Terrace sizes in molecular beam epitaxy

Abstract

The order of magnitude of the typical distance ℓ between steps in MBE-grown crystal surfaces in calculated from simple scaling assumptions in the absence of evaporation. This distance is measurable by diffraction methods and yields access to the surface diffusion constant D. At the lowest non trivial temperatures the characteristic distance is of order (D/F)1/6 where F is the beam flux. At slightly higher temperature, ℓ is given by an algebraic formula which depends on the lifetime τ2 of a bound pair of adatoms at the surface, as well as of the diffusion constant D2 of these pairs. In certain ranges, ℓ varies as F-1/4 or F-1/5. At higher temperatures yet, ℓ is given by a formula which depends on a larger number of parameters. In special cases, our results are in agreement with the classical formulae of Stoyanov and Kashchiev, but disagree with certain recents works. ℓ is found to increase with temperature more rapidly than an Arrhenius exponential. Monte-Carlo simulations are reported and the discrepancy with certain other authors is clarified

The effect of a modulated flux on the growth of thin films

“…We have checked that, as in the case of a continuous flux [3,10], the saturation island density is reached for a surface coverage of about 15%. Then, the total number of cycles needed to reach saturation is n c ∼ f /(6F i d).…”

“…Summary, Perspectives : As anticipated, we have shown that it is not possible to interpret growth experiments under a chopped flux in the framework of usual growth models [3][4][5] …”

“…in order to obtain different film morphologies. A simple example is given by the quantity of islands grown on a substrate at low enough temperatures : it is known that the number of islands at saturation is given by (F/D) 1/3 [3][4][5] where F is the incident flux and D the diffusion coefficient. Then, by increasing the flux or decreasing the diffusion constant (by lowering the substrate temperature), one can adjust the saturation number of islands grown on the substrate.…”

“…Then, the important timescale for growth is given by the time needed for monomers to reach their steady state concentration or to disappear. Since, in the absence of evaporation, the monomers disappear mainly by diffusing randomly until they aggregate with an island [3], their mean lifetime on the surface is given by τ m ∼ l 2 /D where 2l is the mean distance between islands and D the diffusion constant of the monomers.We obtain τ m ∼ 1/(DN) where N is the island concentration. We can predict three regimes of behaviour, depending on the relative magnitude of τ m , d/f and 1/f.…”

“…It is therefore important to understand how growth proceeds in the presence of a modulated flux if one is to be able to interpret experiments performed in these conditions. For example, one may wonder whether the usual growth theories [3][4][5] can be used by replacing the continuous flux by the average value of the chopped flux over a cycle. In the following, we will show that this is not the case, and that the growth of the film is profoundly changed by the modulation of the incident flux for the case of growth with irreversible aggregation (critical island size 1, see [3][4][5][7][8][9].…”