The Analytics user interface guides users in the design, execution and analysis of large statistical experiments using various techniques, including Monte-Carlo process variation. Automated multivariate regression is used to identify important parameters and rank them by their impact on process variation.


Automating Statistical Analysis of Process Variation

The Analytics module automates statistical analysis of process variation directly within SEMulator3D.  Users can automate large statistical design of experiments (DOEs) within SEMulator3D process modeling, to minimize critical defects and maximize yield and device performance. The capabilities in the Analytics module, along with the Expeditor batch execution engine and Analytics add-ons, enable massively parallel quantitative studies of process or design variation to be undertaken. These studies can be used for process assumption validation, design rule generation, yield ramp and other applications.

Process Model Calibration

After identifying important input parameters, the Process Model Calibration (PMC) workflow allows the user to automatically optimize SEMulator3D process model parameters so that the virtual 3D model matches actual physical semiconductors.  This methodology streamlines the process of creating a virtual replica of an actual wafer.

Targets measurements from the virtual semiconductor structure can include metrology, structure search, DTC checks, and electrical analysis. The user enters corresponding target measurements from an actual semiconductor, e.g., critical dimensions from a TEM image.

PMC creates multiple trials beginning at random parameter starting points.  Multiple targets can be simultaneously calibrated and may be weighted with different levels of importance.  Parameter values may also be constrained to be within user determined lower and upper bounds. The optimized parameter values and predicted target values are provided for each trial result.

The figures display a comparison of (a) a SEMulator3D model constructed with a set of initial parameters (figure, left) and (b) a final model built from optimized parameters (figure, right).  The optimized parameters were generated during a PMC indirect optimization study.


Starting Parameters

  • sidewall angle = 3
  • xbias = -1
  • thickness=43


Starting Metrology (Desired Values)

  • Trench_CD = 44.83 (38)
  • GapCD_Top = 23.95 (38)
  • FinCD_Top = 16.89 (12)
  • FinCD_Bot = 27.27 (27)


Optimized Parameters

  • sidewall angle = 4.3
  • xbias = 1.43
  • thickness = 35.78


Optimized Metrology (Desired Values)

  • Trench_CD = 40.73 (38)
  • GapCD_Top = 36.85 (38)
  • FinCD_Top = 12.39 (12)
  • FinCD_Bot = 27.03 (27)

Process Window Optimization

The Process Window Optimization (PWO) workflow provides a streamlined methodology to understand and identify the ranges of input parameters needed to achieve specific user-defined performance metrics or goals.  This workflow can be used to drive semiconductor process decisions.

The specified process window has to be just right, to maximize on-wafer performance and yield. The question is, “How do you know what “just right” is?”  EE Journal published an article “Goldilocks Process Windows” that answers this very question, and explains how SEMulator3D can be used to calculate a process window where yield is maximized.

Cross-correlation and analysis of thousands of test data points is often required to optimize and calibrate process parameters and meet device specifications. Gathering this necessary data using non-optimized, pre-production wafers is very costly. Our blog “Controlling Variability using Semiconductor Process Window Optimization” provides an example of using PWO with SAQP Patterning, which can easily be extended for much more complex cases.

Process Window Optimization can be used to explore a broad range of process parameters without the time and expense of wafer-based experimentation.

PWO inSpec%
The figures above provide an example of Process Window Optimization.  In this example, one process parameter is varied while keeping the others constant to see how the yield varies. Confidence intervals are calculated in SEMulator3D. In our example, the red curve identifies the nominal inSpec% value, and the purple lines indicate the confidence interval.  PWO can identify processes where a small change can result in significant yield degradation or improvement. In our example, we have modifed the etch taper sidewall angle to undersand the impact on in specification % (inSpec%) and yield. Changing the sidewall angle from nominal resulted in unexpected changes of the inSpec%. This study demonstrates that small changes in process parameters can substantially impact yield. Over a large parameter space, this type of analysis would be prohibitively expensive to perform using actual wafer experiments.