斜入射时电子穿过石墨烯的透射率问题的分析

Analysis of Transmissivity of Electrons Passing Through Graphene at Oblique Incidence

针对电子斜入射透过石墨烯的问题,以石墨烯层作为势垒,假设势垒宽度为D,势垒高度为V_0,电子从左往右穿过石墨烯层,能量分别设为E_1、E_2、E_3,其中E_1>E_2>E_3;利用薛定谔方程,通过波函数和其一阶导数在x=0和x=D处的连续性条件,进行求解得到斜入射时电子穿过石墨烯的透射率;运用Matlab绘制不同宽度下的透射率,发现透射率的高低与入射角度无关,只与能量有关;入射能量越高,穿过势垒后的能量越大,即透射率越高,同时,势垒宽度越窄,透过的能量也越高;入射能量为0.7倍势垒高度时,透过1倍、2倍、3倍隧道效应长度的透过率分别为势垒高度的55.5%, 32.0%和15.2%。

For analyzing the situation that electron oblique incidence through graphene, it is assumed that graphene layer is as a barrier.The width of the barrier is D and the height is V0.The energies of the electrons that pass through from the incidence layer, the graphene layer, and the transmissive layer are set to E1,E2 and E3(E1>E2>E3).The transmittance of the electrons is obtained by Schr?dinger equation and the continuities of the wave function and its derivative at x=0 and x=D.The figures of the transmissive are drawn using Matlab.The results show us three aspects.The first one is that the transmittance is independent of the incident angle but related to energy.The second one is that the higher the incident energy is, the greater the energy is after passing through the barrier, that is, the better the transmittance.The narrower the barrier width is, the higher the transmission energy is.The third one is that the transmitted energies are 55.5%, 32.0%, 15.2% of the height of the barrier at the widths of the barrier are 1, 2, 3 times of the length of the tunneling effect when the incidence energy is the 0.7 times of the height of the barrier.