  We performed analytical calculations of the current-voltage and
strain-voltage response of the heterostructure like "charged SPM tip electrode
/ gap / ionic-semiconductor film" caused by the local changes of (a) ions
concentration (stoichiometry contribution); (b) acceptors (donors) charge state
(recharging contribution via ionic radius variation); (c) free electrons
(holes) concentration (electron-phonon coupling via the deformation potential).
The contribution (b) into the strain-voltage SPM was not calculated previously,
while the contribution (c) was not even predicted before, while our estimations
performed for correlated oxides show that strength of (c) appeared comparable
with (a,b). For the case of ion-blocking tip and substrate electrode mainly the
changes in holes (electrons) concentration contribute into the
voltage-dependent mechanical displacement of the film surface, directly
registered by strain SPM. Thus, we predict that the SPM measurements of the
ionic semiconductor surface displacement could provide important information
about the local changes of the acceptors (donors) charge state and electron
(hole)-phonon correlations via the deformation potential. We obtained the great
variety of the nonlinear static and dynamic current-voltage and strain-voltage
hysteresis loops in the ionic semiconductor thin film with mobile acceptors
(donors) and holes (electrons). Some types of the current-voltage hysteresis
with pronounced memory window and double loops are observed experimentally in
the correlated oxides and resistive switching materials like p-La1-xSrxMnO3-d
and La1-xSrxCoO3-d, while predicted strain-voltage hysteresis of
piezoelectric-like and butterfly-like shape requires experimental justification
by SPM.
