Electron Transmission Across Metal-Graphene Heterojunction

In recent years,with the discovery of the salient physical properties of graphene,a growing number of scientists have participated in the study of graphene.Unlike the well-known semiconductor materials,the electronic property of graphene is unique.This unique electronic structure makes graphene own many physical properties.One of the main topics of graphene research in recent years involved graphene heterostructures whose barriers are generally composed of an external scalar potential or vector potential.In this thesis,we mainly study electron transmission across normal metal-graphene heterojunctions.We focused on strained graphene-metal heterojunctions,and the qualitative discussion of the effects of strain,incident energy,incident angle,effective interface hopping on transmission.The thesis mainly consists of the following two parts:(1)In the framework of nearest neighbor tight-binding approximation,we first obtained the effective Hamiltonian of the 2-D metal(square lattice)and the pristine graphene honeycomb lattice under the condition of the conservation of the longitudinal momentum.Secondly,by establishing the boundary conditions of the pristine graphene-normal metal contact interface,the analytical expression for the reflection coefficient of electrons tunneling through the normal metal-graphene interface(heterojunction)were obtained.The change of the reflection coefficient with the incident angle of the electrons as the electrons pass through the interface of the heterojunction was analyzed through numerical calculations,and then the results were compared with the approximate solution at low energy conditions.The incident angle of the electron has a significant effect on the ability of the electron to tunnel through the interface.It was numerically found that reflectance is not symmetrical about the incident angles,which is in contrast to the case of the graphene-graphene junctions(PN junction).The reflectance attains the minimum value at the incident angle of slightly away from 0°,but greaterthan 0°.The increase of the incident energy and effective interface hopping can alter the incident angles where the reflectance attains the minimum values.(2)In the second part of the thesis,stress was applied upon the graphene side to make the pristine graphene to become strained one.The Schr?dinger equation was employed to calculate the lattice equations and energy expressions satisfied by the strained graphene.Furthermore,based on the boundary conditions of the normal metal-strained graphene model,the analytical expression of the reflection coefficient of the electron at the interface was obtained.The numerical computation based on the analytical results was carried out to study the transmission characteristics of electron in the heterojunction.The maximum transmittance was numerically selected from the transmittances to plot the relationship between the maximum transmittance and parameters of incident angles,strains,incident energy,and effective interface hopping.It was concluded that the introduction of strain into graphene can significantly change the transmission capability of electrons.The transmission capability sensitively depends on the applied strain and the effective interface hopping.The increase in incident energy has minor effect on the electron transmission properties,and even can be neglected,while making the maximum transmission angle(corresponding to the maximum transmittance)subject to the wider range of the effective interface hopping.In addition,the evolution behavior of the real and imaginary parts of the wave function under different strains was numerically investigated.A remarkable effect was found that the increase of the strain applied to the graphene side can increase the period of the wave function on the metal side,which can be interpreted by the longitudinal momentum matching.Through the analytical and numerical analysis,it is believed that these results can be extended to qualitatively study more physical properties,such as,Fano factor,conductance,and shot noise in more complex heterostructures.