We have investigated the structural properties of multi-stacked layers of self-organized In0.4Ga0.6As quantum dots (QDs) embedded with GaN0.007As0.993 strain compensation layers (SCLs) grown on GaAs (3 1 1)B substrate by atomic hydrogen-assisted molecular beam epitaxy. Symmetrical lens-shaped QDs are observed along [0 1 (1) over bar], while their shape is asymmetric along [(2) over bar 3 3] with two different dominant facets. Further, QDs are vertically aligned in the growth direction when viewed along [0 1 (1) over bar], while the alignment is inclined at an angle of 22 degrees with respect to the growth direction when viewed along [(2) over bar 3 3]. The inclination angle is in good agreement with the result of resonant diffuse X-ray scattering sheets in reciprocal space mapping around GaAs (3 1 1) lattice point. We believe that the local strain field around QD extends further outward from the lower-angle facet, thereby the vertical alignment is tilted along the direction of stronger strain field. (C) 2009 Elsevier B.V. All rights reserved.