Electrostatic quantum dots with designed shape of confinement potential

In electrostatic (gated) quantum dots, the potential confining the electrons is generated by the electrostatic field, which is created by the external voltages applied to the leads. Changing the geometry of the nanodevice we can obtain a diverse class of confinement potentials. We discuss the choice of the nanodevice parameters, which allows us to get the confinement potentials with the designed shape: from the rectangular potential well to the potential well with smooth edges. In particular, we find the conditions, under which the confinement potential possesses the Gaussian shape or is parabolic in a large region of the quantum dot.