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Final Words

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In this thesis, a basic introduction on the construction of a MOSFET is given. The general output characteristics of the MOSFET are discussed, and the derivation of output characteristics based on square law and bulk charge theories are demonstrated. As the working temperature of a MOSFET is critical, the dependency of threshold voltage, saturation current and electron mobility on the temperature of the device is discussed. It was found that threshold voltage and electron mobility decrease as temperature decreases, whereas the saturation current increase as temperature increases for low values of gate-to-source voltage but decrease similar to electron mobility for higher value of g ate-to-source voltage . The concept of velocity saturation is introduced, and it was found that the MOSFET is a velocity saturated device. An explanation on the working principle of MOSFET as a energy barrier controlled device is given, and with it some critical limitations of MOSFET are discussed such as mi...
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Regression models using multiple predictors

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The regression system in the previous blog post used only one predictor (gate oxide thickness) to predict a value of a response (threshold voltage or transconductance). A more complex system which uses four predictor inputs to determine a response is presented here. The system uses the gate oxide thickness, gate length, gate voltage as standard predictors. Whereas, the saturation current is used as the 4th predictor to determine the threshold and vice versa. A Quadratic SVM Model in addition to the models used in previous system is used for training the data. Below is a snapshot of the dataset used. It has 100 data-points for training and 10 data-points for test. Threshold voltage prediction Training the models for threshold voltage as the response, it is seen that the Squared Exponential Gaussian Process Regression Model has the least RMSE at 0.0097421. The response plots (training data) for various regression models is shown below. Testing the trained models, the following results ar...
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Regression models using single predictor

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  The same datasets used shown in the classification blog post, will be used for training and testing various regression models. The datasets present in an excel spreadsheet are imported as tables in MATLAB. The training data is used to train various relevant regression models. In this use case, there is only one predictor input, which is the gate oxide thickness. The response is either the threshold voltage or transconductance. In all the models, the cross-validation parameter is set to 10. It is done to protect the model from over-fitting by partitioning the dataset into 10 groups and estimating the accuracy in each group. The models vary by virtue of the underlying mathematical function used to estimate the relationship between the predictor(s) and response. The training of various models produces the following. As in the case of classification models, the accuracy of a regression model is computed on the training data itself on MATLAB. The accuracy of a model is expressed in te...
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Classification Models to determine operating region of a MOSFET

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The datasets are imported from an excel spreadsheet to MATLAB in the form of tables. The training data is used to train various classification models.  The training data has 100 data-points, whereas the test data has 15 data data-points. The training is done to determine the region of operation of a MOSFET for a given values of threshold voltage, gate-to-source and drain-to-source voltage. In all the classification models, the cross-validation parameter is set to 5. The training data is divided in to 5 groups to verify the accuracy in each group while also preventing over-fitting the data. The accuracy of a model maybe determined by a confusion matrix. It is a performance measurement for machine learning classification models where there are two or more classes. It is a table with 4 different combinations of predicted and actual classes. It gives the count of prediction of true positives and negatives (correct classifications), false positives and negatives (erroneous classificatio...
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Machine Learning for MOSFET Modelling

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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 ...
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