Grain Growth in Polycrystalline Thin Films of Semiconductors

Grain growth in thin films is usually abnormal, leading not only to an increase in the average grain size, but also to an evolution in the shape of the grain size distribution and to an evolution in the distribution of grain orientations. The latter can be driven by surface, interface or strain energy minimization, depending on film and substrate properties and on deposition conditions, and can lead to different final textures depending on which energy dominates.In semiconductor films, as in other materials, grain growth stagnation coupled with texture-selective driving forces leads to secondary grain growth, the rate of which is higher in thinner films. Self ion-bombardment enhances the rate of pre-stagnation grain growth, and doping of Si with electron donor leads to enhanced pre-stagnation grain growth as well as surface-energy-driven secondary grain growth. The effects of ion-bombardment and dopants on grain growth in Si can be understood in terms of associated increases in point defect concentrations and the effects of point defects on grain boundary mobilities.     

Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation H=(RWL)² between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic () and deterministic () coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent which, for a saturated mound slope, yields . Received: 11 November 1997 / Revised in final form: 28 November 1997 / Accepted: 28 November 1997     

Ehrlich-Schwoebel barrier controlled slope selection in epitaxial growth

We examine the step dynamics in a 1+1-dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step edges. We find that the formation of mounds with a stable slope is closely related to the presence of an incorporation mechanism. We confirm this finding using a solid-on-solid model in 2+1 dimensions. In the case of an infinite step edge barrier we are able to calculate the saturation profile analytically. Without incorporation but with inclusion of desorption and detachment we find a critical flux for instable growth but no slope selection. In particular, we show that the temperature dependence of the selected slope is solely determined by the Ehrlich-Schwoebel barrier which opens a new possibility in order to measure this fundamental barrier in experiments. Received 11 May 1999 and Received in final form 6 November 1999     

Correlation between growth of high-index faces, relative growth rates and crystallographic structure of crystal

According to contemporary crystal growth theories, crystals are bound by low-index faces which are the most slowly growing. However, high-index faces are observed in crystal habits more and more often. In this paper the growth of high-index faces is analysed from a crystallographic perspective. It is shown that the crystallographic structure of a given crystal, expressed by the trigonometric function of appropriate interfacial angles, influences to great degree the crystallisation process and the morphology of crystals, in particular the behaviour of high-index faces. Additionally, it is concluded that at particular crystallographic structure of a crystal, a given high-index face may exist in the habit and develop its size, although it grows much faster than the neighbouring faces. Received 31 July 2001     

Equilibrium shape and size of supported heteroepitaxial nanoislands

We study the equilibrium shape, shape transitions and optimal size of strained heteroepitaxial nanoislands with a two-dimensional atomistic model using simply adjustable interatomic pair potentials. We map out the global phase diagram as a function of substrate-adsorbate misfit and interaction. This phase diagram reveals all the phases corresponding to different well-known growth modes. In particular, for large enough misfits and attractive substrate there is a Stranski-Krastanow regime, where nano-sized islands grow on top of wetting films. We analyze the various terms contributing to the total island energy in detail, and show how the competition between them leads to the optimal shape and size of the islands. Finally, we also develop an analytic interpolation formula for the various contributions to the total energy of strained nanoislands.     

Thermodynamical control of the grain size of LiCoPO4 powders

The control of the grain size distribution of the LiCoPO₄ compound was achieved by a thermodynamically monitored heating regime of the used ceramic route. For this purpose, on the basis of calorimetric (DSC-TG) measurements collected in non-isothermal and isothermal regime and then related to the grain size of the final product via equations, the irreversibility degree of the heating regime was determined. Grain size of the final product was revealed by scanning electron microscopy (SEM), while the purity of the final product was discussed from thermodynamic calculations (DSC and TG) and confirmed by X-ray diffraction analysis (XRD). The purity and the grain size of the product was tested a priori, using a series of heating regimes and then the accuracy of the established model was checked.     

Intermittent granular flow and clogging with internal avalanches

The dynamics of intermittent granular flow through an orifice at the bottom of a granular bin and the associated clogging due to formation of arches blocking the outlet, is studied numerically in two dimensions. When the hole size is less than the grain diameter, only a single grain is removed from the system so that the system self-organizes to a steady state and the distribution of the grain displacements decays as power laws. On the other hand, when hole sizes are within few times of the grain diameter, the outflow distributions are also observed to follow a power law. Received 21 July 1999 and Received in final form 17 September 1999     

On the proximity relation between two surface-melted clusters involved in inter-cluster mass transfer

We explore the way free particles produced by dissociating “particle-hole pairs” on a surface-melted cluster can be transferred to a second, nearby surface-melted cluster. This mass transport is based on an inter-cluster direct transfer mechanism of the particles. We found that in this particular case one cluster may grow at the expense of another, obeying a temporal power law with the exponent 1/2 for the average radius (R∼t ^1/2). The change from the expected universal power law (R∼t ^1/3) is a consequence of the proximity relation between these two clusters which lead to enhance the effective transport rates. Received 4 December 2000     

Shapes of heaps and in silos

Experimental investigations on the shape of a heap formed in a Hele Shaw cell either on a flat base or in a two-dimensional silo are presented. We have focused our attention on the shape dependence on mass flux and initial energy of particles poured into the cell. Two kinds of granular media are considered: glass beads and sand and we shall point out their different behaviors. We described the variations of the angle of repose and of the size of the tail as a function of the experimental parameters. We also report the time evolution of the angle of repose during the formation of the heap. Received 28 September 1998 and Received in final form 20 January 1999     

Observation of Diffusion Process of a Water Droplet Immersed in Protein Solution in Microgravity

Pure liquid-liquid diffusion driven by concentration gradients is hard to study in a normal gravity environment since convection and sedimentation also contribute to the mass transfer process. We employ a Math Zehnder interferometer to monitor the mass transfer process of a water droplet in EAFP protein solution under micro- gravity condition provided by the Satellite Shi Jian No 8, A series of the evolution charts of mass distribution during the diffusion process of the liquid droplet are presented and the relevant diffusion coefficient is determined.     

Discrete nonlinear Schrödinger breathers in a phonon bath

We study the dynamics of the discrete nonlinear Schr?dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. Received 21 January 1999 and Received in final form 20 September 1999     

Kinetics of shape equilibration for two dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time. Received 7 December 1998 and Received in final form 18 March 1999     

Hindered Coulomb explosion of embedded Na clusters — stopping,shape dynamics and energy transport

We investigate the dynamical evolution of a Na₈ cluster embedded in Ar matrices of various sizes from N=30 to 1048. The system is excited by an intense short laser pulse leading to high ionization stages.We analyze the subsequent highly non-linear motion of cluster and Ar environment in terms of trajectories, shapes, and energy flow. The most prominent effects are: temporary stabilization of high charge states for several ps, sudden stopping of the Coulomb explosion of the embedded Na₈ clusters associated with an extremely fast energy transfer to the Ar matrix, fast distribution of energy throughout the Ar layers by a sound wave. Other ionic-atomic transfer and relaxation processes proceed at slower scale of few ps. The electron cloud is almost thermally decoupled from ions and thermalizes far beyond the ps scale.     

Charge transfer between alkali cluster ions and atoms in the 1 to 10 keV collisional energy range

The cross-sections for collisional charge transfer between singly charged free clusters M _n ⁺ (M = Li, Na; n=1...50) and atomic targets A (cesium, potassium) have been measured as a function of collisional relative velocity in laboratory energy range 1–10 keV. For each cluster size, the experimental values of the charge transfer cross-section are fitted with an universal parametric curve with two independent parameters and v_m, the maximum cross-section and the corresponding velocity. For small size clusters (), the characteristic parameters show strong variations with the number of atoms in the cluster. Abrupt dips observed for n=10 and n=22 are attributed to electronic properties. Charge transfer patterns observed for various collisional systems present similarities, which appear more sensitive to cluster quantum size effects than to collision energy defects. In their whole, the and v_m parameters show differences in both their size evolution and their absolute values discussed in term of projectile and target electronic structures. Received 13 April 2000 and Received in final form 29 June 2000     

Energy exchange in structure scattering: a molecular dynamics study for Cs from Pt(1 1 1)

We have employed a classical molecular dynamics simulation to investigate the energy transfer of a heavy projectile ion to a surface, i.e. Cs⁺ impacting onto Pt(1 1 1), for incidence energies between 25 and 100 eV and an incidence angle of 45°. The in-plane scattering results show a continuous increase of the final energy with increasing scattering angle. All scattering intensities have a main supraspecular peak and scattering into subspecular angles increases with increasing incidence energy. The large projectile/target mass ratio causes a high energy loss and a strong angular dependence of the final energy distribution. The trends of the energy transfer and its angular dependence can be understood in terms of a binary collision model, augmented with double collisions and an the image charge correction. Backscattering at high incidence energies leads to a distribution of very low final energies, indicating the onset of surface sputtering. Peaks in the energy spectra arise from impact site dependent scattering and can be assigned to single, double, triple or sputtering type collisions.     

The internal energy of small ammonia clusters in a supersonic beam and after scattering off LiF(100)

The photoionization efficiency (PIE) of neutral ammonia clusters is studied as a function of photon energy. From these curves the internal energies of clusters in the incident supersonic beam and of clusters surviving after scattering off a LiF(100) surface are derived. A supersonic expansion of ammonia seeded in He produces small clusters of various size but with uniform kinetic energy of about 285 meV per monomer molecule. The mass distribution of clusters in the jet and of the scattered particles is measured in a reflecting time-of-flight mass spectrometer by single photon photoionization using vacuum ultraviolet (VUV) laser radiation tunable between and . In the incident beam the internal energies of clusters up to n = 15 do not vary significantly and amount to an average of about . After scattering off LiF(100) the internal energy of clusters up to n = 4 increases with fragment size and amounts to about half a monomer binding energy. Received 18 October 1999 and Received in final form 10 December 1999     

Grain growth and static recrystallization kinetics in Co–20Cr–15W–10Ni (L-605) cobalt-base superalloy

The grain size evolution of cold-rolled L-605 cobalt-base superalloy during ultra-rapid annealing is investigated in this paper. Cold-worked specimens undergo static recrystallization, leading to grain refinement or grain coarsening depending on the annealing time and temperature. The kinetics of grain growth is found to be independent of the initial deformation. The evolution of grain size can be simply described by a grain growth model for high temperatures and long annealing times, and the mobility of interfaces is estimated by modelling. Fast annealing treatment process is a very promising technique to customize grain size and enhance mechanical strength. In particular, the reduction of annealing time is an efficient method to produce a refined microstructure through static recrystallization.     

Spontaneous emission from a four-level system

We examine the decay dynamics of a free four-level system in the -V configuration. Quantum interference strongly manifests itself in this system, as can be seen by looking at the combined spectral distribution of the two emitted photons and at the time evolution of the intermediate-level populations, whose effective lifetimes can become very long under certain conditions for the atomic parameters. This effect is attributable to a population transfer mechanism induced in the time evolution equations by the Fano terms, also responsible for the strong modifications of the spectral correlation between the emitted photons which we analyze in detail. Finally, population trapping can also occur when the two intermediate levels are degenerate. Received: 20 October 1998     

Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t ^1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N ² when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”). The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average). We argue that this mechanism for subaging might hold in other slowly coarsening systems. Received 23 October 2000