High electron mobility transistors (HEMTs) fabricated using AlGaN/GaN heterostructures grown on Si substrate havegained tremendous attention for high-speed and high-power electronic device applications. However, improving the crystal quality of the AlGaN/GaN hetero structure in order to achieve better device performance remains challenging. Recently, the growth technique of SiNx nano-mask grown via metal organic chemical vapor deposition (MOCVD) was applied to improve the quality of the AlGaN/ GaN heterostructure. A reduction in edge-type threading dislocation density was observed, which results in improving2DEG electronic properties. However, the organic precursors involved in the MOCVD technique inadvertently introduce undesirable impurities that could degrade the crystal quality. In addition, the high temperature growth of MOCVD and thicker buffer layer could induce cracks and wafer bowing. This work evidences that theplasma-assisted molecular beam epitaxy (PAMBE) technique can efficiently support the growth of high purity epitaxial film under ultra-high vacuum and lower growth temperature conditions. High-quality GaN grown by PAMBEwith significantly reduced threading dislocation density and defects is confirmed by the X-ray and photoluminescence (PL) measurements. The enormously reduced yellow (YL) and blue luminescence (BL) intensity implies a huge reduction in point defects and impurities compared with the GaN/Si template, improved compressive stress in GaN layer by PAMBE is observed by the Raman scattering. Atomic force microscope (AFM) images also reveal smooth morphology with a root mean square roughness of less than 0.5 nm. Reduced pit density and dislocation are investigated by the scanning electron microscope (SEM) images and X-ray measurement, respectively. The above results are further verified by the cathodoluminescence measurements. In summary, high-quality GaN was grown by PAMBE for the application in high-speed and high-power electronic HEMT devices.