In this paper, the impact of AlGaN barrier thickness (tAlGaN) and substrate leakage on the noise conductance and noise figure in GaN High Electron Mobility Transistor (HEMT) is investigated. The investigation and analysis in this paper are targeting the Low Noise Amplifier (LNA) applications. The noise analysis is carried out using Technology Computer-Aided Design (TCAD) physical simulator. Initially, the DC, RF, and noise simulations are validated against measurements of a GaN device. AlGaN barrier thickness (tAlGaN) is varied and its impact on the minimum noise figure (NFmin) is analyzed. It is observed that the NFmin decreases with tAlGaN reduction at the typical bias conditions of LNA. This observation on the impact of tAlGaN on the NFmin follows Fukui's model, which states that the NFmin decreases with the increase in transconductance. In addition, the impact of the substrate material on noise performance is analyzed. The substrates used for the investigation are Silicon (Si) and Silicon Carbide (SiC). At 40 GHz, it is found that the noise conductance and the NFmin of GaN HEMT on SiC substrate is reduced by 13% and 12%, respectively, in comparison with GaN HEMT on Si substrate. This could be attributed to the lower gate-tosubstrate capacitance of the GaN HEMT on SiC substrate.