Step-mobility

Step-mobility-limited models can be further separated into two limits conserved and non-conserved [20]. This terminology refers to the local conservation of mass transport is said to be conserved if a surface defect generated at a step edge eventually annihilates at the same step or at one of the two adjacent steps. Thus, the motion of adjacent steps is coupled. The 1-D conserved model of Nozieres [21] predicts T a L, independent of Zo. On the other hand, in a non-conserved model the motion of adjacent steps is uncorrelated surface defects generated at a step edge can annihilate at any step edge on the surface. Uwaha [22] has considered this case and found x a L L/zay. In the discussion below, we will use these two limiting cases of step-mobility-limited models [21, 221 to extract the step-mobilities on Si(OOl) and Ge(OOl) surfaces from experiments on relaxation kinetics. 

In this section, we analyze experiments on the relaxation of non-equilibrium Si(OOl) [12, 25] and Ge(OOl) [24] morphologies to extract values for the step-mobility as a function of temperature. Mobilities derived from the relaxation experiments are compared to more direct measurements of step-mobilities using low energy electron microscopy (LEEM) [26] and STM [27,28]. 

Keefe et al. [12] observed that the relaxation of micron-sized 1-D gratings on Si(OOl) is consistent with Eq. 1. But as discussed above, the derivation of Eq. 1 is not strictly valid at r < Tr. We show here that these experiments are also in agreement with dynamics of the conserved, step-mobility-limited model derived by Nozieres [21] ... 

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

Bartelt and Tromp [26] have recently described direct measurement of step-mobilities using low energy electron microscopy (LEEM). We include their data for Si(OOl) in Fig. 6. 

Figure 6. Compilation of step-mobilities derived from several experiments on Si(OOl) and Ge(OOl). The temperatures for the two data points for Ge(OOl) (filled triangles) have been scaled by the ratio of the cohesive energy of Si to Ge, 1.20. The dashed line shows a thermally activated process with an activation energy of 1.8 eV and a prefactor b kQ/k, 0 is the Debye temperature of Si, 650 K, and b = 0.38 nm.

Nevertheless, the 1-D, non-conserved, step-mobility-limited model [22, 24] does appear to fit the data and we will apply it here to extract the step-mobility. For non-conserved transport, the step velocity v is simply related to the gradient in the step chemical potential by the step-mobility h ... 

Step-mobilities for Ge(OOl) using Eq. 14 are included in Fig. 6 by scahng the annealing temperature by the ratio of the cohesive of energy of Si to Ge, 1.20 [32]. In other words, to enable a comparison between the Ge and Si experiments, we assume that activation energies for Si(OOl) are 1.20 times larger than the equivalent activation energies for Ge(OOl). 

Data for step-mobilities shown in Fig. 6 span an impressively large range a factor of 10 " separates step-mobilities measured by STM from the step-mobilities extracted from the relaxation of micron-sized gratings. Some discrepancies exist, but most of the step-mobilities are consistent with a single activation energy of 1.8 eV and an attempt rate given by the frequency of atomic vibrations. We hope that this initial comparison of step-mobility data will help motivate more detailed theoretical analysis and experiments on the coimections between step-mobility and the evolution of surface morphology. 

The 2 1 ratio of base add in the reservoirs is not co-inddental. It is selected to minimize drift of the pH gradient. The pH of the anolyte must be lower than that of the most addic ampholyte likewise, the pH of the catholyte must be higher than the most basic ampholyte. Otherwise, ampholytes wiU migrate into the reservoirs and cause gradient drift. If the EOF is not reduced, a form of cathodic drift occurs as well. An exception to this is when one-step mobilization is employed. 

In a next step, mobile technology can integrate objectively measured variables regarding sleep, such as movements, short awakenings, sleep depth, or relaxation/stress, with subjective information such as desired wake-up time. This integration may allow a smart alarm to wake up a person at the physiologically most suitable moment around the desired wake-up time. Many sleep trackers on the market have this feature, yet they operate on different basic objective information thus, the wake-up time depends on the physiological information obtained (movement, heart-rate fluctuations, EEG, or a combination of those). 

Step Mobile phase Plate length in cm Time in min PTH amino acid identified... 

Parameter in Knox Eqn (11) relates to packed bed Parameter in Knox Eqn relates to diffusion in mobile phase Parameter in Knox Eqn relates to mass transfer between phases Mobile phase concentration at the kih. time step and /th distance step Mobile phase concentration of solute Mobile phase concentration of solute /... 

---