Effects of 2D dissipative tunneling in the recombination radiation spectra of interacting quantum dots in an external electric field

Abstract

Background. Quantum dots (QDs) have unique optical properties that have found wide applications in optoelectronics, biology and medicine. The problem of controlling the spectral – luminescent properties of QDs initiated studies of the mechanisms of interaction of QDs with each other and with the surrounding matrix. Such interactions, under certain conditions, can significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The purpose of this work is to study the effect of 2D dissipative tunneling in the QDs - surrounding matrix system, as well as the paired electrostatic interaction of QDs with (А+ + е) impurity complexes, on recombination radiation associated with the optical transition of an electron from the ground state of QDs to a quasi-stationary A+ state in the external electric field. Materials and methods. The interaction of an electron in the ground state of the QDs and a hole localized at the A+ center was considered in the framework of the adiabatic approximation. The dispersion equations determining the dependence of the binding energy of a hole in an impurity complex (А+ + е) in a spherically symmetric QDs on the magnitude of the external electric field and the parameters of dissipative tunneling are obtained within the framework of the zero radius potential model, in the approximation of the effective mass. The spectral intensity of recombination radiation (SIRI) in QDs with an impurity complex (А+ + е) in an external electric field is calculated in the dipole approximation. The effect of the electric field on the ground state of the electron in the QDs was taken into account in the second order of the perturbation theory. Numerical calculations and plotting of graphs were carried out for InSb-based semiconductor quantum dots using symbolic mathematics Mathcad 14 and Wolfram Mathematica 9. The probability of 2D dissipative tunneling was calculated with exponential accuracy for a model 2D oscillatory potential at a finite temperature, taking into account linear interaction with phonon modes of the environment at one time instanton quasi-classical approximation. Results. It is shown that the field dependence of the binding energy of the quasi-stationary A+ state has an oscillating character associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRI curves have a characteristic fracture corresponding to the 2D bifurcation point that occurs when the tunneling modes in the interacting QDs pair change from synchronous to asynchronous. It is established that in the vicinity of the 2D bifurcation point there are irregular oscillations in SIRI associated with the modes of quantum beats when competing trajectories of tunnel transport appear. It is found that the parameters of dissipative tunneling: temperature, frequency of the phonon mode, the constant of interaction with the contact medium, the constant of interaction of QDs, have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in SIRI. Conclusions. Taking into account the interaction of QDs with the surrounding matrix leads to a significant modification of SIRI, which manifests itself in the form of bifurcation points and quantum beats depending on the parameters of dissipative tunneling. Taking into account the paired interaction of QDs with each other by means of hole pushing in (А+ + е) complexes leads to the suppression of recombination radiation with an increase in the constant interaction.

Keywords

• interacting quantum dots
• impurity complex
• zero-radius potential method
• adiabatic approximation
• dipole approximation
• electric field
• dissipative 2d tunneling
• recombination radiation