J.C. Heyraud

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.

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.

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.

Analysis of the critical behaviour of curved regions in equilibrium shapes of in crystals

Abstract Crystal shapes near {111} facets have been analyzed on indium crystals in their equilibrium shape. These measurements are compared with two theoretical concepts of the critical behaviour of curved regions: the “Pokrovsky-Talapov transition” and the “mean field theory”. Taking into account, on the one hand, the inaccuracy of the experimental determination of the origin of the curved region and, on the other hand, the “window” of validity of the Pokrovsky-Talapov transition theory, the choice between the two theories is difficult. Nevertheless the analytical expression of the mean field theory reproduces surprisingly well all the points of the experimental profile.

Surface decoration: Localization of crystallites along the steps

Abstract The interest of decorating surfaces by metallic particles is to point out defects and in particular, steps. However, the precise localization of these particles is not known. It is shown here, by statistical measurements, that gold and palladium nuclei settle in the upper part of diatomic and monoatomic steps of (100) KCl. This unexpected localization is interpreted by the consideration of the elastic strain field, induced in the substrate by an in-contact crystallite. A crystallite placed near to the lower part of a step finds itself in a repulsive situation. When localized in the upper part, an attractive force counterbalanced by the line tension of the step exists. It is understood that decorating crystallites moving along the steps do not leave them, as it has been revealed by measurements and observations.

Steady-state motion of silicon islands driven by a DC current

The understanding and control of structures at the surface of crystals is a fashionable topic nowadays. The role of an electric heating current in shaping the morphology of vicinal (111) and (001) silicon surfaces during sublimation in ultra-high vacuum is well known. Less known is the behaviour of surface features when the crystal is in contact with its own saturated vapour, and thus at equilibrium. We report here the observation by reflection electron microscopy of two-dimensional, micrometre-sized silicon islands on a resistively heated Si(001) substrate held at equilibrium (vanishing super- and undersaturation) at temperatures between 1000 and 1100°C. Surprisingly, the islands are seen to perform a gliding motion at a constant velocity in or against the current direction, depending on the island reconstruction. The value of the velocity is, on the contrary, independent of island reconstruction and size. A simple model based on adatom electromigration is discussed, that allows us to account for all observed features.

The roughening transition of the Si{113} and Si{110} surfaces – an in situ, real time observation

The roughening transition of the silicon {110} and {113} compact faces has been visualized, in situ and in real time, by transmission electron microscopy (TEM) and reflection electron microscopy (REM) under UHV. By using a silicon evaporation source in the close vicinity of the sample, it has been possible to control the silicon super (or under) saturation over the sample surface and, in particular, to obtain thermodynamic equilibrium at high temperatures (up to, roughly, 1400°C). REM pictures of the {110} and {113} surfaces at their roughening temperatures (thermodynamic equilibrium) are displayed. These roughening temperatures have been determined (1370°C and 1340°C for {110} and {113}, respectively). The kinetic broadening of the roughening of {110} and {113} has been studied by TEM, by observing the growth shapes of small silicon crystals, and by REM, by observing the topography of {110} and {113} surfaces, as a function of the growth temperature. Under our experimental conditions the {110} facet was kinetically roughened less than the {113}. In contrast, REM and TEM showed that the {111} surface does not become rough up to 1400°C.

Surface self-diffusion studied by microscopic measurements of crystallite profile evolutions

Dendritic gold crystallites on graphite are heated in ultra high vacuum up to less than 0.5 of the melting point (Tm). Electron microscopy shows that the gold crystallites change their shapes by surface self-diffusion. The dendritic contours round off while the crystallite remains very flat (20 to 40 A). The increase with time of the radii of dendrite tips is measured statistically. Such an evolution can be described by analogy to the blunting of either metal tips (Nichols and Mullins) or monoatomic cleavage tips (Hoche and Bethge). Using this result, a new technique to measure surface self-diffusion coefficients (D) is proposed. Test measurements have shown that this is an interesting, very sensitive method to measure D (down to 10−13 cm−2 s−1) which enables measurements to be made in an unusual low temperature range (0.25 Tm < T < 0.5Tm). In special cases the dendrites are split by the surface self-diffusion which is qualitatively in agreement wih the theory.