Stability of STM at short distances

Because of the existence of force, under certain circumstances, the STM gap becomes unstable. This problem has been studied extensively by Pethica and Oliver (1987) and Pethica and Sutton (1988), using the classical theory of continuum elasticity. In spite of its simplicity, the theory reproduces the basic features of a large number of the observed phenomena. 

As we have discussed in Chapter 7, the force on the entire range of tip-sample distances under normal STM operating conditions can be described by the Morse curve (Slater, 1963)  

Following Pethica and Sutton (1988), the mechanical loop of STM responses to the force and exhibits an elastic deformation. By formally introduce an elastic constant a, the deformation is 

For a well-designed, rigid STM, the deformation takes place predominately near the end of the tip. In this case, the elastic constant a is 

The observed z-piezo displacement is then the sum of 8z = aF and the true tip-sample displacement Bs. Using Equations (8.18) and (8.19), we find 

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Spring motion-demagnifier 274 Springs 244—249, 373—374 allowable stress 374 materials 247 stiffness 374 Stability of STM at short distances 204—207... 

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