What are the best ways to incorporate process variation into your semiconductor device models?

2 How to model process variation?

There are different ways to model process variation, depending on the type, level, and source of variation. Generally, process variation can be classified into two types: systematic and random. Systematic variation is the deterministic variation that can be correlated across devices or within a device, such as lithography-induced variation, stress-induced variation, and layout-dependent variation. Random variation is the stochastic variation that is independent and uncorrelated across devices or within a device, such as dopant fluctuation, line-edge roughness, and random telegraph noise.

Depending on the level of variation, you can use different modeling techniques to capture the effect of process variation on your device characteristics. For example, you can use corner-based models to represent the extreme values of your device parameters under different process, voltage, and temperature (PVT) conditions. You can also use statistical models to represent the probability distribution of your device parameters under a given PVT condition. Statistical models can be further divided into parametric and non-parametric models. Parametric models assume a specific distribution shape, such as Gaussian, log-normal, or Weibull, and use a few parameters to describe the variation. Non-parametric models do not assume any distribution shape, and use a large number of samples to describe the variation.

Depending on the source of variation, you can use different modeling approaches to incorporate process variation into your device models. For example, you can use physical models to capture the physical mechanisms and effects of process variation on your device characteristics, such as the BSIM models. You can also use empirical models to fit the experimental data and measurements of process variation on your device characteristics, such as the PSP models. Alternatively, you can use behavioral models to abstract the functional relationship between process variation and device characteristics, such as the Verilog-A models.

3 What are the challenges of modeling process variation?

Modeling process variation is not a simple task, as it involves various challenges and trade-offs. Data availability and quality is a key factor for accurately modeling process variation, yet obtaining such data can be costly, time-consuming, and difficult. Additionally, to model process variation comprehensively, you need to consider multiple sources and types of variation, and their interactions and correlations. This can increase the complexity and size of your device models, and reduce the efficiency and speed of your simulation and analysis. Moreover, validating and calibrating your device models against the actual variation behavior and response of your devices can be challenging and error-prone.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?