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Gaussian Process Regression Model for Piezoelectric and Dielectric Constants in Gallium Nitride
Gaussian Process Regression Model for Piezoelectric and Dielectric Constants in Gallium Nitride as a function of Strain and Aluminum doping
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Abstract
Gallium Nitride (GaN) plays a vital role in a variety of high-power applications owing to its high breakdown voltage, drift velocity, and sheet charge density. Specific inverse piezoelectric based degradation mechanisms have been proposed to determine the reliability of GaN-based devices that incorporate the piezoelectric constants in their predictions. However, these constants are highly sensitive to the strain and composition of the material. The lattice mismatch of GaN with its substrates gives rise to different strain levels in the device while different devices have different Aluminum doping levels depending on the application. We used Density Functional Perturbation Theory (DFPT) to calculate the piezoelectric and dielectric constants for different compositions of GaN/AlGaN with varying biaxial in-plane strain and propose a model to predict the various components of their respective tensors as a function of doping and strain values. Here we implement a Gaussian Process Regression(GPR) based model to predict the piezoelectric and dielectric constants given the strain and Aluminum doping percentages. This tool first shows a 1D strain-based model for each doping level to highlight how GPR works. Finally, we look at the complete 2D GPR model which incorporates both composition and strain to predict the piezoelectric and dielectric constants with predictions and uncertainty quantifications. We find that piezo-electric constants which influence the total elastic stored energy under an applied vertical field or a gate voltage vary by almost 100% in a bi-axial strain range of -3% to 3% for a given composition
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