Surface State Spectrum of AlGaN/AlN/GaN Extracted From Static Equilibrium Electrostatics

Abstract

We extract an AlGaN surface state spectrum with a density ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}_{\text{SS}}$ </tex-math></inline-formula> ) ranging between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.4\times10$ </tex-math></inline-formula> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.7\times10$ </tex-math></inline-formula> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> eV <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> . The low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}_{\text{SS}}$ </tex-math></inline-formula> is achieved with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> SiN passivation. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}_{\text{SS}}$ </tex-math></inline-formula> is extracted from ungated AlGaN/AlN/GaN heterostructures with varied AlN thicknesses between 0 and 2 nm: increased AlN thicknesses in heterostructures monotonously increase two-dimensional electron gas (2DEG) densities <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}_{\text{sh}}$ </tex-math></inline-formula> and AlGaN surface potential energies <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${q} {\varphi } _{\text{s}}$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}_{\text{SS}}$ </tex-math></inline-formula> is extracted with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\Delta } {N}_{\text{sh}}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\Delta } {\varphi }_{\text{s}}$ </tex-math></inline-formula> correlations. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}_{\text{SS}}$ </tex-math></inline-formula> extraction methodology in this work features calibrated polarization charge values, Hartree approximation-based 2DEG profile calculation, and incorporated C-doped GaN (C-GaN) substrate impact on 2DEG. We also extract the charge neutrality level at the AlGaN surface, which is ~0.95 eV below conduction band minimum.