Transient heat flow in a graphene-coated glass

In example for the Heat Transport Solver, we look into a transient heat flow in thin films, specifically the time-resolved heating of a thin glass film with a few layers of graphene on top. Detailed modeling instructions are provided in the end.

Requirements

Lumerical products R2018a or newer

The extremely high thermal conductivity of graphene has generated a lot of attention in its use as a heat spreader [1]. In this part of the example we will investigate the time-resolved heat flow in a (glass) thin film with a few layers of graphene on top. The simulation will show that the high conductivity (2000 W/mK) of graphene makes the heat flow at the top layer of glass much faster as compared to the heat flow inside the film. As shown in the schematic below, we assume a 50 nm thickness for the graphene layer. By utilizing the symmetry of the structure, we can perform a 2D simulation instead of a 3D one.

Simulation Setup

Open the graphene_on_thin_film.ldev project file in HEAT.  Alternatively, you can follow the instructions provided in the Modeling Instructions section to create your own project file.  The project file contains two geometric objects, thin_film and graphene.  Note that the length and thickness of both the thin_film and graphene objects are slightly larger than the specifications.  This is because the area of the simulation region gets defined by the area of the (HEAT) solver region so we have made the geometric object larger and have used the length and thickness of the HEAT object to define the dimensions of the simulated thin film / graphene layer.  The material for "thin_film" is set to SiO₂ and the material for the "graphene" object is set to graphene.

Since we want to see the time evolution of the temperature profile, the HEAT solver mode has been changes to "transient".  For more details about how to set up the transient solver please refer to the Modeling Instructions section. There are two thermal boundary conditions (left and right) defined in the "Boundary Conditions" group.  The "left" boundary condition sets the left edge of the thin film at a fixed temperature of 300 K.  The "right" boundary condition raises the temperature on the right edge from 300 K to 400 K at t = 1 us and then keeps it constant at 400 K up to 200 us.  The end time in the temperature table of the "right" boundary condition also sets the end time for the transient simulation.

Modeling Instructions

In this section, we will provide detailed instructions on how to create the HEAT project file that will simulate the time resolved heating of a glass thin film with a few layers of graphene on top.  To get started, first open HEAT and save the blank project file by selecting the "Save" option under the "File" tab.  To be consistent with the provided project file, you can name your project "graphene_on_thin_film.ldev".

Materials

Check the instructions in "Option 1" (Air Cooling of Thin Film) to learn about the material properties of solids and fluids.  For this example, we will create a new "Conductor" type material model for graphene. Click on the Electrical and Thermal button   to open the electrical/thermal material database. Click the (new material)  button on the top left corner of the window and select Conductor.  Select the New Material and edit the properties according to the following table.

After editing the properties of the new material, add it to the simulation as explained in option 1. In addition, SiO2 (glass) needs to be added to the simulation as well.

Geometry

thin_film

From the Structures section of the Design tab, select a RECTANGLE to be added to the Objects Tree. Select the rectangle in the Objects Tree and click on the "Edit Properties" button  to edit the properties of the rectangle according to the following table.

graphene

From the Structures section of the Design tab, select a RECTANGLE to be added to the Objects Tree. Select the rectangle in the Objects Tree and click on the "Edit Properties" button  to edit the properties of the rectangle according to the following table.

Simulation Region

Click on in the Objects Tree and click the  button (on the left of the Objects Tree) to edit its properties according to the following table:

HEAT Solver

In the Solvers section of the Design tab select the   to place a HEAT solver in the simulation environment.  Note that once the solver is selected, all the simulation objects belonging to the HEAT solver become available under a new tab named HEAT.  Select the HEAT object from the Objects Tree and click on the "Edit Properties" button  to edit the properties according to the following table.

Boundary Conditions

left

Here we will use a thermal boundary condition to set the temperature at the left edge of the simulation region to a fixed value of 300 K.  Click the "Temperature" button  from the Boundary Conditions section of the HEAT tab to add a temperature boundary condition. Select the thermal boundary in Objects Tree and click the "Edit" button to edit its properties according to the following table.

right

Here we will use a thermal boundary condition to set a time varying temperature at the right edge of the simulation region.  The temperature will start at 300 K at t = 0 fs, will switch to 400 K at 1e9 fs, and will remain at that value until 1e11 fs.  Click the "Temperature" button  from the Boundary Conditions section of the HEAT tab to add a temperature boundary condition. Select the thermal boundary in Objects Tree and click the "Edit" button to edit its properties according to the following table.

The project file is now set up.  Save the file using the "File" tab and run it by following the instructions provided in the top-level page of the example.

Results and Discussion

Open the graphene_on_thin_film.ldev project file in HEAT.  Run the simulation by clicking the  button under Simulation section of the HEAT tab.  Once the simulation finishes running, results will be saved in the solver region and the icon will change to .  Right-click on the solver object and select "Visualize thermal" to view the temperature profile.  The thermal dataset has multiple results (attributes) saved.  To view the temperature profile, select the "T" attribute from the list of attributes in the visualizer.  The temperature profile will be a function of time which will be shown in the "parameter" table below the image.  Select the "t" parameter and change the time using the slide on the right side of the table.  As shown below, the heat coming from the right edge spread much quickly near the top of the glass film due the presence of the highly conductive graphene layer.  With time, the bottom of the film 'catches up' and the temperature distribution becomes even and linear throughout the film.

Related publications

1. Z. Yan, G. Liu, J. M. Khan, and A. A. Balandin, "Graphene quilts for thermal management of high-power GaN transistors," Nature Comm., vol. 3, art. 827, pp. 1-8, 2012.