships of optical phonons are deduced according to the boundary condition.Finally,the electrostatic potentials of the confined and propagating optical phonons are obtained with the frequency solved from dispersion relationships.In this paper,the confined and propagating optical phonons in wurtzite GaN/In_xGa_1-xN/In_yGa_1-yN core multi-shell nanowires are calculated as an example to test the applicability of the transfer matrix method.The requirements of component and frequency for the existence of the phonons,as well as the dispersion relationship and electrostatic potentical and their modification by mixed crystal are discussed in detail.The results show here are at most six types of confined mode optical phonons in wurtzite GaN/In_xGa_1-xN/In_yGa_1-yN core multi-shell nanowires with given component due to the anisotropy of optical phonons in the wurtzite material.The phonons of each mode exist in specific frequency domains,while their dispersion relationship and electrostatic potential in each domain show different characteristics.When the material components of the layers in nanowire are close to each other,here it means x and y are small enough,there is propagating optical phonons which electrostatic potential is oscillating in all layers of nanowire.Based on the transfer matrix method developed in this work,the dispersion relationship and electrostatic potential of the confined and propagating optical phonons in arbitrary wurtzite cylindrical core multi-shell nanowires can be numerically solved.Then the interaction between the two types of optical phonons and electrons can be discussed further to provide a theoretical guidance for analysis and optimization of optical phonon related performance in nanowire devices.