Building Predictive And Accurate 3D Process Models

How to calibrate a process model to ensure it reflects actual process behavior and can generate silicon-accurate images.


Process engineers and integrators can use virtual process modeling to test alternative process schemes and architectures without relying on wafer-based testing. One important aspect of building an accurate process model is to ensure that the model is calibrated. Having a calibrated model is important, since it provides assurance to the process integrators and engineers that the model will reflect actual process behavior. A calibrated model can also display realistic 3D visualizations of complex process flows and provide accurate results during process window studies and design technology co-optimization.

In order to calibrate a process model, inputs such as critical dimensions, pitch length, line and space length, and other important process flow feature dimensions are needed. This would include process flow steps, such as stack thicknesses for deposition and lithography parameters, and process step parameters such as etch selectivity to help define etch ratios and lateral ratios during virtual process modeling.

There are multiple techniques available to calibrate a process model in SEMulator3D:

  1. Iteratively change parameters in the model and see if the virtual measurement results match actual measurements taken from an XSEM image of a wafer.
  2. Modify metrology masks drawn within the Layout Editor and compare the model results to actual metrology measurements.
  3. Use the Expeditor batch processing engine to vary process parameters automatically and generate bulk virtual metrology measurements. These virtual metrology measurements can then be compared to on-wafer metrology results.

Process model calibration – case study

In this example, an SAQP process model is used to demonstrate Process Model Calibration at the Spacer 1 Oxide Fin CD step (figure 1) [1]. Using a measurement tool for XSEM images via Quartz, top CD, bottom CD, fin height and over-etch distance measurements were obtained, with values of 9.5 nm, 13.8 nm, 42.5 nm and 5.75 nm respectively. For this example, these measurements are the target values for our process model calibration. Using an uncalibrated model, virtual metrology measurements were measured at 11.87 nm, 12.85 nm, 45.7 nm and 5.33 nm respectively. Metrology locations (boxes) were established to measure the Fin CDs (see Figure 1, far left) and to measure the film thickness to verify the fin height.

Fig. 1: Images provided by IMEC. Zoomed in version of Spacer 1 Oxide Fin CD measured via Quartz PCI. Note: the spacer is oxide and the bottom etch stop layer is amorphous silicon [1].

In order to better specify the appropriate mandrel etch in our model, the Analytics Module of SEMulator3D is used to identify the most important process parameter settings, using a full factorial DOE as part of our Process Model Calibration. We then select input factors or parameters to vary in our etch process DOE. The etch sequence, and range of parameter values for the etch sequence, are shown in figure 2.

Fig. 2: Parameter ranges to be used in Etch Process DOE.

Using the parameter ranges shown in figure 2, we generated a virtual DOE that contained 512 different runs (combinations of parameter values) that completed in under one hour. Next, we selected the previously defined metrology targets (Sp1 top CD, bottom CD, fin height and over-etch distance measurements) to determine critical factors influencing these parameters (see figure 3) using regression analysis. After outliers are selected, the user can analyze which process parameters are critical to each of the metrology targets, using the p-values, relative weight and the r squared value of the relevant regression plot. Finally, we defined the calibration targets that we want the process model to match (see figure 3). In our example, these include spacer one top and bottom CD, the fin height and the over etch value. The desired values are set for each target, with an assigned weight representing the relative importance of the targeted item for the calibration. Parameter bounds for the calibration must also be specified.

Fig. 3: Selecting Metrology Targets.

After the parameter bounds are established, the calibration process can be started. Once the calibration process is complete, the process parameter values that should be used in the process model are listed in SEMulator3D. A table of these parameter values can be found in a full case study available on our website. If we use these parameter values, our SAQP process model can then be calibrated for the Spacer 1 Oxide Fin CD step.

Using these calibrated parameter values in our process model, we regenerated a silicon-accurate image of our calibrated Spacer 1 Oxide Fin CD model and compared it to our TEM images (see figure 4). Please note that additional parameters can be used to fully capture the tilt of the fins after the mandrel is pulled out. The virtual metrology target values are shown in figure 5 and are compared to the XSEM measurements.

Figure 4: SEMulator3D model of the Spacer 1 Oxide Fin CD after PMC. The oxide spacer is turquoise, and the red etch stop layer is amorphous silicon. TEM image with the SEMulator3D image aligned to show visual comparison. Note that sidewall angle and line to line measurements can be used with Process Model Calibration to tune for the deformation caused by the mandrel removal.

Figure 5: Table shows XSEM image measurements, measurements for basic calibration before PMC is used, and virtual metrology measurements using Trial-0 parameters from the Process Model Calibration run.


Process model calibration is a key step in ensuring that virtual process models are accurate. Using process model calibration, process window studies and design technology checks can be undertaken with a high degree of confidence in their predictive accuracy.

If you are interested in learning more about this topic, please read the full case study or contact us for additional information.


  1. Efrain Altamirano-Sánchez, Tao S. Zheng, Anil Gunay Demirkol, Gian F. Lorusso, Toby Hopf, Jean-Christophe Everat, William Clark, IMEC (Belgium); Daniel Sobieski, Fung-Suong Ou, Lam Research Corp. (United States); David Hellin, Lam Research (Belgium), “Self-aligned-quadruple-patterning for N7/N5 silicon fins”, Proc. SPIE 9782, Nanopatterning for Advanced Logic and Memory Technology Nodes
  2. Coventor SEMulator3D online product manual, July 2020

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