Level correlation function

Scanning tunnel microscope image of a smooth silicone surface with a step

The level correlation function is a function that can be used to analyze fluctuations at atomic levels of a surface. The fluctuations arise from the fact that atoms attach to or leave a certain point of the stage through diffusion . Depending on the mechanism of the mass transport on the surface , the step correlation function has a certain dependence on time t or on position y along the step.

The step correlation function is usually determined from measurements with a scanning tunneling microscope (STM). A prerequisite is a sample that has atomically smooth surfaces (terraces). The terraces are separated from each other by steps; Adjacent terraces differ in that the higher terrace has one atomic layer more than the lower one.

If an STM tip is used to repeatedly scan along the same line perpendicular to the edge of the step over a fluctuating step, a so-called pseudo-image is obtained from which the step correlation function G (t) is obtained according to the equation

{\ displaystyle G (t) = <(x (t) -x (0)) ^ {2}>}

where the position of the step edge is currently . The angle brackets mean that the mean value has to be determined over many measurements. ${\ displaystyle x (t)}$ ${\ displaystyle t}$

This function is proportional to if the atoms can leave the step edge relatively easily and diffuse over the terrace, on the other hand proportional to or if these processes are restricted or not possible. In the extreme case, the atoms can only diffuse along one step and not leave it, then applies . ${\ displaystyle t ^ {1/2}}$ ${\ displaystyle t ^ {1/3}}$ ${\ displaystyle t ^ {1/4}}$ ${\ displaystyle G (t) \ propto t ^ {1/4}}$

If you have an image of the surface that was recorded faster than the typical time for the fluctuation of a level, the level correlation function can be determined as a function of the location : ${\ displaystyle y}$

{\ displaystyle G (y) = <(x (y) -x (0)) ^ {2}>}

The direction is in the direction of the (middle) course of the step edge. G (y) indicates how “wavy” the step edge appears when looking at the surface. ${\ displaystyle y}$