Co diffusion in the near-surface region of Cu

We present our experimental and theoretical study on Co diffusion in the first few atomic layers of Cu(001). While the diffusion of Co atoms in Cu(001) is usually expected to be intense at a temperature $T\ge 800$ K, in the vicinity of the surface, it is already activated at a considerably lower temperature $T\sim 650$ K whereas the diffusion in the deep bulk region is still inhibited. This intense near-surface diffusion provides an accumulation of Co atoms in the first six atomic layers upon a single stage Co deposition. The details of the near-surface diffusion are studied by analyzing the distribution of the location depth of the buried single Co atoms. The depth of location of single Co atoms is deduced from scanning tunneling microscopy (STM) data. The subsurface Co atoms induce a perturbation of the electron density of states of the surface which is observable as apparent ringlike ripples in the STM images of the atomically flat Cu surface. The depth of location of the buried Co atoms is determined from the diameter of those rings. The largest amount of Co atoms is found to be in the third layer, emphasizing that the near-surface diffusion should be described by diffusion parameters different from those for bulk diffusion. A model that describes the embedding process of Co atoms into Cu(001) layers is developed. The model assumes Co atoms to diffuse via the vacancy and ring-exchange mechanisms. The energy barriers for the interlayer Co diffusion via those mechanisms are calculated using the nudged elastic band method. The model satisfactorily explains the experimental results. Our study reveals that the energy barriers for Co diffusion in the first five atomic layers of Cu(001) are lower than those in the bulk. This defines the region in which Co diffusion should be considered as a near-surface one.

Figure 1

(a) The topographic map of the Cu(001) surface, $15\times 15n{m}^2$, after the deposition of Co at 650 K. The areas with different contrasts are two atomically flat terraces. (b) The surface profile along the line in (a). A single atomic step between the atomically flat terraces is shown in the image.

Figure 2

(a) The ringlike ripples observed in the STM images of the atomically flat terraces after the deposition at 650 K. The arrows show rings with different diameters, corresponding to different location depths of the single Co atoms. The image shows an area of $6.25\times 4.06n{m}^2$. The tunneling set point is ($-0.15$ V,1 nA). (b) The simulated illustration of the relation between the depth of a buried Co atom, $z$, and the diameter of the ripple above it, $d$. The Co atom is represented by the dark blue sphere.

Figure 3

The distribution of the location depth of Co atoms in Cu(001), deduced by analyzing STM data, where Eq. (2) has been implemented. Different symbols and colors (blue-filled triangles and black-filled squares) represent distributions obtained from different samples that were fabricated with a similar procedure. The horizontal error bars across the symbols show the standard deviation of the data distribution. The vertical ones represent the uncertainty of the relative counting frequency as derived from the counting uncertainty. The red-filled circle (pointed by the arrow) is an auxiliary point, showing the estimated depth of the center of atoms in the first atomic layer. The top of the horizontal axis presents the Cu(001) layers to which the depth is attributed. (Inset) The histogram of the distribution of the diameter of the apparent ringlike ripples. The diameters show a clustering around averaged values shown by the numbers above each cluster. The data presented by the histogram were analyzed to obtain the distribution presented by the blue-filled triangles.

Figure 4

The illustration of the diffusion via the vacancy mechanism. The Co atom is represented by the blue sphere while the Cu atoms by the orange ones. (a) A Co atom jumps into a vacancy. (b) A simultaneous shift of two neighboring atoms (a Co-Cu dimer) due to a vacancy jump.

Figure 5

The illustration of the migration of a Co atom via the exchange mechanism. The Co atom is represented by the blue spheres while Cu by the orange ones. (a) The exchange between a Co and a Cu atom. (b) The cyclic exchange that involves three atoms. Described by the picture is the cyclic exchange of a Co-Cu-Cu trimer in (111) plane.

Figure 6

The distributions of Co atoms in Cu(100) at 650 K for different time durations as calculated using Eq. (14). The black-filled squares, the red-filled circles, and the blue-filled triangles correspond to the time durations of 30 seconds, 10 minutes, and 55 minutes, respectively. The straight lines are guides to the eyes. (Inset) The calculated concentration of Co atoms in the second (the violet curve) and third (the magenta curve) layers for the first 60 seconds. During this period, the amount of Co in the other layers is negligible. The gray area indicates the time during the deposition. The arrow shows the time when the concentration in the third layer equals to the concentration in the second layer.