Analytically Modeling the Effect of Buffer Charge on the 2DEG Density in AlGaN/GaN HEMT

Abstract

In this article, an analytical model of the buffer charge (BC) effect is presented for the 2-D electron-gas (2DEG) density ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S}{)}$ </tex-math></inline-formula> prediction in AlGaN/GaN high-electron-mobility-transistor (HEMT). Through applying Gauss’ Law, the buffer doping concentration ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}_{\text {bu}}{)}$ </tex-math></inline-formula> and energy level ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {bu}}{)}$ </tex-math></inline-formula> dependent BC density ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{\text {BC}}{)}$ </tex-math></inline-formula> is analytically expressed. Then, the contributions of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{\text {BC}}$ </tex-math></inline-formula> on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S}$ </tex-math></inline-formula> are included in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S}$ </tex-math></inline-formula> calculation. We propose and utilize the one-variable quadratic equation method to analytically express the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{\text {BC}}$ </tex-math></inline-formula> according to the understanding of AlGaN/GaN device semiconductor physics. Substituting the obtained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{\text {BC}}$ </tex-math></inline-formula> , we establish the quantitative analytical relationship between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S}$ </tex-math></inline-formula> and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}_{\text {bu}}$ </tex-math></inline-formula> under different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {bu}}$ </tex-math></inline-formula> cases, which enhances the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S}$ </tex-math></inline-formula> prediction model of the AlGaN/GaN HEMT. Compared to the conventional method without considering the BC effect, the established analytical model better predicts the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}_{S} - {N}_{\text {bu}}$ </tex-math></inline-formula> curves with the various <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {bu}}$ </tex-math></inline-formula> and is in good agreement with the experimental data. Verified by the simulation and experiment, the proposed analytical model serves as beneficial guidance for the epitaxial structure design, leakage (or breakdown) and dynamic ON-resistance performance investigation, and device or circuit simulation model implementation for AlGaN/GaN HEMT.