It has been repeatedly proposed that the electrostatic interaction between electrons in a periodic planar array of polarizable quantum dots can lead to spontaneous polarization as in ferroelectricity or anti-ferroelectricity. This conclusion is not questioned, but some cautionary comments are made. Densely populated metallic dots cannot produce a spontaneous polarization; suitably shaped dots, each with a single mobile electron, can. A spontaneous polarization in an array of limited extent generates a depolarization field arising from the divergence of polarization at the ends of the array. Existing theories ignore this. Ferroelectric polarization cannot arise from identical electronic displacements in an array of dots with a quadratic confinement potential.
