中文摘要：

基于各向异性弹性理论的有限元方法，研究了金字塔形自组织Ge／Si半导体量子点应变能随高宽比变化的规律：系统的应变能随着高宽比的增大而逐渐减小,并通过自由能（应变能与表面能之和）讨论了量子点的平衡形态。结果表明，对于固定体积的量子点，存在一个高宽比值，称之为平衡高宽比，使得系统的自由能最低。同时，还给出了量子点的应力、应变、流体静应变及双轴应变分布，这些可以作为阐明应变自组织量子点实验的理论基础。

英文摘要：

The dependence of total strain energy of a pyramidal self-assembled Ge/Si semiconductor quantum dot on the aspect ratio, is investigated. The free energy consisting of the strain energy and surface energy is defined, and used to study the equilibrium shape of the systems. The results show that the strain energy of the system decreases with the increasing aspect ratio, and under the requirement of minimum total free energy, the quantum dot with a given volume will take a particular height-to-width aspect ratio, i. e. the equilibrium aspect ratio. Meanwhile, the distributions of the stress, hydrostatic strain and biaxial strain are presented. These can serve as a basis for interpretation of experiments on strain self-assembled quantum dots.