Figure 2

Three approaches to enhancing electron wave transmission through an example barrier of width \({{w}}_{2}=0.5\,{nm}\) and height \({{V}}_{2}=10\,{eV}\) by adding a pre-barrier of width \({{w}}_{1}\) and height \({{V}}_{1}\). The incident electron energy is \({E}\,=\,8\,{eV}\). For (a) (b) (c), the transmission probability is shown on the right as a function of the thickness of the pre-barrier, and the transmission probability for the “uncoated” rectangular barrier is also shown. (a) Using the optical analogy as previously applied, the pre-barrier has negative height \({{V}}_{1}=-10\,{eV}\) and acts as a potential well, giving a marginal transmission enhancement. (b)The pre-barrier has positive height \({{V}}_{1}=7\,{eV}\) just below the incident electron kinetic energy and gives a significant enhancement of transmission. This case is unexpected in having an unfamiliar optical analogue. (c) The barrier is above the incident electron energy and gives no enhancement of transmission. (d) The maximum transmission probability as a function of the pre-barrier height, illustrating each of the three cases (a–c). ε′ is the real part of the optically analogous permittivity \({\boldsymbol{\varepsilon }}={\boldsymbol{\varepsilon }}^{\prime} +i{\boldsymbol{\varepsilon }}^{\prime\prime} \) for pre-barrier having \({\boldsymbol{\varepsilon }}^{\prime\prime} =0\) for all three cases.