Double-crystal x-ray diffraction rocking curves and two-dimensional reciprocal space mapping (2D-RSM) are utilized to characterize the degree of strain relaxation, lattice parameters and assessment of defect propagation in two growth approaches to yield relaxed germanium buffer layers on silicon substrates. Two schemes are investigated: direct epitaxy of a single relaxed buffer layer (SE-RBL) and step-graded multiple relaxed buffer layers (GM-RBLs). The characteristics of these two growth schemes offer prospects of a much thinner grown layer compared with previously reported approaches. Two-dimensional reciprocal space mapping shows that an SE-RBL with a thickness of less than 0.35 µm has a superior quality over the GM-RBLs. A high relaxation factor (R = 0.986 ± 0.002) is obtained from the asymmetric (113) 2D-RSM of the SE-RBL with 100% Ge content. Further, the ratios of full width at half maximum of the layer to substrate FWHM (L/S) of nearly unity for both ω and ω/2θ scan directions imply a very high-quality crystalline relaxed buffer layer is realized. The 2D-RSM of the material deposited using the GM-RBL scheme, the first of its kind regarding the total grown thickness (approximately 6 µm), also show a mosaic final Ge buffer layer with an indication of reduction of dislocation density.