Buried Pd slows self-diffusion on Cu(001)

Using low-energy electron microscopy, we determine that self-diffusion of the Cu(001) surface is slowed by the presence of a $c$($2\times 2$)-Pd buried surface alloy. We probe surface diffusion using Cu-adatom island-ripening measurements. On alloyed surfaces, the island decay rate decreases monotonically as the Pd concentration is increased up to $\sim$0.5 monolayer (ML), where the $2\times 2$ buried alloy is Pd saturated. We propose that the Pd slows island ripening by inhibiting the diffusion of surface vacancies across terraces. For dilute alloys ($\lesssim$0.2-ML Pd), this conclusion is supported by density-functional theory calculations, which show that surface vacancies migrate more slowly owing to an attraction to isolated buried Pd atoms. The results illustrate a fundamental mechanism by which even a dilute alloy thin-film coating may act to inhibit surface-diffusion-mediated processes, such as electromigration.

Figure 1

Schematic representation of the growth and composition of the $c$($2\times 2$)-Pd buried surface alloy

Figure 2

LEEM characterization of $c$($2\times 2$)-Pd buried surface alloy. The image contrast is sensitive to the surface composition and the electron energy, (a) 14.5 eV and (b) 20.5 eV ($0.4\pm 0.05$-ML Pd, field of $\mathrm{view}=3$ $\mu$m). (c) A schematic drawing identifying various structures on the surface. (d) Intensity-versus-electron energy ($I$-$V$) curves on terraces of the Pd-Cu alloy structure for pure Cu and 0.1-, 0.2-, and 0.4-ML Pd concentrations. The peak at $\sim$20.5 eV grows nearly in proportion to the Pd concentration. (e) $I$-$V$ measurements before and after annealing a 0.4-ML Pd alloy. Pd diffusion into the bulk is tracked by $I$-$V$ measurements. After annealing (1.5 h, 240 ${}^{\circ }$C), the double-peak near 20 eV indicates significant Pd in the fourth layer below the surface.

Figure 3

Decay of a small island isolated on top of a larger island ($T=310{}^{\circ }$C, $e^{-}\mathrm{energy}=2$ eV). (a) LEEM images of the island decay. An arrow points to a defect on the microchannel plate in the imaging system. (b) Area versus time of the small island. The broken blue line is a line fit to the experimental data, shown to emphasize that the island decay in the experiments is nonlinear.

Figure 4

(a) Ripening of a group of islands on the pure Cu(001) surface at $T=240{}^{\circ }$C (field of $\mathrm{view}=1.6$ $\mu$m, $e^{-}\mathrm{energy}=2$ eV). (b) The area-versus-time relationships for all the islands along with the prediction of Eq. (4). Note that larger islands grow in direct response to the decay of relatively smaller islands in the neighborhood.

Figure 5

(a) Decay of isolated islands at various temperatures. The red solid curves are fits by the diffusion-limited model. (b) Temperature dependence of $D{c}^{\infty }$ determined by fitting island decay measurements. The values of $\kappa D{c}^{\infty }$ are calculated from island decay rates given in Ref. 4. Note that $D{c}^{\infty }$ has been shortened simply to $Dc$ on the vertical axis.

Figure 6

Decay of an isolated island on the $0.06\pm 0.03$-ML Pd alloy surface is in the diffusion-limited regime of Eq. (2) ($T=230{}^{\circ }$C, field of $\mathrm{view}=1.6$ $\mu$m, $e^{-}\mathrm{energy}=2$ eV).

Figure 7

Ripening of a small island group on the 0.2-ML Pd alloy surface at $T=240{}^{\circ }$C with fits by Eq. (4). The gray dotted line shows the calculated evolution of islands 3 and 4 (field of $\mathrm{view}=1.6$ $\mu$m, $e^{-}\mathrm{energy}=2$ eV).

Figure 8

Slowing of island decay with increasing Pd concentration. (a) Dependence of $D{c}^{\infty }/D_o{c}_o^{\infty }$ on Pd coverage at $T=240{}^{\circ }$C. Here $D{c}^{\infty }$ is the measured diffusion coefficient, obtained from fits to island-ripening curves, for a given Pd coverage, and $D_o{c}_o^{\infty }(=20000$ s${}^{-1})$ is the rate for the clean surface. The solid lines are the results of our KMC simulation. The red line is the calculated value of $D/D_o$, including only the change in the effective migration barrier and ignoring changes in the vacancy formation energy and concentration $c$. The blue line is the complete result for $D{c}^{\infty }/D_o{c}_o^{\infty }$, including the Pd-coverage-dependent migration barrier and the formation energy. Note that $D{c}^{\infty }$ has been shortened simply to $Dc$ on the vertical axis. (b) Estimate of the change in the activation barrier for island decay versus Pd concentration. The solid lines are the results of our Monte Carlo simulations. The red line includes changes in the effective migration barrier and ignores changes of the vacancy formation energy. The blue line is the calculated value of $\Delta E_a$, including changes in the effective migration barrier and formation energy.

Figure 9

Values of $D{c}^{\infty }$ versus temperature for the pure Cu(001) surface (blue) and the $0.06\pm 0.03$-ML Pd alloy (red). Values from isolated island decays [Fig. 5b] are shown in black along with data from decay of island groups. Note that $D{c}^{\infty }$ has been shortened simply to $Dc$ on the vertical axis.

Figure 10

(Left panel) A DFT optimized vacancy in the outer layer of a Cu(001) film. (Right panel) Midpoint of a vacancy diffusion event, amounting to displacement to a second-layer bridge site of a surface-layer atom initially adjacent to the vacancy.

Figure 11

(Left panel) A DFT optimized vacancy in the outer layer of a Cu(001) film. As the concerted diffusion event proceeds, the dark, second-layer atom, A, will rise, moving northwest, while the light atom, B, moves down to replace it. (Right panel) A geometry close to the transition state, whose energy is 0.63 eV higher than that of the structure shown in the left panel.

Figure 12

(Left panel) A DFT optimized vacancy in the outer layer of a Cu(001) film, adjacent to a second-layer substitutional Pd impurity atom. The Cu atoms are light in color; the Pd atom is dark. Vacancy diffusion in the $-y$ direction amounts to displacement of the Cu atom, labeled A, in the $+$$y$ direction. (Right panel) Midpoint of atom A's minimum energy trajectory. Note that largely because the radius of a Pd atom exceeds that of a Cu by about 0.1 Å, A is displaced into contact with two Cu atoms on the left, in contrast to the symmetric transition geometry of Fig. 10. (Lower panel) A schematic representation of the effective potential for hopping past the Pd site.