Mathematically it is possible to describe step flow growth just like dendritic growth as a moving boundary problem. Thus we got the idea to adapt our program to investigate structures evolving during that process which is industrially so important for example to grow thin films in a layer by layer fashion during MBE. From the dendrite problem heritage we found it natural to adress the question of anisotropy on steps - a question which before that to our knowledge was only mentioned very briefly by Saito and Uwaha in 1994. To gain confidence in the numerical correctness of our program and the physicality of the structures simulated thereby we started out reproducing well known results at the threshold of instability for an isolated step. Next we worked our way further in the region of instability supporting our findings with further analysis and comparison to structures found in directional solidification. Clearly this can only be a first step. It leads directly to the question if the structures arising in this approach will survive with the diffusive and elastic interaction between steps if we eventually focus on a step train. Since our work only started last autumn more work has to be done regarding this point. However during the East West Surface Sience Conference 1999 in Sofia we got the feedback that our approach is promising and will be useful to deal with a lot of open questions such as lateral structures of steps or backwards meandering during step bunching to only mention a few.
| A few of our first simulation results | |
|---|---|
| frameplot.mpg | The movie puts together some of our first simulations. Unfortunatly before the conference we ran out of time, thus there are only a few sequences for several steps. Clearly it is the main goal of our simulations to describe the behaviour of a full vicinal surface as a step train, thus we are working with up to ten steps at the moment and will report on that next. |
| ~16.7 Mb 2000 frames | |
| Sofia.ps.gz | Here you find the contribution for the workshop proceedings. From the text you will gain a better understanding of our numerical procedure and what's special about our approach. |
| ~687 Kb, gzipped |
The colors in the movie account for different values of the concentration field. It is interesting that it is easier to find the KS behaviour of splitting and reunion of stable cells for several steps than for one step only, even though analytically the KS regime can be derived for both. The reason is probably a new Goldstone mode appearing for more than one step.