Local structural and compositional determination via electron scattering: Heterogeneous Cu(001)-Pd surface alloy

We have measured the structure and chemical composition of ultrathin Pd films on Cu(001) using low-energy electron microscopy. We determine their local stoichiometry and structure, with $8.5\mathrm{nm}$ lateral spatial resolution, by quantitatively analyzing the scattered electron intensity and comparing it to dynamical scattering calculations, as in a conventional low-energy electron diffraction (LEED)-IV analysis. The average $t$-matrix approximation is used to calculate the total atomic scattering matrices for this random substitutional alloy. As in the traditional LEED analysis, the structural and compositional parameters are determined by comparing the computed diffraction intensity of a trial structure to that measured in experiment. Monte Carlo simulations show how the spatial and compositional inhomogeneity can be used to understand the energetics of Cu-Pd bonding.

Figure 1

Top view (left column) and side view (right column) of CuPd surface structures on Cu(001) at different temperatures. (a) $p(1\times 1)$ Pd overlayer below $173\mathrm{K}$, (b) $c(2\times 2)$ overlayer at room temperature, and (c) $c(2\times 2)$ underlayer above about $423\mathrm{K}$.

Figure 2

$13.1\mathrm{eV}$ LEEM image after a deposition of $\approx 0.6$ ML Pd on Cu(001) at $473\mathrm{K}$. The image shows dendritic islands (one indicated by an arrow) and significant contrast variation near steps. Scale bar: $1\mu \mathrm{m}$.

Figure 3

Sequence of LEEM images recorded during the deposition of Pd on Cu(001) at $473\mathrm{K}$. The electron beam energy was $13.5\mathrm{eV}$ for the images in column (a) and $20.5\mathrm{eV}$ for the images in column (b). The images are labeled by the elapsed deposition time and the total Pd coverage. The marked line in column (a) is used for the near-step heterogeneous structure study. The rectangular area in column (b) is used for the uniform structure study on the terrace. Scale bar: $500\mathrm{nm}$.

Figure 4

Diffraction pattern for clean Cu(001) at $46.2\mathrm{eV}$ measured in the LEEM. The diffuse intensity in the left of the image is due to secondary electrons, which are not filtered out of the image.

Figure 5

(Color online) Measured (solid) and best-fit calculated (dotted) IV curves for clean Cu(001) at $473\mathrm{K}$. The same scaling factor is used for all three beams.

Figure 6

(Color online) Comparison between the (00) beam intensity measured in LEEM (solid), LEED (dash-dotted), and the best fit (dotted) to the LEEM curve.

Figure 7

(Color online) Analysis of the Pd concentration on the terrace (averaged over the white rectangle in Fig. 3). (a) Measured (solid) and computed (dotted) image intensity as a function of electron beam energy at four different Pd coverages. (b) Corresponding time evolution of the Pd concentrations $c_i(i=1,2,3)$ for the first three surface layers. $\mathit{fit}̱c_2$ is the fitting curve of $c_2$ according to Eq. (2) with a flux of $0.9\mathrm{ML}∕\mathrm{h}$. $s̱c_1$ and $s̱c_2$ are simulated uptake curves for $c_1$ and $c_2$.

Figure 8

(Color online) Measured Pd concentration profiles across an advancing step and equilibrated concentration distributions in the first two layers from Monte Carlo simulations. $c_i(i=1,2,3)$ are measured data for the $i\text{th}$ layer. $s̱c_i(i=1,2)$ are the simulated profiles. Each panel corresponds to one deposition time. The chemical potential $\mu$ is shown and $ϵ=-25\mathrm{meV}$. The arrows point to the step edge position.

Figure 9

(Color online) The computed equilibrium structure of an alloy with $c_1+c_2=0.58$, $c_3=0.33$, and $ϵ=-25\mathrm{meV}$. Cu atoms are shown as lighter balls (red online), Pd atoms as darker balls (blue online).

Figure 10

(Color online) Determination of errors in $c_2$ and $c_3$. IV curves at three positions on the line across a step ($A$, $B$, and $C$) are shown at the bottom of each panel. The measured curve is shown as a dark solid line (black online), the best-fit curve is shown as a dotted line, and a computed curve with a worse fit is shown as a gray solid line (green online). The residual ${\mid \Delta I\left(E\right)\mid }^2$ is shown on the top of each panel. The dotted ones are for best-fit data and the solid curves for worse-fit data. The contour plots in the upper right corner of each panel show $R_2$ as a function of $c_2$ and $c_3$. The solid square indicates the values of $c_2$ and $c_3$ for the best-fit point, and the solid circle marks the values for the worse fit. The increment in the $R_2$ contours is 0.005.