Abstract
We studied electronic tunnelling through a potential barrier between two quantum wells in one- and two-electron systems numerically. We solved a one-dimensional Schrodinger eigenvalue equation by the QL and finite difference methods. We found that taking E-Ec as the control parameter, where E is the strength of the external electric field and Ec is the tunnelling electric field, power laws apply to the tunnelling probability, the first moment and the second moment for both one- and two-electron systems. We carried out a scaling analysis of the electronic tunnelling problem and found that the amount of increase or decrease in the probability density of electron in each quantum well is scaled. We derived the relationship between the scaling exponents, which agreed with the numerical result. We also found that in the case of two-electron systems, the system energy and the information entropy change discontinuously when an electron tunnels, whereas in the case of one-electron systems, they change continuously in the tunnelling electric field.
Published Version
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