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New Results In Tunnelling And Image Theory

We have reformulated elastic tunnelling theory to avoid WKB approximations, in order to form a complete set of basis functions for calculating the effects of adatoms and surface defects on tunnelling. The method of calculation starts with an exact solution of the tunnelling boundary value problem for a linear potential, and then incorporates image effects by perturbation theory. The exact linear banier solution is in the form of a contour integral representation of the 1-D Schrodinger boundary value problem, using a contour which satisfies the outgoing current boundary condition at infinite distance from the surface. This unperturbed solution is valid at all points from the crystal surface outward, including classical turning points, and can be put into closed form by saddle point methods which become exact asymptotically. The reformulated tunnelling wave function requires using a realistic non-classical nonsingular image "potential", corresponding to clamping the electronic bulk states at the surface. We discuss realistic image potentials for both metals and dielectrics in terms of polarization selfenergy. The role of the effective mass is discussed in the context of virtual excitation Pf clamped electronic states. Differences with the Fowler-Nordheim theory are discussed. Preliminary discussion is given also of adatom effects on tunnelling and the noise spectrum at low frequencies.