Physics-Based Core Model For GaN HEMT Considering Spatial Nonlinearity And Thermal Effect

The high-power AlGaN/GaN HEMT devices are undergoing rapid development and are proving to be an excellent candidate for power and RF application due to high electron concentration,high saturation velocity,high-power and high-frequency capabilities.While these devices have high capabilities,their implementation in IC design is limited by reliability issues and the lack of fast and accurate models that capture their physics and performance.The current literature includes various models,but many are non-physical or too complex for IC design.The MVGS and ASM models have made attempts to fill this gap,but challenges still need to be addressed,such as electron concentration calculation,channel temperature,and selfheating effect,and the gradual channel approximation.To address these challenges,this research proposes a new analytical model that accurately describes the electron concentration as a function of applied voltages,which can be achieved using coupled Poisson and Schrodinger.While numerical solutions of the Poisson and Schrodinger are accurate,they are computationally expensive,making analytical solutions more desirable.Therefore,a new mathematical approximate solution for coupled Poisson and Schrodinger has been developed by this research,which considers the presence of the positive charge,complex barrier structure,and doping profile,fermi-level pinning due to the polarization charge and discontinuity of the band,and charge conservation law.This model is able to predict the electron concentration over a wide range of applied voltages with higher accuracy than other models and can predict the effect of barrier structure and doping profile on the threshold voltage.Existing physics-based compact models calculate the self-heating process as a secondary effect using a linear RC circuit,which does not consider the nonlinearity of the self-heating process and scaling effect.Also,extracting thermal resistance from numerical simulations can be computationally expensive.Several models have been developed to analytically estimate the channel temperature,but they are still limited in their scalability and do not consider the interaction between the gate fingers.To overcome these limitations,this dissertation proposes a new analytical solution for the three-dimensional heat transfer equation,which predicts the maximum channel temperature of a general GaN HEMT structure with n-gate fingers,different substrate materials,and non-linear thermal conductivity.This model provides a comprehensive understanding of the temperature distribution within the device and enables the estimation of the thermal stability of the device under various operating conditions.Additionally,the model can be incorporated into the spice program without the need for additional numerical simulation for thermal resistance.Finally,the Gradual-Channel Approximation(GCA)is used as the basis to derive the core equations in physics-based compact models,such as the ASM and MVGS models.While GCAbased physical models can achieve a good fit with output device performance,they cannot reveal a deep insight into device physics,such as predicting the maximum vertical electric field and lattice temperature,which are important for device reliability and optimization.To overcome the limitations posed by the gradual channel approximation,this dissertation proposes a closed-form analytical model for the charge,potential,and electric field distributions within the gated region of the GaN HEMT.The model is based on the solution of the Poisson equation along with current continuity equation.Additionally,an analytical equation for the channel current based on the drift-diffusion approximation is proposed.This model considers the non-uniform electric field,electrical potential,and electron concentration distributions within the device and enables accurate predictions of the device’s performance under different operating conditions.Lastly,an analytical model for the GaN HEMT intrinsic charge is proposed.The model considers the electron concentration distribution and enables the calculation of basis-dependent capacitances.