# Laser Chemical Vapor Deposition (LCVD)

During LCVD, the spot on the substrate under laser irradiation is at a very high temperature (1200 K or higher). Temperature gradients in the source gases will cause natural convection in the chamber. The concentration of the gas mixture near the hot spot on the substrate is affected by the chemical reaction taking place on the substrate. Concentration differences in the chamber become another force driving natural convection in the chamber. For the case of LCVD by a stationary laser beam, Lee et al. (1995) concluded that the effect of natural convection on the thin film deposition rate was negligible and that the heat and mass transfer in the gases were dominated by diffusion. In the SALD process, a laser beam scans the substrate and induces chemical reaction; the resulting product forms a line on the substrate. These lines, formed by multiple laser scans, are subsequently interwoven to form a part layer. To thoroughly understand the effects of various physical phenomena – including natural convection – on the SALD process,

Figure 1: Physical model of Laser Chemical Vapor Deposition.

natural convection during LCVD with a moving laser beam was investigated by Zhang (2003).

The physical model of LCVD under consideration is illustrated in Fig. 1. A substrate made of Incoloy 800 with a thickness of h is located in the bottom of a chamber. Before the vapor deposition starts, the chamber is evacuated and then filled with a mixture of H2, N2, and TiCl4. A laser beam moves along the surface of the substrate with a constant velocity, ub. The initial temperature of the substrate, Ti, is below the chemical reaction temperature. Vapor deposition starts when the surface temperature reaches the chemical reaction temperature. The chemical reaction that occurs on the top substrate surface absorbs part of the laser energy and consumes the TiCl4. A concentration difference is thereby established and becomes the driving force for mass transfer. The physical model of the LCVD process includes: natural convection, heat transfer in the substrate and gases, and chemical reaction, as well as mass transfer in the gases.

The laser beam travels with a constant velocity ub along the surface of the substrate, constituting a typical moving heat source problem. If the substrate is sufficiently large in comparison to the diameter of the laser beam, which has an order of magnitude of 10-3 m, a quasi-steady state occurs. The system appears to be in steady-state from the standpoint of an observer located in and traveling with the laser beam. By simulating LCVD with a moving laser beam in the moving coordinate system, the computational time will be substantially shortened, thereby enabling numerical simulation for a significant number of cases.

Heat transfer in the substrate and gases is modeled as one problem with different thermal properties in each region. In the substrate region, the velocity is set to zero in the numerical solution. The advantage of modeling the heat and mass transfer in the substrate and the gases as one problem is that the temperature distribution in the substrate and gases can be obtained by solving one equation. This eliminates the iteration procedure needed to match the boundary condition at the substrate-gas interface. Since the model geometry is symmetric about the xz plane, only half of the problem needs to be investigated. For a coordinate system moving with the laser beam, as shown in Fig. 1, the laser beam is stationary but the substrate and the chamber move with a velocity -ub. The heat and mass transfer in the substrate and gases is governed by eqs. (1)-(5) $\frac{D\rho }{Dt}+\rho \nabla \cdot \mathbf{V}=0$ and $\rho \frac{D{{\omega }_{i}}}{Dt}=-\nabla \cdot {{\mathbf{J}}_{i}}+{{{\dot{m}}'''}_{i}}\begin{matrix}, & i=1,2,...N-1 \\\end{matrix}$ from Governing Equations of Chemical Vapor Deposition, with buoyancy forces due to temperature and concentration gradients accounted for, but the Soret effect neglected (Zhang, 2003). For the substrate region, the thermal properties are those of Incoloy 800, the substrate material. For the gaseous region, the thermal properties are determined by the individual thermal properties of H2, N2, and TiCl4 as well as their molar fractions [see eq. ($\mu =\sum\limits_{i=1}^{N}{\frac{{{x}_{i}}{{\mu }_{i}}}{\sum_{j=1}^{N}{{{x}_{i}}{{\phi }_{ij}}}}}$) - ($k=\sum\limits_{i=1}^{N}{\frac{{{x}_{i}}{{k}_{i}}}{\sum_{j=1}^{N}{{{x}_{i}}{{\phi }_{ij}}}}}$)]. The mass diffusivity of TiCl4 in the gas mixture is determined by the Stefan-Maxwell equation, using the binary diffusivity of TiCl4 with respect to all other species, which is calculated using the hard sphere model.

The heat flux at the substrate surface due to laser beam irradiation and chemical reaction is expressed as

${q}''=\frac{2P{{\alpha }_{a}}}{\pi r_{0}^{2}}\exp \left[ -\frac{2({{x}^{2}}+{{y}^{2}})}{r_{0}^{2}} \right]-\varepsilon \sigma ({{T}^{4}}-T_{\infty }^{4})+{{\rho }_{TiN}}\Delta {{H}_{R}}{{u}_{b}}\frac{d\delta }{dx}\begin{matrix} , & z=h \\ \end{matrix} \qquad \qquad(1)$

where ΔHR is chemical reaction heat, and dδ / dt is the deposition rate. For a chemical reaction in the order of unity, the deposition rate is expressed as

$\frac{d\delta }{dx}=-\frac{{{\gamma }_{TiN}}{{K}_{0}}}{{{u}_{b}}{{\rho }_{TIN}}}\exp \left( -\frac{E}{{{R}_{u}}{{T}_{s}}} \right){{\omega }_{s}} \qquad \qquad(2)$

where ωs represents the concentration of TiCl4 at the surface of the substrate. The constant K0 in eq. (2) is defined as ${{K}_{0}}={{({{\omega }_{{{H}_{2}}}})}_{i}}{{({{\omega }_{{{N}_{2}}}})}_{i}}^{1/2}K_{0}^{'}$.

The coefficient γTiN in eq. (2) is a sticking coefficient defined as

{{\gamma }_{TiN}}=\left\{ \begin{align} & 1\begin{matrix} \begin{matrix} \begin{matrix} {} & {} & {} \\ \end{matrix} & {} & {} \\ \end{matrix} & {} & {} & T<{{T}_{m}} \\ \end{matrix} \\ & 1+({{T}_{m}}-{{T}_{s}})/({{T}_{M}}-T)\begin{matrix} {} & {{T}_{m}}\le T\le {{T}_{M}} \\ \end{matrix} \\ & 0\begin{matrix} \begin{matrix} \begin{matrix} {} & {} & {} \\ \end{matrix} & {} & {} \\ \end{matrix} & {} & {} & T>{{T}_{M}} \\ \end{matrix} \\ \end{align} \right. \qquad \qquad(3)

where Ts is the surface temperature of the substrate, Tm is a threshold temperature below which the product of the chemical reaction can fully stick to the substrate, and TM is another threshold temperature above which no product of chemical reaction can be stuck on the substrate. If the surface temperature is between Tm and TM, the product of chemical reaction can only be partially stuck on the substrate. The values of Tm and TM are chosen as 1473 K and 1640 K, respectively (Conde et al., 1992).

The boundary conditions of the velocities are

$u=-{{u}_{b}}\begin{matrix} , & v=w=0, & \left| x \right| \\ \end{matrix}\to \infty \qquad \qquad(4)$

$v=\frac{\partial u}{\partial y}=\frac{\partial w}{\partial y}=0\begin{matrix} , & y=0 \\ \end{matrix} \qquad \qquad(5)$

$u=-{{u}_{b}}\begin{matrix} , & v=w=0, & y \\ \end{matrix}\to \infty \qquad \qquad(6)$

(a) P=300W, ub=1.2mm/s
(b) P=360W, ub=1.2mm/s
Comparison of cross-sections (Zhang, 2003)

$u=-{{u}_{b}}\begin{matrix} , & v=w=0, & z=0, \\ \end{matrix}\infty \qquad \qquad(7)$

The governing equations are discretized using the finite volume method (Patankar 1980); the SIMPLEC algorithm (Van Doormaal and Raithby, 1984) was employed to handle the linkage between velocity and pressure. The results show that the effect of natural convection on the shape of deposited film is negligible for the laser power of P = 300 W [see Fig. 2(a)]. When the laser power is increased to 360W, the effect of natural convection on the shape of the cross-section becomes important, although the cross sectional area is almost unchanged [see Fig. 2(b)]. A groove is observed on the top of the deposited film for P = 360 W due to a low sticking coefficient.

Zhang (2004) presented a parametric study on shape and cross-sectional area of the thin film produced by LCVD with a moving laser beam. The effect of natural convection on the LCVD process is neglected because it has little effect on the shapes of deposited film, and it has no effect on the cross-sectional area of the thin film. The effects of laser scanning velocity, laser power, and radius of the laser beam on the shapes of the deposited film were investigated. The results showed that a groove could be observed on the top of the film in conjunction with higher laser power and lower scanning velocity. The cross-sectional area, calculated by

${{A}_{c}}=\frac{2}{r_{0}^{2}}\int_{0}^{\infty }{\delta dy} \qquad \qquad(8)$

at different processing parameters, is shown in Fig. 3. It decreases with increasing scanning velocity. It also increases with increasing laser power and decreasing laser beam radius. The following empirical correlation on the dimensionless cross-sectional area is obtained (Zhang, 2004):

${{A}_{c}}={{a}_{0}}+{{a}_{1}}{{\left( \frac{Bi}{Pe} \right)}^{1.35}} \qquad \qquad(9)$

Figure 4: Dimensionless cross-sectional area vs. scanning velocity

where

${{a}_{0}}=\left\{ \begin{matrix} \text{-2}\text{.136}\times \text{1}{{\text{0}}^{\text{-5}}}+\text{6}\text{.126}\times \text{1}{{\text{0}}^{\text{-6}}}\text{Bi} & {{r}_{0}}=1.0\text{ mm} \\ \text{-9}\text{.206}\times \text{1}{{\text{0}}^{\text{-5}}}+\text{9}\text{.352}\times \text{1}{{\text{0}}^{\text{-5}}}\text{Bi} & {{r}_{0}}=0.8\text{ mm} \\ \end{matrix} \right. \qquad \qquad(10)$

${{a}_{1}}=\left\{ \begin{matrix} \text{8}\text{.343}\times \text{1}{{\text{0}}^{\text{-7}}}+\text{1}\text{.423}\times {{10}^{\text{-5}}}\text{Bi} & {{r}_{0}}=1.0\text{ mm} \\ \text{-2}\text{.587}\times \text{1}{{\text{0}}^{\text{-5}}}+\text{4}\text{.372}\times \text{1}{{\text{0}}^{\text{-5}}}\text{Bi} & {{r}_{0}}=0.8\text{ mm} \\ \end{matrix} \right. \qquad \qquad(11)$

The Biot number and Peclet number are defined as

$\text{Bi}=\frac{{{\alpha }_{a}}P}{\pi {{r}_{0}}{{k}_{s}}({{T}_{c}}-{{T}_{i}})} \qquad \qquad(12)$

$\text{Pe}=\frac{{{u}_{b}}{{r}_{0}}}{{{\alpha }_{s}}} \qquad \qquad(13)$

where αa is the absorptivity of the laser beam on the substrate surface, P is the laser power, r0 is the radius of the laser beam, Tc is the chemical reaction temperature, Ti is the initial temperature of the gases, and ub is the laser scanning velocity. The thermal conductivity ks and the thermal diffusivity αs in eqs. (12) – (13) are those of the substrate (Incoloy) at chemical reaction temperature.

## References

Conde, O., Kar, A., and Mazumder, J., 1992, “Laser Chemical Vapor Deposition of TiN Dot: A Comparison of Theoretical and Experimental Results,” Journal of Applied Physics, Vol. 72, pp. 754-761.

Lee, Y.L., Tompkins, J.V., Sanchez, J.M., and Marcus, H.L., 1995, “Deposition Rate of Silicon Carbide by Selected Area Laser Deposition,” Proceedings of Solid Freeform Fabrication Symposium 1995, pp. 433-439.

Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC.

Van Doormaal, J.P., and Raithby, G.D., 1984, “Enhancements of the Simple Method For Predicting Incompressible Fluid Flows,” Numerical Heat Transfer, Vol. 7, pp. 147-163.

Zhang, Y., 2003, “Quasi-Steady State Natural Convection in Laser Chemical Vapor Deposition with a Moving Laser Beam,” ASME Journal of Heat Transfer, Vol. 125, No. 3, pp. 429-437.

Zhang, Y., 2004, “A Simulation-Based Correlation of Cross-Sectional Area of the Thin Film Produced by Laser Chemical Vapor Deposition with a Moving Laser Beam,” ASME Journal of Manufacturing Science and Engineering, Vol. 126, No. 4, pp. 796-800.