InxGa1-xAs self-organized quantum dots with x=1.0, 0.5, and 0.35 have been grown by molecular beam epitaxy. The areal density, distribution, and shapes have been found to be dependent on x. The dot shape changes from a round shape for x=1.0 to an elliptical shape for x less than or equal to 0.5. The major axis and minor axis of the elliptical InxGa1-xAs dots are along the [(1) over bar 10] and  directions, respectively. The ordering phenomenon is also discussed. It is suggested that the dot-dot interaction may play important roles in the self-organization process. (C) 2000 American Institute of Physics. [S0021-8979(00)10701-7].