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We performed analytical calculations of the current-voltage andstrain-voltage response of the heterostructure like "charged SPM tip electrode/ gap / ionic-semiconductor film" caused by the local changes of (a) ionsconcentration (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 estimationsperformed for correlated oxides show that strength of (c) appeared comparablewith (a,b). For the case of ion-blocking tip and substrate electrode mainly thechanges in holes (electrons) concentration contribute into thevoltage-dependent mechanical displacement of the film surface, directlyregistered by strain SPM. Thus, we predict that the SPM measurements of theionic semiconductor surface displacement could provide important informationabout the local changes of the acceptors (donors) charge state and electron(hole)-phonon correlations via the deformation potential. We obtained the greatvariety of the nonlinear static and dynamic current-voltage and strain-voltagehysteresis loops in the ionic semiconductor thin film with mobile acceptors(donors) and holes (electrons). Some types of the current-voltage hysteresiswith pronounced memory window and double loops are observed experimentally inthe correlated oxides and resistive switching materials like p-La1-xSrxMnO3-dand La1-xSrxCoO3-d, while predicted strain-voltage hysteresis ofpiezoelectric-like and butterfly-like shape requires experimental justificationby SPM.

Strain-voltage and current-voltage Scanning Probe Microscopy (SPM) response of ionic semiconductor thin films: probing of deformation potential