Case Studies-Vacancy Diffusions

Before we move on to the next section about Cl extraction by hydrogen atoms from Cl-saturated Si(100) surface, we need to look at a number of cases to get an idea of the experiment. There have been several studies regarding the structures and kinetics of vacancies on Si surfaces. In 1993, MIT’s J. Wang, T. Arias and J. Joannopoulos identified the possible mechanisms contributed to the low formation energy and the stability of dimer vacancies on the Si(100) surface, as: (i) the need to eliminate dangling bonds in the second layer and (ii) the need for atoms to readjust in order to relax the strain [3]. Later in the same year, N. Kitamura et al. reported on thermal vacancy diffusions by real-time STM observations on the Si(001)-(2x1) surface where they tracked the motion of single dimer vacancy jumps using a novel method of repeated line scans [19]. They then obtained the activation energy of 1.7eV for the vacancy diffusions through an Arrhenius plot (Fig 1.17).

They concluded that the motion of vacancies is predominantly one dimensional along the dimer rows. They also believed that the single dimer vacancy jump is preceded by a place exchange mechanism between the atom pairs from the top and the second layers.

Fig. 1.17 An Arrhenius plot for the single dimer vacancy jump rate. From this plot they obtained an activation energy of 1.7eV. (Ref. [19]).

Vacancy diffusion has also been seen on other material and structures other than Si(100). For example, a recent report on surface diffusion of single vacancies on the Ge(111)-c(2x8) surface by means of variable temperature scanning tunneling microscope is also been observed [10]. The vacancies were deliberately created with the STM at different sample temperatures by slight tip-sample contacts (Fig1.18). They have found that the diffusion of such generated vacancies is a thermally activated motion. The vacancies have higher mobility along the parallel direction to the adatom rows than in the perpendicular direction to them. They found that the activation energy barrier along the rows is slightly lower than the activation energy barrier that is perpendicular to them (0.83eV vs. 0.95eV, respectively). They have also plotted the Arrhenius relation for the diffusion coefficient D at different temperatures and measured the activation energy and the prefactor of the system to be 0.88eV and , respectively (Fig. 1.19).

Ed D₀

1 3 .

1014 s⁻

Fig.1.18 (a) Schematic representation of the extraction procedure of a single Ge atom. (b) and (c) are constant current images showing a region before and after the creation of a single vacancy.

(Image Adopted from Ref. [10]).

Fig. 1.19 TheArrhenius plot for the diffusion coefficient D at different temperatures. The measured activation energy and prefactor of the system was 0.88eV and10^14.3s⁻¹respectively. (Ref. [10]).

For a more interesting case we will be looking at vacancy diffusions on the Cu(100) surface experiment done by van Gastel et al. [11-12] few years back. In the experiment they deposited indium atoms on a clean copper surface. The indium atoms embedded on the outermost atomic layer of the surface, and with the help of STM they traced the particles at room temperature to reveal the mobility of the atoms in the surface. The indium atoms rapidly incorporated in the outermost atomic layer, where each one replaces a single copper atom. They soon discover that the embedded indium atoms are mobile as they actually jumped over multiple lattice spacings, and the jumps where separated by a relatively long intervals of about 100 seconds at room temperature. The neighboring indium atoms also seem to jump simultaneously, causing a concerted motion. These are shown in figure 1.20.

In order to explain this unusual behavior of the indium atoms they assumed the motion is assisted by an ‘invisible particle’ that is rapidly diffusing on the surface. This particle will randomly diffuse two-dimensionally on the surface and will have a high chance of bump into the indium atoms several times, thereby making the In atoms being displaced at a distance of more than one lattice spacing in a time too short to be observed by STM. This long jump could also happen to other indium atoms simultaneously due to its fast movement.

Fig. 1.20 STM images of the Cu(001) surface at room temperature illustrating the diffusions of the embedded indium atoms. Image (a) shows five of the embedded indium atoms. Image (b) shows

There could be three possibilities responsible for the assisting role, namely an adsorbed residual gas molecule, single copper atoms on top of the surface, and the vacancies. In the case of diffusions of an embedded indium atom assisted by an adsorbed molecule from the residual gas in the vacuum system, the rate of the long jump would not agree with the rate of the adsorption of the gas molecules should it depends on it. The length of the long jump also depends on the residence time of the gas molecules residing at the indium atoms, in which the time of residence of the molecules goes down exponentially with temperature, so the jump length of the In atoms should do he same. Lastly, after desorption of the residual gas molecule, it should no longer be present on the surface and is therefore not available to assist the indium atoms in making the long jumps. The case with the exchange of the copper atoms, most indium atoms, immediately after the desorption on top of the surface, stays close to the steps rather than inserting themselves into the first copper layer, resulting a homogeneous population of the terraces with indium. This thus rules out the possibility and they concluded that surface vacancies are the ones responsible for the diffusions on the Cu(001) surface with indium atoms. They also concluded that the reason why one can not ‘see’ the vacancies is because the probability for even a single vacancy to be present in the scanning area is very low, and the rate at which each vacancy moves is much higher than the imaging rate of the STM. The short range attraction between the indium atom and the vacancy makes the jump length of the indium atom somewhat larger than that of the copper atoms. The distribution of the waiting times between successive jumps is purely exponential, which shows that subsequent (long) jumps are the effect of the passage of different vacancies. Vacancy diffusion mechanism is the main transport mechanism on the surface with measured activation energy of 0.699eV and a frequency prefactor of 10^10.4Hz(Fig. 1.21).

Fig. 1.21 Arrhenius plot of the long jump rates of the embedded indium atoms. The activation energy and the prefactor calculated were 0.699eV and10^10.4Hzrespectively. (Ref. [12]).