Lateral Size Effect Research Articles

The Fractal Geometry of TiAlNiAu Thin Film Metal System and Its Sheet Resistance (Lateral Size Effect)

This paper investigates the relation between the geometry of metric space of a TiAlNiAu thin film metal system and the geometry of normed functional space of its sheet resistances (functionals), which are elements of the functional space. The investigation provides a means to describe a lateral size effect that involves a dependency in local approximation of sheet resistance Rsq of TiAlNiAu metal film on its lateral linear dimensions (in (x,y) plane). This dependency is defined by fractal geometry of dendrites, or, more specifically, it is a power-law dependency on fractal dimension Df value. The revealed relation has not only fundamental but also a great practical importance both for a precise calculation of thin film metal system Rsq values in designing discreet devices and ICs, and for controlling results at micro- and nanoscale in producing workflow for thin metal films and systems based on them.

Lateral Size Effect of Graphene Oxide on Its Surface-Enhanced Raman Scattering Property.

The lateral size effect of graphene oxide (GO) on surfaced-enhanced Raman scattering (SERS) property is systematically investigated by using size-fractionalized GO. For the size fractionalization without changes of chemical structure, large-sized GO (LGO) and small-sized GO (SGO) are separated from the as-synthesized GO (AGO) by centrifugation and membrane filtration, respectively. The size-fractionalized GO sheets are immobilized on a solid substrate for the parallel comparison of their SERS property. As a result, we find that LGO shows considerably higher SERS property than SGO for typical Raman probes such as rhodamine 6G and crystal violet. Furthermore, the lateral size effect of GO derivatives is consistently observed when they are hybridized with plasmonic silver nanoparticles. These results indicate that LGO is superior to AGO and SGO as a SERS platform, and it is also quantitatively confirmed by calculating their enhancement factor.

Lateral size effect of reduced graphene oxide on properties of copper matrix composites

Graphene/copper composite using graphene oxide sheets with three kinds of lateral sizes (~0.92 μm, ~5.49 μm and ~13.73 μm) were prepared via molecular level mixing method and spark plasma sintering process. The lateral size effects of graphene on the structure, mechanical performance, thermal and electrical conductivities of the composites were investigated while the volume fraction of graphene remained 2.5 vol%. For microstructure, small-sized graphene sheets (denoted as SRGO) tend to distribute randomly in the composites while middle-sized (denoted as MRGO) and large-sized graphene sheets (denoted as LRGO) are prone to form the carbon-rich aggregate with micro-layered structure. MRGO/Cu composite has the highest tensile yield strength (663 MPa) while SRGO/Cu composite exhibits the most excellent thermal and electrical conductivities (334 W/(m × K), 82 %IACS) among the three composites. This work provides a better understanding the formation mechanism of hierarchical layered graphene/Cu composite and can further promote the development of architectural design of graphene based composites.

Effect of the Two-Dimensional Magnetostrictive Fillers of CoFe2O4-Intercalated Graphene Oxide Sheets in 3-2 Type Poly(vinylidene fluoride)-Based Magnetoelectric Films.

In the last decade, magnetoelectric (ME) polymer films have been developed by including zero-dimensional or one-dimensional magnetostrictive fillers in a piezoelectric polymer matrix. Existing reports on ME polymer films reveal that the shape of the magnetostrictive fillers is a critical determinant of the polymeric phase conformation, strain transfer between the piezoelectric and magnetostrictive phases, and dipole alignment in the films. In this study, to investigate the effect of two-dimensional (2D) magnetostrictive fillers on piezoelectric, magnetic, and magnetoelectric responses, 3-2 type ME films were prepared using CoFe2O4-intercalated graphene oxide (CFO-i-GO) fillers and poly(vinylidene fluoride) (PVDF) polymers. The 2D fillers of CFO-i-GO were hydrothermally synthesized by CFO intercalation into the interlayers of GO sheets with different lateral sizes, which were controlled by ultrasonication treatment. It was found that the large-lateral-size GO (LGO), medium-lateral-size GO (MGO), and small-lateral-size GO (SGO) fillers in the PVDF-based ME films exhibited a lateral size effect on CFO intercalation, polymeric phase conformation, dipole alignment, and magnetoelectric responses. A maximum ME coefficient (αME) of 3.0 mV/cm∙Oe was achieved with a strong linearity (r2) of 0.9992 at an off-resonance frequency (f) of 1 kHz and applied direct current (dc) magnetic field (Hdc) of ± 1000 Oe. The 3-2 type polymer-based ME films with reliable ME responses have potential for use in high-feasibility ME devices for biomedical sensing applications.

Nano/micro-structures and mechanical properties of ultra-high performance concrete incorporating graphene with different lateral sizes

The performance of cement-based materials can be controlled and tailored by adjusting the characteristics of reinforced nano inclusions. Therefore, the lateral size effect of graphene on the nano/micro-structures of ultra-high performance concrete (UHPC) was explored, and then the mechanical properties were investigated to analyze the structure–property correlation of composites in this paper. The test results show that due to nucleation site effect and the formation of core–shell elements, incorporating graphene with lateral size of > 50 µm improves the polymerization degree and mean molecule chain length of C-S-H gel by 242.6% and 56.3%, respectively. Meanwhile, the porosity and average pore volume of composites is reduced by 41.4% and 43.4%. Furthermore, graphene can effectively inhibit the initiation and propagation of cracks by crack-bridging, crack-deflection, pinning and being pulled-out effect, and the wrinkling characteristic is conductive to the enhancement of pinning effect. These improvements on nano- and micro- structures result in that the compressive strength, compressive toughness and three-point bending modulus of UHPC are increased by 43.5%, 95.7% and 39.1%, respectively, when graphene with lateral size of > 50 µm and dosage of 0.5% is added. Compared to graphene with lateral size of > 50 µm, graphene with average lateral size of 10 µm has less folds and larger effective size, then reducing the distance between core–shell elements. Hence, the addition of graphene with average lateral size of 10 µm leads to 21.1% reduction for Ca(OH)2 crystal orientation index, as well as 30.0% increase for three-point bending strength. It can be, therefore, concluded that the lateral size of graphene obviously influences the nano/micro-structures of UHPC, thus leading to the significantly different reinforcing effects of graphene on mechanical behaviors of UHPC.

Слоевое сопротивление TiAlNiAu тонкопленочной металлизации омических контактов к нитридным полупроводниковым структурам

AbstractThe relation between the geometry of the metric space of the thin-film TiAlNiAu metallic system surface and the geometry of the functional space of the sheet resistances R _ sq of this system is established. Based on the results obtained, the lateral size effect observed in the local approximation is described, which manifests itself in the dependence of the sheet resistance R _ sq of a TiAlNiAu metallic film on its lateral (in the ( x , y ) plane) linear sizes. The dependence of the R _ sq value on the linear sizes is shown to be determined by the fractal geometry of the forming dendrites, specifically, by the power dependence of a variation in the linear sizes on the fractal dimension D _ f . The obtained regularity is of great practical importance for accurate calculation of the R _ sq values ​​of thin-film metal systems in designing discrete devices and integrated circuits and for controlling the technological processes of fabricating thin metallic films and systems based on them at the micrometer and nanometer scales.

Sheet Resistance of the TiAlNiAu Thin-Film Metallization of Ohmic Contacts to Nitride Semiconductor Structures

The relation between the geometry of the metric space of the thin-film TiAlNiAu metallic system surface and the geometry of the functional space of the sheet resistances Rsq of this system is established. Based on the results obtained, the lateral size effect observed in the local approximation is described, which manifests itself in the dependence of the sheet resistance Rsq of a TiAlNiAu metallic film on its lateral (in the (x, y) plane) linear sizes. The dependence of the Rsq value on the linear sizes is shown to be determined by the fractal geometry of the forming dendrites, specifically, by the power dependence of a variation in the linear sizes on the fractal dimension Df. The obtained regularity is of great practical importance for accurate calculation of the Rsq values ​​of thin-film metal systems in designing discrete devices and integrated circuits and for controlling the technological processes of fabricating thin metallic films and systems based on them at the micrometer and nanometer scales.

Lateral size effect of graphene on mechanical properties of aluminum matrix nanolaminated composites

A lateral size effect of reinforcement on mechanical properties is investigated for aluminum matrix nanolaminated composites reinforced with reduced graphene oxide (rGO). rGO sheets with remarkably different lateral size are chosen to cover the critical value estimated by the shear lag model. Tensile tests with loading along the in-plane direction of the nanolaminated structure demonstrate that lateral size has significant influence on mechanical properties. A good balance between strength and ductility is realized by the largest lateral size of rGO.

Lateral Size Effects of Two-dimensional IrO<sub>2</sub> Nanosheets towards the Oxygen Evolution Reaction Activity

The oxygen evolution reaction of anode catalyst is an important reaction in polymer electrolyte membrane water electrolysis. Recent research has focused on understanding the factors governing the catalytic properties of nanostructured IrO2 in order to decrease the use of expensive and precious IrO2. We demonstrate here the equivalent diameter (De) effect (lateral size effect) of IrO2 nanosheets for the oxygen evolution reaction. IrO2 nanosheets with four different De from 110 to 260 nm and same thickness (∼1.5 nm) were prepared. The electrical double layer capacitance, which should be proportional to the electrochemically active surface area, of IrO2 nanosheets was independent of De. On the other hand, the pseudo-capacitance, which is related to surface redox processes, and the oxygen evolution reaction activity increased with decreasing De. The enhanced oxygen evolution reaction activity is discussed based on the electrochemically active surface area and edge effect.

The interaction between Lateral size effect and grain size when scratching polycrystalline copper using a Berkovich indenter

It has been reported previously that, for single and polycrystalline copper (fcc), the indentation size effect and the grain size effect (GSE) can be combined in a single length-scale-dependent deformation mechanism linked to a characteristic length-scale calculable by a dislocation-slip-distance approach (X. D. Hou and N. M. Jennett, ‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). Recently, we identified a ‘lateral size effect (LSE)’ in scratch hardness measurements in single crystal copper, where the scratch hardness increases when the scratch size is reduced (A. Kareer, X. D. Hou, N. M. Jennett and S. V. Hainsworth ‘The existence of a lateral size effect and the relationship between indentation and scratch hardness’ Philos. Mag. published online 24 March 2016). This paper investigates the effect of grain size on the scratch hardness of polycrystalline copper with average grain sizes between 1.2 and 44.4 μm, when using a Berkovich indenter. Exactly the same samples are used as in the indentation investigation by Hou et al. (‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). It is shown that, not only does the scratch hardness increase with decreasing grain size, but that the GSE and LSE combine in reciprocal length (as found previously for indentation) rather than as a superposition of individual stresses. Applying the same (as indentation) dislocation-slip-distance-based size effect model to scratch hardness yielded a good fit to the experimental data, strongly indicating that it is the slip-distance-like combined length-scale that determines scratch hardness. A comparison of the fit parameters obtained by indentation and scratch on the same samples is made and some distinct differences are identified. The most striking difference is that scratch hardness is over four times more sensitive to grain size than is indentation hardness.

The existence of a lateral size effect and the relationship between indentation and scratch hardness in copper

Indentation size effects (ISEs) are well known in static indentation of materials that deform by dislocation-based mechanisms. However, whilst instrumented indentation techniques have become rapidly established as a means of determining the near-surface mechanical properties of materials, scratch testing has been much less widely used. Hardness is used in wear models as a proxy for the yield stress, and the design of materials and hard coatings has often sought to exploit size-derived performance enhancements through length-scale engineering. Yet, it is not known directly whether (or not) length-scale effects also apply to scratch (and thus wear) performance at small scales, or what the functional form of this effect is. This work directly demonstrates that there is a lateral size effect (LSE) and shows that there are questions to be answered if the use of hardness as an indicator of wear performance is to remain valid. We report on constant load scratch experiments using a Berkovich indenter on single-crystal, annealed copper, using a range of applied normal forces and compare results from three scratch hardness calculation methods to indentation hardness (ISO 14577:2002) measured on the same sample at the same loads. Scratch tests were performed with the Berkovich indenter aligned either edge forward or face forward to the scratch direction. In all cases, we demonstrate that there is a very significant (approximate factor of two) effect of scratch size (an LSE) on scratch hardness. The results also show that the deformation mechanisms occurring in scratch tests are different to those occurring beneath a static indentation and that different mechanisms dominated for different stylus orientations (face-forward vs. edge-forward orientation). This is, to our knowledge, the first direct demonstration of an LSE akin to the ISE in metallic materials. The results have significant implications for using static indentation as a predictor of deformation during wear processes.

Lateral grain size effect on exchange bias in polycrystalline NiFe/FeMn bilayer films

This study explores the effect of lateral grain size on the exchange bias in the magnetron sputtered NiFe(5nm)/FeMn(20nm) bilayer films. The thicknesses of ferromagnetic (NiFe) and antiferromagntic (FeMn) layers were kept constant in the study. The lateral grain size variation was induced by increasing Ta buffer layer thickness. The cross-sectional transmission electron microscopy revealed that bilayers deposited on thicker Ta buffer layers have larger lateral grain diameter. Grain-to-grain epitaxy from buffer layer controls lateral grain size at NiFe/FeMn interface. A large increase in exchange bias field was observed with increasing thickness of Ta buffer layer, which is attributed to the enhanced ferromagnetic/antiferromagnetic coupling originated from larger interface lateral grain area.

Lateral Size Effect on Electrochemical Capacitor Performance of Reduced Graphite Oxide Nanosheets

The lateral size of individual graphene sheets is expected to impact the electrochemical properties of reduced graphite oxide nanosheets (rGOns). The size effect on the specific capacitance of rGOns was investigated by breaking down the size of rGOns using high-frequency ultrasonification. The specific capacitance of rGOns prepared by hydrogen reduction of GOns with an average equivalent diameter of 280 nm was 242 F g−1 in 0.5 M H2SO4 and 205 F g−1 in 0.5 M Na2SO4. The specific capacitance was 30% higher to that of larger-sized GOns with diameter of 920 nm. The area normalized capacitance ranged between 70 to 138 µF cm−2, with larger-sized rGOns affording higher values. The cause of this size-effect is discussed based on the microstructure of the rGOns electrode as well as the edge/plane ratio.

Atomic force microscopy study of the potential distribution over a locally metallized n-GaAs surface

Investigations of the potential of the free surface of gallium arsenide and of the surface coated (locally or entirely) by thin layers of gold or platinum have been carried out using atomic force microscopy in the Kelvin mode. The results obtained show that the potential measured in the metal-probe system corresponds as a whole to its contact potential difference (CPD). CPD values measured for the gallium arsenide-probe system depend on the type of processing that may be related to the influence of the processing on the electron affinity of a semiconductor. The lateral size effect consisting in the presence of a significant (about 10 µm) transition zone (aureole) between the metal contact and the GaAs free surface has been found. In this region the potential varies gradually between values of the potential of the metal contact and the free surface of the semiconductor. The potential of a contact depends on its dimensions (diameter and thickness) and on the substrate material’s (GaAs) properties.

Lateral and vertical size effects on nanoindented microstructures

In this paper we study numerically the size effect of different constitutive relationships based on bulk silicon subjected to nanoindentation. The constitutive relationships of multilinear kinematic hardening rules are considered in order to capture elastic-perfectly plastic to strain-hardening characteristics. The size effect is estimated from the hardness of the varied contact depths normalized by that of the standard size sample that has been previously validated. Both lateral and vertical sample size effects of the microstructure are evaluated by varying respective size with an identical indentation depth. The contact depths equaling to 1/10th of the sample thickness bring around ±10% of the vertical size effect, while those equaling to one quarter lead to approximately ±20%. A softer material with an elastic-perfectly plastic characteristic generates a smaller vertical size effect because of the continuum mechanism occurs only at the near field. Narrowing down the lateral width, leads to lower loads due to no lateral boundary could conduct. Hard samples are less affected by the lateral size effect than soft ones.

Structure-functional property relationships in rf-sputtered vanadium dioxide thin films

The study of metal-insulator transition (MIT) in VO2 thin films synthesized by means of rf sputtering from a VO2 target is presented. A comparison with conventional reactive sputtering from a V target is also given. Detailed x-ray diffraction analysis, electrical resistance switching, and infrared optical reflectance measurements confirm that our sputtering technique yields high-quality VO2 films. We discuss in depth how synthesis conditions affect MIT parameters derived from temperature dependence of electrical resistance. Sharp MIT is observed in films sputtered on technologically important Si substrates. The choice of Si (or sapphire) substrates results in the transition temperature above (below) the values obtained for single VO2 crystals. The MIT becomes narrower and stronger in thinner films. This is consistent with the assumption that the increased width of the MIT in thin films with respect to single crystals is the result of averaging of the transition parameters over a distribution of crystallites in the film. The measurements of MIT in VO2 patterned into devices do not reveal a noticeable lateral size effect down to 20 μm devices, encouraging use of the phase transition in switching electronic devices. The effect of substrate temperature and ambient during the sputtering on MIT is discussed. While VO2 films are found to be stable in ambient environment with time, the additional exposure to UV radiation near room temperature is shown to enhance the oxidation kinetics and produce changes in film resistance. Using UV radiation as an additional tool to control the oxidation process during VO2 synthesis may allow the synthesis temperature to be lowered and an improvement in material quality. We anticipate these results may be of relevance to synthesizing functional oxide films with potential applications in electronics and sensors.

Lateral Size Effect in the Lifetime Measurement by Frequency-Dependent Surface Photovoltage Technique*

Effective lifetimes measured with the frequency-dependent surface photovoltage method, decrease in proportion to the quantity of excess carriers escaping from the photocarrier injection point towards the lateral surfaces where they recombine. It has been experimentally found that the separation between the sandpaper-lapped surfaces and the photocarrier injection point has to be longer than 8 times the diffusion length L of minority carriers in order to keep measurement errors under 10%, while it may be more than 1.4L for the chemically etched surfaces.

Dendritic crystallization of amorphous germanium by in situ thermal pulse annealing

Phase transformation of amorphous-germanium thin film has been carried out on amorphous substrate by in situ thermal-pulse annealing in a high vacuum chamber directly after evaporation. The microstructure of the resultant film was shown to depend markedly both on the annealing ambient and on the time of exposure (te) for the as-deposited films under full-powered (<102 W/cm2) incoherent broadband irradiation. The heating rate was estimated to be not less than 102 K/s. The surface morphology of the sample was examined by atomic force microscopy (AFM), scanning electron microscopy, and optical microscopy. For samples annealed in air, hillock growth mode was observed, while for samples annealed in vacuum, a transition from the microgranular to dendritic grain growth, depending sensitively on te, was clearly evident. Surprisingly, the length of the crystallized dendrites could be as long as ≃104 μm, being at least ≃104 times larger than the thickness of the film. The dendritic morphology, the implied growth rate, and the condition of crystallization lead us to suggest that the Ge film may exist in a supercooled semiconductive liquid phase just before crystallization. X-ray diffraction analysis revealed that grains were crystallized dominantly with a random orientation for te<2.84±0.05 s, while a sharp transition to a preferred 〈110〉 crystal orientation occurred at the critical te of 3.22±0.05 s, corresponding to a maximum temperature (Tm) of 577 °C reached by the system. This transition is consistent with the appearance of dendrites in AFM micrographs. More interestingly, an anomalous lateral size effect of the substrate on the misalignment of the 〈110〉 crystal direction of different grains with respect to the substrate normal was observed from the x-ray rocking curves. Careful inspection of the AFM images found that the giant dendrites broke up into individual columnar grains as the substrate width went down in size.

Optical characteristics of GaAs/AlGaAs ridge-quantum-well-wires grown by MBE on nonplanar substrates

With conventional photolithography and wet chemical etching, we have realized GaAs/AlGaAs buried ridge-quantum-well-wires (RQWWs) with vertically stacked wires in lateral arrays promising for device application, which were grown in situ by a single-step molecular beam epitaxy growth and formed at the ridge tops of mesas on nonplanar substrates. Confocal photoluminescence (CPL) and polarization-dependent photoreflectance (PR) are applied to study optical characteristics of RQWWs. Lateral bandgap modulation due to lateral variation of QW layer thickness is demonstrated not only by CPL but also by PR. As one evidence for RQWWs, a large blue shift is observed at the energy level positions for electronic transitions corresponding to quantum wells (QWs) at the ridge tops of mesas compared with those corresponding to QWs on nonpatterned areas of the same sample. The blue shift is contradiction with the fact that the GaAs QW layers at the tops of the mesas are thicker than those on nonpatterned areas. The other evidence for RQWWs, optical anisotropy is provided by the polarization-dependent PR, which results from lateral quantum size effect existing at the tops of the mesas.

Growth and characterization of InAs microclusters in InP and InAsP/InP heterostructures by low pressure MOCVD using tertiarybutylarsine

InAs microclusters embedded in an InP matrix and InAs x P 1– x /InP (0.1 ≤ x≤0.3) strained multiple quantum wells (SMQW) have been prepared by LP-MOCVD using tertiarybutylarsine (TBAs) as a substitute for AsH 3. The relatively large cracking efficiency of TBAs resulted in low As/In ratios (from 4.3 to 8.8) for InAs/InP structures and low As/P ratios (from 1×10 -3 to 3.5×10 -3 for InAs x P 1– x /InP (0.1 ≤ x ≤0.3). High-resolution X-ray diffraction (HRXRD) and photoluminescence (PL) show that the TBAs-grown material is of high quality. The HRXRD patterns of InAs microclusters embedded in the InP matrix demonstrate that the InAs unit cell is tetragonally distorted in accordance with the elasticity theory. For InAs microclusters embedded in the InP matrix, the 7 K emission PL peak shifts from 1.35 to 1.39 eV when the InAs coverage is reduced from 0.8 to 0.2 monolayers, a clear indication of a lateral size effect. Picosecond time resolved PL shows a weak coupling of excitons confined by these InAs microclusters. We report also the results of a study of the interface roughness of InAs x P 1– x /InP heterostructures. HRXRD, PL, absorption and photoconductivity (PC) measurements for InAsP/InP SMQW reveal that the InAsP/InP interface is very sensitive to growth procedure. For nonoptimal growth procedures a large density of interface states is created, probably as a consequence of compositional modifications within the interface region. The optical measurements clearly resolve the fundamental intersubband transitions in the InAsP/InP SMQW, including heavy hole-light splittings, even at room temperature.