Fractional order capacitance behavior due to hysteresis effect of ferroelectric material on GaN HEMT devices

In recent years, gallium nitride (GaN) high electron mobility transistors (HEMTs) have come to the forefront of the semiconductor industry because of their exceptional performance in both high-power and high-frequency utility. Accurate capacitance modeling is crucial to optimize performance and facilitate energy-efficient electronic circuit design. In order to reflect the complex nature of the aluminum scandium nitride (AlScN) gate capacitance in GaN HEMTs this study investigates the use of the unique Grünwald-Letnikov model based on fractional order calculus. The proposed model presents a powerful approach to accurately characterize capacitance since fractional order derivatives allow modeling of non-integer order systems. Quantitative assessment of the Grünwald-Letnikov model's accuracy is performed through various error metrics, including mean absolute error (MAE), root mean square error (RMSE), maximum percentage error (MPE), mean absolute percentage error (MAPE), and mean squared error (MSE), by comparing the model's predictions to experimental data. Notably, this model demonstrates remarkable consistency in error metrics, with maximum values of MPE = 0.21%, MAE = 0.05%, MAPE = 0.33%, MSE = 0.01%, and RMSE = 0.09% for the forward scan, and MPE = 0.32%, MAE = 0.04%, MAPE = 0.39%, MSE = 0.01%, and RMSE = 0.08% for the backward scan. These metrics affirm the model's precision in capturing the nuanced capacitance characteristics of GaN HEMT devices. Hence, herein for the first time, the novel Grünwald-Letnikov model, augmented by fractional order calculus, proves to be a robust tool for accurately characterizing GaN HEMT capacitance. Its ability to seamlessly account for the complexities introduced by using ferroelectric material highlights its potential for advancing semiconductor design and optimizing device performance.