An experimentally justified confining potential for electrons in two-dimensional semiconductor quantum dots

We propose a confinement potential for electrons in a two-dimensional (2D) quantum dot that is more physically motivated and better experimentally justified than the commonly used infinite range parabolic potential or few other choices. Because of the specific experimental setup in a 2D quantum dot involving application of gate potentials, an area of electron depletion is created near the gate. The resulting positively charged region can be most simply modeled as a uniformly charged 2D disk of positive background charge. Within this experimental setup, the individual electrons in the dot feel a confinement potential originating from the uniformly positively charged 2D background disk. Differently from the infinitely high parabolic confinement potential, the resulting 2D charged disk potential has a finite depth. The resulting 2D charged disk potential has a form that can be reasonably approximated as a parabolic potential in the central region of the dot (for low energy states of the electrons) and as a Coulomb potential (that becomes zero at large distances). We study the electronic properties of the 2D charged disk confinement potential by means of the numerical diagonalization method and compare the results to the case of 2D quantum dots with a pure parabolic confinement potential.