Keywords: Atom-solid interaction, scattering, diffraction; Diffusion; Computer simulations
 
 
 
 
 

*Fax: +36 1 242 43 16, E-mail: vargag@ phy.bme.hu, Home page: http://goliat.eik.bme.hu/~vargag/

@Poster 2000 varga

Abstract

On the solid surfaces evolution of condensation seeds can be observed by Scanning Tunneling Microscope (STM). Present work discusses a quantum mechanical model that describes these phenomena. Solid surface is characterized as a set of contours of the time dependent interaction potential. The seeds are the special places on this potential map that attract the impurity atoms. The places of the seeds are determined by the usage of the wave-packet method on the fluctuating potential surface. This method means that the impurity atoms are described as an ensemble of independent particles by Gaussian wave packet. Time dependent Schrödinger equation is governed the time propagation of Gaussian wave packet. The time dependent Schrödinger equation is solved by numerically [1][2]. The propagation of the wave packet provides the condensation seed from the probability density function (PDF). The places of local maximum of PDF correspond to the condensation seeds. The model computations show a realistic dynamic model of seed evolution on solid surfaces.
 
 

For example, rhodium epitaxy on TiO2(110)-(1x2) surface show a special seeding process [3]. To demonstrate the seeding process let us show some images (Fig. 1) that has been taken by STM [3]. Further experimental results of nanoparticles fabrication can be found in [4][5].

• Deposition: Fig. 1A and B show the surface morphology of rhodium at two coverages on 300 K.
• Seeding: the sample was annealed at 1100 K.
• Growing: Fig. 1C and D show the exposition further to rhodium of 1 Ml equivalent at 1100 K in UHV. One can see nanoparticles.

Figure 1 Rh particles on TiO2(110)-(1x2) at 300 K. (A) 0.003ML of Rh and (B) 0.020 ML of Rh. Both surfaces were annealed at 1100 K and grown by post-deposition of 1ML equivalent of Rh (C, D). Fig. 1E shows the morphology of the surface when it was post-deposited at 300 K and annealed at 1100K. The size of images is 100nm x 100nm

The main aim is to give the skeleton of a physical model that describes the "seeding" and "growing" process (SGP).
 
 

Deposition:

• Atomic beam is modelled by Gaussain wave-packet.
• Atom-solid surface interaction is characterised by interaction potential
• Time evolution is governed by time dependent Schrödinger equation.
• Deposition points can be identified by the local maximum of probability density function (PDF) at the surface. Deposition points appears where the attractive part of the interaction potential is strong enough (electron change is possible).

At high temperature on the surface special seeding points are developed. What is the reason of this phenomenon? At high temperature the thermal motion becomes relevant. In that case around the deposition points the attractive part of the atom-solid surface interaction energy remains significant. However, the attractive part (low temperature) of the interaction potential outside of the deposition points becomes strongly time dependent - it is alterning between repulsive and attractive values - at high temperature. This effect leads to the evolution of seeding points.

• Based on the above mentioned process an atom-solid surface time dependent interaction energy function has to be chosen that has strongly attractive values in the seed points.

Growing:

• An interaction energy function has to be chosen with special seeding points.
• Atom exposition beam is described by a Gaussian wave-packet.
• The time evolution of the state function is governed by time dependent Schrödinger equation.
• The shape of the probability density function provides the shape of the particle clusters. (See Fig.)

Very first computations show the effectiveness the above outlined model. The computation results provides similar clusters of particles to Fig. 1. However difficulties arise. Hard problem is to give appropriate interaction potential and energy function. There is no answer how the interaction energy changes when the cluster increases. Some kind of adaptive method should be developed.
 
 

References

[1] G. Varga, Surface Science, (1999) vol. 441 p. 472-478.

[2] G. Varga, Applied Surface Science, (1999) vol.144-145 p. 64-68.

[3] A. Berkó, F. Solymosi, Surface Science, (1998) p. 281-289.

[4] A. Berkó, G. Klivényi and F. Solymosi, Journal of Catalysis, (1999) vol 182 p. 511-514.

[5] A. Berkó, T. Bíró and F. Solymosi, J. Chem. Phys B (2000) vol. 104 p. 2506-2510.