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A comprehensive model is proposed that can be used to select a proper conductive atomic force microscopy (CAFM) probe for use in stable scanning tunnelling microscopy (STM) operation. This type of operation mode could be useful for scanning and patterning heterogeneous surfaces with both conductive and insulating parts using electrical principles in a non-contact fashion. The model includes elastic contact deformation, intermolecular forces, electrostatic attraction and tunnelling current generation between the tip and the sample and the snap-into contact criterion of the probe. Using the model, snap-into contact distances of the probes with varying stiffness values under different bias voltages are found, and is verified with experiments. It is shown that, for a given sample and tip materials, an optimal bias voltage for STM operation with CAFM cantilevers exists. The results also show that, to successfully utilise CAFM probes as STM end-effectors, there is a minimum normal stiffness limit for a given bias voltage. For operation on metal surfaces using metal-coated probes with tip radius values smaller than 50 nm, the model predicts that probes with high stiffness values ( 24 N/m) enable both STM and AFM operations reliably with potential resolution reduction in AFM force sensing. The model also implies that probes with longer tips are better for minimising the electrostatic attraction between the cantilever and the substrate. The model would help researchers to select proper CAFM probes, which could enable simultaneous AFM and STM imaging and manipulation capabilities for tip-based nanofabrication applications.