The double-layer criterion, consisting of necessary conditions for the existence of double-layer solutions, is derived for both extended and localized parallel electric fields along converging geomagnetic field lines in the presence of backscattered and trapped electrons. According to the criterion, the parallel electric field is either distributed from ~0.5 RE to less than ~1.5 RE altitudes in the case of an extended double-layer or concentrated in a few Debye lengths at an altitude above ~ 0.5RE but below a few RE in the case of a localized double-layer. The lower limit on the altitude is determined by the supersonic transition altitude of the polar wind. The upper limit is controlled by the number density of the backscattered primary electrons and the electric potential profile near the upper boundary.