On-chip integrated photonics with operating wavelength at short-wave infrared region is becoming popular for its potential advantages in extending the telecommunication bandwidth and the application in gas sensing. As an important component of integrated optoelectronic chips, high-performance waveguides have attracted widespread attention. In this work, high-performance Ge waveguides were designed and fabricated on the Ge-on-Si platform, in which germanium films were epitaxially grown by the chemical vapor deposition process. The propagation loss for the waveguide was measured to be 2.34 dB/cm at the wavelength of 2 μm through the cut-back method. The quantitative relationship between the waveguide propagation loss and sidewall roughness as well as material defect density was established by introducing an empirical coefficient m. The m value was calculated to be 3.8 × 10−4 dB for the waveguide with a fixed Ge thickness of 1.5 μm by fitting the experimental propagation loss data at an operating wavelength of 2 μm. This formula provides a significant reference for future design of waveguide dimension structures, where defect induced absorption loss is non-negligible.