Machine Learning for MOSFET Modelling

Although the MOSFET is not a recent technology, it remains as an attractive option for large-scale ICs. As process geometries are scaled down further in the nanometre range, the need for high performance computing is increasing as the supply voltages are reducing. Hence, accurate modelling of the MOSFETs is a key enabler. As a method of achieving high performance, major semiconductor companies have adopted approaches apart from scaling of a device or replacing traditional materials, such as 3D packaging at various device levels. A consequence of this is that the electrical behaviour of the device changes compared to the traditional approach. Hence, modelling of these device requires complex equations.

Owing to ever evolving technologies of the MOSFETs, development of models to characterize the new transistor behaviours has become an essential component of the design flow, and complex and interdependent equations makes modelling arduous. Artificial Neural Networks (ANN) have emerged as a capable tool for modelling and optimization. ANNs have the potential to make the use of equations redundant, instead ANNs possess the universal approximation property which imparts them the ability to learn arbitrary input-output relationships and predict any input-output relationships for which they are trained to. They make use of pre-processed data to train models.

Unsupervised Machine Learning (ML) is to model the underlying pattern or distribution in the input dataset(s) in order to learn more about the dataset(s). Unsupervised ML usually only have input data and no output. No inference is made from the data.

Supervised Machine Learning is a type of learning where there are at-least one input variable (predictors) and at-least one output (responses). It makes use of an algorithm to learn the relationship (mapping function) between the inputs and outputs in the training datasets. The requirement is to approximate the mapping function as efficiently as possible, so that when a new input data is given, the system can predict the output for that data as accurately as possible. The process of algorithm learning is supervised by the training datasets. The algorithm iteratively makes predictions on the training data and learns, the outputs are supervised by the training data itself. Hence the name supervised machine learning. Supervised ML is further grouped as classification, when the output is a category type and regression, when the output is a real value.

Classification Models

Classification refers to a predictive modelling task where a class label is predicted for the given input data. A classification model will use the training dataset and calculate how to effectively map examples of input data to specific class labels. Hence, the training dataset must be sufficiently representative of the problem and have many examples of each class label. Class labels are generally string values.

Regression Models

Regression Analysis is a subgroup of supervised ML. It models the relationship between a certain number of inputs (predictors or features) and continuous target variables, the outputs (responses). A common type of regression model is a linear regression model. This type of regression algorithm will model the relationship between a single feature and a continuous valued response. The algorithm will model this relationship by setting an arbitrary line and computing the distance from the line to the data points. This distance between the set line and the actual data points i.e. the vertical lines, are the residuals or prediction’s errors. The regression algorithm will keep moving the position of the line through each iteration, trying to find the best-fitting line with the minimum errors.

However, as seen in previous blog posts, the dependencies between any transistor parameters are not necessarily linear. Hence, there arises a need for a model which can learn non-linear relationships as well. Since different models form an internal equation based on a different underlying mathematical concept, the accuracy and effectiveness of models vary. Although based on the type of training data, certain models may be deemed more effective than the others, there is no definitive method of determining what type of model might be suitable for a particular use case or a given set of data.