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In this article, high composition (>35%) thick (>30 nm) barrier AlGaN/AlN/GaN HEMT structure grown on a sapphire substrate with ultra-low sheet resistivity (<250 \Omega / \Box ) is reported. Optimization of growth conditions, such as reduced growth rate, low carbon incorporation, and thickness optimization of different epitaxial layers allowed to grow a crack-free high composition and thick AlGaN barrier layer HEMT structure. A significantly high two-dimensional electron gas (2DEG) density of 1.46 \times 10^{13} cm^{-2} with a room temperature mobility of 1710 cm^{2}/V.s is obtained by Hall measurement using the Van-Der-Pauw method. These state-of-the-art results show great potential for high-power Ga-polar HEMT design on the sapphire substrate.