COMSOL 6.4 - Boat Reactor for Low-Pressure Chemical Vapor Deposition

Boat Reactor for Low-Pressure Chemical Vapor Deposition

Chemical vapor deposition (CVD) is an important step in the process of manufacturing microchips. A common application is the deposition of silicon on wafers at low pressure. Low-pressure reactors such as shown in Figure 1 below are used to get a high diffusivity of the gaseous species, which results in a uniform deposition thickness, because the process becomes limited by the deposition kinetics (Ref. 1 and Ref. 2).

Figure 1: Schematic of a boat reactor and principle of the deposition process.

The gas, in this case silane (SiH4), enters the reactor from the left and reacts on the wafers to form hydrogen and silicon. The remaining mixture leaves the reactor through the outlet on the right. The deposition of silicon on the wafers surface depends on the silane concentration. Further details can be found in Elements of Chemical Reaction Engineering by H. Scott Fogler (Ref. 1).

This example models the coupled reaction kinetics, fluid, and mass transport in a low-pressure boat reactor to describe the rate of deposition as a function of the operating conditions.

Model Definition

Figure 2 shows the modeled domain of the boat reactor which is simplified as a 2D axisymmetric geometry. To further simplify the geometry and to save computational memory, the wafer bundle is modeled as a porous medium. The temperature in the reactor is assumed to be constant.

Figure 2: Model geometry including the domain and boundary labels.

The specific surface area (m2/m3) of the wafer bundle porous medium is calculated as the area per volume by assuming a pitch between the wafers as seen in Figure 3 below.

Figure 3: Specific surface area of wafer bundle calculation.

The wafer bundle porosity is the wafer volume per bundle volume:

Chemistry

In the wafer bundle, silane gas reacts to form solid silicon which is deposited on the wafers:

The reaction rate, Ri (mol/(m3·s)), is expressed as a first order reaction as follows:

(1)

where cSiH4 is the local concentration (mol/m3) and k is the rate constant (m/s) which is based on experimental results (Ref. 2) as follows:

where a (m/s) and b (1/Pa) are experimental kinetic parameters (based on Ref. 2) which depend on temperature as follows:

where kB is the Boltzmann constant (J/K) and T is the reactor temperature (K).

A crucial characteristic of the reactor performance is the growth rate of the silicon layers on the wafers known as the deposition rate, ΔSi (m/s), which is calculated as follows:

where MSi is the molar mass (kg/mol) and ρSi is the density (kg/m3) of silicon.

The reacting gas species are diluted in inert nitrogen gas which is assumed to well represent the properties of the mixture.

Fluid Flow

The flow in the reactor is modeled as laminar fluid flow. Flow inside the wafer bundle is neglected such that the reacting gas are only be transported by diffusion. This is justified since only transport in the radial direction is permitted by the physical wafers. And only dilute gas species, silane and hydrogen, experience a net transport through the wafer bundle from the deposition process. The inlet velocity is assumed to be fully developed with an average velocity and there is no slip at the reactor walls, support boat and along the wafer bundle.

Mass transport

The diffusion, convection, and reaction of each gaseous species i in the diluted solution is described as follows:

where Di is diffusion coefficient (m2/s), ci is the concentration (mol/m3), u is the velocity vector (m/s), and Ri is the reaction rate (mol/(m3·s)), as defined in Equation 1. The reaction is defined only in the wafer bundle domain and therefore the reaction rate term is zero in the free flow domain. Since the gases do not diffuse through the physical wafers, the axial diffusion in the porous medium representing the wafer bundle is neglected by setting the z-component of the diffusivity matrix to zero. The inlet concentration of silane is defined from the ideal gas law at the operating conditions and there is no mass flux perpendicular to the support boat or the reactor wall boundaries.

Results and Discussion

Figure 4 shows the velocity profile in the reactor, indicating that the velocity in the wafer bundle is much smaller than in the free flowing domain. Figure 5 shows the concentration profile in the wafer bundle of the silane gas, which dictates the deposition rate and thickness of silicon.

Figure 4: Velocity profile in boat reactor 600°C, 25 Pa.

Figure 5: Silane concentration profile in wafer bundle at 600°C, 25 Pa. Lines indicate the concentration isocontours.

Figure 5 shows the concentration of the silane in the wafer bundle which is used to estimate the deposition rate of silicon on the wafers as shown in Figure 6 below. The highest concentration of silane is obtained near the reactor inlet and close to the free-fluid channel. The relative variation in silane concentration over the wafer bundle domain is 3.6%.

Figure 6: Variation in deposition rate with temperature, total pressure, and location in wafer bundle. The asterisks represent the minimum expected deposition rate whereas the squares represent the maximum expected deposition rate in the wafer bundle. The colors of the lines represent operating pressures.

Figure 6 shows that the variation in the deposition rate of silicon increases as the operating temperature and pressure of the reactor increases. Therefore, operating at lower pressures and higher temperatures is favorable to ensure a uniform deposition rate over the wafer bundle due to the higher diffusivity of the gaseous species.