First Principles Study Of Energy Bands,Dielectric Properties And Phonon Spectra Of Two-dimensional Transition Metal Dichalcogenides

Since the discovery of graphene in 2004,scientists have been searching for other new types of two-dimensional(2D)atomic crystals.2D compound crystals with a similar hexagonal honeycomb structure such as hexagonal boron nitride(hBN)and transition-metal dichalcogenides(TMDs)started attracting more research attention.While graphene is a semimetal,in terms of electrical conductivity,hBN is an insulator,and TMDs are semiconductors.Also hBN and TMDs are both polar crystals,very different from graphene.While TMDs in bulk form are rich in nature,monolayers and multilayers of a TMD can be made by stripping,dissolving or chemical vapor deposition.Bulk TMDs are centrosymmetric semiconductors with an indirect bandgap.When TMDs are thinned to one layer,interestingly,the monolayers become non-centrosymmetric with a direct bandgap,in which spin and valley are coupled,thus making it possible to control valley and spin by light in valleytronic devices.Monolayer and multilayer TMDs have also other novel properties in mechanics and electronics.In recent years,therefore these semiconductors have emerged as a new type of 2D materials and become a hot topic of experimental,theoretical and also computational studies in condensed matter physics.In electronic devices such as field effect transistors,the electron mobility is a key parameter which sets the upper limit for the operation speed.Recent experiments have however obtained very low mobilities in monolayer TMDs(in the range 1–200 cm²/Vs at room temperature for monolayer MoS₂),which are in fact lower than in the TMD multilayers.Therefore,the multilayers may have advantage over monolayers for next generation transistors.A detailed knowledge of the material properties such as the band structure and dielectric properties are essential and fundamental to the calculation of the mobility due to microscopic electron-phonon scattering.Calculations of energy bands and dielectric constants have been focused on TMD monolayers and bilayers;to the best of our knowledge,however there have been no calculations for multilayer TMDs.In general,the dielectric constants of a 2D TMD calculated from first principles vary with the vacuum layer thickness;this problem has been overcome recently by Laturia et al using the principle of equivalent capacitance,and the accurate and meaningful dielectric constants have been obtained after removing the vacuum layer contribution for monolayer and bilayer TMDs.In this thesis,the electronic and dielectric properties of multilayer TMDs are studied comprehensively based on first-principles calculations.The energy bands,electron effective masses,dielectric constants and susceptibilities,Born effective charges are calculated using the Vienna Ab-initio Simulation Package(VASP),with an emphasis put on how these quantities vary with the number or thickness of the multilayer.As usual a vacuum layer is introduced to perform supercell calculations for the 2D materials.Some interesting results have been obtained and are summarized as follows.The dielectric tensor calculated from the VASP contains the contribution of the vacuum layer,and therefore the values of its elements(i.e.in-plane and out-of-plane dielectric constants)change when the vacuum layer thickens or narrows.To eliminate the vacuum layer effects we use the formulas of Laturia et al and obtained reliable in-plane and out-of-plane dielectric constants which become independent of the vacuum layer.Our caclulation shows these dielectric constants are almost invariable with the layer number.The2 D susceptibility is another useful dielectric property of 2D materials.Due to the local field effects,the 2D in-plane susceptibilities of TMD multilayers are one order of magnitude greater than the out-of-plane susceptibilities.This is because the dipole moments on an ion induced by the local field and macroscopic field are parallel(antiparallel)for in-plane(out-of-plane)polarization.The in-plane susceptibility of an N-layer TMD is equal to the monolayer susceptibility multiplied by N,as the electric field is independent of z,i.e.homogeneous across the multilayer.The outof-plane multilayer susceptibility deviates from the simple N times monolayer susceptibility relation--the deviation increases as the layer number N goes up--probably because of the interlayer van der Waals interactions.The Born effective charge(BEC)tensor is a key quantity in lattice dynamics,measuring the coupling of electrostatic fields and lattice displacements and the splitting between the longitudinal and transverse optical phonon modes(long-range Coulomb interaction).The BEC values can be used to evaluate some lattice dynamical properties with a simple model rather than performing complicated numerical calculations.Our result shows that the in-plane BEC varies little with the number of TMD layers and therefore can be taken as a constant for simple model calculations.The transition metal ions have a negative BEC because valence electron screening of the ion-core potentials is weaker at the Mo atoms(take MoS₂ for example),thus raising their electronegativity and leading to electron transfer from S to Mo atoms.There are large variations with layer number for out-of-plane BEC,possibly because there are mirror charges in the supercell calculations,but unfortunately the current VASP has not dealt with them effectively.Monolayers of MoS₂,WS₂ and hBN have a direct bandgap whereas their multilayers and bulk crystals are semiconductors with an indirect bandgap(hBN is an insulator).The monolayer bandgap and bulk bandgap have a similar value to those in the literature.The effective mass is also a key electronic property apart from the bandgap.A bulk TMD and its multilayers have a very similar electron effective mass for a conduction or valence band,which is very different from that of its monolayers.Such a large effective mass change may be associated with the direct-to-indirect bandgap transition of these semiconductors.The above properties such as dielectric constants,BEC and effective mass,for monolayer and bilayer TMDs we calculated are in agreement with the reported data in the literature.No data of the multilayers are available so far.The results we obtained in this thesis are very useful for the study of electron transport(mobility)and optical properties of hBN and TMDs.Phonon spectra of both acoustic and optical vibrations in monolayer,bilayer MoS₂,WS₂ and MoS₂/WS₂ heterostructure are compared and analyzed in detail.The in-plane optical mode frequencies are increased as the layer number increases.i.e.,from monolayer to bilayer or heterojunction;in particular,the polar modes have a more layer frequency increase(4 %)than the non-polar modes(2%).These are explained in terms of the effects due to van der Waals interactions and long-range Coulomb interactions.