Abstract
Energy level structure and direct light absorption in a cylindrical quantum dot (CQD), having thin falciform cross section, are studied within the framework of the adiabatic approximation. An analytical expression for the energy spectrum of the particle is obtained. For the one-dimensional “fast” subsystem, an oscillatory dependence of the wave function amplitude on the cross section parameters is revealed. For treatment of the “slow” subsystem, parabolic and modified Pöschl-Teller effective potentials are used. It is shown that the low-energy levels of the spectrum are equidistant. In the strong quantization regime, the absorption coefficient and edge frequencies are calculated. Selection rules for the corresponding quantum transitions are obtained.
Highlights
Optical experiments with self-assembled quantum dots (QDs) have demonstrated strong carrier confinement
Note that in the limit case when L1 ! 0 the falciform cross section becomes a segment of a circle and we arrive at the following well-known result: the transitions are allowed between the energy levels having quantum numbers in z-direction nz 1⁄4 n0z; in y-direction, n 1⁄4 n0 and, different parity
In the oscillatory quantum number values, transitions are allowed between the levels either having N 1⁄4 N0 and equal parity quantum numbers, N À N0 1⁄4 2t: Partial reduction of number of selection rules in the case of falciform cross section of cylindrical-well QD is due to oscillatory character of the dependence of wave function’s amplitude (10) on cross section parameters of the QD
Summary
Optical experiments with self-assembled quantum dots (QDs) have demonstrated strong carrier confinement. We suggest a more realistic model of one-dimensional effective potential which we represent in the form of modified Poschl-Teller potential (see Fig. 2) [11, 12] In dimensionless quantities, this potential has the following form: p2n2 kðk À 1Þ kðk À 1Þ e1ðxÞ 1⁄4 VPTðxÞ 1⁄4 L2 À c2ðchðx=cÞÞ2 þ c2 : ð17Þ Here k and c are parameters describing the depth and width of corresponding quantum well, respectively. This potential has the following form: p2n2 kðk À 1Þ kðk À 1Þ e1ðxÞ 1⁄4 VPTðxÞ 1⁄4 L2 À c2ðchðx=cÞÞ2 þ c2 : ð17Þ Here k and c are parameters describing the depth and width of corresponding quantum well, respectively Note that they depend on the quantum number n of the ‘‘fast’’ subsystem. A series of transformations results in the following expressions for the wave function and energy spectrum of CC:
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