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The influence of the atomic-scale inhomogeneities of the pairing interactionstrength on the superconducting order parameter and the conductance spectrameasurable by STM is studied in the framework of weak-coupling BCS-like theoryfor two-dimensional lattice model. First of all, it is found that theinhomogeneity having the form of atomic-scale regions of enhanced pairinteraction increases the ratio of the local low-temperature gap indifferential conductance spectra to the local temperature of vanishing the gap$2\Delta_g/T_p$. Even in the framework of mean-field treatment this ratio isshown to be larger than the one corresponding to the homogeneous case. It isshown that the effect of thermal phase fluctuations of the superconductingorder parameter can further increase this ratio. Taking them into account inthe framework of a toy model we obtained the ratio $2\Delta_g/T_p$ to be $\sim7-8$. It is found that the additional atomic-scale hopping element disorder andweak potential scatterers, which can also take place in cuprate materials, haveno considerable effect on the statistical properties of the system, includingthe distribution of the gaps, $T_p$ and the ratio $2\Delta_g/T_p$. The secondconsequence of the atomic-scale order parameter inhomogeneity is theanticorrelation between the low-temperature gap and the high-temperaturezero-bias conductance. The obtained results could bear a relation to recent STMmeasurements.

Influence of the atomic-scale inhomogeneity of the pair interaction on extracted from the STM spectra characteristics of high-$T_c$ superconductors