Nanoscale physics
Effect of the electric field and the acceptor impurity on the energy spectrum of spherical quantum dot
I.V. Bilynskyi2, R.Ya. Leshko1, Kh.O. Metsan1 
1 Drohobych Ivan Franko State Pedagogical University, 3 Stryiska Str., 82100 Drohobych, Ukraine.
E-mail: kristik98@gmail.com
2 Kryvyi Rih State Pedagogical University, 54 Gagarin av., 50086 Kryvyi Rih, Ukraine 

Modern nanotechnologies give the opportunity to get various nanoscale objects with different properties. Every time, the use of those nanoobjects leads to improving the operation parameters of different devices. It is very important to control the mentioned properties with high accuracy. Ways to solve this range of problems include the change of the QD size, doping, and applying external fields.
    In this work we propose a model for determining the hole spectrum in the multiband model in the electric field with the presence of acceptor impurity. We investigate a heterosystem where the dielectric permittivity of each layer does not differ. That is why we do not consider the polarization and deformations effects, and we use the average value of dielectric permittivity.
    For the hole and acceptor states we use the multiband effective mass models. For considered nanosystem GaAs/AlxGa1−xAs the Luttinger model with spherical approximation comfortably can be used.
We place the hydrogen impurity at a distance D from the center of the QD. The external electric field Fel is applied to the heterosystem and we considered three cases of electric field directions.
We consider the case of the quantum dot (QD) with the central and off-central acceptor impurities in the electric field. The shift of the impurity from the center also causes the shift of the absorption band into the low-energy region when we applied electric field to a quantum dot. The presence of the impurity in the QD center decreases the energy levels in compare with the case of the impurity absence.
As a result of research, the spectrum of holes in a multiband model in an electric field in different directions is determined. The dependence of the hole energy spectrum on the radius of the quantum dot and the location of the impurity from the center of the quantum dot is shown. The dependence of the energy spectrum of central and non-central acceptor impurity in the electric field and without it is obtained.