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Flexocoupling impact on the size effects of the spontaneous polarization,effective piezo-response, elastic strain and compliance, carrier concentrationand piezo-conductance have been calculated in thin films of ferroelectricsemiconductors with mixed-type conductivity under applied pressure. Analysis ofthe self-consistent calculation results revealed that the thickness dependencesof aforementioned physical quantities, calculated at zero and nonzeroflexoelectric couplings, are very similar under zero applied pressure, butbecome strongly different under the application of external pressure pext. Atthat the differences become noticeably stronger for the film surface undercompression than under tension. The impact of the Vegard mechanism on the sizeeffects is weaker in comparison with flexocoupling except for the thicknessdependence of the piezo-conductance. Without flexoelectric coupling the studiedphysical quantities manifest conventional peculiarities that are characteristicof the size-induced phase transitions. Namely, when the film thickness happroaches the critical thickness hcr the transition to paraelectric phaseoccurs. The combined effect of flexoelectric coupling and external pressureinduces polarizations at the film surfaces, which cause the electric built-infield that destroys the thickness-induced phase transition to paraelectricphase at h= hcr and induces the electret-like state with irreversiblespontaneous polarization at h<hcr. The built-in field leads to noticeableincrease of the average strain and elastic compliance under the film thicknessdecrease below hcr that scales as 1/h at small thicknesses h. The changes ofthe electron concentration by several orders of magnitude under positive ornegative pressures can lead to the occurrence of high- or low-conductivitystates, i.e. the nonvolatile piezo-resistive switching.

Flexocoupling impact on the size effects of piezo- response and conductance in mixed-type ferroelectrics-semiconductors under applied pressure