单晶锗横向外延生长的相场法模拟

       成熟的半导体工艺可将锗异质集成到硅晶圆上，因此在不增加成本的前提下能够充分利用锗优异的光电特性。锗在图案化硅衬底上横向外延生长所呈现出的特殊结构和生长动力学为光电领域的研究和器件制造提供了新思路，但其生长机理尚未被深刻认识。由于化学气相沉积过程的复杂性，很难直接观察和测量生长过程中发生的演化现象，因此本文利用相场法对生长过程进行了研究。
       相场模型以金兹堡-朗道自由能和非平衡热力学为基础，耦合了浓度场和相场的演化方程，利用有限元方法进行求解。其中，浓度场的构建在模拟几何域内引入了竖直向下的锗原子通量。我们发现横向外延生长过程中晶体的形貌演化主要受气相原子的表面沉积，以及在能量最小化驱动下的表面原子迁移所控制。特殊形貌和生长行为由以下两种机理调制：
       各向异性至各向同性转变由掩膜曲率诱导，曲率决定了晶体表面原子迁移方向。横向生长初期晶体几何特征与掩膜相似，原子倾向于迁入大曲率掩膜对应的晶体表面位点以降低表面积与表面能。在曲率诱导下，横向生长初期为各向异性生长模式，直至生长前端呈现曲率相同的圆形，生长模式转变为各向同性。
       孔洞的形成受晶体表面原子浓度调制。横向生长前期表面存在稳定的浓度梯度层，当生长前端相互靠近时，原子供给不足以维持前端匀速推进。在几何屏蔽效应作用下，生长前端下侧停止生长，上侧继续生长直至合并，这种差速生长行为导致合并点下方形成孔洞。此外，我们引入锗的各向异性晶面能还原了孔洞内部晶面构造。

       Mature semiconductor processes allow the heterogeneous integration of germanium onto silicon wafers, so that the excellent optoelectronic properties of germanium can be fully utilized without increasing manufacturing costs. The special structure and growth kinetics shown in the lateral epitaxial growth of germanium on patterned silicon substrates provide new ideas for research and device fabrication in the field of optoelectronics, but the growth mechanism has not yet been well understood. Due to the complexity of the chemical vapor deposition process, it is difficult to directly observe and measure the evolutionary phenomena occurring during the growth process, so we study the growth process using the phase field method in this thesis.
       The phase field model is based on Ginzburg-Landau free energy and nonequilibrium thermodynamics, coupled with the evolution equations of the concentration field and the phase field, and solved using the finite element method. The concentration field is constructed by introducing a vertical downward germanium atomic flux in the simulation domain. We find that crystal morphology evolution is mainly controlled by the surface deposition of gas-phase atoms, and surface atom migration driven by energy minimization. The specific morphology and growth behavior are modulated by two mechanisms:
       The anisotropic-isotropic transition of growth mode is induced by the curvature of the mask, which determines the direction of atomic migration on the crystal surface. In the early stage of lateral growth, the crystal geometry is similar to that of the mask, and the atoms tend to migrate into the crystal surface sites corresponding to the mask with large curvature to reduce the surface area and surface energy. Under curvature induction, the lateral growth shows anisotropic growth mode until the growth fronts have a circular shape with the same curvature, and then the growth mode switches to isotropic way.
       The formation of the cavity is modulated by the atomic concentration on the crystal surface. In the early stage of lateral growth, there is a steady concentration gradient layer on the surface. When the growth fronts are close to each other, the atomic supply is not sufficient to maintain the uniform advancement of the growth fronts. Under the effect of geometric shielding, the lower sides of the growth fronts stop growing, while the upper sides continue growing until coalescence. This behavior of growing at different speeds leads to the formation of a cavity underneath the coalescence point. In addition, we introduce the anisotropic crystal surface energy of germanium to reproduce the inner structure of the cavity.

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