Critical terrace width for step flow growth: Effect of attachment-detachment asymmetry and step permeability

Abstract

A general expression for the critical terrace width for step flow growth accounting for both the step permeability and the asymmetric incorporation of atoms to ascending and descending steps is derived. It covers both cases of diffusion and attachment-detachment limited regimes of growth at high and low temperatures. It is found that when at least one of the excess step-edge barriers is equal to zero, only diffusion-limited behavior regime is allowed. The step permeability does not affect both limiting cases at high and low temperatures. Comparing the theory with experimental data for the Si͑111͒͑7 ϫ 7͒ surface leads to the conclusion that the nucleation process in the interval 700-850 K takes place in an attachment-detachment limited regime with critical nuclei consisting of one and three atoms below and above 750 K, respectively. Step flow and two-dimensional island nucleation and growth ͑2DNG͒ are two basic mechanisms of crystal growth. 1 A crystal grows exclusively by step flow when the temperature is sufficiently high so that the mean free path of the adatoms is longer than the mean terrace width. Decreasing temperature leads to a drastic decrease of the adatom diffusivity, which gives rise to island nucleation and growth on the terraces. 1,2 The interplay of surface diffusion and step attachment in growth produces an adatom concentration on terraces that generally increases with increasing spacing between step sinks. Consequently, a transition between step flow and 2DNG occurs as a function of terrace width. This transition is characterized by a quantity called the critical terrace width. Since growth involves a number of thermally activated processes, it is not surprising that the critical terrace width also displays an Arrhenius behavior as a function of deposition temperature. [3][4][5] Island nucleation occurs with greatest probability at the points where the adatom concentration is the highest. 6 Therefore, a full understanding of the transition between step flow and 2DNG requires accurate knowledge of the adatom concentration profile on a terrace. The latter is determined during growth by several factors. This includes the relative importance of diffusion and step attachment, i.e., the ratelimiting step, which is characterized in opposite extremes as attachment-detachment limited ͑ADL͒ and diffusion-limited ͑DL͒ regimes. Asymmetry of the kinetic coefficients for step attachment from opposite sides of a step 7 and step permeability 2,8 are also known to affect the adatom concentration profile. Therefore, the critical terrace width should depend on the rate-limiting step, the kinetic coefficient asymmetry, and step permeability, and may be used, in principle, to determine these important microscopic details. Various models of the critical terrace width have been presented that loosely correspond to the different extremes of the ratelimiting step. 4,9,10 However, these models did not take into account the kinetic coefficient asymmetry or step permeability. In this paper, we develop a more general model ...

Adatom diffusion on vicinal surfaces with permeable steps

“…In the case of equidistant steps and symmetric attachmentdetachment kinetics the adatom concentrations on both sides of the steps are equal. There is no gradient of the concentration and the rates of step crossings of ascending and descending steps are equal [18,34]. This results in a dynamic equilibrium of step crossings in both directions which is not expected to have an effect on the surface stability as it leads to an effective vanishing of the step permeability.…”

“…The latter should contribute significantly to the transformation of the non-primitive vicinals consisting of alternating single layer S A and S B steps into the primitive surfaces consisting of only double layer, D B , steps [10][11][12]. That is why the phenomenon of step permeability has been given considerable theoretical attention until now mostly in connection with the problem of bunching of steps on vicinal crystal surfaces [5,[13][14][15][16] and the critical terrace width for step flow growth [17,18].…”

Real-time observation of self-interstitial reactions on an atomically smooth silicon surface

“…According to theory, surface morphology can be affected by the kinetic limitations during twodimensional island growth or decay [27,[47][48][49]. The rate-limiting kinetics can be characterized as diffusion-limited (DL) or attachment-detachment limited (ADL) depending on the relative importance of the surface diffusion or the attachment-detachment of the adatoms at the step edge, respectively [50].…”

Зарождение двумерных островков на Si(111) при высокотемпературном эпитаксиальном росте

“…При достижении критической величины i * зародыш становиться стабильным и толь-ко увеличивается в размерах. Для описания экспери-ментальных данных воспользуемся развитой на основе классического представления теорией, опубликованной в работе [12], где рассматривается процесс зарождения одиночного островка на террасе между ступенями. За-висимость критического расстояния между ступенями D crit от потока материала на поверхность имеет следую-щий вид:…”