Effect of deposition rate on morphology evolution of metal-on-insulator films grown by pulsed laser deposition

Ag films were grown by pulsed laser deposition on insulating $\mathrm{Si}{\mathrm{O}}_2$ and mica substrates and exhibited a morphological progression beginning with nucleation of three-dimensional islands and culminating in a continuous, electrically conducting film. The rate of advancement through this progression with increasing pulse frequency was studied with experiments and with kinetic Monte Carlo (KMC) simulations. Experiments at 93 and $135°\mathrm{C}$ give exponents of $-0.34$ and $-0.31$, respectively, for the scaling of the electrical percolation thickness with pulse frequency. Simulations predicted an exponent of $-0.34$, in excellent agreement with the experiments. Both of these values agree well with the previously reported analytic value of $-0.33$ for the scaling of the morphology transition thickness with average flux in continuous deposition. Simulations also predicted that data collapse for island density vs amount deposited would be observed for experiments run at the same value of the parameter $B∕f$ at constant amount deposited per pulse, where $B$ is the kinetic rate constant for coalescence and $f$ is the pulse frequency. Measurements of the percolation transition were consistent with this prediction. These findings indicate that the elementary processes included in the KMC simulation—substrate terrace diffusion, irreversible aggregation of hemispherical islands, and two-island coalescence, but neglecting the effects of kinetic energy—are sufficient to explain the behavior observed when the pulse rate is varied at constant kinetic energy.

Figure 1

AFM images of morphological progression of PLD deposited Ag on mica. Scale bars are $1\mu \mathrm{m}$. Principal stages are (a) island growth and coalescence, (b) percolation, and (c) hole filling.

Figure 2

(Color online) Experimental film thickness at electrical percolation transition vs pulse frequency for (a) $135°\mathrm{C}$, (b) $93°\mathrm{C}$, and (c) $40°\mathrm{C}$. The data are well fitted by a power law with a single exponent of about $-0.33$ for (a) and (b). Several power-law fits to the data are provided in (c) as a guide to the eyes. The uncertainty in measured percolation thickness is $\pm 8\%$ for all points.

Figure 3

(Color online) KMC simulations of elongation transition. (a)–(c) Film thickness at elongation transition vs pulse frequency for three different ratios of substrate surface diffusion constant $D$: (a) $D=1.6\times {10}^5{a}^2∕\mathrm{s}$ (fast diffusion), (b) $D=1.7\times {10}^3{a}^2∕\mathrm{s}$ (slow diffusion), and (c) $D=1.0\times {10}^{-2}{a}^2∕\mathrm{s}$ (essentially no diffusion). Other parameters: (a) and (b) $I=0.025$ ML/pulse and $B=500a^4∕\mathrm{s}$. (c) $I=0.01$ ML/pulse and $B=10a^4∕\mathrm{s}$ (diamonds) and $B=1a^4∕\mathrm{s}$ (crosses). (d) Value of $\zeta$ [Eq. (5)] at the moment of the elongation transition, for the conditions of (a)–(c). Panels (a) and (b) adapted from Ref. 15.

Figure 4

(Color online) Data collapse for equal values of $B∕f$. (a) $B∕f=10a^4$ and $D=1.6\times {10}^5{a}^2∕\mathrm{s}$. (b) $B∕f=5a^4$ and $D=1.0\times {10}^{-2}{a}^2∕\mathrm{s}$. Scatter at low pulse number is noise associated with the operation of the island counting algorithm in the absence of a clear minimum below which “small” sizes could be neglected.