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Chemical Vapor Deposition of GaAs
Introduction
This example illustrates the modeling of a reactor for chemical vapor deposition (CVD). CVD is an important process for the electronics industry in which a thin film is grown on a substrate by allowing molecules and molecular fragments to adsorb and react on a surface. Combining detailed chemical reaction kinetics with transport models of a CVD reactor allows for realistic modeling of the deposition process. Such simulations in turn minimize the large number of expensive and time-consuming trial runs typically required for a reactor design.
In the CVD process described here, triethyl-gallium (Ga(C2H5)3) first decomposes into a gas phase. The reaction products, along with arsine (AsH3), then adsorb and react on a substrate to form GaAs layers. The CVD system is modeled using momentum, energy, and mass balances including a detailed description of the gas phase and adsorption kinetics (Ref. 1).
The model highlights the usability of the Reaction Engineering and Chemistry interfaces together with the Reversible Reaction Group feature for simulation of reaction/transport systems in well-mixed (0D) and space-dependent reactors.
In the Reaction Engineering interface you can easily study the transient behavior of different sets of reactions in a perfectly mixed system. The Chemistry interface collects reaction kinetics and calculates transport and thermal parameters, which can seamlessly be coupled with other interfaces. In this application, you also utilize the Reversible Reaction Group feature for CHEMKIN import and organization of the complex system of bulk and surface reactions that are involved in the CVD process. The space-dependent reactor model accounts for mass transport, heat transfer, and fluid flow in the CVD reactor using the Transport of Diluted Species, Heat Transfer in Fluids, and Laminar Flow interfaces.
Model Definition
Chemistry
In this model, the reaction kinetics together with most species transport and thermal properties are imported from CHEMKIN files using the Reversible Reactions Group feature available in either the Reaction Engineering or Chemistry interface. The CHEMKIN reaction kinetics file includes the following reactions making up the CVD process.
1
The gas phase decomposition of Ga(C2H5)3:
(1)
(2)
(3)
2
Gas phase radical reactions:
(4)
(5)
(6)
(7)
(8)
(9)
3
Growth of GaAs at the surface by the adsorption of gas phase species and the subsequent reaction of the surface-bonded molecular fragments. These surface reactions involve the Ga and As species. SA and SG represent surface sites, corresponding to dangling bonds of As or Ga atoms, respectively.
(10)
(11)
(12)
(13)
(14)
4
Surface reactions of carbon and hydrogen fragments:
(15)
(16)
(17)
(18)
(19)
(20)
5
Surface reactions leading to GaAs growth:
(21)
(22)
The reaction rates (SI unit: mol/(m3·s)) corresponding to the chemistry just described involve the mass action law
Here, and denote the forward and reverse rate constants, respectively. The concentration of species i  is denoted ci (SI unit: mol/m3). The stoichiometric coefficients are denoted νij, and are defined as negative for reactants and positive for products. The temperature dependence of the reaction rates is included through Arrhenius expressions for the rate constants:
In this equation, A denotes the frequency factor, T the temperature (K), n the temperature exponent, E the activation energy (SI unit: J/mol), and Rg the ideal gas constant, 8.314 J/(mol·K). The frequency factor is expressed in the units , where α is the order of the reaction.
With the CHEMKIN import, the chemical species automatically adapts the following labels, where _1(ads) indicates adsorbed surface species and _Ga_ indicates adsorption at gallium (Ga) sites instead of the more common arsenic (As) sites Figure 1.
Figure 1: Species labels used in the model.
Model Analysis
The analysis follows these steps: First, study of the reaction kinetics in an ideal batch reactor using the Reaction Engineering interface. Afterward, setup of a space-dependent model with the following interfaces to investigate the effects of momentum, heat, and mass transport within the system:
•
Chemistry
•
Transport of Diluted Species
•
Heat Transfer in Fluids
•
Laminar Flow
Figure 2 shows the CVD reactor model geometry. The reactor is 40 cm long and 10 cm high. Located in the center is the substrate, 5 cm across and tilted 10° with respect to the vertical position. Gas enters the reactor at the inlet with a velocity of 0.4 m/s and at a pressure of 4000 Pa.
Figure 2: The modeling domain consists of the CVD reactor and the substrate surface.
Results and Discussion
As noted, the first step in the modeling process is to enter the complete set of gas phase reactions, Equation 1 to Equation 9, into the Reaction Engineering interface for analysis. Figure 3 shows the species concentrations as functions of time in a perfectly mixed batch reactor kept at 900 K.
Figure 3: The complete set of gas phase reactions including decomposition reactions of gallium species as well as radical reactions. The chemistry occurs in a perfectly mixed batch reactor held at 900 K. Radical species are not shown in the graph.
As a test, omit the radical reactions given by Equation 4 to Equation 9 from the set of gas phase reactions. Once again analyze the kinetics of the reactions describing gallium species decomposition (Equation 1 to Equation 3) at 900 K. The results appear in Figure 4.
Figure 4: A reduced set of gas phase reactions including only the decomposition reactions of gallium species. Reactions occur in a perfectly mixed system held at 900 K.
Reducing the gas phase reaction set does not affect the reactions of the gallium species. However, excluding the radical reactions has a considerable influence on the carbon-species distribution. For the reduced reaction set, ethene and ethyl radicals are the main carbon products; for the full reaction set the main products are ethene and methane. The various species have different characteristics with respect to surface adsorption and reaction. Furthermore, the net concentration of carbon species is higher for the full reaction set. Both these factors can significantly influence the growth of surface layers. For a first study of geometrical effects on the reacting system, you can bring the reduced reaction model into the actual geometry of the CVD reactor and then solve the space-dependent problem.
The first results from the space-dependent model are displayed below. Figure 5 shows the fluid velocity and Figure 6 the temperature distribution in the reactor domain. The gas mixture enters the reactor with a velocity of 0.4 m/s and a temperature of 300 K with the substrate held at a constant temperature of 900 K. Notice the large effect that the heating plate has on the temperature and the expansion this causes in the fluid. This effect is seen in the average velocity, which increases downstream after the position of the substrate.
Figure 5: The gas phase velocity in the reactor domain.
Figure 6: The temperature distribution in the reactor domain.
In Figure 7 shows the concentration distribution of the triethyl-gallium species in the reactor domain, while Figure 8 displays the concentration profile along the reactor centerline for triethyl-gallium together with that of the final product gallium hydride. Triethyl-gallium is stable at the inlet temperature (300 K) and then rapidly decomposes near the hot substrate.
Figure 7: Concentration distribution of triethyl-gallium in the reactor domain.
Figure 8: Concentration profiles of triethyl-gallium (blue line) and gallium hydride (green line) along the reactor centerline.
Figure 9 shows the arsine concentration change along the reactor centerline. This species does not decompose in the gas phase. The decrease in concentration at the substrate surface (at the 0 length coordinate) is due to the adsorption of arsine at the surface.
Figure 9: Composition change of arsine along the reactor centerline. Arsine is adsorbed at the substrate surface, which is located at the center of the length scale.
Figure 10 and Figure 11 depict a few of the transport properties calculated in the Chemistry node which are coupled to the physics interfaces of the space-dependent model. Figure 10 shows the diffusivity of triethyl-gallium (bottom) and arsine (top). Figure 11 shows the thermal conductivity of the hydrogen carrier gas. All variables are plotted as functions of temperature.
Figure 10: The diffusivities of triethyl-gallium (bottom) and arsine (top) as functions of temperature.
Figure 11: The thermal conductivity of the hydrogen carrier gas.
Reference
1. N.K. Ingle, C. Theodoropoulos, T.J. Mountziaris, R.M. Wexler, and F.T.J. Smith, “Reaction kinetics and transport phenomena underlying the low-pressure metalorganic chemical vapor deposition of GaAs”, J. Crystal Growth, vol. 167, pp. 543–556, 1996.
Application Library path: Chemical_Reaction_Engineering_Module/Reactors_with_Mass_and_Heat_Transfer/gaas_cvd
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  0D.
2
In the Select Physics tree, select Chemical Species Transport>Reaction Engineering (re).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Time Dependent.
6
Click  Done.
Global Definitions
Load the model parameters from a text file.
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file gaas_cvd_parameters.txt.
The 25 reactions describing the GaAs vapor deposition are available in a kinetics CHEMKIN file. Both bulk and surface reactions are present in this process.
Reaction Engineering - Gas Phase Reactions, Full Set (re)
Use the Reversible Reaction Group to import the kinetics CHEMKIN file.
1
In the Model Builder window, under Component 1 (comp1) click Reaction Engineering (re).
2
In the Settings window for Reaction Engineering, type Reaction Engineering - Gas Phase Reactions, Full Set (re) in the Label text field.
Reversible Reaction Group 1
1
In the Reaction Engineering toolbar, click  Reversible Reaction Group.
2
In the Settings window for Reversible Reaction Group, click to expand the CHEMKIN Import for Kinetics section.
3
Select the Import CHEMKIN data check box.
4
Click  Browse.
5
Browse to the model’s Application Libraries folder and double-click the file gaas_cvd_reaction_kinetics.txt.
6
Click  Import.
Delete the imported solid species C because it neither takes part in any reactions nor behaviors as third body.
Species: C
In the Model Builder window, under Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re) (re) right-click Species: C and choose Delete.
Species Group 1
First, investigate the bulk reactions at 900 K.
1
In the Model Builder window, expand the Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re) (re)>Species Group 1 node, then click Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re) (re).
2
In the Settings window for Reaction Engineering, locate the Energy Balance section.
3
In the T text field, type 900[K].
Remove the imported reactions associated with surface reactions and move reaction 9 to the model builder tree.
Reversible Reaction Group 1
1
In the Model Builder window, click Reversible Reaction Group 1.
2
In the Settings window for Reversible Reaction Group, locate the CHEMKIN Import for Kinetics section.
3
Clear the Import CHEMKIN data check box.
4
Click to expand the Move Reaction and Species section. In the Move reaction (with the number) from table text field, type 9.
5
Click  Create Reaction.
Remove reactions 10 to 25 from the Reaction table by clicking the Delete button.
Reaction 9 contains H2 which is the solvent in this process. When moving the reaction from the table a separate feature for the species H2 is created. This can now be accessed and set as solvent.
Species: H2
1
In the Model Builder window, click Species: H2.
2
In the Settings window for Species, locate the Type section.
3
From the list, choose Solvent.
Initial Values 1
Initially, only GaC6H15 and H2 exist in the reactor.
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Volumetric Species Initial Values section.
3
In the table, enter the following settings:
Species
Concentration (mol/m^3)
GaC6H15
c_GaC6H15_init
H2
c_H2_init
Study (re)
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study (re) in the Label text field.
3
In the Home toolbar, click  Compute.
Results
Gas Phase Concentrations, Full Set (re)
In the Settings window for 1D Plot Group, type Gas Phase Concentrations, Full Set (re) in the Label text field.
Global 1
Select the species concentrations that are plotted in Figure 3.
1
In the Model Builder window, expand the Gas Phase Concentrations, Full Set (re) node, then click Global 1.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_GaC6H15 - Concentration - mol/m³.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_GaC4H10 - Concentration - mol/m³.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_GaC2H6 - Concentration - mol/m³.
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_GaH2 - Concentration - mol/m³.
6
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_C2H4 - Concentration - mol/m³.
7
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_C2H5 - Concentration - mol/m³.
8
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_C2H6 - Concentration - mol/m³.
9
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Full Set (re)>re.c_CH4 - Concentration - mol/m³.
10
Click to expand the Coloring and Style section. From the Width list, choose 2.
11
Find the Line markers subsection. From the Marker list, choose Cycle.
12
From the Positioning list, choose Interpolated.
13
Click to expand the Legends section. From the Legends list, choose Manual.
14
In the table, enter the following settings:
Legends
GaC6H15
GaC4H10
GaC2H6
GaH2
C2H4
C2H5
C2H6
CH4
15
Click the  x-Axis Log Scale button in the Graphics toolbar.
16
Click the  y-Axis Log Scale button in the Graphics toolbar.
Gas Phase Concentrations, Full Set (re)
1
In the Model Builder window, click Gas Phase Concentrations, Full Set (re).
2
In the Settings window for 1D Plot Group, click to expand the Title section.
3
From the Title type list, choose None.
4
Locate the Axis section. Select the Manual axis limits check box.
5
In the y minimum text field, type 1e-8.
6
In the y maximum text field, type 1e-1.
7
Locate the Legend section. From the Layout list, choose Outside graph axis area.
8
From the Position list, choose Right.
9
In the Gas Phase Concentrations, Full Set (re) toolbar, click  Plot.
To reduce the model before simulating the process in a 2-dimensional model, study whether it is possible to remove the non-gallium species and reactions and yet obtain approximately the same results.
To do so, modify the existing reaction model by first removing reactions of non-gallium species from the Reversible Reaction Group. Then solve the mass balances and compare the results with the full reaction model.
Reaction Engineering - Gas Phase Reactions, Full Set (re) (re)
In the Model Builder window, under Component 1 (comp1) right-click Reaction Engineering - Gas Phase Reactions, Full Set (re) (re) and choose Copy.
Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)
1
In the Model Builder window, right-click Component 1 (comp1) and choose Paste Reaction Engineering.
2
In the Messages from Paste dialog box, click OK.
3
In the Model Builder window, click Reaction Engineering - Gas Phase Reactions, Full Set (re) 1 (re2).
4
In the Settings window for Reaction Engineering, type Reaction Engineering - Gas Phase Reactions, Reduced Set (re2) in the Label text field.
Reversible Reaction Group 1
Remove reactions 4 to 8 from the Reaction table by clicking the Delete button.
1: 2H+H2=>2H2
1
In the Model Builder window, expand the Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2) (re2) node.
2
Right-click 1: 2H+H2=>2H2 and choose Disable.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve check box for Reaction Engineering - Gas Phase Reactions, Full Set (re) (re).
4
Find the Studies subsection. In the Select Study tree, select General Studies>Time Dependent.
5
Click Add Study in the window toolbar.
6
In the Home toolbar, click  Add Study to close the Add Study window.
Study (re2)
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Study (re2) in the Label text field.
3
In the Home toolbar, click  Compute.
Results
Gas Phase Concentrations, Reduced Set (re2)
Select the species concentrations that are plotted in Figure 4.
1
In the Settings window for 1D Plot Group, type Gas Phase Concentrations, Reduced Set (re2) in the Label text field.
Global 1
1
In the Model Builder window, expand the Gas Phase Concentrations, Reduced Set (re2) node, then click Global 1.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_GaC6H15 - Concentration - mol/m³.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_GaC4H10 - Concentration - mol/m³.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_GaC2H6 - Concentration - mol/m³.
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_GaH2 - Concentration - mol/m³.
6
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_C2H4 - Concentration - mol/m³.
7
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Reaction Engineering - Gas Phase Reactions, Reduced Set (re2)>re2.c_C2H5 - Concentration - mol/m³.
8
Locate the Coloring and Style section. From the Width list, choose 2.
9
Find the Line markers subsection. From the Marker list, choose Cycle.
10
From the Positioning list, choose Interpolated.
11
Locate the Legends section. From the Legends list, choose Manual.
12
In the table, enter the following settings:
Legends
GaC6H15
GaC4H10
GaC2H6
GaH2
C2H4
C2H5
13
Click the  x-Axis Log Scale button in the Graphics toolbar.
14
Click the  y-Axis Log Scale button in the Graphics toolbar.
Gas Phase Concentrations, Reduced Set (re2)
1
In the Model Builder window, click Gas Phase Concentrations, Reduced Set (re2).
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
Locate the Axis section. Select the Manual axis limits check box.
5
In the y minimum text field, type 1e-8.
6
In the y maximum text field, type 1e-1.
7
Locate the Legend section. From the Layout list, choose Outside graph axis area.
8
From the Position list, choose Right.
9
In the Gas Phase Concentrations, Reduced Set (re2) toolbar, click  Plot.
A comparison of Figure 3 and Figure 4 reveals that the gallium-related reactions remain approximately the same. This means that you can go on to set up a space-dependent CVD model based on the reduced model instead of the one comprising all bulk species.
Move on to the space-dependent model. This CVD model is in 2D and you set up the necessary reactions using the Chemistry interface and the Reversible Reaction Group feature. Mass transport, heat transfer, and fluid flow are accounted for with Transport of Diluted Species, Heat Transfer in Fluids, and Laminar Flow interfaces, respectively.
Add Component
Right-click Results>Gas Phase Concentrations, Reduced Set (re2) and choose Add Component>2D.
First, draw the 2D geometry.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.4.
4
In the Height text field, type 0.1.
5
Locate the Position section. From the Base list, choose Center.
6
Click  Build Selected.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Position section.
3
In the y text field, type -0.025.
4
Locate the Size and Shape section. In the Width text field, type 1e-3.
5
In the Height text field, type 0.05.
6
Locate the Rotation Angle section. In the Rotation text field, type -10.
7
Click  Build Selected.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object r1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to add subsection. Click to clear the  Activate Selection toggle button.
5
Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
6
Select the object r2 only.
Form Union (fin)
In the Geometry toolbar, click  Build All.
Select the Chemistry interface and the Reversible Reaction Group feature to set up all necessary reaction kinetics and define some species parameters.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Chemical Species Transport>Chemistry (chem).
4
Click Add to Component 2 in the window toolbar.
5
In the Home toolbar, click  Add Physics to close the Add Physics window.
Chemistry (chem)
Reversible Reaction Group 1
1
Right-click Component 2 (comp2)>Chemistry (chem) and choose Reversible Reaction Group.
Aside from CHEMKIN import of reaction kinetics, also use CHEMKIN import of transport and thermal properties. In this manner, several thermal and transport properties available in the Chemistry interface can be utilized in the other interfaces.
2
In the Settings window for Reversible Reaction Group, click to expand the CHEMKIN Import for Kinetics section.
3
Select the Import CHEMKIN data check box.
4
Click  Browse.
5
Browse to the model’s Application Libraries folder and double-click the file gaas_cvd_reaction_kinetics.txt.
6
Click  Import.
Species: C
1
In the Model Builder window, under Component 2 (comp2)>Chemistry (chem) right-click Species: C and choose Delete.
2
In the Model Builder window, click Chemistry (chem).
3
In the Settings window for Chemistry, click to expand the Calculate Transport Properties section.
Species Group 1
1
In the Model Builder window, under Component 2 (comp2)>Chemistry (chem) click Species Group 1.
2
In the Settings window for Species Group, click to expand the CHEMKIN section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file gaas_cvd_transp.txt.
5
Click  Import.
Species Thermodynamics 1
1
In the Model Builder window, expand the Species Group 1 node, then click Species Thermodynamics 1.
2
In the Settings window for Species Thermodynamics, click to expand the CHEMKIN Import for Thermodynamic Data section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file gaas_cvd_thermo.txt.
5
Click  Import.
Remove the bulk reactions that were considered redundant in the 0D model investigation of the system.
Reversible Reaction Group 1
1
In the Model Builder window, under Component 2 (comp2)>Chemistry (chem) click Reversible Reaction Group 1.
2
In the Settings window for Reversible Reaction Group, locate the CHEMKIN Import for Kinetics section.
3
Clear the Import CHEMKIN data check box.
Remove reactions 4 to 8 from the Reaction table by clicking the Delete button.
Continue with moving the reactions containing surface species to the model builder tree. This enables access to all surface species. Additionally, do the same with the hydrogen reaction (reaction 17).
4
Click to expand the Move Reaction and Species section. In the Move reaction (with the number) from table text field, type 9.
5
Click  Create Reaction.
Repeat this with reactions 10 to 25.
Disable reaction 17 ( Ga_1(ads)+As_Ga_1(ads)=>GaAs ) and select H2 as solvent.
17: Surface: Ga_1(ads)+As_Ga_1(ads)=>GaAs
In the Model Builder window, right-click 17: Surface: Ga_1(ads)+As_Ga_1(ads)=>GaAs and choose Disable.
Species: H2
1
In the Model Builder window, right-click Species: H2 and choose Enable.
2
In the Settings window for Species, locate the Type section.
3
From the list, choose Solvent.
The surface species concentrations are considered constant. To account for this, lock the concentrations for these.
Species: GaAs
1
In the Model Builder window, click Species: GaAs.
2
In the Settings window for Species, click to expand the Constant Concentration/Activity section.
3
Select the Keep concentration/activity constant check box.
Repeat the same lock operation for GaC2H5_1_surf, GaC2H6_1_surf, Ga_1_surf, As_Ga_1_surf, C2H5_1_surf, C2H5_Ga_1_surf, H_1_surf, and H_Ga_1_surf.
4
In the Model Builder window, collapse the Chemistry (chem) node.
Component 2 (comp2)
Add a Transport of Diluted Species interface to model the mass transport of the bulk species diluted in solvent. When available, use the transport parameters from the Chemistry interface. Additionally, show the Advanced physics option. This is needed to choose the conservative form for the convective term in the mass transfer interface. The conservative form should be used for systems including convection and non-negligible changes in density.
Add Physics
1
In the Physics toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Chemical Species Transport>Transport of Diluted Species (tds).
4
Click Add to Component 2 in the window toolbar.
5
In the Physics toolbar, click  Add Physics to close the Add Physics window.
6
Click the  Show More Options button in the Model Builder toolbar.
7
In the Show More Options dialog box, select Physics>Advanced Physics Options in the tree.
8
In the tree, select the check box for the node Physics>Advanced Physics Options.
9
Click OK.
Transport of Diluted Species (tds)
1
In the Settings window for Transport of Diluted Species, click to expand the Advanced Settings section.
2
From the Convective term list, choose Conservative form.
3
Click to expand the Dependent Variables section. In the Number of species text field, type 8.
4
In the Concentrations table, enter the following settings:
cGaC4H10
cC2H5
cH
cC2H4
cAsH3
cGaH2
cGaC2H6
cGaC6H15
Set the constant (locked) concentrations in the Chemistry interface main node.
Chemistry (chem)
1
In the Model Builder window, under Component 2 (comp2) click Chemistry (chem).
2
In the Settings window for Chemistry, locate the Species Matching section.
3
From the Species solved for list, choose Transport of Diluted Species.
4
Find the Bulk species subsection. In the table, enter the following settings:
Species
Type
Molar concentration
Value (mol/m^3)
AsH3
Variable
cAsH3
Solved for
C2H4
Variable
cC2H4
Solved for
C2H5
Variable
cC2H5
Solved for
GaAs
Constant
User defined
0
GaC2H6
Variable
cGaC2H6
Solved for
GaC4H10
Variable
cGaC4H10
Solved for
GaC6H15
Variable
cGaC6H15
Solved for
GaH2
Variable
cGaH2
Solved for
H
Variable
cH
Solved for
H2
Solvent
User defined
c_H2_init
5
Find the Surface species subsection. In the table, enter the following settings:
Species
Species concentration type
Surface concentration (mol/m^2)
As_Ga_1(ads)
Constant
c_Assurf_Ga
C2H5_1(ads)
Constant
c_C2H5surf
C2H5_Ga_1(ads)
Constant
c_C2H5surf_Ga
GaC2H5_1(ads)
Constant
c_GaC2H5surf
GaC2H6_1(ads)
Constant
0
Ga_1(ads)
Constant
c_Gasurf
H_1(ads)
Constant
c_Hsurf
H_Ga_1(ads)
Constant
c_Hsurf_Ga
Transport of Diluted Species (tds)
Transport Properties 1
1
In the Model Builder window, under Component 2 (comp2)>Transport of Diluted Species (tds) click Transport Properties 1.
2
In the Settings window for Transport Properties, locate the Diffusion section.
3
From the Source list, choose Chemistry.
4
From the DcGaC4H10 list, choose Diffusion coefficient , GaC4H10 in H2 (solvent) (chem).
5
From the DcC2H5 list, choose Diffusion coefficient , C2H5 in H2 (solvent) (chem).
6
From the DcH list, choose Diffusion coefficient , H in H2 (solvent) (chem).
7
From the DcC2H4 list, choose Diffusion coefficient , C2H4 in H2 (solvent) (chem).
8
From the DcAsH3 list, choose Diffusion coefficient , AsH3 in H2 (solvent) (chem).
9
From the DcGaH2 list, choose Diffusion coefficient , GaH2 in H2 (solvent) (chem).
10
From the DcGaC2H6 list, choose Diffusion coefficient , GaC2H6 in H2 (solvent) (chem).
11
From the DcGaC6H15 list, choose Diffusion coefficient , GaC6H15 in H2 (solvent) (chem).
Reactions 1
1
In the Physics toolbar, click  Domains and choose Reactions.
2
In the Settings window for Reactions, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Reaction Rates section. From the RcGaC4H10 list, choose Reaction rate for species GaC4H10 (chem).
5
From the RcC2H5 list, choose Reaction rate for species C2H5 (chem).
6
From the RcH list, choose Reaction rate for species H (chem).
7
From the RcC2H4 list, choose Reaction rate for species C2H4 (chem).
8
From the RcAsH3 list, choose Reaction rate for species AsH3 (chem).
9
From the RcGaH2 list, choose Reaction rate for species GaH2 (chem).
10
From the RcGaC2H6 list, choose Reaction rate for species GaC2H6 (chem).
11
From the RcGaC6H15 list, choose Reaction rate for species GaC6H15 (chem).
Surface Reactions 1
Create a Surface Reactions feature and apply it at the substrate surface. Then prescribe the surface reaction rates to model the deposition on the substrate.
1
In the Physics toolbar, click  Boundaries and choose Surface Reactions.
2
Select Boundaries 4–7 only.
3
In the Settings window for Surface Reactions, locate the Surface Reaction Rate section.
4
From the J0,cGaC4H10 list, choose Surface reaction rate for species GaC4H10 (chem).
5
From the J0,cC2H5 list, choose Surface reaction rate for species C2H5 (chem).
6
From the J0,cH list, choose Surface reaction rate for species H (chem).
7
From the J0,cC2H4 list, choose Surface reaction rate for species C2H4 (chem).
8
From the J0,cAsH3 list, choose Surface reaction rate for species AsH3 (chem).
9
From the J0,cGaH2 list, choose Surface reaction rate for species GaH2 (chem).
10
From the J0,cGaC2H6 list, choose Surface reaction rate for species GaC2H6 (chem).
11
From the J0,cGaC6H15 list, choose Surface reaction rate for species GaC6H15 (chem).
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
Select Boundary 1 only.
3
In the Settings window for Inflow, locate the Concentration section.
4
In the c0,cAsH3 text field, type c_AsH3_in.
5
In the c0,cGaC6H15 text field, type c_GaC6H15_in.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Select Boundary 8 only.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the cAsH3 text field, type c_AsH3_in.
4
In the cGaC6H15 text field, type c_GaC6H15_in.
Component 2 (comp2)
Add a Heat Transfer in Fluids interface to model the heat transfer and heat generation in the reactor. When available, use the thermal parameters from the Chemistry interface.
Add Physics
1
In the Physics toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Heat Transfer>Heat Transfer in Fluids (ht).
4
Click Add to Component 2 in the window toolbar.
5
In the Physics toolbar, click  Add Physics to close the Add Physics window.
Heat Transfer in Fluids (ht)
Fluid 1
1
In the Model Builder window, under Component 2 (comp2)>Heat Transfer in Fluids (ht) click Fluid 1.
2
In the Settings window for Fluid, locate the Heat Conduction, Fluid section.
3
From the k list, choose Thermal conductivity (chem).
4
Locate the Thermodynamics, Fluid section. From the Fluid type list, choose Gas/Liquid.
5
From the ρ list, choose Density (chem).
6
From the Cp list, choose Heat capacity at constant pressure (chem).
7
From the γ list, choose User defined.
Heat Source 1
1
In the Physics toolbar, click  Domains and choose Heat Source.
2
Select Domain 1 only.
3
In the Settings window for Heat Source, locate the Heat Source section.
4
From the Q0 list, choose Heat source of reactions (chem).
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundaries 1–3 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type T_in.
Temperature 2
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundaries 4–7 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type T_surf.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Select Boundary 8 only.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T_in.
Component 2 (comp2)
Add a Laminar Flow interface to model the fluid flow. When available, use the fluid parameters from the Chemistry interface.
Add Physics
1
In the Physics toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Fluid Flow>Single-Phase Flow>Laminar Flow (spf).
4
Click Add to Component 2 in the window toolbar.
5
In the Physics toolbar, click  Add Physics to close the Add Physics window.
Laminar Flow (spf)
1
In the Settings window for Laminar Flow, locate the Physical Model section.
2
From the Compressibility list, choose Compressible flow (Ma<0.3).
3
In the pref text field, type 0[atm].
Fluid Properties 1
1
In the Model Builder window, under Component 2 (comp2)>Laminar Flow (spf) click Fluid Properties 1.
2
In the Settings window for Fluid Properties, locate the Fluid Properties section.
3
From the ρ list, choose Density (chem).
4
From the μ list, choose Dynamic viscosity (chem).
Inlet 1
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
Select Boundary 1 only.
3
In the Settings window for Inlet, locate the Boundary Condition section.
4
From the list, choose Fully developed flow.
5
Locate the Fully Developed Flow section. In the Uav text field, type u_in.
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
Select Boundary 8 only.
3
In the Settings window for Outlet, locate the Pressure Conditions section.
4
In the p0 text field, type p_0.
5
Select the Normal flow check box.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the p text field, type p_0.
Chemistry (chem)
Finish the space-dependent model setup by coupling the interfaces.
1
In the Model Builder window, under Component 2 (comp2) click Chemistry (chem).
2
In the Settings window for Chemistry, locate the Model Input section.
3
From the T list, choose Temperature (ht).
4
From the p list, choose Absolute pressure (spf).
Set the density dependent on both pressure and temperature.
5
Locate the Mixture Properties section. From the Density list, choose User defined.
6
In the ρ text field, type chem.p/R_const/chem.T*chem.M_H2.
Multiphysics
Nonisothermal Flow 1 (nitf1)
In the Physics toolbar, click  Multiphysics Couplings and choose Domain>Nonisothermal Flow.
Reacting Flow, Diluted Species 1 (rfd1)
In the Physics toolbar, click  Multiphysics Couplings and choose Domain>Reacting Flow, Diluted Species.
Mesh 1
1
In the Model Builder window, under Component 2 (comp2) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Finer.
4
Click  Build All.
Study (re)
Step 1: Time Dependent
1
In the Model Builder window, under Study (re) click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Physics and Variables Selection section.
3
In the table, clear the Solve for check boxes for Reaction Engineering - Gas Phase Reactions, Reduced Set (re2) (re2), Chemistry (chem), Transport of Diluted Species (tds), and Heat Transfer in Fluids (ht).
Root
Solve the model for stationary conditions by selecting the Stationary study type.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve check boxes for Reaction Engineering - Gas Phase Reactions, Full Set (re) (re) and Reaction Engineering - Gas Phase Reactions, Reduced Set (re2) (re2).
4
Find the Studies subsection. In the Select Study tree, select General Studies>Stationary.
5
Click Add Study in the window toolbar.
6
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2D Model
1
In the Model Builder window, click Study 3.
2
In the Settings window for Study, type Study 2D Model in the Label text field.
3
In the Home toolbar, click  Compute.
Results
Velocity (spf)
To create Figure 5, follow these steps:
1
In the Model Builder window, under Results click Velocity (spf).
2
In the Settings window for 2D Plot Group, locate the Color Legend section.
3
From the Position list, choose Bottom.
4
In the Velocity (spf) toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Temperature (ht)
To reproduce Figure 6, do the following:
1
In the Model Builder window, click Temperature (ht).
2
In the Settings window for 2D Plot Group, locate the Color Legend section.
3
From the Position list, choose Bottom.
4
In the Temperature (ht) toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Concentration, GaC6H15 (tds)
You can reproduce Figure 7 as follows:
1
In the Model Builder window, click Concentration, GaC6H15 (tds).
2
In the Settings window for 2D Plot Group, locate the Color Legend section.
3
From the Position list, choose Bottom.
Streamline 1
1
In the Model Builder window, expand the Concentration, GaC6H15 (tds) node, then click Streamline 1.
2
In the Settings window for Streamline, locate the Streamline Positioning section.
3
From the Positioning list, choose On selected boundaries.
4
In the Number text field, type 10.
5
Locate the Selection section. Click to select the  Activate Selection toggle button.
6
Select Boundary 1 only.
7
Click the  Zoom Extents button in the Graphics toolbar.
8
In the Concentration, GaC6H15 (tds) toolbar, click  Plot.
The pressure variation in this model is small. For clarity, plot the relative pressure instead of the total pressure.
Contour
1
In the Model Builder window, expand the Results>Pressure (spf) node, then click Contour.
2
In the Settings window for Contour, locate the Expression section.
3
In the Expression text field, type p-p_0.
4
In the Pressure (spf) toolbar, click  Plot.
To produce the remaining figures, illustrating various results along the reactor centerline, use a Cut Line 2D dataset.
Cut Line 2D 1
1
In the Results toolbar, click  Cut Line 2D.
2
In the Settings window for Cut Line 2D, locate the Line Data section.
3
In row Point 1, set x to -0.2.
4
In row Point 2, set x to 0.2.
5
Click  Plot.
Concentration Profiles GaC6H15 and GaH2
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Concentration Profiles GaC6H15 and GaH2 in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Line 2D 1.
4
Locate the Legend section. From the Position list, choose Upper right.
GaC6H15
1
Right-click Concentration Profiles GaC6H15 and GaH2 and choose Line Graph.
2
In the Settings window for Line Graph, type GaC6H15 in the Label text field.
3
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Transport of Diluted Species>Species cGaC6H15>cGaC6H15 - Concentration - mol/m³.
4
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Geometry>Coordinate>x - x-coordinate.
5
Click to expand the Coloring and Style section. From the Width list, choose 2.
6
Click to expand the Legends section. Select the Show legends check box.
7
From the Legends list, choose Manual.
8
In the table, enter the following settings:
Legends
GaC6H15
GaH2
1
In the Model Builder window, right-click Concentration Profiles GaC6H15 and GaH2 and choose Line Graph.
2
In the Settings window for Line Graph, type GaH2 in the Label text field.
3
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Transport of Diluted Species>Species cGaH2>cGaH2 - Concentration - mol/m³.
4
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Geometry>Coordinate>x - x-coordinate.
5
Locate the Legends section. Select the Show legends check box.
6
From the Legends list, choose Manual.
7
In the table, enter the following settings:
Legends
GaH2
Concentration Profiles GaC6H15 and GaH2
1
In the Model Builder window, click Concentration Profiles GaC6H15 and GaH2.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
In the Concentration Profiles GaC6H15 and GaH2 toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Concentration Profile AsH3 Change
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Concentration Profile AsH3 Change in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Line 2D 1.
4
Locate the Legend section. From the Position list, choose Upper right.
Line Graph 1
1
Right-click Concentration Profile AsH3 Change and choose Line Graph.
2
In the Settings window for Line Graph, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Transport of Diluted Species>Species cAsH3>cAsH3 - Concentration - mol/m³.
3
Locate the y-Axis Data section. In the Expression text field, type cAsH3-c_AsH3_init.
4
Click to expand the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Change in arsine, AsH<sub>3</sub>, concentration compared to initial conditions in the reactor.
6
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Geometry>Coordinate>x - x-coordinate.
7
Locate the Coloring and Style section. From the Width list, choose 2.
8
Locate the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
AsH3
11
In the Concentration Profile AsH3 Change toolbar, click  Plot.
The Chemistry node calculates the diffusivities, the thermal conductivity, and other fluid properties, including their temperature dependence. Next, plot the diffusivities along the reactor centerline for two of the species as functions of the temperature.
Diffusivities vs. Temperature
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Diffusivities vs. Temperature in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Line 2D 1.
4
Locate the Legend section. From the Position list, choose Lower right.
GaC6H15
1
Right-click Diffusivities vs. Temperature and choose Line Graph.
2
In the Settings window for Line Graph, type GaC6H15 in the Label text field.
3
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Transport of Diluted Species>Species cGaC6H15>tds.Dav_cGaC6H15 - Average diffusion coefficient - m²/s.
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Heat Transfer in Fluids>Temperature>T - Temperature - K.
6
Locate the Coloring and Style section. From the Width list, choose 2.
7
Locate the Legends section. Select the Show legends check box.
8
From the Legends list, choose Manual.
9
In the table, enter the following settings:
Legends
GaC6H15
10
In the Diffusivities vs. Temperature toolbar, click  Plot.
AsH3
1
In the Model Builder window, right-click Diffusivities vs. Temperature and choose Line Graph.
2
In the Settings window for Line Graph, type AsH3 in the Label text field.
3
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Transport of Diluted Species>Species cAsH3>tds.Dav_cAsH3 - Average diffusion coefficient - m²/s.
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Heat Transfer in Fluids>Temperature>T - Temperature - K.
6
Locate the Coloring and Style section. From the Width list, choose 2.
7
Locate the Legends section. Select the Show legends check box.
8
From the Legends list, choose Manual.
9
In the table, enter the following settings:
Legends
AsH3
Diffusivities vs. Temperature
1
In the Model Builder window, click Diffusivities vs. Temperature.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
Locate the Grid section. Select the Manual spacing check box.
5
In the x spacing text field, type 100.
6
In the y spacing text field, type 1e-3.
7
Locate the Legend section. From the Position list, choose Lower right.
8
In the Diffusivities vs. Temperature toolbar, click  Plot.
Thermal Conductivity H2
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Thermal Conductivity H2 in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Line 2D 1.
4
Locate the Legend section. From the Position list, choose Lower right.
Line Graph 1
1
Right-click Thermal Conductivity H2 and choose Line Graph.
2
In the Settings window for Line Graph, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 2 (comp2)>Heat Transfer in Fluids>Material properties>ht.kmean - Mean effective thermal conductivity - W/(m·K).
3
Locate the x-Axis Data section. From the Parameter list, choose Expression.
4
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 2 (comp2)>Heat Transfer in Fluids>Temperature>T - Temperature - K.
5
Locate the Coloring and Style section. From the Width list, choose 2.
6
Locate the Legends section. Select the Show legends check box.
7
From the Legends list, choose Manual.
8
In the table, enter the following settings:
Legends
H2
Thermal Conductivity H2
1
In the Model Builder window, click Thermal Conductivity H2.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
In the Thermal Conductivity H2 toolbar, click  Plot.