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Probing the electrical properties of multilayer grapheneKhodkov, Tymofiy January 2012 (has links)
Graphene is a new two-dimensional (2D) material with unique electrical transport, optical and mechanical properties. However, monolayer graphene (MLG) is a gapless semiconductor, which limits its relevance for transistor applications where a large on/off ratio of the current is required. In this work the investigation of transport properties of few-layer graphene (FLG) is presented. These 2D electronic systems offer a novel solution to the problem concerned the absence of an energy gap in single layer graphene, since they exhibit an electric field and stacking-dependent band gap in the energy dispersion. Thus far, a clear observation of a band-gap in multilayer graphene (e.g. Bernal-stacked bilayers) in transport measurements was hindered by the presence of disorder. Here we develop a reliable and effective method of fabrication of high-quality suspended double-gated graphene devices, which are of crucial importance for probing the low energy dispersion of few-layer graphene. The current annealing technique, described in details, improves transport characteristics like carrier mobility, which is typically higher than ∼ 104 cm2/Vs for our multilayer devices. Electrical transport experiments on suspended dual-gated ABC-stacked trilayer are performed. We report the direct evidence of the opening of a tunable band-gap with an external perpendicular electric field, ranging from 0 meV up to 5.2 meV for an electric field of 117 mV/nm. Thermally activated transport is observed in these samples over the temperature range 0.5 - 80 K. The values of energy gap extracted from both temperature dependence of minimum conductivity measurements and non-linear I –V characteristics correlate well. Our experimental results are in a good agreement with theoretical approximation, based on self-consistent tight-binding calculations. The high quality of our ABC trilayer samples is also demonstrated by a particularly high on/off ratio of the current (250 at applied electrical displacement as low as 80 mV/nm), which makes these devices promising for future semiconductor electronics. FLG samples with reduced disorder allow us to observe quantum Hall effect (QHE) at magnetic field as low as 500 mT. We present the first study of electric field- induced new QH states in ABC trilayer graphene (TLG). The transitions between spin-polarized and valley polarized phases of the sample at the charge neutrality point are investigated. Resolved novel broken symmetry states along with observed Lifshitz transition in rhombohedral TLG display exciting phenomena attributed to rich physics in these interactive electronic systems.
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Propriedades eletrônicas de tricamada de grafeno e nanofitas de carbono tensionadas / Electronic properties of trilayer graphene and strained carbon nanoribbonsSena, Silvia Helena Roberto de January 2012 (has links)
SENA, Silvia Helena Roberto de. Propriedades eletrônicas de tricamada de grafeno e nanofitas de carbono tensionadas. 2012. 112 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-15T18:11:54Z
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Previous issue date: 2012 / Graphene is a truly two-dimensional crystal with a gapless linear electronic spectrum at low energies (E<1 eV) which, along with the chiral nature of its charge carriers, is responsible for a variety of unusual properties. As a result of its uniqueness, a great effort has been made in order to understand all its fundamental properties and try to generate a new technology of them. In this thesis we theoretically study two types of graphene-related systems: graphene nanoribbons and trilayer graphene (TLG). Concerning the former, a tight-binding model is used to study the energy band of graphene and graphene ribbon under simple shear strain. The ribbon consists of lines of carbon atoms in an armchair or zigzag orientation where a simple shear strain is applied in the $x$-direction keeping the atomic distances in the $y$-direction unchanged. Such modification in the lattice gives an energy band that differs in several aspects from the one without any shear and with pure shear. The changes in the spectrum depend on the line displacement of the ribbon, and also on the modified hopping parameter. It is also shown that this simple shear strain tunes the electronic properties of both graphene and graphene ribbon, opening and closing energy gaps for different displacements of the system. The modified density of states is also shown. On the latter subject, the continuum model is used in order to investigate the electronic spectrum of three coupled graphene layers (graphene trilayers) in the presence of an external magnetic field. We obtain analytical expressions for the Landau level (LL) spectrum for both the ABA and ABC types of stacking, which exhibit very different dependence on the magnetic field. While the LL spectrum of ABA TLG is found to be a superposition of a monolayer-like and bilayer-like spectra, the ABC TLG present a nearly B^{3/2} field dependence. We show that layer asymmetry and an external gate voltage can strongly influence the properties of the system. In addition, the cyclotron resonance energies, the corresponding oscillator strengths, and the cyclotron absorption spectrum for trilayer graphene are calculated for both ABA and ABC stacking. A gate potential across the stacked layers leads to (1) a reduction of the transition energies, (2) a lifting of the degeneracy of the zero Landau level, and (3) the removal of the electron-hole symmetry. / Grafeno é um cristal bidimensional cujo espectro eletrônico a baixas energias (E <1 eV) apresenta dispersão linear e ausência de gap que, juntamente com a natureza quiral dos portadores de carga, são responsáveis por uma variedade de propriedades incomuns. Como resultado da sua natureza singular, um grande esforço tem sido feito para entender todas as suas propriedades fundamentais e tentar gerar uma nova tecnologia baseada nesse material. Nesta tese, nós realizamos um estudo teórico de dois tipos de sistemas: nanofitas de grafeno e tricamadas grafeno (TCG). No que diz respeito ao primeiro sistema, um modelo de ligação forte (tight-binding) é utilizado para estudar as bandas de energia do grafeno e fitas de grafeno sujeitas a uma tensão de cisalhamento. A fita é constituída por linhas de átomos de carbono cujas bordas estão orientadas nas direções conhecidas como “armchair” ou “zigzag”. Uma tensão de cisalhamento simples é aplicada na direção x de forma que as distâncias interatômicas na direção y são mantidas inalteradas. Esta modificação na rede cristalina origina bandas de energia que diferem em vários aspectos do sistema original sem qualquer deformação. As mudanças no espectro dependem do deslocamento entre linhas adjacentes da fita, bem como do parâmetro de “hopping” modificado. Mostra-se também que este cisalhamento simples modifica as propriedades eletrônicas de ambos os sistemas, fitas de grafeno e grafeno, abrindo e fechando gaps de energia para diferentes deslocamentos do sistema. A densidade de estados modificada também é mostrada. Por fim, o modelo contínuo é utilizado a fim de investigar o espectro electrônico de três camadas de grafeno acopladas (tricamada de grafeno), na presença de um campo magnético externo. Nesse contexto, obtemos expressões analíticas para os nveis de Landau para ambos os tipos de empilhamento: Bernal (ABA) e romboédrico (ABC), verificando-se uma forte dependência dos níveis de energia com o tipo de empilhamento. Embora o espectro de Landau para tricamadas ABA seja uma sobreposição dos espectros de uma monocamada e de uma bicamada, tricamadas com empilhamento ABC apresentam uma dispersão do tipo B3/2 com o campo magnético. Foi mostrado que uma assimetria entre as camadas, que pode ser introduzida por um potencial externo, pode influenciar fortemente as propriedades do sistema. Além disso, as energias de ressonância cíclotron, assim como forças de oscilador correspondentes, e o espectro de absorção para tricamadas de grafeno são calculadas para ambos os tipos de empilhamento. Verificou-se que um potencial de porta aplicado através das camadas leva a (1) uma redução das energias de transição, (2) um levantamento da degenerescência do nível de Landau n=0, e (3) a quebra de simetria entre elétrons e buracos.
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A slow-release organophosphate-filled trilayer polyolefin filmMadzorera, Tatenda Panashe January 2017 (has links)
The development of pyrethroid resistance in mosquitoes threatens the goal of malaria elimination in Africa. Alternative insecticides, e.g. organophosphates, can be considered to control pyrethroid resistant mosquitoes. The problem associated with the deployment of organophosphate-based insecticides is their high volatility. Conventional application forms have a fairly short residual efficacy. This study aimed at extending the residual efficacy of an organophosphate insecticide by using a polymer matrix as a slow release device. A multilayer film blower was used to produce a trilayer film. The middle layer comprised poly(ethylene-co-vinyl acetate), i.e. EVA polymer, impregnated with malathion. This was sandwiched by two low density polyethylene (LDPE) outer layers. These acted as semi-permeable membrane-like barriers that slowed down the release of the contact insecticide to the surfaces of the film. In theory, such a film could be deployed as a long-lasting insecticide-treated wall lining in pyrethroid resistant settings. Scanning electron microscopy (SEM) confirmed the trilayer film structure of the blown film. The malathion release from the film was tracked with Fourier transform infrared spectroscopy (FTIR). The malathion absorption band in the FTIR spectra disappeared gradually over time. Confocal Raman analysis showed a malathion concentration gradient across the thickness of the polyethylene layers. These results suggested diffusion-controlled transport through the LDPE membranes. Bioassays indicated that the residual efficacy of the malathion, against mosquitoes, was increased to about six months. This means that trilayer films, impregnated with an organophosphate, may have potential as alternative mosquito control interventions in pyrethroid resistant settings. / Dissertation (MEng)--University of Pretoria, 2017. / Chemical Engineering / MEng / Unrestricted
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Propriedades eletrÃnicas de tricamada de grafeno e nanofitas de carbono tensionadas / Electronic properties of trilayer graphene and strained carbon nanoribbonsSilvia Helena Roberto de Sena 19 December 2012 (has links)
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Grafeno à um cristal bidimensional cujo espectro eletrÃnico a baixas energias (E <1 eV) apresenta dispersÃo linear e ausÃncia de gap que, juntamente com a natureza quiral dos portadores de carga, sÃo responsÃveis por uma variedade de propriedades incomuns. Como resultado da sua natureza singular, um grande esforÃo tem sido feito para entender todas as suas propriedades fundamentais e tentar gerar uma nova tecnologia baseada nesse material.
Nesta tese, nÃs realizamos um estudo teÃrico de dois tipos de sistemas: nanofitas de grafeno e tricamadas grafeno (TCG). No que diz respeito ao primeiro sistema, um modelo de ligaÃÃo forte (tight-binding) à utilizado para estudar as bandas de energia do grafeno e fitas de grafeno sujeitas a uma tensÃo de cisalhamento. A fita à constituÃda por linhas de Ãtomos de carbono cujas bordas estÃo orientadas nas direÃÃes conhecidas como âarmchairâ ou âzigzagâ. Uma tensÃo de cisalhamento simples à aplicada na direÃÃo x de forma que as distÃncias interatÃmicas na direÃÃo y sÃo mantidas inalteradas. Esta modificaÃÃo na rede cristalina origina bandas de energia que diferem em vÃrios aspectos do sistema original sem qualquer deformaÃÃo. As mudanÃas no espectro dependem do deslocamento entre linhas adjacentes da fita, bem como do parÃmetro de âhoppingâ modificado. Mostra-se tambÃm que este cisalhamento simples modifica as propriedades eletrÃnicas de ambos os sistemas, fitas de grafeno e grafeno, abrindo e fechando gaps de energia para diferentes deslocamentos do sistema. A densidade de estados modificada tambÃm à mostrada. Por fim, o modelo contÃnuo à utilizado a fim de investigar o espectro electrÃnico de trÃs camadas de grafeno acopladas (tricamada de grafeno), na presenÃa de um campo magnÃtico externo. Nesse contexto, obtemos expressÃes analÃticas para os nveis de Landau para ambos os tipos de empilhamento: Bernal (ABA) e romboÃdrico (ABC), verificando-se uma forte dependÃncia dos nÃveis de energia com o tipo de empilhamento. Embora o espectro de Landau para tricamadas ABA seja uma sobreposiÃÃo dos espectros de uma monocamada e de uma bicamada, tricamadas com empilhamento ABC apresentam uma dispersÃo do tipo B3/2 com o campo magnÃtico. Foi mostrado que uma assimetria entre as camadas, que pode ser introduzida por um potencial externo, pode influenciar fortemente as propriedades do sistema. AlÃm disso, as energias de ressonÃncia cÃclotron, assim como forÃas de oscilador correspondentes, e o espectro de absorÃÃo para tricamadas de grafeno sÃo calculadas para ambos os tipos de empilhamento. Verificou-se que um potencial de porta aplicado atravÃs das camadas leva a (1) uma reduÃÃo das energias de transiÃÃo, (2) um levantamento da degenerescÃncia do nÃvel de Landau n=0, e (3) a quebra de simetria entre elÃtrons e buracos. / Graphene is a truly two-dimensional crystal with a gapless linear
electronic spectrum at low energies (E<1 eV) which, along with
the chiral nature of its charge carriers, is responsible for a
variety of unusual properties. As a result of its uniqueness, a
great effort has been made in order to understand all its
fundamental properties and try to generate a new technology of
them.
In this thesis we theoretically study two types of
graphene-related systems: graphene nanoribbons and trilayer
graphene (TLG). Concerning the former, a tight-binding model is
used to study the energy band of graphene and graphene ribbon
under simple shear strain. The ribbon consists of lines of carbon
atoms in an armchair or zigzag orientation where a simple shear
strain is applied in the $x$-direction keeping the atomic
distances in the $y$-direction unchanged. Such modification in the
lattice gives an energy band that differs in several aspects from
the one without any shear and with pure shear. The changes in the
spectrum depend on the line displacement of the ribbon, and also
on the modified hopping parameter. It is also shown that this
simple shear strain tunes the electronic properties of both
graphene and graphene ribbon, opening and closing energy gaps for
different displacements of the system. The modified density of
states is also shown. On the latter subject, the continuum model
is used in order to investigate the electronic spectrum of three
coupled graphene layers (graphene trilayers) in the presence of an
external magnetic field. We obtain analytical expressions for the
Landau level (LL) spectrum for both the ABA and ABC types of
stacking, which exhibit very different dependence on the magnetic
field. While the LL spectrum of ABA TLG is found to be a
superposition of a monolayer-like and bilayer-like spectra, the
ABC TLG present a nearly B^{3/2} field dependence. We show that
layer asymmetry and an external gate voltage can strongly
influence the properties of the system. In addition, the cyclotron
resonance energies, the corresponding oscillator strengths, and
the cyclotron absorption spectrum for trilayer graphene are
calculated for both ABA and ABC stacking. A gate potential across
the stacked layers leads to (1) a reduction of the transition
energies, (2) a lifting of the degeneracy of the zero Landau
level, and (3) the removal of the electron-hole symmetry.
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Charge Storage Effect in a Trilayer Structure Comprising Germanium NanocrystalsHeng, C.L., Choi, Wee Kiong, Chim, Wai Kin, Teo, L.W., Ho, Vincent, Tjiu, W.W., Antoniadis, Dimitri A. 01 1900 (has links)
A metal-insulator-semiconductor (MIS) device with a trilayer insulator structure consisting of sputtered SiO₂ (~50nm)/evaporated pure germanium (Ge) layer (2.4nm)/rapid thermal oxide (~5nm) was fabricated on a p-type Si substrate. The MIS device was rapid thermal annealed at 1000°C. Capacitance-voltage (C-V) measurements showed that, after rapid thermal annealing at 1000°C for 300s in Ar, the trilayer device exhibited charge storage property. The charge storage effect was not observed in a device with a bilayer structure without the Ge middle layer. With increasing rapid thermal annealing time from 0 to 400s, the width of the C-V hysteresis of the trilayer device increased significantly from 1.5V to ~11V, indicating that the charge storage capability was enhanced with increasing annealing time. High-resolution transmission electron microscopy results confirmed that with increasing annealing time, the 2.4nm amorphous middle Ge layer crystallized gradually. More Ge nanocrystals were formed and the crystallinity of the Ge layer improved as the annealing time was increased. When the measurement temperature was increased from –50°C to 150°C, the width of the hysteresis of the MIS device reduced from ~10V to ~6V. This means that the charge storage capability of the trilayer structure decreases with increasing measurement temperature. This is due to the fact that the leakage current in the trilayer structure increases with increasing measurement temperature. / Singapore-MIT Alliance (SMA)
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From Hopping to Ballistic Transport in Graphene-Based Electronic DevicesTaychatanapat, Thiti 08 October 2013 (has links)
This thesis describes electronic transport experiments in graphene from the hopping to the ballistic regime. The first experiment studies dual-gated bilayer graphene devices. By applying an electric field with these dual gates, we can open a band gap in bilayer graphene and observe an increase in resistance of over six orders of magnitude as well as a strongly non-linear behavior in the transport characteristics. A temperature-dependence study of resistance at large electric field at the charge neutrality point shows the change in the transport mechanism from a hopping dominated regime at low temperature to a diffusive regime at high temperature. / Physics
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Spin and Charge Transport in Monolayer and Trilayer Graphene in the Quantum Hall RegimeStepanov, Petr 28 September 2018 (has links)
No description available.
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Optimisation des modes de Lamb à vitesse de groupe nulle engendrés par laser et évaluation locale de structures collées / Optimization of laser source for enhanced generation of zero-group velocity Lamb modes and local evaluation of bonded structuresBruno, François 08 June 2017 (has links)
Les structures planes supportent la propagation de modes de Lamb, dont certains présentent une vitesse de groupe nulle et une vitesse de phase finie. Ces modes ZGV, favorablement engendrés et détectés par ultrasons laser, donnent lieu à des résonances locales étroites qui sont sensibles à l'épaisseur, aux propriétés élastiques et aux conditions de surface. Dans le premier volet de cette thèse, l'optimisation spatiale de la source laser (Faisceau rectangle ou Gaussien, anneau à profil rectangle ou Gaussien obtenu à l'aide d'un axicon) est étudiée afin d'améliorer la génération d'un mode de Lamb de longueur d'onde λ. Il est démontré que le rayon optimal d'un faisceau Gaussien est égal à λ/π. Les résultats théoriques sont en bon accord avec les simulations semi-analytiques et les mesures réalisées à la fréquence du mode ZGV S1S2 dans une plaque de Duralumin. Le second volet est dédié au contrôle de plaques collées par résonance ZGV. Ces structures sont décrites par un modèle rhéologique adhésif faisant intervenir des raideurs d'interface. La sensibilité des fréquences ZGV aux paramètres de la couche d'adhésif et aux raideurs d'interface est étudiée. La mesure des résonances ZGV a conduit à l'obtention des cartes de raideurs et d'épaisseur de colle. Elle a également permis de différencier des assemblages à tenue mécanique contrôlée / For some Lamb modes propagating in plane structures, the group velocity vanishes while the phase velocity remains finite. These modes are associated with local and narrow resonances and are sensitive to thickness, elastic properties and boundary conditions. Laser ultrasound techniques are well suited to generate and detect these resonances. In the first part of this thesis, spatial optimization of laser sources (Top-Hat and Gaussian beam, rectangular and Gaussian ring produced by an axicon-lens system) are studied in order to enhance the generation of a Lamb mode at wavelength λ. Optimal radius of a Gaussian beam is demonstrated to be λ/π. Theoretical results are shown to be in a good agreement with semi-analytical simulation and experimental results performed in a Duralumin plate at the S1S2-ZGV mode frequency. The second part of this work is dedicated to the use of ZGV resonances for the inspection of bonded plates. Trilayers are described by rheological model where interfaces are modelized by stiffnesses. The sensitivity of ZGV frequencies to the interfacial stiffnesses as well as adhesive layer parameters has been studied. Stiffnesses and adhesive thickness maps have been extracted from ZGV resonance measurements. In addition, ZGV mode measurements have been shown to allow the differenciation of controled bond strengh samples
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Electrodes multifeuillets de type oxyde/métal/oxyde à transparence accordable pour cellules solaires organiques / Multilayer electrodes of Oxide/Metal/Oxide type with tunable transparency for organic solar cellsBou, Adrien 08 December 2015 (has links)
Parmi les filières de cellules photovoltaïques, les cellules solaires organiques suscitent un intérêt industriel par leur faible coût financier et de production énergétique et leur application possible sur des substrats flexibles de type plastique. L'ITO (Indium Tin Oxide) est l'électrode transparente conductrice (ETC) la plus utilisée pour ces cellules ainsi que pour d'autres dispositifs optoélectroniques. Cependant, ce matériau n'est pas sans présenter certains inconvénients (rareté de l'indium, structure non adaptée à des substrats flexibles,…), et la recherche d'alternatives à l'ITO est une préoccupation actuelle de la communauté scientifique internationale. Une possibilité est alors offerte par des structures multicouches de type Oxyde|Métal|Oxyde. Le rôle des deux couches d’oxydes est d’accorder, en ajustant les épaisseurs, la position, l’intensité et la largeur de la fenêtre spectrale de transmission. Des travaux numériques et expérimentaux couplés ont été effectués en particulier sur les structures SnOx|Ag|SnOx, TiOx|Ag|TiOx et ZnS|Ag|ZnS. Par microstructuration de telles électrodes ou bien par incorporation d’un bicouche Cu|Ag comme feuillet métallique au coeur de la structure, il est possible d’améliorer leurs performances optiques en amplifiant et en élargissant la fenêtre spectrale de transmission, sans dégrader leur haute conductivité. L’intégration d’électrodes SnOx|Ag|SnOx et TiOx|Ag|TiOx au sein de cellules solaires organiques inverses a été entrepris. Des résultats photoélectriques très prometteurs ont été obtenus avec la structure TiOx|Ag|TiOx qui permet d’atteindre des performances de niveau quasi-équivalent aux cellules de référence à base d’ITO. / Among all variants of photovoltaic thins films, organic solar cells generate a major industrial interest due to low manufacturing costs, reasonable levels of energy production and suitability to flexible substrates like plastic. ITO (Indium Tin Oxide) is the most used Transparent Conductive Electrode (TCE) for organic solar cells as well as other optoelectronic devices. However, this material is not without drawbacks (scarcity of indium, non-suitability to flexible substrates...), and the search for alternatives to ITO is actively pursued by the international scientific community. One possibility is offered by Oxide|Metal|Oxide multilayer structures. By reaching the thin metal layer percolation threshold and by varying its thickness, it is possible to obtain very high conductivity and transparency of this multilayer in the visible spectral range. The role of both oxide layers is to tune the position, intensity and width of the spectral transmission window by adjusting the oxides’ thicknesses. Coupled experimental and numerical works were lead in particularly on SnOx|Ag|SnOx, TiOx|Ag|TiOx and ZnS|Ag|ZnS structures. By microstructuring such electrodes, or by incorporating a Cu|Ag bilayer as metal sheet at the core of the structure, it is possible to increase the optical performances by amplifying and expanding the spectral transmission window without degrading the high conductivity. The integration of SnOx|Ag|SnOx and TiOx|Ag|TiOx electrodes in inversed organic solar cells was undertaken. Very promising photoelectric results were obtained with the TiOx|Ag|TiOx structure which allows to reach performances close to that obtained with ITO-based reference cells.
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Contact Mechanics Of Layered StructuresMath, Souvik 01 1900 (has links)
Contact mechanical study of layered structures is useful to various fields of
engineering, such as - mechanical engineering, civil engineering, materials engineering and biomechanics. Thin hard film coating on a compliant substrate used in cutting tool industry is an example of a layered structure. The protective coating saves the substrate from fracture and wear. However, due to film material brittleness, fracture in the films is of concern. We have developed an analytical model for a film-substrate bilayer system under normal contact loading, which helps us to obtain the stress distribution in the film and fracture behaviour.
Our contact model is based on Hankel’s Transform technique, where we assume
a Hertzian pressure boundary condition. At each depth of penetration of the indenter in
the film-substrate system, we estimate effective modulus of the system based on Gao’s approach. We have validated our analysis by surface strain measurements and
photoelastic stress study in the film on a substrate.
Experimental observations from literatures show the dependence of different
fracture modes in a thin hard film with columnar structure on film thickness and substrate plasticity. We perform fracture analysis, a parametric study of the fracture modes in the film under contact loading. When the film thickness is small and the substrate is relatively hard (e.g. tool steel), the film and the substrate deform conformally under contact loading and the columns of TiN slide against each other into the substrate. On the other hand, when the film is thicker and the substrate is soft (e.g. mild steel or aluminium), the strain mismatch between the film and substrate acts as an added traction at the interface and drives cracks, such as radial tensile stress driven bending cracks that start from the interface at the center of indentation; maximum shear stress driven inclined
shear crack that starts inside the film and propagate at an angle to the indentation axis and tensile stress driven edge crack that starts from the free surface outside the contact. We can draw a fracture map based on these calculations which provides a guide to select film thickness depending on the substrate hardness, so that the benign mode of damage, i.e., columnar shear occurs in the film.
Apart from generating the fracture map, we can obtain rationale for different
fracture phenomenon in the film by studying the indentation stress field. Principal tensile stresses, responsible for driving edge cracks from the free surface outside the contact, become compressive as one approaches the substrate if the substrate is compliant. The cracks therefore do not penetrate deep into the film rather curve away from the axis of indentation. At the transition zone from one mode of damage to other in the fracture map, different modes of fracture may co-exist. The whole column may not shear, rather the shear can start from somewhere in the middle of the film, where the shear stress is maximum and it can end without reaching the interface. The indentation energy is then dissipated in other forms of damage.
The contact analysis is further applied to TiN /AlTiN multilayered films having
similar elastic properties. Experimental observations suggest that with decreasing layer thickness the fracture resistance of the multilayers increase and some plastic yielding occurs at the top layers of the film. However no substantial change in strain capacity (Hardness/ Young’s Modulus) of the film is observed. Hence we attribute the increase of fracture resistance of multilayers to film plasticity and mimic it by reducing the modulus of the film. The analysis validates the propensity of edge cracking and transgranular cracking as they decrease with increasing number of layers in a multilayer.
We next extend our bilayer analysis to a more general trilayer problem where the
moduli of the layers vary by several orders. The test system here is a mica-glue-glass
system which is used in surface force apparatus experiments. Gao’s trilayer analysis is used to fit the experimental data obtained from surface force apparatus experiments, where a glass sphere indents the trilayer. The parallel spring model used in Gao’s approximation is found to be inadequate to rationalize the experimental data. We have modified Gao’s formulations by reducing the problem to a bilayer problem where the layers are the first layer (in contact) and an equivalent layer which has properties determined by a rule of mixture of the properties of all the layers excluding the top layer set out as a set of springs in series. The modified formulations give a better fit to the experimental data and it is validated from nanoindentation experiments on the same system. The formulation is used to obtain the compression of the glue, which contributes
significantly to the deformation of the trilayer system in the SFA experiments. Thus, the analysis can be used to deconvolute the influence of glue in the actual mechanical response of the system in an SFA experiment, which has so far been neglected.
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