Nanoscale physics

Electric field effect on photoionization cross-section of hydrogenic impurity in lens shaped quantum dot
Holovatskyi I. V., Holovatsky V. A., Makhanets O. M. 

 Institute of Physical, Technical and Computer Sciences, Chernivtsi National University after Yuriy Fed’kovych. Kotsiubynsky str, 2, Chernivtsi-58002, Ukraine 
E-mail: v.holovatsky@chnu.edu.ua
Epitaxial quantum dots can be made in various forms. In the process of self-assembled growth, quantum dots are often obtained in the form of lenses of different heights [1]. Their geometric shape is close to half of an oblate ellipsoid or a spherical segment. To improve optical and electronic characteristics, they are often doped with impurities. These impurities can change the energy levels of the quantum dots, which affects their properties such as light absorption, fluorescence, and other optical characteristics. Ionization of shallow impurities can be useful in solar cells because it can promote more efficient photon absorption and generation of electron–hole pairs.
In this work, theoretical studies of the influence of a uniform electric field on the optical properties of lens shaped quantum dots are carried out within the framework of two models:  a spherical segment and a hemiellipsoidal model. The energy spectrum and wave functions of the electron at different values of the electric field and the ratio of the height to the width of the quantum dot were obtained. The binding energy of a shallow donor impurity localized on the axis of the quantum dot was calculated. The effect of the electric field on the oscillator strengths of intersubband quantum transitions and the photoionization cross-section of the impurity was studied. The Schrödinger equation was solved using the finite element method with COMSOL Multiphysics Software for both quantum dot models. Good convergence of the results obtained for different geometries of the lenticular quantum dot in the case of the same volume has been demonstrated. In addition, for the hemiellipsoidal model of quantum dots, the calculation was performed using the matrix method on the orthonormal basis of the exact solutions of the Schrödinger equation, obtained in the absence of an impurity and an electric field. The obtained result completely coincides with the result of the numerical solution of the Schrödinger equation using the COMSOL Multiphysics software.

1.	Zhou X, Zhai L, Liu J. Epitaxial quantum dots: a semiconductor launchpad for photonic quantum technologies. Photonics Insights. 2023;1(2):1-31.