Adatom concentration

Figure Bl.26.24. The change of work fimction of the (100) plane of tungsten covered by Na, K and Cs, and work fiinction of alkali metals (dashed-dotted line) versus adatom concentration n (Kiejna A and Wojciechowski 1981 Prog. Surf. Sci. 11 293-338).

The rate of mass transport is the product of these two factors, the density of atoms and the diffusion coefficient per atom, as shown in Fig. 6. Over a large temperature interval up to the mass transport coefficient is almost perfectly Arrhenius in nature. The enhanced adatom concentrations at high temperatures are offset by the lower mobility of the interacting atoms. Thus, surface roughening does not appear to cause anomalies in the... 

The incorporation of the adatoms at the steps should be fast because no charge transfer is involved hence the adatom concentration should attain its equilibrium value ... 

The interpretation of this data on metals in terms of microscopic mechanisms of surface atom transport is not totally understood. The original papers[ 11] proposed that during surface transport the controlling process was adatom terrace diffusion between steps with the adatom concentration being that in local equilibrium with the atomic steps. This may indeed be the case, but in light of other experiments on adatom diffusion[13] and exchange processes at steps[14] the possibility of step attachment/detachment limited kinetics caimot be raled out. 

There are other ways to obtain many of these results. Decades ago Mullins (1957, 1959, 1963) showed the fruitfulness of formulating the problem in terms of a step chemical potential. Bales and Zangwill (1990) used the linear kinetic approximation that the step velocity is proportional to the difference between the adatom concentration near the step edge... 

Figure 4. Early time adatom concentration profile for 7 =0.56r A = 32a (a) concentration, C vs. position, (b) schematic illustrating lower step interaction energy upon creation of adatoms on the top terrace (i) and higher step interaction energy upon creation of adatoms on the bottom terrace (ii).

Fig. 7.138. Adatom concentration profiles, c M/c, between two steps of growth, (a) for different cathodic (upper part of the plot) and anodic (lower part of the plot) overpotentials at X = 0.31 8. (b) For different surface diffusion (sd) rates 0.1 8step < < 3.1 8step atTo mV cathodic and anodic...

Note that in this specific model, desorption is neglected, and sites get regenerated upon adsorption, so the classic Langmuir blocking of sites is uncommon for MBE modeling. Furthermore, the diffusion-adsorption model for the terrace is only approximate since interactions between molecules are not accounted for. As a result, this hybrid model cannot handle nucleation between terraces, and applies only to small supersaturations or high temperatures [note that for high temperatures, one needs to include desorption in Eq. (2)] where the adatom concentration on terraces is relatively low. 

The adatom concentration at equilibrium, o,ads [atoms cm ], is determined by the Gibbs energy AGdispi [J mol ] of the displacement reaction of atoms from kink positions to free" adsorption sites on the surface, where it can form an adatom [2.1] ... 

The equilibrium adatom concentration is a well-defined thermodynamic quantity characteristic for the respective crystal face. It does not depend on the profile of the surface, particularly on the presence of steps as long as Wfree ... 

The equilibrium adatom concentration Co,ads. as expected from eq. (2.24), is independent of the ion activity and the actual value of the equilibrium potential... 

If, however, for any reason, the electrode potential deviates from the equilibrium potential and the balancing equilibrium with kink atoms is blocked, as, e.g., in the absence of steps and kink sites (cf. also Section 2.3), the adatom concentration may change until a dynamic equilibrium between deposition and dissolution is reached diss,free ads dep.free > free Th adatom concentration, ads, or Cads, becomes a function of electrode potential, E, or overpotential rj = E- E y z+, so that... 

At more negative potentials, i.e., at higher (negative) overpotentials tj, the adatom concentration increases because the flux of ions from the solution increases accordingly. 

If the potential of an atomically smooth (non-stepped) singular face is changed, e.g., to a value more negative than the reversible potential, the enhanced deposition rate dep,free will increase the adatom concentration above its equilibrium value Co,ads until the opposite reaction of dissolution idiss,ads reestablishes the balance. The adatom concentration Cads(r/) increases and becomes a function of overpotential as given by eq. (2.29). 

In the presence of steps, in the close vicinity of the step edge, the kink-adatom exchange reaction will keep the adatom concentration at its equilibrium value Co,ads- At a distance from the step greater than the mean displacement yilsd (cf. eq. (2.35)), however, adatoms deposited on the face cannot reach the step edge during their lifetime on the surface, so that the adatom concentration will remain unaffected by the presence of the step and equal to Cads( )-... 

This causes a diffusion flux, I>sd(cads - fo,ads) /, of adatoms towards the step edge, where the adatoms are rapidly incorporated into kink positions. Therefore, the adatom concentration at the step edge is kept at the equilibrium value Co,ads- At room temperatures, where the average kink distance, i k (cf. eq. (2.5)), is low and smaller than the mean displacement of adatoms, diffusion along the steps can be neglected and the diffusion process can be treated as linear. The incorporation of atoms in the step results in a step propagation with a rate Vsd [cm s ] determined by the flux Dsd Acads/Asd [mol cm s ] and the area 0 hU) occupied by one mole. 

The current is strongly localized around the steps, as seen for instance on Fig. 2.13b, and the adatom concentration is uniform over the surface with the exception of that in the close vicinity of the step edges (Fig. 2.12b for Asd Q.ft step) The surface diffusion process controls the reaction rate and the current density is proportional to the step density Ls-... 

In an ordered monolayer, both the surface area, A, and the surface adatom concentration, r, may be expressed in terms of a characteristic lattice parameter, r, as a common independent variable. Therefore... 

Through statistical fluctuation in the local adatom concentration, these clusters grow or decay. 

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