PC3D

The Default Example (PERC 2D)

Move the downloaded PC3D Excel file to your desktop and open the file. Depending on your operating system, you may have to enable macros and/or disable protected mode. If you have difficulty opening or running the program, please make sure that you are using a version of Excel dated 2010 or later. The default setup is for a 2D model of a Passivated Emitter and Rear Cell (PERC).

Start by clicking Solve (Dashboard!A5) {This notation means cell A5 on the Dashboard sheet}. This button solves the current problem at the current contact voltage (Dashboard!G1). The contact voltage is the forward voltage applied between the positive and negative contacts to the solution volume. It differs from the device's terminal voltage when an external series resistance (Device!T8) has been added to account for additional series resistance between the solution volume and the device terminals.

There are numerous plots available using the buttons in the upper-right region of the Dashboard sheet. Some of them have multiple options that you can select from drop-down lists. Some of the plots only have meaning at the front and rear surfaces. The layout plot is special in that it is not a solution result, but rather a pictorial representation of the metal contacts and diffused regions on each surface (gray for metal, orange for n-type, blue for p-type, and green for undoped surfaces). For 2D problems, all of the solution information is contained in the Face view (looking at the wafer edge-on), but you can select Top or Side view to get a feel for the different view perspectives.

You can use the Image sheet to see what the solution plotted on the Dashboard looks like when it is expanded (unfolded) across multiple symmetry planes. The aspect ratio of the expanded image will match the dimensions of the solution volume, so what you see is a realistic enlargement of the device. You can then stretch or squeeze it if you prefer, and copy it to the clipboard for pasting into other documents.

Exploring Other Examples

You can load any of the example files available on this website (or that you may create yourself) using the Load button in the upper-left corner of the Dashboard sheet. Browse to the folder location where you moved the example file and select it. The parameters that define that example will be loaded into the spreadsheet. Note that the sea-green numerical solution cells in the spreadsheet are not changed when you load a new example file, but all of the yellow and orange user-input values are set. There is a brief description of each example in the upper-right corner of the Device sheet.

3D problems take several times longer to solve than a similar 2D problem, and much longer if you select the highest resolution (Dashboard!D2). For most problems, Auto resolution provides the shortest solution time while maintaining three-digit accuracy.

Visualizing a 3D solution utilizes the full flexibility of the contour plot on the Dashboard sheet. Once the problem solution is finished, you can view any two-dimensional slice through the volume. You can look at the solution volume from the front face, left side, or top surface. You can examine the solution at any distance (position) into the solution volume, as measured from the surface closest to your point of view. You can also "fly though" the solution volume from the near side to the far side using the Scan button adjacent to the contour plot. Note that the color bands in the contour plot are normally scaled based on the range of the plotted value in the visible plane, but when Scanning through the volume, the contour bands are scaled based on the range of the value throughout the entire solution volume.

Defining Your Own Device

Most of the user-definable input cells have a comment attached to them to explain briefly what that value represents. The presence of these comments is indicated by a small red triangle. You read the comment by moving your cursor to the cell with the red triangle. These comments replace the need for a Help file. You may also see a green triangle in the upper-left corner of some input cells. This indicates that those cells contain a spreadsheet formula rather than a numerical value. You can use formulas to make some input values depend on other input values that you supply.

The numerical solution volume is a small portion of the solar cell that is replicated across the surface of the wafer with mirror symmetry on all four edges. For a cell with metal gridlines on the front surface, the solution volume typically spans from the middle of a gridline to halfway between gridlines. Frequently, it is adequate to leave the larger busbars out of the solution, which makes a fast two-dimensional (2D) solution possible. When there are three-dimensional features such as point contacts on the rear surface, the solution volume must be carefully chosen to represent the mirror symmetry of these features. Use the Image sheet to view the extended symmetry of your layout. PC3D allows you to illuminate the solution region non-uniformly, and that may require a 3D solution even if the cell itself has 2D symmetry. Bulk defects, when enabled, may also require a 3D solution. PC3D will automatically detect if a 3D solution is required (as indicated in Dashboard!C2).

Once you have identified your solution volume, use the Device sheet to specify the dimensions of this volume and the dimensions of the surface features, including metal contacts and diffused regions. The surface can be divided into as many as 25 distinct areas (5 partitions in each axis). This partitioning can be different on the front and rear surface. The partitioning has no effect on the solution other than to define the dimensions of each feature on the surface. There is one exception. When using the Auto mode for Resolution (Dashboard!B2), the resolution it selects depends in part on the dimensions of the partitions, so keeping them roughly similar when that's possible will avoid invoking unnecessarily high resolution, which is slower.

If something goes wrong and the program stops working, try clicking the Reset button (Dashboard!K4). If that's not enough, try quitting and re-starting the Excel program. Because PC3D is not a protected file, you may have inadvertently corrupted the spreadsheet. In that case, return to this website and download a fresh copy of the Excel file.

To save your work, you have two choices. You can save the device parameters in a text file similar to the example problems by clicking on Save (Dashboard!A3) and giving your file a short but descriptive filename. Or, you can save the Excel file itself using either the main Excel menu or the diskette icon in the upper-left corner. Saving the Excel file stores your numerical solution preferences, batch solution results, and any notes you've entered along with the device parameters (You can even add additional sheets to the Excel file, but do not change the names or the layout of any of the original sheets). Whereas saving the text file stores only the device parameters, it requires far less disk storage and has the important advantage that it is portable to new versions of PC3D as they become available.

PC3S

Many PC3D users quickly progress to the point where they want to explore the impact of changing various surface parameters (e.g. Jo1, sheet resistance, and spectral transmission). While these parameters are ideally obtained from experimental devices, you can use PC3S to approximately predict the impact of physical changes to the device structure, such as texture depth, doping profile, surface recombination velocity, and optical coatings. PC3S has a user interface that is an adaptation of the one used for PC3D, so once you are comfortable with PC3D, you will feel at-home with PC3S.

When you first download and open the file, the default example is a nitride-passivated n+ emitter on a pyramidally textured surface with 0.5 volts dark bias. You will see the doping profile shown in the plot. What you are looking at is a side-on (face-view )cross-section through half of a pyramid. The aspect ratio of the plot is scaled to fit the square plot region, so the texture angle looks shallower than it really is. To see it in correct aspect ratio, go to the Image tab and click on Create Image. Notice that the doping density is higher near the pyramid peak. That's because this particular example assumes a fixed-source gaussian diffusion (Device!J8), and near the peak there is plenty of source dopant around and not much volume for it to diffuse into.

Similar to PC3D, the first thing to try is clicking the Solve button on the Dashboard tab. When the 3D solution is complete (40 seconds on my laptop), you'll see a plot of recombination rate. Significant recombination occurs both in the space-charge region snaking below the surface and in the heavily doped region near the surface. Click on Scan (above the plot). Your point of view will move forward through the pyramid from its peak down its back slope. Now click the Current button near the upper-right corner of the spreadsheet. Notice the current crowding beneath the pyramid peak. Changing the Carrier from Combined to either Electrons or Holes reveals that the current crowding is associated with the holes.

There are many interesting 3D effects to investigate, but the primary purpose of PC3S is to calculate the surface parameters for input to PC3D. These are obtained using the three Macro buttons: Recombination, Sheet Rho, and Spectral. Try each one. If you haven't changed the device parameters, you should get the same results shown when you first loaded the Excel program. On my computer, the solution time (Dashboard!B21) is 100 seconds for Recombination, 160 seconds for Sheet Rho, and 40 seconds for Spectral. The details of spectral transmission (reflectance, absorption, and collection) are shown in the Data tab. The calculated recombination and sheet rho parameters should be typed into PC3D's Device tab for the portions of the surface that have the structure that was simulated in PC3S. The spectral transmission column calculated in PC3S (Dashboard!L11:L29) can be cut-and-pasted directly into the corresponding spectral transmission column in PC3D's Device tab.

A few PC3S examples are available for download from this website. A partner to the passivated-n+ example is the metal-contacted n++ example. The two together can be used in PC3D to simulate the front surface of a selective-emitter cell. Other examples are the front surface of an n-type heterojunction cell (complete with a-Si and ITO optical absorption), and a planar aluminum-oxide passivated surface as found on the rear of a PERC device.