Nanoscale physics

Electron energy in quantum dots with different configurations
Tovstyuk C.C.
Lviv Polytechnic National University. Bandery str. 12, Lviv-79013, Ukraine. 
E-mail: cctovstyuk@gmail.com

In this paper, we compare the electron energіes in quantum dots of different geometrical configurations. These results can be used in many-particle interaction [1,2]. They are also necessary for finding the thermodynamic functions of electron gas. Comparing the obtained results for infinite cubic and spherical quantum dots (CQD and SQD) we see the similar values ​​of the electron energy in them. In particular, for an electron CQD  1 nm3 and a SQD with the diameter  1.4 nm, the largest energy deviations are for the main and first excited states (about 32%.)  For other quantum states (4< n< 32) the deviation does not exceed 16%. Since, in electronic devices people use mainly the very lowest levels of energy, we found SQD with the nearest to CQD results for 4 lowers energies (they differ as 7,5%; 5.3%; 4%:1%, accordingly).   It means that for devices where only several energy levels are used, the geometrical form of QD is not so important as its size, while the difference between the energies contains a multiplier. When analyzing a large number of energy levels, we see the difference in the energy changes in QD of different configurations. We also found different velocity of energy change from level to level. The electron energy in CQD for lower levels is somewhat greater than the energy in SQD. As the number of levels increases, this difference decreases. Starting from level 13, we see an inverse tendency - the domination of energies in SQD over energies in CQD. In this problem we do not get a limit on quantum number l  and have levels 1p,1d, 1f…That is why we get a large number of closely spaced energy levels (with (n,l): (2,1); (1,4); (2,2); (1,5); (3,0)) for SQD. 

1.	Tovstyuk C.C., Tovstyuk K.D., Danylevych O.O. The permutation group theory and electrons interaction // International Journal of Modern Physics B.-2003.-17.-P. 3813-3831.
2.	Buryi O.A., Tovstyuk C.C., Danylevych O.O. Exciton spectra and their renormalization by electron-phonon interaction // Ukr. Phys. Journal.-2005.-50.-P. 1240-1246.