Optical properties of black phosphorus: from bulk crystal to atomic layers


Black phosphorus is a small gap semiconductor (about 0.3 eV) that has recently joined the family of two-dimensional materials. Due to its modulable band gap from mid-infrared to visible depending on the thickness, its strong anisotropy in the atomic plane as well as the high mobility of charge carriers it is promised to a high application potential in the field of optoelectronics. The objective of this thesis was to study the optical properties of the black phosphorus crystal and its atomic layers.

After a description of the different instrumental developments realized during this thesis, the methods of
fabrication of the samples are discussed. Two points have to be mastered: The elaboration of thin layers and their protection from environmental conditions to avoid their oxidation. In a first part, several methods known as “Top-Down”(mechanical exfoliation, gold assisted exfoliation, ion etching) are compared on the basis of the quality, the size, the thickness of the obtained samples as well as the ease of the operating mode execution. In a second part, two methods of thin film protection are presented: alumina passivation (by ALD or aluminum evaporation) and encapsulation of BP flakes into hBN flakes (hBN / BP / hBN heterostructures).

The strong anisotropy of black phosphorus makes the identification of the orientation of the crystallographic axes a key point in the study of the material. For this purpose, a procedure has been proposed using polarized Raman spectroscopy. It has been confronted and validated by different experimental means (TEM observations, EBSD) and theoretical means (modeling of the Raman intensity in thin films). The vibrational properties have also been studied as a function of the number of atomic layers. Several effects have been noticed at high (> 100 cm-1) and low (< 100 cm-1) frequencies and are attributed to dimensionality reduction and resonance phenomena. Thanks to the peculiar excitation conditions used in this study, a large number of modes related to inter-plane vibrations are for the first time identified and have been shown to be accurate indicators of crystallite thickness. The photoluminescence of the bulk crystal is for the first time studied at room and cryogenic temperatures.

Several band-edge emission components have been identified as excitonic, including a fine line due to the free exciton. The analysis of their behavior as a function of temperature as well as a calculation of the binding energy of the free exciton taking into account the anisotropy of the medium have made it possible to establish a new reference value for the black phosphorus gap at 0.287 eV at 2 K. The photoluminescence study of the exfoliated crystals revealed the disappearance of the fine line of luminescence in favor of a wide band. This change is attributed to the density of defects introduced by the mechanical exfoliation as evidenced by a broadening of Raman bands. The photoluminescence band was followed as a function of the thickness of the exfoliated layers down to 8 atomic layers. Below a threshold thickness evaluated at 25 nm, a shift of the band towards high energies is highlighted, and is very well described by a quantum confinement model. No significant difference is observed between the alumina passivated and hBN encapsulated samples, which indicates that the dielectric effects are not predominant in the thickness range studied.

Phd Candidate:
Etienne Carré

Christophe TESTELIN – Directeur de recherche, CNRS, Sorbonne Université – Rapporteur
Laëticia MARTY – Chargée de recherche, CNRS,Université Grenoble Alpes – Rapporteur
Bruno MASENELLI – Professeur des universités, INSA Lyon – Examinateur
Aurélie PIERRET – Ingénieure de recherche, CNRS, École Normale Supérieure Paris – Examinatrice
Pierre SENEOR – Professeur des universités, CNRS, Université Paris Saclay – Examinateur
Annick LOISEAU – Directrice de recherche, ONERA, Sorbonne Université – Directrice de thèse
Julien BARJON – Professeur des universités, UVSQ – Directeur de thèse
Ingrid STENGER – Maîtresse de conférences, UVSQ – Encadrante


Thursday 23th June 2022, 14h30
Salle Contensou, ONERA, 29 Avenue de la Division Leclerc,92320, Chatillôn

Modelling of the propagation of a short crack in ductile material coupling phase-field method and dislocation dynamics


The propagation of short cracks in FCC metals is strongly influenced by microstructures, in particular associated with the linear defects of the crystals, i.e. dislocations.

In this work, a new coupling between two methods at the mesoscale is proposed to investigate the interaction of moving cracks with three-dimensional dislocation microstructures. First, crack propagation is predicted by a phase field model. In this approach, cracks are described by some continuous damage field that evolves so as to minimize the total free energy, including stored elastic energy and surface energy associated with the crack. Second, dislocation microstructures are handled by a Dislocation Dynamics (DD) model that describes plastic deformation by the movement of dislocations under external loading.

To couple both models, the DCM (Discrete-Continuous Model) approach is used, where dislocations are described by continuous fields (eigenstrain or Nye tensor) in an elastic solver. Fast Fourier Transform (FFT) based solvers are used for their computational efficiency. Particular discretization schemes have been adopted to minimize the smoothing of dislocation cores, usually performed in MDC approaches. The different schemes are carefully analyzed with respect to the quality of the predicted fields. In addition, the resulting model is implemented using efficient parallelization solutions.

Thanks to this new coupling, we have been able to study the elastic shielding on crack propagation according to the nature of the slip systems and the dislocations density. We have also been able to investigate phenomena and ingredients rarely accounted for, such as dislocation cross slips close to the crack front or the influence of the number of sources. This mesoscale method constitutes a breakthrough for the thorough analysis of physical mechanisms controlling the early stages of fracture in metallic materials.

Keywords : Crack, Plasticity, Multiphysics modelling, Dislocation Dynamics, Phase Field

Phd Candidate:
Luis Eon

Stéphane Berbenni – Directeur de Recherche CNRS, LEM3, Metz – Rapporteur
Samuel Forest –  Directeur de Recherche CNRS, CDM, Evry  – Rapporteur
Véronique Doquet – Directrice de Recherche CNRS, LMS, Palaiseau  – Examinatrice
Lionel Gélébart – Ingénieur-chercheur HdR,  CEA/DEN, Gif-sur-Yvette – Examinateur
Rénald Brenner – Directeur de Recherche CNRS, D’Alembert, Paris – Examinateur
Yoann Guilhem – Maître de conférences, LMPS, Gif-sur-Yvette – Examinateur
Riccardo Gatti – Chargé de Recherche CNRS, LEM, Châtillon – Encadrant de thèse
Benoît Appolaire – Professeur des Universités, IJL, Nancy – Directeur de thèse


Tuesday 14th June 2022, 10h00
Salle Contensou, ONERA, 29 Avenue de la Division Leclerc,92320, Chatillôn

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