Theoretical Study Of Electronic Transport And Photoelectric Properties Of Black Phosphorus And A Generalization Of Formula For Magneto-optical Conductivities In Electron Gas Systems

Since the discovery of graphene,the investigation of atomically thin electronic ma-terials has quickly become an important field of research in condensed matter physics and micro-nano electronics.These newly developed two-dimensional?2D?materials are often of unique and have important electrical,optical,mechanical and thermal prop-erties and have been proposed as advanced materials for new generation of related de-vices.Particularly,black phosphorus has an anisotropic band structure which is dif-ferent from other 2D materials.Recently,few-layer black phosphorus has been used to fabricate field effect transistors.As we know that the transport mobility and on/off ratio are the two main parameters that determine the properties of the field effect tran-sistor.What's more,the electron?hole?-impurity scattering and electron?hole?-phonon scattering can both affect the mobility properties of black phosphorus.At low temper-atures,we mainly consider the electron-impurity scattering effect.From the point of practical application,the investigation of the effect of impurity scattering on the elec-tron transport mobility of monolayer black phosphorus is very essential and significant.In addition,as the black phosphorus has a direct band gap and the band-gap energy is in the visible and infrared regime,which means that black phosphorus can be applied in photoelectric devices.However,the properties of optical conductivity and transmission of monolayer black phosphorus have little focused investigation.It is found that the Drude model can't be used to describe the optical conductivity of thin film made up of nano-structure materials.In order to solve this problem,in 2001,Smith proposed the Drude-Smith model with considering electron backscattering or localization effect.Unfortunately,the Drude-Smith model under magnetic field has not been generated since the Smith's work.Hence,the magneto-optical properties and electron backscattering effect in metal-insulator transition material are not yet studied.In the thesis,we theoretically study the electronic transport and photoelectric prop-erties of monolayer black phosphorus and develop the Drude-Smith model under mag-netic field.Base on the above discussions,the main contents of my thesis are focused on:Firstly,we theoretically study the electronic and transport properties of n-type monolayer black phosphorus at low temperatures.We firstly apply the k · p method to study the band structure of monolayer black phosphorus and energy spectrum and wave function are obtained.The exact energy spectrum and the energy spectrum at long wavelength limit are denoted as Model ? and Model ?,respectively.Then,the density of states,chemical potential?i.e.,Fermi level at zero temperature?and the in-verse screening length are calculated.The Fermi's golden rule is applied to calculate the electronic transition rate for impurity scattering of an electron.The response of the system to the external field is studied via the Boltzmann equation.In order to solve the Boltzmann equation,momentum balance equation is applied.Then the electron trans-port mobilities for monolayer black phosphorus are calculated.From the calculation results,we find that the density of states for Model ? is a unit step function which is much like with that in a parabolic semiconductor based electron gas system.The elec-tron density of states for Model I is a litter larger than that for Model ?.We attribute this behavior of the electron density of states for Model ? to the nonparabolic energy spec-trum.For the Fermi level,the calculation result of Model ? is almost same with Model?.The inverse screening length is a constant for Model ?,which is different from that Model I.The electron mobilities obtained from Model ? and Model ? are both in line with the experimental data.A large anisotropy exists for the mobilities along x direc-tion and y direction.The transport mobility along x direction is always larger than that y direction for various electron densities at a fixed impurity density.This is mainly due to the fact that the effective mass along the x direction is much lighter than that along y direction.We also study the impurity scattering effect on the electron mobilities.It is found that with increasing the impurity density,the electron mobility decreases.Secondly,we study the optical conductivity and transmission in monolayer black phosphorus.The electron-photon interaction Hamiltonian,which is dependent on po-larization direction of the radiation field,is obtained from k · p model.The electronic transition rate induced by electron-photon interaction is calculated by using Fermi's golden rule.The Boltzmann equation is applied to study the response to the external radiation field.For the reason that there is no simple and analytical solution to Boltz-mann equation,so the energy balance equation approach is employed to approximately solve this problem.Then the energy transfer rate for the electron in the conduction band is obtained.With the energy transfer rate we calculate the optical conductance and transmission coefficient.From the calculation results,we find that the optical con-ductivity?transmission?along x direction is always larger?smaller?than that along y direction.The optical conductivity along x direction with a rapid increase is sensitive than that y direction.We also study the optical conductivity at different levels of chem-ical potential.When increasing the chemical potential,the conductivity decrease and the absorption edge has a blue shift.Thirdly,a generalization of Drude-Smith formula for magneto-optical conductivi-ties is represented.The modified longitudinal and transverse current response function with considering an electron in a material may suffer the first and subsequent collisions due to backscattering mechanism are proposed.Then the corresponding longitudinal conductivity ?xx???and transverse conductivity ?xy???can be obtained through the Fourier transformation from current response functions.For sake of demonstration,we take the electron effective mass to be m*= 0.065me and the relaxation time to be?=0.5 ps in the calculations.From the calculation results,we can find that the lon-gitudinal and transverse current response functions oscillate with a frequency ?c,and decay exponentially with increasing time in the presence of the magnetic field.The electronic backscattering effect can change the feature of the time decay.The cyclotron resonance effect can be observed in real part of longitudinal conductivity Re?xx???.In the presence of the backscattering effect with a?0,the cyclotron resonance peak splits into two peaks and the peak position becomes the valley position.When the backscat-tering effect becomes strong,the splitting of the peak for cyclotron resonance becomes more obvious.The presence of backscattering effect does not change the basic features of real part of transverse conductivity Re?xy???.However,a stronger backscattering effect can lead to a higher peak and a deeper valley for Re?xy???.The presence of the backscattering mechanism can change the features of Im?xy???significantly.With de-creasing the coefficient a the valley in Im?xy???around the cyclotron frequency ???c looks deeper.Finally,the magneto-optical Drude-Smith formulas are applied to study the properties of dielectric function of VO₂ in the THz regime.It is found that the backscattering effect changes the features of dielectric function of VO₂ to a great ex-tent.