*3.2. Study of the Effect of the Head-Substrate Deposition Gap on the Deposition Mode*

Using the calculation of the velocity and the pressure obtained in the CFD computation, the concentration of each reactant was calculated along the gap, and more importantly, in the immediate region above the surface of the substrate for different deposition gaps. Figure 3 shows the concentration of the different reactants obtained along the length of the substrate (30 mm).

One can observe that, for a gap of 150 μm, the separation of reactants is well achieved (Figure 3a). In the concentration plot, the colors that represent the concentration of reactants are well separated along the geometry, with dark blue color (i.e., no precursor) below and next to the inert gas inlet channels, thus indicating a well-defined ALD regime. On the other hand, when the deposition gap is increased to 750 μm, the concentration is no longer well defined, as shown by the light blue color in the regions between each precursor. Thus, with this deposition gap, the deposition occurs in CVD regime (Figure 3b). In addition, to clearly compare different deposition gaps, first we plot the concentration of reactants in the carrier gases at the immediate region above the substrate, and then we quantified the amount of "overlap" between the plot of each precursor (indicated by the gray region in Figure 3). Again, a deposition gap of 150 μm shows almost no overlap, whereas a deposition gap of 750 μm clearly shows a much greater overlap.

**Figure 3.** Concentration plot along the immediate region above the substrate for a deposition gap of (**a**) 150 and (**b**) 750 μm. Under each plot, a 2D plot along the whole geometry of the gap is shown, with a color code that corresponds to the concentration of reactants along the whole gap geometry.

Furthermore, in order to quantify the overlap for each deposition gap value, we calculated the ratio between the area under the curve of the overlap (where both reactants are present at the same time represented by the gray region in Figure 3) and the area under the curve of the sum of both concentrations, yielding a "percentage of overlap".

With this approach, further calculations of the percentage of overlap as a function of the deposition gap were made and are shown in Figure 4. This graph shows that, as the gap is increased, the overlap increases as well. Nevertheless, at a deposition gap value of around 750 μm the gases mainly flow out through the sides of the head, rather than being confined on top of the substrate, and therefore there is a change in the slope of the curve and a lower overlap than it would be expected takes place.

**Figure 4.** (**a**) The percentage of overlap, i.e., the percentage in which there exist both reactants at the same time, creating thus a CVD regime reaction on the surface of the substrate; (**b**) The total concentration of all the gases (both separated and overlapped) at the immediate area above the substrate vs. head-surface deposition gap.

Figure 4 also shows a plot of the total concentration of all reactants in the immediate region above the surface of the substrate, as measured by integrating the sum of the concentration of both reactants at the line of the substrate. The concentration reaches a maximum at ~750 μm, which means that, at that deposition gap, the flow is preferentially directed towards the surface of the substrate, rather than at the lateral outflow regions. Nevertheless, the overlap percentage at that deposition gap is ~13%, which indicates the existence of a CVD component taking place. Logically, as the deposition gap increases, the flow tends to be directed to the lateral outflow regions rather than be captured at the injection head exhaust, making the extraction of the surplus of reactants difficult, leading to a release of chemicals to the atmosphere, which should, of course, be avoided.

Study of the CVD Mode as a Consequence of Precursor Crosstalk

On a SALD reactor, reactions take place on the surface of the substrate, thus generating the desired films. Such reactions, in principle through chemisorption, take place as a consequence of the presence of a certain concentration of a reactant above the surface, and this depends on the pressure at each point, and of the substrate surface temperature.

In the case of an ALD deposition, the film deposition happens in two sequential half-reactions on the surface. Each half-reaction is self-limited to the surface sites available. In the case of SALD, if we assume a correct separation of the reactants, a static substrate, and a correct extraction of the reactant surplus, regardless of the time of injection of gases, the concentration of adsorbed reactant molecules in the surface should not be higher than the concentration of available sites. The surface coverage (θ) can be explained with the help of a Langmuir isotherm [18]:

$$\theta = \frac{k\_{ads}P}{k\_{des} + k\_{ads}P} = \frac{(\text{number of occupied sites})}{(\text{total number of sites})}; 0 \le \theta \le 1\tag{2}$$

where *kads* and *kdes* represent, respectively, the rate of adsorption/desorption of the reactant to/from the surface, and *P* is the precursor partial pressure.

Furthermore, the reaction probability depends on the surface coverage, since, as more sites are occupied, the sticking probability β of a reactant diminishes:

$$
\beta = \beta\_0 (1 - \theta) \tag{3}
$$

where β<sup>0</sup> is the "bare reaction probability", given by the intrinsic properties of the reactant. Equation (3) is taken from [19], which also mentions that the saturation time of the reactant (our ALD precursor in this case) is inversely proportional to the precursor pressure and to β0.

In contrast to an ALD deposition, in a CVD deposition, the reactants are present in the gas simultaneously, which will induce both a surface chemical reaction, due to both chemisorption and thermal activation of the reaction, and at a lower rate, at the gas phase. In the substrate surface, this CVD reaction will induce a competition among the reactants for the available surface sites. The reactants may react to be chemisorbed or may be desorbed from the surface. To describe this phenomenon, the Langmuir-Hinshelwood reaction rate equation can be used [18]:

$$R\_{\rm AB} = \frac{\mathbf{k}\_{\rm react} \mathbf{K}\_{\rm A} \mathbf{K}\_{\rm B} P\_{\rm A} P\_{\rm B}}{(1 + \mathbf{K}\_{\rm A} P\_{\rm A} + \mathbf{K}\_{\rm B} P\_{\rm B})} \tag{4}$$

where kreact, KA, and KB are reaction constants corresponding to the whole reaction, and to reactant A and B, respectively, and *P*<sup>A</sup> and *P*<sup>B</sup> are the partial pressures of each reactant. To express the partial pressure of each reactant in terms of its concentration, we can assume an ideal gas behavior and express them as:

$$P\_{\mathbf{A}} = \frac{n\_{\mathbf{A}}}{n} P = \,\,\mathbf{x}\_{\mathbf{A}} P \,\,\tag{5}$$

and

$$P\_\mathcal{B} = \begin{array}{c} \frac{m\_\mathcal{B}}{n}P = \ \ x\_\mathcal{B}P \end{array} \tag{6}$$

where *n*<sup>A</sup> and *n*<sup>B</sup> are the numbers of moles of each reactant, *n* is the total number of moles of the solution and *x*<sup>A</sup> and *x*<sup>B</sup> are the partial fractions of each reactant. Hence, substituting in Equation (4), we can obtain:

$$R\_{\rm AB} = \frac{\mathbf{k\_{react}} \mathbf{K\_A} \mathbf{K\_B} \mathbf{x\_A} x\_\mathbf{B} P}{\left(\frac{1}{2} + \mathbf{K\_A} \mathbf{x\_A} + \mathbf{K\_B} x\_\mathbf{B}\right)}\tag{7}$$

In Equation (7), the reaction rate of each reactant is considered, as well as a reaction rate of the reaction as a whole. This equation indicates that the reaction rate is not self-limited and will, therefore, continue as long as there is a non-zero concentration for both reactants. It also implies that if at any point the mass fraction of any of the reactants is zero, the reaction rate will also be zero and hence, no reaction would occur.

With this in mind, several time-dependent simulations were carried out in Comsol Multiphysics® to observe the appearance of a CVD deposition regime for different values of the deposition gap. The surface concentration obtained in such CVD regime is characterized by Equation (1) (Section 2), while the reaction rate *R*AB comes from Equation (7). The pressure and the mass fraction of each reactant are calculated before the time-dependent surface chemistry reaction study, in the laminar flow study presented in Section 3.1, and in the concentration simulation of each reactant in the flow, respectively. As the CVD reaction is not self-limited, such time-dependent simulation was limited to 1 s. The reaction rate used for the CVD surface reaction has a value of 1.5 × <sup>10</sup>−<sup>5</sup> mol·s·kg−1·m−<sup>1</sup> [18].

Figure 5 shows the result of simulations of a time-dependent surface reaction. On top, a plot that corresponds to the amount of ZnO film deposited as a result of CVD taking place is shown. Under each plot, a 2D color plot of the CVD reaction rate can be seen. It is clear that the highest value of reaction rate *R*AB would lead to a thicker, CVD regime deposition. Confirming previous simulations described above, as the deposition gap increases, the diffusion of reactants presents more "overlap" and hence, the reaction rate is higher, leading to a higher CVD component in the process, which in turn yields higher surface concentration as the gap is increased (Figure 5a).

**Figure 5.** Results of the CVD surface reaction on the substrate calculated with a time-dependent multiphysics simulation. The plots shown correspond to the surface concentration that results from different gaps. Under each plot, a surface plot of the CVD reaction rate that corresponds to the plot directly above is shown, with OP and MP representing the outlets of the reactants; (**a**) deposition gap of 750 μm, (**b**) deposition gap of 425 μm, and (**c**) deposition gap of 150 μm.

To obtain evidence of the existence of the CVD and ALD regime with a simple change in gap, depositions of ZnO were made at different values of the gap. Figure 6 shows experimental results as evidence of the ability to modify the growth regime in our SALD system. Figure 6a presents the increase of growth rate as the gap value increases. The values for growth rate are in accordance with those reported for a self-limited (ALD) growth of ZnO [20–22]. The increase of the growth per cycle (GPC) with the gap value confirms the transition from an ALD regime (with small gap values) to a CVD regime (with higher gap values). Figure 6b shows the XRD spectra of ZnO films grown with different gap values for the same number of cycles. The peaks correspond to those of crystalline ZnO and one can observe that, as the gap value increases, the intensity of the peaks increases as well, indicating that thicker films are obtained in the same deposition time as the gap is increased.

**Figure 6.** Experimental results for a deposition of ZnO using di-ethyl zinc (DEZ) and water as co-reactants. (**a**) Growth per cycle (GPC) evolution with different gap values; (**b**) X-ray diffraction patterns for ZnO films grown with different gap values, showing the crystalline peaks corresponding to wurzite ZnO (ICSD #82028).

#### *3.3. Efficiency of the Deposition System Exhaust*

Using the same method described above, the exhaust efficiency was studied. In the geometry of our SALD deposition head, one assumes that all inputs will be directed towards the exhausts and that all surplus of reactant concentration is directed towards the exhausts (empty arrows in Figure 2). Nevertheless, to ensure this, the exhaust outlet must have the same outflow rate as the sum of all the inflow of gases (i.e., mass balance). Failure to achieve this, i.e., due to a bad design or to a partial or total blockage of the exhausts, may induce a CVD regime even with a small deposition gap. We define exhaust efficiency as the efficiency in which the incoming gaseous reactants and by-products are extracted from the reaction zone. A high exhaust efficiency may be achieved by a properly designed outlet/exhaust area ratio, or alternatively with, for example, properly chosen pumping in the exhausts. Here, we use a geometrical approach to such efficiency by calculating the outlet/exhaust area ratio, as explained below.

The result of simulations is shown for different exhaust efficiencies in Figure 7. We quantify an exhaust efficiency as the ratio between the total cross-section area of the exhausts and the total cross-section area of the gas outlets. An ideal ratio would be where the exhaust and the outlet have the same total area, in which case we consider an exhaust efficiency of 100%. As the exhaust efficiency decreases, there is more diffusion of the reactant concentrations, even when the deposition gap is at a "close-proximity" of 150 μm. Interestingly, the diffusion of reactant concentrations has a slightly different behavior in this case than in the case of an increase of deposition gap. As the exhaust efficiency decreases, the CVD reaction rate appears to be more localized. This leads to a localized deposition in the CVD regime, and with time, four overlapped regions appear in localized points over the substrate.

To evaluate the behavior of the exhaust efficiency in real conditions, an experimental "static deposition" was performed to observe the behavior of the real SALD. The deposition head was placed at 150 μm and all flows (precursor, oxidant and separation nitrogen) were injected as usual. The movement of the substrate was suppressed, and the pattern deposited was compared to simulations.

Figure 8 shows a "static deposition" using DEZ as metallic precursor and H2O as the oxidant. The deposited sample shows four well-defined stripes roughly at the location under the oxidant, similar to the plot of the exhaust efficiency of 4.5% shown in Figure 7. The exhaust/outlet ratio measured on the physical exhausts and outlets of the geometry of our SALD system (measured as the ratio of the total cross-section area available for exhaust and the total cross-section area of gas outlets in our deposition head) is 10.1%, which may explain the four lines pattern observed in our "static deposition". In order to improve the exhaust efficiency, one could envision either a change of the geometry of the deposition head or a forced exhaust using a pump. While it should be noted that adding a pump to the system will affect the fluid dynamics in the system, it may substantially change the deposition.

**Figure 7.** CVD regime deposition with different exhaust efficiencies. It can be seen that the exhaust efficiency has a drastic influence on the appearance of CVD regime: with an exhaust efficiency of ∼45%, almost no appearance of CVD regime can be observed, at ∼13% CVD regime appears in some regions, and at ∼4% CVD regime is more pronounced and more localized.

**Figure 8.** Simulation and experimental result of a static deposition experiment made with the SALD set-up at LMGP: (**a**) CVD deposition simulated for an exhaust efficiency of ~4% shown previously in Figure 7, and (**b**) optical photography of the pattern obtained after performing an experimental "static deposition" on a Si substrate with DEZ and H2O; (**c**) Scanning electron microscope (SEM) cross-section image showing a ZnO thickness of ~75 nm for one of the lines in the pattern obtained after a 30 s long "static deposition".

#### *3.4. CVD Regime Influenced by a Tilt in the Deposition Gap*

Finally, the CVD surface reaction was used to assess the influence of a tilt on either the substrate or the head. Since our SALD system uses a "close-proximity" approach where the deposition gap should be around 150 μm, a slight misalignment is expected to affect the distribution of gases (flows and pressures) and thus the deposition and homogeneity of the films. Figure 9 shows a CVD surface reaction of a tilted substrate by 0.3◦.

**Figure 9.** Simulation results for a tilt of 0.3◦: (**a**) Schematic of the rotation of the substrate with respect to the deposition head, about its center point, which leads to a difference of ±75.8 μm on each side of the substrate for a 30 mm length head. Below, the velocity of the flow is shown; (**b**) concentration of reactants above the surface; and (**c**) 2D concentration distribution in the gap. The concentration slightly favors the section with a higher deposition gap, (**d**) surface concentration of a film deposited as a consequence of the appearance of a CVD regime, and (**e**) 2D distribution of the CVD reaction rate.

As it can be seen in Figure 9, the influence of a small tilt can greatly affect the deposition. The 0.3◦ tilt along the middle of the substrate for a 30 mm long deposition head causes a difference of ~75.8 μm at each extreme of the substrate, which changes the effective deposition gap, causing the deposition regime to change locally. Nevertheless, counter-intuitively to what was expected, the CVD reaction rate is higher in the section in which the deposition gap is narrower. This may be explained by the fact that, as the deposition gap decreases, the velocity, and hence the diffusion of the reactants, becomes higher, and the reactants have a higher chance of interacting between them creating a higher CVD reaction rate. As the gap widens, the velocity decreases and the flows are better separated by the nitrogen separation line and the exhausts, reducing the concentration of reactants and therefore the CVD reaction rate.

#### **4. Conclusions**

In the present work, Comsol Multiphysics® was used to study the influence of several geometrical parameters on the deposition regime when using a close-proximity SALD system. We confirmed that the deposition gap is crucial for the determination of an ALD or a CVD deposition regime and studied the influence of the "close-proximity" approach in the fluid dynamics. For a large deposition gap (i.e., larger than ~500 μm), the separation of the flows is not achieved and intermixing of gas concentration appears. CVD regime can, therefore, be tuned simply by changing the value of the deposition gap. Hence, we present a simple and versatile way to tune the SALD deposition process by controlling simple parameters such as the head-substrate gap in the system.

With respect to the CVD surface reaction, simulations were performed to study the CVD reaction rate at the surface of the substrate. Using the intermixing of concentrations calculated, two parameters were considered to determine the CVD reaction rate, and therefore, the CVD surface film formation, namely, the deposition gap and the exhaust efficiency. As expected, as the deposition gap is increased, the CVD reaction rate is also increased, and it gives place to a non-self-limited surface reaction on the substrate. Ina1s simulation, a surface concentration of a film deposited in a CVD regime was plotted and a higher surface concentration was observed with a higher deposition gap. Concerning the exhaust efficiency, the ratio between the cross-section area of the exhausts with respect to the cross-section area of the outlets was investigated since this would define the exhaust efficiency for the surplus of precursor (and by-products of the surface reaction) present at the moment of deposition. Interestingly, with a ratio of 4.5%, well localized intermixing of reactants was formed, leading to a four-stripes deposition pattern that is in accordance with the deposition obtained in a static experiment of a "static-deposition" performed. This would indicate that probably the exhaust efficiency of the current deposition head geometry must consider an exhaust/outlet ratio of less than 10%, which is a value consistent with the real geometry of the deposition head used experimentally. Furthermore, with a precise mechanical design (of the gap and the inlets and exhausts of the deposition head) and with an optimized exhaust pumping, this behavior can be exploited as an approach for a selective area CVD or ALD deposition of materials.

Finally, the influence on a head-substrate tilt was studied. This is important since mis-alignment between the deposition head and the substrate is often difficult to avoid, and doing as such would require high-precision equipment, increasing the complexity of the instrumentation. Simulations show that a slight tilt of only 0.3◦ is enough to change the deposition regime from one side of the substrate to the other. The simulations performed regarding the tilt influence have the aim to show the sensibility of the SALD to the positioning and portray the need of high precision on the system to precisely control the deposition.

The simulations performed in this study justify the need of high-precision and alignment of the geometry used. The parallelism of the system needs to be ensured as much as possible so that the deposition regime can be well controlled. In the current study, no movement of the substrate was studied but the same approach can be readily applied to evaluate the influence of the movement on the deposition regime, as well as on the precision requirements of the geometry.

As observed here, the geometry of the system is crucial to understand and control the deposition of thin films with SALD. With the correct geometry, area-selective deposition of films with properties comparable to ALD deposited films is possible, creating new advantages for SALD such as patterned mask-less film deposition, subsequent depositions for a multi-layer scheme, or a deposition with well optimized flows and concentrations to optimize the usage of ALD precursors.

**Author Contributions:** Conceptualization, C.M.d.l.H. and V.H.N.; Methodology, C.M.d.l.H. and V.H.N.; Validation, J.-M.D., C.J. and D.M.-R.; Investigation, C.M.d.l.H. and V.H.N.; Writing–Original Draft, C.M.H.; Writing–Review & Editing, C.M.d.l.H., V.H.N., J.-M.D., D.B., C.J. and D.M.-R.; Supervision, D.B., C.J. and D.M.-R.; Funding Acquisition, D.M.-R.

**Funding:** This work was benefited from funding from the Consejo Nacional de Ciencia y Tecnología (CONACYT) from Mexico (No. 456558). The authors thank the "ARC Energies Auvergne-Rhône Alpes", for their economic support through a Ph.D. grant, and the Agence Nationale de Recherche (ANR, France) via the project DESPATCH (No. ANR-16-CE05-0021). This work benefited from the facilities and expertise of the OPE)N(RA characterization platform of FMNT (FR 2542, fmnt.fr) supported by CNRS, Grenoble INP, and UGA. DMR acknowledges funding through the Marie Curie Actions (FP7/ 2007–2013, Grant No. 631111). This project was financially supported by "Carnot Energies du Futur" (ALDASH project). This project has received funding from the European Union's Horizon 2020 FETOPEN-1-2016-2017 research and innovation programme under grant agreement 801464.

**Acknowledgments:** The author thanks Dominique De Barros for his support in the development of the SALD system at LMGP.

**Conflicts of Interest:** The authors declare no conflict of interest.
