Abstract
Modern semiconductor technology has in recent years made it possible to fabricate ultrasmall structures that confine electrons on scales comparable to their de Broglie wavelength. If the confinement is only in one spatial direction such systems are called quantum wells. In quantum wires the electrons can move freely in one dimension but are restricted in the other two. Structures that restrict the motion of the electrons in all directions are called quantum dots. The number of electrons, N,in a quantum dot can range from zero to several thousand. The confinement length scales R 1, R 2, R 3 can be different in the three spatial dimensions, but typically R 3 ≪ R 1≈ R 2≈ 100 nm. In models of such dots R 3 is often taken to be strictly zero and the confinement in the other two dimensions is described by a potential V with \(V\left( x \right)\to\infty for |x|\to\infty,x =\left( {{x^2},{x^2}} \right) \in {R^2}.\) A parabolic poten-tial, \(V = \frac{1}{2}\omega {\left| x \right|^2}\) is often used as a realistic and at the same time computationally convenient approximation.
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Yngvason, J. (1999). Quantum dots. In: Dittrich, J., Exner, P., Tater, M. (eds) Mathematical Results in Quantum Mechanics. Operator Theory Advances and Applications, vol 108. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8745-8_12
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DOI: https://doi.org/10.1007/978-3-0348-8745-8_12
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