Epitaxial growth on a surface vicinal to a high-symmetry crystallographic plane occurs through the propagation of atomic steps, a process called step-flow growth. In some instances, the steps tend to form close groups (or bunches), a phenomenon termed step bunching, which corresponds to an instability of the equal-spacing step propagation. Over the last fifty years, various mechanisms have been proposed to explain step bunching, the most prominent of which are the inverse Ehrlich–Schwoebel effect (i.e., the asymmetry which favors the attachment of adatoms from the upper terrace), elastically mediated interactions between steps (in heteroepitaxy), step permeability (in electromigration-controlled growth), and the chemical effect (which couples the diffusion fields on all terraces). Beyond the discussion of the influence of each of these mechanisms taken independently on the propensity to bunching, we propose a unified treatment of the effect of these mechanisms on the onset of the bunching instability, which also accounts for their interplay. This is done in the setting of the so-called quasistatic approximation, which by permitting mostly analytical treatment, offers a clear view of the influence on stability of the combined mechanisms. In particular, we find that the Ehrlich–Schwoebel effect, elastic step-interactions and the chemical effect combine in a quasi-additive fashion, whereas step permeability is neither stabilizing nor destabilizing per se but changes the relative influence of the three aforementioned mechanisms. In a companion paper, we demonstrate and discuss the importance of another mechanism, which we call the dynamics effect, that emerges when relaxing the simplifying but questionable quasistatic approximation.

在高对称晶面附近的表面上的外延生长通过原子台阶的传播发生，这一过程称为阶梯流生长。在某些情况下，台阶倾向于形成紧密的组（或束），这种现象称为台阶束，它对应于等距台阶传播的不稳定性。在过去的五十年里，已经提出了各种机制来解释阶梯聚束，其中最突出的是逆 Ehrlich-Schwoebel 效应（即，有利于吸附原子从上阶地附着的不对称性），阶梯之间弹性介导的相互作用（在异质外延中）、阶梯渗透性（在电迁移控制的生长中）和化学效应（在所有阶地上耦合扩散场）。除了讨论这些机制中的每一种对聚集倾向的影响之外，我们还建议统一处理这些机制对聚集不稳定性开始的影响，这也解释了它们的相互作用。这是在所谓的准静态近似的设置中完成的，通过允许大部分分析处理，提供了对组合机制稳定性影响的清晰视图。特别是，我们发现 Ehrlich-Schwoebel 效应、弹性阶梯相互作用和化学效应以准加性方式结合，而阶梯渗透率本身既不稳定也不不稳定，但改变了上述三种机制的相对影响。在一篇配套论文中，我们展示并讨论了另一种机制的重要性，