A Measurement of a Surface Self-diffusion Coefficient by Scanning Tunneling Microscopy

A technique is described to measure a surface self-diffusion coefficient (D) of a metal (gold) by scanning tunneling microscopy. Micro-hills formed on a gold face show a shape evolution by a diffusion transport of kink site atoms. D is determined via a measurement of the hill apex radius as a function of time and includes corrections of image errors. The technique shows that STM can be used to study diffusion and it opens the possibility of measuring diffusion at lower temperatures where D could not be measured previously. 1. I n t r o d u a In scanning tunneling microscopy (STM), changes of the shape of surface structures with time have often been interpreted in terms of rnatter transport by surface self-diffusion /1//2//3//4/. It may be interesting to improve this type of observation in order to develop a technique to determine surface self-diffusion coefficients. Such a technique is described in this paper. As a test example the diffusion coefficient of gold is determined. 2. 9. . f' i 2.1. Basis of the method To determine a surface self-diffusion coefficient by mass transport, two conditions have to be fulfilled : (1) The initial surface shape should be simple in order to facilitate the mathematics of the shape evolution and (2) the driving force should be capillarity, because this force can be determined from measurable geometrical data. Both conditions are fulfilled only in a few cases, specifically, sinusoidal profile decay /5N6/ and the tip blunting technique /7//8//9//15//16/. The STM technique which we will describe can be considered as a new version of the tip blunting technique. The microscope we used is a high stability bimorph STM /12/. The phenomenon of the growth of micro-hills takes place on STM specimens. A hill or tip grows when the horizontal sweep is stopped and the Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989838 -. .--p -l : Shape evolution of a gold tip (hill) with time (300 K). STM micrograp hs. (a) t = 0 (shape 95 minutes after hill formation). (b) t = 174 minutes. voltage is varied in a special manner (details to be described elsewhere, see also /10/). The radius of curvature at the hill apex (summit) increases with time and temperature. In the case of gold tip growth occurs even at 300 K. This increase in tip radius with time can be interpreted as a classical blunting of a conical tip /11//7//9/. The numerical value of the cone angle a, which is between 0 and 10" in classical experiments, is about 45" in the case of the STM hill blunting (Fig.4) (although the apparent angle is only about 15' (Fig.1)). Nevertheless, both shape evolutions are describable by the same equation for the surface diffusion coefficient D /11//7//8//9/ : A, is a known constant which varies with the measurable cone angle a / I l l , y is the mean surface free energy of the solid, R is the atomic volume and v is the number of diffusing atoms per cm2 ( v = R ~ / ~ ) . RI and R2 are the measured tip radii at times t l and t2, respectively. 2.2. lmaae errors and its correction In order to determine hill apex radii (equ.1) three types of corrections are made which concern : (1) profile irregularities, (2) a slope error and (3) the image distortion error. Profile irreaularit ie~ Hill profiles as in fig.1 show many small irregularities. The tip apex radii in equation 1 are mean radii and should not be confounded with the radii of such irregularities. Consequently the profile irregularities can simply be ignored here in a graphical manner (see fig.3 a and b) without a discussion of its origin (probably irregularities of the emitting regions of the STM tip). tip positions to visualize A and B Fia. 2 : Scheme the STM image. 1 1xP-l apparent distance AB / \ '\.--apparent hillprofile real distance \ I '\ of -the STM slope eiror. A distance as AB appears too large in Fia. 3 : Examples of image corrections : a) Profile with irregularities (see fig. 1) (which are probably artefacts). b) The smoothed profile of (a) has an apex radius which is the basis to determine R for equation 1. c) This profile has a typical slope error (see also fig. 1 and 2) : There are two minimum radii somewhat outside the hill apex and the apex radius appears as a maximum. Three arbitrary hill diameters are indicated by e l ,