In contrast to what has been assumed by Gomer [4], the electron-adatom interaction must not he small. This can change the instant current by an order of magnitude.

However, the form of time dependence of the temporary current correlation function appears to be similar to the one obtained in [4]. The difference is in the values of coefficients in these expressions.

2.3 How and where to use these formulas

The analytical results, presented above, are valid for the diffusion of adatoms independently moving along the flat substrate surface. At a first glance, the account for the lattice structure of the surface could significantly change the resulting equations. However, it is not the case when a large number of adatom sites contribute to a current peak as shown e.g., in Fig 1(a), i.e., the tip is not too sharp. Substituting the flat surface for the lattice is then somewhat similar to substituting the integral for the sum when there are many terms with a slow dependence on their number. In the case when only a few sites contribute to the current peak, Eqs. (7) and (1) could also be applied but to <I> and K(t) averaged over the lateral coordinates of the tip within an area larger than the surface unit cell.

The treatment of random I(t) dependence found from experiment can give the average current, <I>, and the correlation function, K(t). The current through the bare barrier, 7o, coincides with the value of I(t) outside peaks (see Fig. 1(b)). Therefore Io can be directly measured. 'The conventional method make it possible to determine the absolute value of wave numbers in the barrier region, and the width of the tunneling gap, d giving thereby an estimate for Q. Then the values for cf n can be found from K(0); with an estimate for a this gives the adatom density n. The values Dx and Dy might be found by treating the curve K(t)/K(0), using an estimate for Q. However, this is usually too much! We do not need to estimate Q if we are interested only in the activation energies of surface diffusion, but not in pre-exponential factors, if the tipsample configuration is temperature-independent.

2.4 Distinguishing isotropic and anisotropic diffusion

Using the data for K(t) we could distinguish between isotropic and strongly anisotropic (one-dimensional) diffusion: linear i-dependence should be obtained for l/K(t) or l/K(t)2 for isotropic or one-dimensional diffusion, respectively. Alternatively, one may judge the kind of diffusion from the low-frequency spectra: -ln(o) dependence is typical of isotropic diffusion, while l/Ja) is a fingerprint of strongly anisotropic diffusion. These simple recipes can be used to gain this valuable qualitative information.

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