Francis Bailly

Critical thickness in heteroepitaxial growth of zinc-blende semiconductor compounds

It is assumed that the critical layer thicknesses (CLT) in strained heteroepitaxial layers of zinc-blende semiconductor compounds depend on an energy balance relation between the strain energy and the deformation energy induced by the misfit dislocations. The first energy is evaluated by theoretical means and confirmed by calculation. In order to calculate the latter energy, we have developed an interfacial misfit dislocation model in association with a computer simulation method based on Keatings valence force field approximation. In this way the energy of the relaxed grown layer is obtained in the case of a complete network of two-dimensional misfit dislocations. The computer simulation results are compared with published experimental data. The predicted values are in excellent agreement with the experimental CLT measurements for CdTe on CdZnTe substrates as well as for GeSi on Si substrates, over the entire alloy compositional range. It is shown that the CLT depends in fact only on lattice mismatch η. The η-3/2 law of variation of the CLT found in this way may thus be considered as quite general and is extended to GaInAs/GaAs, GaSbAs/GaAs and GaInAs/InP systems.

Randomness and determinism in the interplay between the continuum and the discrete

This paper provides a conceptual analysis of the role of the mathematical continuum versus the discrete in the understanding of randomness as a notion with a physical meaning or origin. The presentation is ‘informal’ as we will not write formulas; however, we will refer to non-obvious technical results from various scientific domains, and we will also propose a conceptual framework for understanding randomness (and predictability), which we believe is, essentially, original. As a matter of fact, unpredictability and randomness may be conveniently identified in various physico-mathematical contexts. This will allow us to explore these concepts in continuous versus discrete frameworks, with particular emphasis on the relationships and differences between classical approaches and quantum theories in Physics.

CONFIGURATIONAL ENTROPY IN OCTAGONAL TILING MODELS

We calculate the configurational entropy of random tilings obtained by elementary flips from a perfect octagonal tiling with an octagonal boundary. We map the problem of generating all configurations onto a partition problem. We calculate numerically the number of configurations and the associated entropy. We give some exact expressions in restricted cases and upper bounds for the entropy in the asymptotic case.

ZnO growth by chemically assisted sublimation

Abstract Residual water present in gases or gaseous mixtures such as H 2 , Ar or H 2 + H 2 O is shown to act as sublimation activator of the vapour phase transport of ZnO. The thermodynamic constants of the water activated sublimation are determined through close spacing vapour transport experiments using a theoretical model. The variation of the growth rate as a function of temperature is found to be not linear. Finally, some optical and structural properties of the layers are studied and compared to those of bulk crystals. No photoluminescence emission that could be attributed to HO or O 2 are detected.

Orgons andbiolons in theoretical biology: Phenomenological analysis and quantum analogies

In this paper we define two types of formal biological entities corresponding to biological levels of organization, thebiolons and theorgons, the properties of which are phenomenologically analyzed and discussed.We examine then, in a rather speculative manner, how some characteristics of these entities may suggest analogies between properties of biological systems and some special features of quantum systems.These analogies are principally related to the specific roles played by these entities (relatively to matter-energy, for orgons, and to information, for biolons) in a biological system. They are funded on the formal equivalence between the temporal variations associated to the development of the orgons and the biolons, respectively, and the statistical distribution over the available energy levels of the two main types of quantum entities, the fermions and the bosons (the former being associated to the constitution of matter and the latter to the effects of interactions).This formal comparison leads us to put into correspondences the developmental duration in biological systems with the energetic structuration in quantum ones and the related characteristic times of the former with the temperature of the latter. We discuss briefly these correspondences.

Setting up of misfit dislocations in heteroepitaxial growth and critical thicknesses

In a previous work we have shown that the critical layer thickness (CLT) in heteroepitaxial growth of zinc-blende semiconductor compounds, as defined by the minimal energy configuration between the coherent deformation of the layer and the full misfit dislocation (MD) system, varies clearly only with the lattice mismatch η as η−32. We report new results regarding situations defined mainly by the fact that the MD array is, as often observed experimentally, not complete in length or in density. In the simplest case the interfacial MD have a maximum length but only along one direction and the layer is partially relaxed, with a strain energy roughly linear as a function of thickness. Pseudo CLT are found to be smaller than the one of a completely relaxed layer. In the situation of an incomplete interfacial cross-shaped MD, dislocation loops with threading dislocation (TD) lines are assumed and the system involves strain energy value always higher than that of a full MD system. It is shown that the setting up of the full MD system is not progressive but is rather a brutal one, as in a phase transition. Another observation is that partial MD systems lead to apparent CLT different from a complete MD network. In the case of low density MD array, i.e. with MD infinite in length and located at various distances from each other, stepped stages in the setting up of the total system are also found when varying the array density. The apparent CLT are submitted to change from 0.7tc up to 1.4tc, where tc is the equilibrium CLT in an ideal unit cell. Phenomenological models are proposed with results which are in good agreement with the computational data.

About the emergence of invariances in physics: from substantial conservation to formal invariance

The role and place of relativity principles and related symmetries in physics are emphasized. It is proposed to organize part of a formalized epistemology around such invariance principles.

Remarks about the program for a formalized epistemology

The question of relationships between mathematical structures and language analysis in epistemology is considered briefly in the framework of a program for a formalized epistemology.

The characterization of systems identity in the Physical and the Biological Sciences

Abstract Our aim in this paper is to try to characterize systems as they may be circumscribed and defined in natural sciences, mainly physics and biology. The first part will be devoted to a more or less abstract determination of what may be called a system in these domains, in relationship with representations induced by empirical results or with the conceptual systems required by the theoretical approaches. In the second part we will discuss examples from an analysis of complicated situations as modelized by the mathematical behavior of dynamical systems applied to physical or biological situations. Finally, in the third part, we will examine to what extent physics and biology themselves may be considered as systems (knowledge systems or cognitive systems) and in which sense— with respect to their goals, languages and methods—it is possible to speak of a systemic identity about them.

Phenomenology of Incompleteness: From Formal Deductions to Mathematics and Physics

This paper is divided into two parts. The first proposes a philosophical frame and it “uses” for this a recent book on a phenomenological approach to the foundations of mathematics. Godel’s 1931 theorem and his subsequent philosophical reflections have a major role in discussing this perspective and we will develop our views along the lines of the book (and further on). The first part will also hint to the connections with some results in Mathematical physics, in particular with Poincare’s unpredictability (three-body) theorem, as an opening towards the rest of the paper. As a matter of fact, the second part deals with the “incompleteness” phenomenon in Quantum physics, a wording due to Einstein in a famous joint paper of 1935, still now an issue under discussion for many. Similarities and differences w.r. to the logical notion of incompleteness will be highlighted. A constructivist approach to knowledge, both in mathematics and in physics, underlies our attempted “unified” understanding of these apparently unrelated theoretical issues.