Numerical modeling of the plasma plume propagation and oxidation during pulsed laser deposition of complex oxide thin films

Pulsed laser deposition is widely used to synthesize complex oxide thin films with advanced functional properties because of the versatility of the process, although the actual processes and mechanisms that take place are highly dynamic and nontrivial. Detailed understanding of the plume dynamics is required to achieve enhanced control of the growth of complex oxide thin films. However, analytical models of the plasma plume proposed in previous studies, the so-called shockwave model, drag model, and adiabatic thermalization model, only apply to a specific pressure regime and only focus on the propagation of the plasma front. Numerical modeling of the plasma dynamics has previously been pursued for the one-dimensional propagation of a Si plasma plume in a noble background gas. Here we have explored a more generalized numerical model for the dynamics of a ${\mathrm{TiO}}_2$ plasma plume by extending to three dimensions, multiple elements in the plasma plume, and including chemical reactions in an oxygen environment without the use of adaptive parameters, other than used for the description of the initial plume shape. Comparison between the simulations and the self-emission measurements of the ${\mathrm{TiO}}_2$ plasma plume shows good agreement. Our model enables detailed simulation of the oxidation state of the arriving particles (Ti, TiO, and ${\mathrm{TiO}}_2$) on the substrate surface depending on oxygen background pressure. Interestingly, low pressures of about 0.02 mbar result in fast oxygen particles arriving prior to the slower titanium particles, which could significantly influence the oxidation state of the initial substrate surface. The enhanced number of collisions for higher pressures of about 0.1 mbar leads to a large amount of the low-mass oxygen particles coming to a standstill 1–2 cm away from the ablated target. Furthermore, the three-dimensional nature of our model has enabled simulation of the lateral variations in composition of the deposited particles on the substrate surface. Although negligible variations in the Ti:TiO and Ti:${\mathrm{TiO}}_2$ ratios are present for high pressures over deposition areas with diameters up to 5 cm, significant variations can be observed for low pressures. These insights could play an important role in upscaling pulsed laser deposition from a scientific laboratory-based scale to an industrial large-area scale.

Figure 1

Polar grid for the numerical model with $r=0$ and 0.05 m for the positions of target and substrate, respectively.

Figure 2

The distributions of the initial velocities for the titanium and oxygen particles within the ${\mathrm{TiO}}_2$ plasma plume, assumed to be Gaussian distributed. The medians of the distributions were estimated using Eq. (1), while the distribution width is determined from the measured velocities of the center and the front of the visible Ti plasma plumes and is assumed to be equal for Ti and O.

Figure 3

Schematic side (a) and top (b) view of the PLD system with the OES camera setup.

Figure 4

Self-emission measurements of a PLD plume after different time intervals (in $\mu \mathrm{s}$), ablated from a ${\mathrm{TiO}}_2$ target at an oxygen pressure of 0.02 mbar. Locations of substrate and target are indicated by blue and red lines. Experimental (circles) and simulated (line) propagation of the plasma front.

Figure 5

One-dimensional simulation of the distribution of the Ti and O particles within the ${\mathrm{TiO}}_2$ plasma plume at an oxygen background pressure of 0.02 mbar at different times and the specific number of collisions. The colors black, blue, and green represent the number of particles that collided zero, one, or two times, respectively. The red line is the sum of all the particles.

Figure 6

Self-emission measurements of a PLD plume after different time intervals (in $\mu \mathrm{s}$), ablated from a ${\mathrm{TiO}}_2$ target at an oxygen pressure of 0.1 mbar. Locations of substrate and target are indicated by blue and red lines. Experimental (circles) and simulated (line) propagation of the plasma front.

Figure 7

One-dimensional simulation of the distribution of the Ti and O particles within the ${\mathrm{TiO}}_2$ plasma plume at an oxygen background pressure of 0.1 mbar at different times and the specific number of collisions. The colors black, blue, and green represent the number of particles that collided zero, one, or two times, respectively. The red line is the sum of all the particles.

Figure 8

3D simulations of the plasma plume propagation exhibiting the densities of Ti and O particles, integrated over the direction normal to the figure, at 3 $\mu \mathrm{s}$ after ablation for oxygen background pressures of (a) 0.02 and (b) 0.1 mbar.

Figure 9

Time-resolved optical emission spectroscopy of a PLD plume ablated from a ${\mathrm{TiO}}_2$ target at oxygen pressures of 0.02, 0.05, and 0.1 mbar. Spectra are shown for different time intervals (in $\mu \mathrm{s}$), corresponding to propagation distances shortly after ablation from the target, halfway between target and substrate, and directly before arrival on the substrate.

Figure 10

Simulated results of the accumulated amount of particles and their oxidation state arriving at the substrate 18 $\mu \mathrm{s}$ after ${\mathrm{TiO}}_2$ ablation for different oxygen pressures.

Figure 11

Simulated results of the lateral variations in (left) Ti:TiO and (right) Ti:${\mathrm{TiO}}_2$ ratios of deposited particles on the substrate surface for different oxygen background pressures 18 $\mu \mathrm{s}$ after ${\mathrm{TiO}}_2$ ablation. The lines are Gaussian distributions fitted to the simulated data. Inset shows the deposited area as distance ($d$) from the center.