Measurements of Surface Diffusivity and Coarsening during Pulsed Laser Deposition

Pulsed laser deposition (PLD) of homoepitaxial ${\mathrm{SrTiO}}_3⟨001⟩$ was studied with in situ x-ray specular reflectivity and surface diffuse x-ray scattering. Unlike prior reflecivity-based studies, these measurements access both time and length scales of the evolution of the surface morphology during growth. In particular, we show that this technique allows direct measurements of the diffusivity for both inter- and intralayer transport. Our results explicitly limit the possible role of island breakup, demonstrate the key roles played by nucleation and coarsening in PLD, and place an upper bound on the Ehrlich-Schwoebel barrier for downhill interlayer diffusion.

Figure 1

Diffuse x-ray scattering for the PLD of ${\mathrm{SrTiO}}_3⟨001⟩$. (a)–(c) Depositions of $\sim 11\mathrm{ML}$ at $1000°\mathrm{C}$, $790°\mathrm{C}$, $695°\mathrm{C}$, respectively. (d)–(f) The corresponding first ML. Vertical lines represent the laser pulses (first pulse at 5 s). (g)–(i) Scattering line shape at $t=16.5\mathrm{s}$ for each temperature. $I_{\mathrm{fit}}$ (red, solid) consists of $I_{\mathrm{diff}}$ (green, dash-dotted), $I_{\mathrm{spec}}$ (black, solid), and $I_{\mathrm{bg}}$ (black, dashed).

Figure 2

(a) The peak position of the diffuse lobes, $q_0$ (green or gray) and the correlation length, $\xi$ (black) at $850°\mathrm{C}$ are shown for the first ML. Vertical lines represent laser pulses (first pulse at 5 s). (b) $I_{\mathrm{spec}}$ (black) and $I_{\mathrm{isl}}$ (green or gray) are shown. The characteristic diffusion times, ${\tau }_{\mathrm{isl}}$ and ${\tau }_{\mathrm{spec}}$ are determined by fitting $I_{\mathrm{spec}}$ and $I_{\mathrm{isl}}$.

Figure 3

Length scale for diffusion, $L_D^2$ vs ${\tau }_{\mathrm{spec}}$ for $1000°\mathrm{C}$ (●), $850°\mathrm{C}$ (○), 785° (*), and $695°\mathrm{C}$ (□). The linear relationship shows that diffusion is the rate-limiting process.

Figure 4

(a) Arrhenius behavior of the diffusivity at $\theta \approx 0.8\mathrm{ML}$; (inset) ${\tau }_{\mathrm{spec}}$ is obtained from the specular relaxation at high coverage, during interlayer transport. (b) Diffusivity at $\theta \approx 0.25\mathrm{ML}$; (inset) ${\tau }_{\mathrm{isl}}$ is determined by fitting the time evolution of $I_{\mathrm{isl}}$.