We have grown the high quality and compressively strained Ge epilayers on a Si substrate with 40-nm width SiO2 trench patterns at a growth temperature of 600 degrees C. Based on (224) reciprocal space mapping measurements of Ge samples with a different thickness, the residual in-plane strain value along the trench direction decreased from -0.74% to -0.42% with increasing thickness of the Ge layer from 150 nm to 180 nm. In addition, the compressive strain along the trench direction (epsilon(-)(110)) was larger than that in the direction perpendicular to the trench (epsilon(110)) regardless of the thickness. For example, when Ge was overgrown on a SiO2 trench, the epsilon(-)(110) and epsilon(110) values were -0.42% and similar to 0%, respectively. We conclude that the asymmetric strain relaxation behavior of Ge is related to the SiO2 trench patterns, which prevent the dislocations from gliding. Defects such as a microtwin and/or stacking fault were generated during the coalescence of Ge films having different lattice constants in each Ge layer arising from the different relaxation values. A local strain in Ge, with a high spatial resolution of 2.5 nm, was measured along the two directions by means of a nanobeam electron diffraction method, thus confirming asymmetric strain relaxation and the results are in good agreement with reciprocal space mapping results. (C) 2014 Elsevier B.V. All rights reserved.