  Recent experimental researches on semiconductors with mobile dopants (SMD)
have reported unconventional hysteretic current-voltage (I-V) curves, which
form dynamically in either one of the two opposite directions, the
counter-figure-eight and figure-eight ways. However the fundamental theory for
the formation of the two directions is still absent, and this poses a major
barrier for researches oriented to applications. Here, we introduce a
theoretical model to explain the origin of the two directions, and find that
the two ways originate from the spatial inhomogeneity of the dopant
distribution in SMD. The counter-figure-eight (figure-eight) way of the
hysteretic curve is obtained when dopants are driven from far from (near) the
Schottky interface to the opposite side in the SMD. This finding indicates that
the directions of hysteretic curve in SMD can be controlled.
