Thermodynamics of an APCVD Reactor
An APCVD reaction is governed by both kinetics and thermodynamics. Kinetics defines the chemical reactions with respect to the reaction rates, effect of various variables, rearrangement of atoms, formation of intermediate species, etc. On the other hand, thermodynamics is the driving force that shows the direction the reaction is going to continue. Chemical thermodynamics is concerned with the interrelation of various forms of energy and the transfer of energy from one chemical system to another under the first and second laws of thermodynamics. In the case of APCVD, this transfer occurs when gaseous compounds are introduced into the reaction chamber.
The Gibbs free energy of a reaction (ДС,) can be used to determine the initial feasibility of the reaction for a given pressure and temperature. For the calculation of the ДСГ, the Gibbs free energy of formation contributions (AGf) for both product and reactant species need to be determined. The Gibbs free energy for a deposition is expressed in the following differential equation, where T is the temperature in kelvin and Д H° is the standard enthalpy of formation at 298 K, S° is the entropy at 298 K, and Cr is the heat capacity.
A positive ДС, means the reaction will lead to a thermodynamically adverse outcome. A negative ДG, means the reaction will lead to a thermodynamically favorable outcome.
In the event where many different reaction routes are considered possible by the thermodynamic laws, the one giving rise to the most negative ДС, will dominate. The equilibrium constant К for any such reaction mechanism can be found by
Once К is found for the various allowed reaction mechanisms, the partial pressure or activity of the gaseous precursor species can be calculated by the law of mass action, as follows:
All possible reaction routes, such as vapor pressure or aerosol saturation, homogeneous or heterogeneous reaction, precursor adsorption, desorption/removal of by-products produced, and surface diffusion, need to be considered. The film growth rate is estimated by the slowest—the rate determining—step of deposition.
Figure 8.11 Symmetry plane of a laminar flow APCVD reactor (LFR- APCVD).
CVD Reactor Geometry
A detailed design of an APCVD reactor is depicted in Fig. 8.11. The reactor consists of metallic flanges (stainless steel 316L), a graphite heater, a quartz tube, and of course the substrate to be deposited, which in this case is a conductive glass (FTO). The quartz tube (cylindric geometry) is held between the two flanges. One flange is connected to a custom-made inlet, and the second flange is connected to a conical outlet section, leading to the exhaust. The inlet is made from an aluminum-bronze alloy for better corrosion resistance while it is used within various precursors, so that it does not face functional complications. The inlet part holds a specially designed baffle to spread the flow entering from a 1/4" pipe over the width of the reactor. The graphite block placed below the glass substrate has three heating elements capable of setting up and supporting high temperatures.
Generally, in every CFD model, the target is to avoid spending a great amount of computer time and power to model the completely detailed part, in our case study the reactor, as described in the opening paragraph of this subchapter. The most crucial parts of the
Figure 8.12 Components used in the computational fluid dynamics simulation.
reactor are selected as the domain for CFD simulation, specifically, the inlet part inside the quartz tube, the glass substrate that is heated by the graphite block, and the wall surroundings of the quartz tube, as seen in Fig. 8.12. Hence, due to symmetry, only half of the needs will be simulated. Additionally, some important assumptions are taken into consideration while simulating the model:
- • There are no gas leaks in any part of the APCVD reactor. In the experimental procedures that took place in the laboratories of Delta Nano-Engineering Solutions Ltd. (DNES Ltd.), when ink was used to visualize the flow patterns inside the APCVD reactor, only a negligible amount of the ink leaked through.
- • The temperature of the walls of the quartz tube will be set according to the experimental parameters that were completed before and after the CFD simulation.
The inlet flow is assumed to be uniform due to the small geometry of the latter.
Methodologies of CFD Simulation Steps Analysis
To support a close relationship between the experimental setup and the CFD model, it is important to highlight how and which important part of the system in question would be examined. This is highly significant since computer power and time need to be saved to ensure time- and cost-efficient results. Apart from evaluating
Figure 8.13 Velocity profile of the fluid in a quartz tube (circular) of the APCVD reactor (laminar flow distribution).
a simulation model, it is important to envisage how it will really work as a physical system in order to "interpret" the working order in terms of mathematical expressions calculations. This is imperative because since the fluid flow in the APCVD reactors is principally three dimensional, the mathematical expression of the transport equations should be constructed properly. For the requirements of this chapter, a steady-state simulation was considered (Poiseuille flow), as seen in Fig. 8.13, which stood for the conditions after the flow field has developed inside the APCVD reactor, long enough for it to reach equilibrium. Moreover, the physics of the system to be simulated during CFD modeling must be determined. Critical factors that influence the effect of the outcomes can be turbulence flow, heat transfer, chemical species transport, and radiation phenomena. Fluid physics, such as thermal sources, velocity profiles, and chemical sources, are essential details that need to be modeled appropriately for the simulation to run and produce results efficiently.
Reaching meticulous and descriptive results within the prerequisites of the research hypothesis is essential in order to get a full and clear picture of what is really going on inside and outside, occasionally, the reactor's system boundaries. Consequently, the aims of transport phenomena in chemical processes are three closely related topics: fluid dynamics, heat transfer, and mass transfer. Fundamentally, fluid dynamics involves the transport of momentum, heat transfer involves the transport of energy, and mass transfer is concerned with the transport of mass of various chemical species. The CFD code, as a numerical simulation of fluid flow, is used to describe the complex behavior of fluids by numerically solving the laws that govern the movement of fluids in or around a part of the system or subsystem.
The important CFD simulation steps can be summarized as follows:
- 1. Creation of the geometrical model (ID, 2D, or 3D)
- 2. Designation of boundary conditions on volumes and/or surfaces that may occur
- 3. Mesh generation of the model
- 4. Conduction of quality checks before the first simulation
- 5. Performance of the simulation process
- 6. Outcome evaluation of refinement of the grid; discretization of the model into a larger number of discrete elements
- 7. Modification of the simulation and reoccupation as needed
- 8. Postprocess analysis of the simulation results and conclusions