Quick Tutorial - A Three-Dimensional Scheme

In this tutorial, you will learn to:

  • Create a three-dimensional reaction scheme
  • Configure the properties of each compartment
  • Define transport processes between compartments
  • Load initial concentration values from an external file
  • Set the simulator parameters
  • Run the simulation
  • Display the simulation results

This section leads you through the procedure for simulating a system combining reaction and diffusion in an initially inhomogeneous volume. If you've never used Kinetiscope before, this tutorial will help you become familiar with Kinetiscope's different menus and functions.

Post-Exposure Bake Process of a Chemically-Amplified Photoresist

In a chemically amplified photoresist, a thin polymeric film is patternwise-exposed to UV light to create a small quantity of an acidic catalyst from a non-acidic precursor. In a subsequent heating step, this initial latent image of acid catalyzes the cleavage of labile groups pendant to the polymer chain. Each catalyst causes multiple cleavage reactions during the thermal treatment, hence the term chemical amplification.

The imaging chemistry for TBOC resist, a model system, is as follows:

PAG + TBOCSt + hν ⇢ tBOCSt-H+
tBOCSt-H+ ⇢ HOSt-H+ + C4H8(gas)
tBOCSt + HOSt-H+ ⇄ tBOCSt-H+ + HOSt

where PAG is the photo-acid generator, tBOCSt is the polymer repeat unit para-(tert-butoxycarbonyloxy)styrene, PHOSt is para-hydroxystyrene, and the -H+ suffix indicates protonation.

After imagewise exposure, the photoresist film composition is highly nonuniform. In consequence, the imaging properties depend on the complex interplay between the acid-catalyzed chemistry and diffusion of the photogenerated acid.

This tutorial reaction scheme is a simplified description of the chemistry and physics of the post-exposure bake step for TBOC resist. In addition to the imaging chemistry and gradient-driven diffusion of photogenerated acid, it also provides for:

  • volume change due to the volatilization of gaseous reaction products;
  • equilibration of the proton among species of different basicity; and
  • dependence of the acid diffusion kinetics on the changing composition of the polymer film.

Creating a New Reaction Scheme

You will create a new reaction scheme based on a three-dimensional reactor model and save it as a file named tutorial3.rxn.

When you first create a three-dimensional reaction scheme, you specify the type of model and select the concentration, time, length, and energy units to be used throughout. You also set up the array of compartments and transfer paths that comprise the reaction system.

When you later save your input, you specify its file name and the directory where it will be stored.

We will construct a two-dimensional array of compartments. The array represents a cross-section or a slice through the photoresist film. It will include, along the X-direction, two periods of an extended pattern of exposed lines separated by unexposed spaces. The exposing light enters the film from the top surface in the Z-direction. The film's bottom surface rests on an unspecified transparent substrate.

To create the reaction scheme:

  1. Select File | New Scheme | Three-dimensional Model... from the menu bar of Kinetiscope's main window,
    or
    Click the (New three-dimensional model) push button on the main window's tool bar.

    A Create Three-Dimensional Scheme Dialog appears.

  2. Select the following units for time, energy, concentration and length using the four drop-down list boxes: sec, kcal, mole/liter, cm.

    Make the selections by clicking the left mouse button on the drop-down list boxes and selecting the appropriate entry.

    The dialog should look like this:

    This is the only time that the units for a particular file can be specified. The units that are selected here must be used consistently for all input data, and are used for plotting the simulation results.
  3. Click Next > to move to the second page of the dialog.
  4. When first created, all compartments in a three-dimensional reaction scheme have the same height, width and depth. On the second page you specify those initial dimensions.

    Enter the following values for the initial dimensions of the compartments:
    x 3.2787e-8 cm
    y 1.0e-6 cm
    z 1.0e-5 cm

    The dialog should look like this:

  5. Click Next > to move to the last page of the dialog.
  6. The total reaction volume to be simulated is represented by a three-dimensional array of compartments. On this page you define the numbers of columns, rows and layers in that array.

    Use the up/down arrows on the spin boxes to adjust the array. For this scheme we will use 10 rows of compartments to represent the film's thickness and 244 columns of compartments to capture the pattern formation, all configured as 1 layer representing the slice. Set the Compartment Array to have
    Columns 244
    Rows 10
    Layers 1

    You may type these values directly into the data entry fields next to the spin boxes.

  7. Periodic boundary conditions are used to connect transfer paths from one face of the array to its opposing face. Since the pattern we are simulating is part of a much larger line-space array, we use periodic boundary conditions in this scheme to account for effects of the extended line-space array.

    To enable periodic boundary conditions in the X direction, check the Connect left and right check box in the Periodic Boundary Conditions area.

    The dialog should look like this:

  8. Click Finish.

You now are returned to Kinetiscope's main window, where a new three-dimensional scheme window named untitled1 - 3D model has been added.

Scaling the Scheme Diagram

The scheme diagram contains 2440 compartments, represented as cubes, each connected to all its neighbors by transfer paths represented as hexagonal shapes located at the inter-compartmental interfaces.

Upon creation the scheme diagram is scaled so that all objects are visible. You can zoom in to the scheme diagram to see the details of individual objects. We will do this to facilitate editing.

To scale the scheme diagram:

  1. Click the (Zoom to full scale) push button on the scheme window's tool bar.
  2. Use the horozontal and vertical scroll bars to bring into view the upper left compartment (named C1 R1 L1, meaning Column 1, Row 1, Layer 1).
The screen should look like this:

If you hover with the mouse cursor over a compartment or transfer path, a tool tip will appear with a brief summary of its contents.

Saving your Reaction Scheme

As you modify your reaction scheme, remember to periodically save your changes. This will help prevent accidental loss of data.

To save a reaction scheme under a name you specify:

  1. Select File | Save As... from the menu bar of the main window, or click the push button on the main window's tool bar. A File Save Dialog appears.
  2. Use the File Save Dialog to navigate to the directory you have selected for your files, and enter the name tutorial3.
  3. Click the Save push button on the File Save Dialog.

If you make an undesired change (for example, accidentally delete a step), you now can recover by selecting File | Revert to Saved... from the menu bar of the main window, or clicking the push button on the main window's tool bar.

Entering the Reaction Conditions

Different combinations of conditions can be chosen using the drop-down list boxes on the Reaction Conditions Page. Not all combinations of them are allowed (or physically meaningful). Kinetiscope will display an error message if an unsupported combination is selected.

You will simulate this system at a constant process temperature of 90 °C (363 °K). The film shrinks during this process, a consequence of the formation and evolution of butene, a gas at the process temperature. To account for the effect this has on the system kinetics we use variable volume reaction conditions.

  1. Select the Reaction Conditions tab.
  2. Select

    Volume is variable

    for the top left list box.

  3. Leave the bottom left list box in the

    Pressure is constant

    state; variable pressure is not allowed for this type of scheme.

  4. Select

    Temperature is constant

    for the top right list box.

  5. In the Temperature data entry field, type

    363.0.

  6. Leave the middle right list box in the

    Voltage is off

    state.

  7. Leave the lower right list box in the

    External stimulus is off

    state.

All reaction conditions have now been set. Your scheme window should look like this:

You will next edit both compartments and transfer paths.

Configuring the Compartments

In this tutorial we define the reaction mechanism in one compartment and then propagate it to all compartments by a copy-and-paste operation.

Entering the Reaction Mechanism

  1. Click on the Scheme tab.
  2. Double-click on compartment C1 R1 L1.

    The compartment is then highlighted with a cross-hatch pattern and the Compartment Editor Dialog opens.

  3. On the Compartment Editor Dialog, click on the Reaction Steps tab.
  4. Click the (Add a reaction step) push button on the Compartment Editor Dialog's tool bar.

    The Reaction Step Editor Dialog that appears is used to enter your reaction mechanism. Later, you may also edit previously entered mechanisms from this dialog.

    The individual reaction steps are entered much as you would write them on a piece of paper. The generalized format for a non-reversible reaction is:

    x A + y B + z C => w D + v E

    where x, y, z, w, and v are stoichiometric coefficients, and A, B, C, D and E are mnemonics that you choose for the various reactants and products. You must separate coefficients from their species mnemonic by a blank space. Also note that the right arrow is typed in as => using the characters "equals" "greater than" (with no spaces between them). For more on this, see the detailed discussion in the section entitled Entering the Reaction Equation.

  5. Type in the first reaction equation in the Equation data entry field of the Reaction Step Editor Dialog:

    PTBOCH => PHOSTH

    Beneath the data entry field are two drop-down list boxes for specifying additional data options.

    Use the list box in hte Rate Constants area to specify the format of the rate constant of the current reaction step. Kinetiscope's default setting is the temperature independent form, where the rate constant is specified as a single value in the scheme's pre-selected units. Temperature dependent rate constants are entered in Arrhenius form. The general Arrhenius form is:

    k  = A Tm e-Ea/RT (1)

    where A is the pre-exponential A factor, m is the temperature exponent, Ea is the activation energy, R is the gas constant and T is the absolute temperature.

    You will enter the rate constant for this reaction in Arrhenius form.

  6. Use the mouse to select

    Temperature-dependent

    on the list box in the Rate Constants area.

    A set of data entry fields for specifying the three Arrhenius parameters is then displayed. Here you will enter the A, m and Ea values for this reaction step. Only the Forward Activation Parameters data entry fields are active because the reaction step is not reversible.

  7. Type the following values in the Forward Activation Parameters data entry fields of the Reaction Step Editor Dialog:
    Prefactor A 2.089e18
    Temperature exponent m 0.0
    Activation energy Ea 28.67

    The drop-down list box in the Rate Laws area is used to specify how the rate of the reaction step is to be calculated. When the rate law corresponds directly to the reaction equation as written, the simulator can derive it from the stoichiometry of the reaction equation.

    Under circumstances when it differs from the stoichiometry, you may modify the rate law by setting the drop-down list box to User-defined rate law. Selecting this option displays and activates the (Edit the rate law expression) push button.

    Kinetiscope's default behavior is to derive the rate from the stoichiometry of the reaction equation. For more detail, see the section entitled Entering the Rate Law.

  8. Use the mouse to select

    Derived from stoichiometry

    on the list box in the Rate Laws area.

    You have now completed entering the data for the first reaction step. The window should look like this:

  9. Click OK to close the Reaction Editor Dialog.

    You return to the Compartment Editor Dialog.

  10. Repeat steps 3-9 once more, adding the following reversible reaction step:

    Equation PTBOCH + PHOST <=> PTBOC + PHOSTH
    Rate Constant Form Temperature-dependent
    Forward Prefactor A 1.439
    Forward Temperature Exponent m 0.0
    Forward Activation Energy Ea -2.319
    Reverse Prefactor A 40.0
    Reverse Temperature Exponent m 0.0
    Reverse Activation Energy Ea 0.0
    Rate Laws derived from stoichiometry

    This completes entry of the reaction steps in this compartment.

    We now configure the compartment itself.

  11. On the Compartment Editor Dialog, click on the Compartment Details tab
  12. Click the white square next displaying the current Compartment Color. This opens a Select Color Dialog. Use that to choose an orange shade and close the Select Color Dialog.
  13. In the Volume Settings area of the Compartment Editor Dialog, under Dimensions that can vary with volume, check the Y check box.
  14. Click OK.

    The Compartment Editor Dialog is dismissed and the first compartment displays the new color.

    The screen should look like this:

Copying the Reaction Mechanism to All Compartments

  1. Click the right mouse button over compartment C1 R1 L1.

    A context menu appears.

  2. Choose the Copy menu item.

    This places a copy of this compartment on Kinetiscope's internal clipboard.

  3. Again click the right mouse button over compartment C1 R1 L1.

    A context menu appears.

  4. Choose the Select | All Compartments menu item.

    All compartments in the scheme diagram are selected, indicated by cross-hatching.

  5. Click the (Paste) push button on the scheme window's tool bar.

    A Replace Compartments Dialog appears.

  6. On the Replace Compartments Dialog, leave all four check boxes checked.
  7. In the Naming area of the Replace Compartments Dialog, select the Preserve the current name radio button.
  8. Click the OK push button on the Replace Compartments Dialog.

    The dialog is dismissed and the reaction mechanism is added to all selected compartments; all now display the new color.

The scheme window should look like this:

Configuring the Transfer Paths

We use a similar process to configure the transfer paths: we will enter the transfer steps in one transfer path and then copy those transfer steps into all transfer paths of the system.

Entering Diffusion Steps

  1. Double-click the left mouse button on the transfer path between the compartment named C1 R1 L1 and compartment (named C2 R1 L1 ).

    The transfer path is highlighted with a cross-hatch pattern and the Transfer Path Editor Dialog appears.

  2. Click the (Add a transfer step) push button on the Transfer Path Editor Dialog's tool bar.

    The Transfer Step Editor Dialog appears.

  3. Set the controls on theTransfer Step Editor Dialog to the following settings:
    Transfer Type Exchange Diffusion
    Transferred Species PTBOCH
    Exchanged Species PTBOC
    Direction Bidirectional
    Rate Constant Form Temperature-dependent
    Prefactor A Forward 1.9e8
    Temperature Exponent m Forward 0
    Activation Energy Ea Forward 36.5
    Prefactor A Reverse 1.9e8
    Temperature Exponent m Reverse 0
    Activation Energy Ea Reverse 36.5
  4. Click the OK push button on the Transfer Step Editor Dialog.

    This returns you to the Transfer Path Editor Dialog.

  5. Repeat steps 2-4 one more time, entering the following values:
    Transfer Type Exchange Diffusion
    Transferred Species PHOSTH
    Exchanged Species PHOST
    Direction Bidirectional
    Rate Constant Form Temperature-dependent
    Prefactor A Forward 9.0e-3
    Temperature Exponent m Forward 0
    Activation Energy Ea Forward 22.1
    Prefactor A Reverse 9.0e-3
    Temperature Exponent m Reverse 0
    Activation Energy Ea Reverse 22.1
    You have now entered all transfer steps and are viewing the Transfer Path Editor Dialog.
  6. Click the black square push button displaying the current Transfer Path Color.

    This opens a Select Color Dialog.

  7. Use the Select Color Dialog to choose a blue shade and close the color dialog.

    This serves to visually differentiate this transfer path from others in the reaction scheme.

    The screen should look like this:

  8. Click OK to dismiss the Transfer Path Editor Dialog.

Copying the Diffusion Steps to All Transfer Paths

To configure the remaining transfer paths we will copy the blue transfer path we have just edited into those still empty.

  1. Single click the right mouse button on the blue transfer path.

    It becomes highlighted with a cross-hatch pattern.

  2. Click the (Copy object) push button on the scheme window's tool bar.

    This places a copy of the transfer path on Kinetiscope's clipboard.

  3. Click the right mouse button over compartment C1 R1 L1.

    A context menu appears.

  4. Choose the Select | All Transfer Paths menu item.

    All transfer paths in the scheme diagram are selected, indicated by cross-hatching.

  5. Click the (Paste) push button on the scheme window's tool bar.

    A Replace Transfer Paths Dialog appears.

  6. On the Replace Transfer Paths Dialog, leave both check boxes checked.
  7. In the Naming area of the Replace Transfer Paths Dialog, select the Preserve the current name radio button.
  8. Click the OK push button on the Replace Transfer Paths Dialog.

    The dialog is dismissed and the transfer steps are added to all selected transfer paths; all now display the new color.

The scheme window should look like this:

Note: You may save your changes by clicking the (Save) push button on the main window's tool bar.

Setting Species Data

Since we have chosen variable volume conditions, we need to supply information about the density of each species.

  1. On the scheme window, click the Species Data tab.

    You will see a table of the four species you have defined in the reaction scheme, each with a default molar density of 1.0 mole/liter.

  2. Enter new values for the molar densities of each species.

    In the table of species data, double-click on the entry for a species in the Molar Density column. Type the new value and then press the Enter key.

    Enter the following values in this way:
    PHOST 11.9
    PHOSTH 11.9
    PTBOC 5.91
    PTBOCH 5.91

Setting Initial Concentrations

We will now set initial species concentrations.

The photoresist polymer initially is in the TBOCST form. We will first initialize all compartments to be pure TBOCST.

We will then set the initial concentration of photogenerated acid (represented as TBOCSTH) to a different value in each compartment, using data read from an external text file. This text file was created using spreadsheet calculations that reproduce the distribution of photogenerated acid from the imagewise exposure. The spreadsheet is distributed with Kinetiscope, in the extradata directory. It is provided in two formats: Microsoft Excel format (as Image Calculation Example.xlsm) and OpenOffice/LibreOffice format(as Image Calculation Example.ods).

For more detail on the format of the text file see here.

All other species will be left at their default concentration of zero.

To set the TBOCST initial concentration:
  1. Click the Scheme tab to activate that page.
  2. Click the (Advanced functions) push button on the scheme window's tool bar.

    The Advanced Functions Dialog appears.

  3. Click on the Set Concentrations tab of the Advanced Functions Dialog.
  4. In the Species list box, select

    PTBOC.

  5. In the Default Concentration data entry field, type

    5.91

    mole/liter.

  6. Click the Apply push button in the Default Concentration area.

    The concentration of PTBOC has been set in all compartments.

To set the TBOCSTH initial concentration:
  1. On the Set Concentrations Page of the Advanced Functions Dialog, click the (Open file) push button.

    A File Open Dialog appears.

  2. Using the File Open Dialog, navigate to the Kinetiscope/extradata directory, select the file name TBOCH-init-conc.txt and click Open.
  3. In the Species list box, select

    PTBOCH.

  4. Click the Apply push button in the File with Concentration Data area.

    The concentration of PTBOCH has been set in all compartments.

All reaction conditions have now been set. The final step before simulation is to edit the simulation settings.

Entering the Simulation Settings

A number of parameters must be specified to configure the simulator. These settings are listed in three groups: General Settings, which include the total number of particles representing molecules and the recording interval; Limits, which allow you to set stopping points for the simulation; and Equilibrium Detect, settings for the Kinetiscope equilibrium detection and emulation system. You access the simulation parameters on the Simulation Settings Page.

To enter the simulation settings:
  1. Select the Simulation Settings tab.
  2. Set the data entry field for the Total Number of Particles to

    791500.

    This parameter specifies the initial number of particles in the simulation. They are apportioned among all species which have a nonzero initial concentration. The number should be large enough to accommodate the dynamic range of concentrations that will occur in the simulation. A larger number will also reduce stochastic noise. There is a trade-off between these benefits and the larger amount of computer time required to reach a given point in the simulation (see the Example Simulation Simulation Precision: Parallel Reactions ).

  3. Set the data entry field for the Record State at Intervals of to

    30000.

  4. Set the data entry field for the Random Number Seed to

    12947.

    The next group of parameters control the limits of the simulation.

  5. Set the data entry field for the Maximum Number of Events to a value of

    0 events.

    Setting this parameter to zero disables it.

  6. Set the data entry field for the Maximum time in Simulation to

    1000 seconds.

    Setting this parameter to zero disables it.

    The third set of simulation settings are the Equilibrium Detect settings. This is used for systems with reversible reaction steps which may come into equilibrium during a simulation.

  7. Uncheck the box in the Equilibrium Detect area.

Your screen should now appear like this:

Running the Simulation

Now you are ready to run the simulation.

  1. Select the Scheme tab.
  2. Click the (Start a simulation) push button on the scheme window's tool bar.

    A Simulator Window opens that tells you that the simulation is running. You can track the reaction as it progresses, with this window displaying the internal elapsed time in the simulation, the number of events that have occurred, how long the simulation has been running, and the number of times the system state has been recorded for later analysis:

  3. Click the OK push button on the simulator window when the simulation completes.

    If you do not click OK, the window will close automatically after 5 seconds. When you return to Kinetiscope's main window, the status display at the bottom of the tutorial3 scheme window now tells you that the simulation has finished, and the reason why the simulation stopped.

    Note: Kinetiscope automatically saves your reaction file with the new simulation results when the simulation is complete.

This simulation takes approximately eight minutes to complete on a mid-range microcomputer.

Viewing the Simulation Results

A view of the composition of the entire image is most informative in this simulation. We will view this by creating a surface plot window.

  1. Click the Scheme tab on the scheme window
  2. Click the (Zoom to show all) push button on the scheme window's tool bar.
  3. Click on an empty area of the scheme diagram to clear any selection, and then click the (Create Results Window) push button on the scheme window's tool bar.

    The Surface Plot Style Dialog is invoked.

  4. In the Plot Format area of the Surface Plot Style Dialog, click the Surface radio button.
  5. In the Parameter to View area, select concentration.
  6. In the Species to View area, click on PHOST in the list box.
  7. Click the OK on the Surface Plot Style Dialog.

    The dialog is dismissed and a new results window displays a graph of concentrations of all PHOST at zero elapsed time, as a function of the compartments' positions.

  8. On the results window, click the (Play animation) push button in the set of animation tools below the graph.

    This starts an time-lapse view of the evolution of the PHOST concentration during the photoresist's post-exposure bake process. The spatial image defined the lithographic process and represented by the PHOST compositional profile becomes progressively better defined with elapsed time, then begins to degrade with over-processing and ultimately disappears at long elapsed times.

You may view the graph from different angles by grabbing the figure with the mouse cursor using the left mouse button and moving the mouse cursor to rotate.

You may modify the graph in other ways also. Click the right mouse button over the figure and then choose the Modify... item from the context menu that appears to invoke a Three-Dimensional Plot Settings Dialog.

Next Steps

You have now completed this tutorial. You should now know the basics for simulating a three-dimensional reaction scheme using Kinetiscope.

Other tutorials lead you through the procedures for setting up other types of reaction systems: