Abstract
In this paper by solving Dirac equation, we present an analytical solution to calculate energy levels and wave functions of mono- and bilayer graphene quantum dots. By supposing circular quantum dots, we solve Dirac equation and obtain energy levels and band gap with relations in a new closed and practical form. The energy levels are correlated with a radial quantum number and radius of quantum dots. In addition to monolayer quantum dots, AA- and AB-stacked bilayer quantum dots are investigated and their energy levels and band gap are calculated as well. Also, we analyze the influence of the quantum dots size on their energy spectrum. It can be observed that the band gap decreases as quantum dots’ radius increases. On the other hand, increase in the band gap is more in AB-stacked bilayer quantum dots. Using the obtained relations, the band gap is obtained in each state. Comparing the energy spectra obtained from the tight-binding approximation with those of our obtained relations shows that the behavior of the energies as function of the dot size is qualitatively similar, but in some cases, quantitative differences can be seen. As quantum dots radius increases, the analytical results approach to the tight-binding method results.
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Tamandani, S., Darvish, G. & Faez, R. Analytical Calculation of Energy levels of mono- and bilayer Graphene Quantum Dots Used as Light Absorber in Solar Cells. Appl. Phys. A 122, 37 (2016). https://doi.org/10.1007/s00339-015-9547-8
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DOI: https://doi.org/10.1007/s00339-015-9547-8