J.J. Métois

Equilibrium shape and temperature; Lead on graphite

The equilibrium shape of micron-sized lead crystallites lying on a graphite cleavage plane has been obtained under UHV at 4 temperatures. By using the Wulff theorem, the surface free energy anisotropy at these temperatures has been determined. As is known from previous work. this anisotropy decreases as the temperature increases, but it is shown here that the anisotropy is not a linear function of the temperature.

Migration brownienne de cristallites sur une surface et relation avec l'épitaxie: I. Partie expérimentale

Abstract During the condensation of crystalline substance A on a crystalline surface (B), the crystallites (A) which appear, are usually supposed to be immobile. Experiments with gold (A), diameters between 10–30A, adhering on the (100) surface of KCl (B), show that crystallites (A) have a measurable brownian translation motion even at 70°C. The diffusion coefficient of the crystallites is strongly temperature dependent, so that an activation enthalpy of migration can be defined, which is a function of the crystallite size. The crystallites A are in motion only if A and B are not in epitaxial relation. During the translation motion, the crystallites rotate and obtain their epitaxial order.

Migration brownienne de cristallites sur une surface et relation avec l'épitaxie: II. Partie théorique

Abstract The thermal migration of small crystal buildings on a crystalline substrate is considered from two points of views. In the first the surface self diffusion of the atoms on the crystallites is supposed to be able to move the crystallites. In the second, special atomic configurations located in the interface crystallites-substrate are rendered responsible of these motions. Both hypotheses are formulated and compared with some experiments given in the fore going paper. The second theory is in qualitative accordance with these experiments so that the formation of an epitaxy is now better understood.

The meandering of steps and the terrace width distribution on clean Si(111): An in-situ experiment using reflection electron microscopy

In situ reflection electron microscopy experiments have been done on steps in thermodynamic equilibrium on clean Si(111) surfaces (900° C). Isolated steps and step trains (mean step separation from 20 to 140 nm) have been studied. From the thermal fluctuations of isolated steps we deduce a value of (roughly) 1 × 10 −10 Jm−10 for the line tension of a step at 900°C. The terrace width distribution has a standard deviation which varies linearly with the mean separation between steps up to mean step distances of 70 nm at least. Over the whole range of step mean separation the distributions are best fitted by a Gaussian law. This is attributed to step interactions decaying as Ax−2 (x normal distance to the step edge). The value of A is determined (A = 4.6 × 10−30 J mat(900°C). The nature of these interactions is briefly discussed.

Equilibrium step dynamics on vicinal surfaces

The time τ necessary for the formation of bumps due to thermal fluctuations on steps of vicinal surfaces is evaluated in various relevant cases. Formulae already derived by Mullins and Bales and Zangwill and other expressions recently published by Bartelt et al., are found as special cases. For Si(111) at 900°C we predict that τ is proportional to the step-step separation l and to the square of the fluctuation wavelength L. This prediction is found to be in reasonable agreement with direct experimental observations of equilibrium step fluctuations.

The equilibrium shape of silicon

Abstract In order to obtain the equilibrium shape of silicon, small monocrystalline silicon columns (diameter ∼ 1–5 μ m, height ∼ 10 μ m) have been formed on a silicon (111) substrate by photolithography. Indashsitu observation, in a UHV transmission electron microscope, of the shape changes of these columns upon heating them shows that the equilibrium shape of clean silicon can be installed over the apices, once the columns have become bulbous by evaporation and surface diffusion. Equilibrium profiles, along the 〈110〉 and 〈112〉 zones, have been visualised indashsitu at 1323 K, recorded and analysed. Well-characterised {111} and {113} facets exist on the equilibrium shape at this temperature. They are separated by rounded regions that display a tangential merging into the facets. Hence, all orientations belong to the equilibrium shape at 1323 K. The γ-plot has been constructed for the 〈110〉 zone. It shows cusps at 〈111〉 and 〈113〉 and rather broad minima at 〈110〉 and 〈100〉. However, within the resolution of our micrographs, it is not possible to decide whether flat facets exist at 〈110〉 and 〈100〉 or whether the crystal surface is merely slightly rounded. The anisotropy of the surface specific free energy is found surprisingly weak (∼ 4% maximum). Within the experimental accuracy (∼ 1%), the hierarchy is γ 111 ≥ γ 110 > γ 113 > γ 100 , the relative anisotropies with respect to {111} being 0.99, 0.98 and 0.97 for {110}, {113} and {100} respectively. An order of magnitude for the step-free energy β has been obtained ( β 111 ≈ 3 × 10 −11 J m −1 , β 113 ≈ 1 × 10 −11 J m −1 ). Our results are compared to those obtained by other authors by using voids in silicon.

Surface free energy anisotropy measurement of indium

Abstract The equilibrium shape of In crystallites shows {111}, {001}; and {100} plane faces. The facets are connected by curved surfaces with smooth edges. The Wulff construction allows the surface free energy anisotropy to be measured in the main zones of the crystal, i.e. 〈001〉, 〈100〉, 〈110〉 and 〈011〉. The higher surface free energy is found in the 〈011〉 direction. Within the accuracy of the measurements the {001} and {100} faces show the same energy.

Anomalous 13 422 diffraction spots from {111} flat gold crystallites: (111) surface reconstruction and moiré fringes between the surface and the bulk

Abstract This paper describes very flat {111} gold crystallites grown on graphite. The diffraction patterns of such crystallites show the “usual” 1 3 422 anomalous spots. It is shown that these spots are in fact split in such a way that each 1 3 422 spot is surrounded by an hexagonal array of additional spots, aligned in the 〈110〉 directions. When seen by TEM, the crystallites show 〈112〉 periodic contrasts which are not normal moire fringes or misfit dislocations between gold and graphite. An interpretation following Yagi et al. is proposed which connects these 2 kinds of anomalies: they should result from the surface superstructure 23 × 1 of clean (111) gold face, described very recently by Melle and Menzel.

Complementary data obtained on the metal-semiconductor interface by LEED, AES and SEM: Pb/Ge(111)

Abstract AES, LEED and scanning electron microscopy analysis performed on the Pb/Ge(111) system under UHV lead to the following main results. The Pb/Ge(111) system exhibits the Stranski-Krastanov growth mode. The stoichiometry of the complete 2D layer is one. This monolayer undergoes a reversible phase transformation √3 × √3 ⇄ 1 × 1 at around 300°C. The value of the bonding energy of one lead atom on (111)Ge is found to be equal to φ Pb − Ge = 31 ± 2 kcal mol . The adhesion energy of a 3D lead crystallite on (111)Ge has been estimated to be β = 918 ± 9 erg cm 2 .

Impact of the growth on the stability–instability transition at Si (111) during step bunching induced by electromigration

Abstract The central result of this work is the definite proof that the mechanisms of the direct current induced step bunching in the middle and high temperature domains are different. We used the recently developed technique for reflection electron microscopy (REM) observation of Si surfaces during equilibrium and during crystal growth to document the impact of the growth on the process of step bunching induced by direct current heating of an Si crystal. We found completely different effects of crystal growth on the stability of the vicinal surfaces in the two temperature domains 1160–1240°C and 1260–1320°C. In the high temperature domain step bunching takes place at step-down direction of the electric current during sublimation, equilibrium and growth; whereas in the 1160–1240°C domain bunching takes place at step-up current during sublimation and at step-down current during growth. These findings support the concept of local mass transport in the high temperature domain — the surface migration of adatoms is effectively interrupted at each step by a high rate exchange between the adlayer and the crystal phase. At 1160–1240°C the mass transport is global — adatoms easily cross the steps without taking part in the crystal–adlayer exchange. Since earlier studies of other researchers support the concept of local mass transport in the low temperature domain, 900–1050°C, a difficult question arises — why do the properties of the steps, with respect to the mass transport over the crystal surface, have a temperature dependence which is not monotonous? To explain the transition from local mass transport in the low temperature domain to global mass transport in the middle temperature domain we advance a hypothesis for a transition from a low temperature state of adsorption (Takayanagi-like adatoms, existing above the (7×7)↔(1×1) transition) to a high temperature state of adsorption (adatom with three dangling bonds) with much lower activation energy for desorption.