Statistical simulation
When photonic integrated circuits are fabricated, random and systematic process variations impact the performance of devices across wafers. As a result, some devices will meet the performance requirements, while others won't. Statistical simulations help circuit designers predict what to expect.
Monte Carlo analysis is used to predict the distributions of the performance figures of merits and the yield. Here the simulation of a circuit is repeated ~100-1000 times, each time setting the statistical parameters of the models to values randomly sampled from their process distributions. In the example shown below, an MMI is parameterized by wafer thickness (delta_height) and etch (delta_width), and the distribution in the transmission from ports opt_1 to opt_2 is obtained.
In corner analysis, the circuit designer studies the circuit performance when the statistical parameters are at combinations of extreme values. For example, one could study the circuit performance when both the wafer thickness and waveguide width are three standard deviations above their respective means.
Statistical compact modeling
A PDK designer working with CML Compiler considers the following:
What are my statistical parameters? The statistical parameters can be physical (the root cause of performance variability) or they can be the performance variability itself.
What are my corners? These are the extreme values of the statistical parameters. This data must be provided to CML Compiler to enable the model for corner analysis. CML Compiler puts this data into a data file (".lib") that is loaded by the Corner Utility in INTERCONNECT.
What is the probability distribution of my statistical parameters? The distributions of the statistical parameters are defined for local and global variations. The Gaussian or Pearson IV parameters for the process (mean, sigma, etc) must be provided to CML Compiler to enable Monte Carlo analysis. CML Compiler puts this data into a data file (".lib") that is loaded by the Monte Carlo Utility in INTERCONNECT.
How is my model sensitive to my statistical parameters? The sensitivity describes how the statistical parameter perturbs the model data. CML Compiler embeds this data within the photonic model.
How does this all come together? CML Compiler generates compact models that are sensitive to the statistical parameters. It also provides the simulators what is needed to randomly sample statistical parameter values from distributions for a given process, or set the parameters to sets of corner values.