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A new equivalent circuit model for electrographic recording on dielectric paper with a backing electrode is presented. It is shown that the conductivity of a thin layer between the dielectric layer and basepaper is more important than bulk conductivity in the basepaper.

Graphene oxide and reduced graphene oxide thin films are very promising materials because they can be used in optoelectronic devices and in a growing range of applications such as touch screens and flexible displays. In this work, graphene oxide (GO) and thermally reduced graphene oxide (rGO) thin films, deposited on Ti/glass substrates, have been obtained by electrophoretic deposition. The morphological and the structural properties of the samples have been investigated by micro-Raman technique, X-ray reflectometry, and SEM analysis. In order to study the optical and electrical properties, variable angle spectroscopic ellipsometry and impedance analysis have been performed. The thermal annealing changes strongly the structural, electrical, and optical properties, because during the thermal processes some amount of sp3 bonds originally present in GO were removed. In particular, the annealing enhances the Ohmic behavior of the rGO film increasing its conductivity and the estimated optical density. Moreover...

In this work, charge transport through interpoly thin nitride/oxide stacked films, including nitride/oxide dual- and oxide/nitride/oxide tri-layer films, was studied. Extensive experimental results, concerning current conduction in single oxide layer, single nitride layer, nitride/oxide dual-layer, and oxide/nitride/oxide tri-layer films are presented. An effective investigation of the various mechanisms that can explain current conduction and charge trapping in these dielectrics was performed. To this aim, different approaches to transport modeling, namely, a classical current continuity model, a transmission model, and a two-step trap assisted model are proposed. The gains and trade offs offered by each model are pointed out. A comprehensive model for the conduction mechanisms in thin nitride/oxide stacked films is proposed.

To develop excellent silicon oxide film using low temperature method, ion plating (IP) oxide is investigated. Physicochemical characterizations of the IP oxide are studied using ellipsometry, Fourier transform infrared spectrometry, and P-etch rate measurement. The IP oxide is a high-density dielectric with strained bonds. Electrical characterizations are also analyzed using capacitance–voltage and current–voltage techniques through metal-oxide-semiconductor capacitors. The IP oxide has a low leakage current, a high breakdown field, and low interface state density. In addition, IP oxide annealed in N2 ambient is also studied. After high-temperature annealing, the characteristics of IP oxide become comparable to those of thermal oxide. The novel oxide film is successfully applied as a gate insulator to low-temperature processed (⩽620 °C) polysilicon thin-film transistors.

Efficient control of intercalation of epitaxial graphene by specific elements is a way to change properties of the graphene. Results of several experimental techniques, such as X-ray photoelectron spectroscopy, micro-Raman mapping, reflectivity, attenuated total reflection, X-ray diffraction, and X-ray reflectometry, gave a new insight into the intercalation of oxygen in the epitaxial graphene grown on 4H-SiC(0001). These results confirmed that oxygen intercalation decouples the graphene buffer layer from the 4H-SiC surface and converts it into the graphene layer. However, in contrast to the hydrogen intercalation, oxygen does not intercalate between carbon planes (in the case of few layer graphene) and the interlayer spacing stays constant at the level of 3.35–3.32 A. Moreover, X-ray reflectometry showed the presence of an oxide layer having the thickness of about 0.8 A underneath the graphene layers. Apart from the formation of the nonuniform thin oxide layer, generation of defects in graphene caused by...

Suspended graphene has the highest measured thermal conductivity of any material at room temperature. However, when graphene is supported by a substrate or encased between two materials, basal-plane heat transfer is suppressed by phonon interactions at the interfaces. We have used frequency domain thermoreflectance to create thermal conductance maps of graphene contacts, obtaining simultaneous measurements of the basal-plane thermal conductivity and cross-plane thermal boundary conductance for 1–7 graphitic layers encased between titanium and silicon dioxide. We find that the basal-plane thermal conductivity is similar to that of graphene supported on silicon dioxide. Our results have implications for heat transfer in two-dimensional material systems, and are relevant for applications such as graphene transistors and other nanoelectronic devices.

Resist residue from the device fabrication process is a significant source of contamination at the metal/graphene contact interface. Ultraviolet Ozone (UVO) treatment is proven here, by X-ray photoelectron spectroscopy and Raman measurement, to be an effective way of cleaning the metal/graphene interface. Electrical measurements of devices that were fabricated by using UVO treatment of the metal/graphene contact region show that stable and reproducible low resistance metal/graphene contacts are obtained and the electrical properties of the graphene channel remain unaffected.

This study elucidates the correlation among conductivity of graphene and interface aspects in GaN light-emitting diodes (LEDs). Using a multilayer graphene of low sheet resistance, it is demonstrated that graphene alone can make ohmic contact with p-GaN without necessitating additional interlayer. Large-area blue LED with relatively low contact resistance in the order of 10−2 ohm-cm2 and improved forward voltage of 3.2 ± 0.1 V was realized irrespective of the use of the interlayer. The results from parallel evaluation experiments performed by varying the layer numbers of graphene with ultrathin NiOx interlayer revealed that the poor lateral conductivity of monolayer or few layer graphene can be well compensated by the interlayer. A combination of three layer graphene and NiOx offered device with enhanced electro-optical performance. But the Schottky barrier associated with the inadequate adhesion of transferred graphene dominates all the benefits and becomes a major bottleneck preventing the formation of low resistance stable ohmic contact.

The electronic properties of epitaxial graphene (EG) on SiC (0001) depend sensitively on the surface morphology of SiC substrate. Here, 2–3 layers of graphene were grown on on-axis 6H-SiC with different step densities realized through controlling growth temperature and ambient pressure. We show that epitaxial graphene on SiC (0001) with low step density and straight step edge possesses fewer point defects laying mostly on step edges and higher carrier mobility. A relationship between step density and EG mobility is established. The linear scan of Raman spectra combined with the atomic force microscopy morphology images revealed that the Raman fingerprint peaks are nearly the same on terraces, but shift significantly while cross step edges, suggesting the graphene is not homogeneous in strain and carrier concentration over terraces and step edges of substrates. Thus, control morphology of epitaxial graphene on SiC (0001) is a simple and effective method to pursue optimal route for high quality graphene and will be helpful to prepare wafer sized graphene for device applications.

GaN-based nanorod light-emitting diodes (LEDs) with multilayer graphene (MLG) transparent electrodes have been fabricated. Two types of nano-LEDs with graphene on and under the metal pads are fabricated and their performances are investigated. And LEDs with graphene on the metal-pads exhibiting lower forward voltage and higher electroluminescence intensity are obtained. Using scanning electron microscope and Raman spectroscopy, we have demonstrated that graphene transferred after the metal deposition remains intact and has much less damages than graphene under the metal during the fabrication of LEDs with nanorods.

Integration of graphene with other materials by direct growth, i.e., not using mechanical transfer procedures, is investigated on the example of metal/graphene/dielectric heterostructures. Such structures may become useful in spintronics applications using graphene as a spin-filter. Here, we systematically discuss the optimization of synthesis procedures for every layer of the heterostructure and characterize the material by imaging and diffraction methods. 300 nm thick contiguous (111) Ni-films are grown by physical vapor deposition on YSZ(111) or Al2O3(0001) substrates. Subsequently, chemical vapor deposition growth of graphene in ultra-high vacuum (UHV) is compared to tube-furnace synthesis. Only under UHV conditions, monolayer graphene in registry with Ni(111) has been obtained. In the tube furnace, mono- and bilayer graphene is obtained at growth temperatures of ∼800 °C, while at 900 °C, non-uniform thick graphene multilayers are formed. Y2O3 films grown by reactive molecular beam epitaxy in UHV covers the graphene/Ni(111) surface uniformly. Annealing to 500 °C results in crystallization of the yttria with a (111) surface orientation.

Graphene grown by chemical vapor deposition can be used as the conductive channel in metal oxide semiconductor field effect transistors, metallic electrodes in capacitors, etc. However, substrate-induced corrugations and strain-related wrinkles formed on the graphene layer impoverish the properties of these devices by lowering the conductance and increasing their variability. Using the scanning electron microscopy, Auger electron spectroscopy, scanning tunneling microscopy, and atomic force microscopy, we investigated the morphology of as-grown and transferred graphene sheets on different substrates. We show that while the compressive strain (from the growth process) in the graphene sheet on flat substrates is minimized by generating wrinkles, and on rough substrates, it can be minimized by improving the graphene-substrate adhesion, leading to lower densities of wrinkles. This method paves the way to the design of wrinkle-free graphene based devices.

The study of epitaxial graphene layers grown on SiC by two techniques, namely, the traditional Si sublimation method and the recent chemical vapor deposition (CVD) using temperature induced shift of the Raman 2D line, is presented. The measurements of thermal shift rate of 2D line on 4 H-SiC(0001) allowed us to determine notable differences in interaction of graphene with SiC substrate. The obtained results show that graphene layers grown by Si sublimation of 4 H-SiC(0001) are pinned strongly to the substrate. In contrast, the layers of graphene grown on 4 H-SiC(0001) substrates by CVD showed much weaker pinning. It was found that the film consisting of two or three graphene layers grown by CVD was already unpinned and thus showing Raman shift expected for freestanding graphene. The obtained differences in pinning of epitaxial graphene layers are explained in terms of basic growth mechanism differences between these two methods: graphene growth by Si sublimation is a “bottom-up” process and by CVD—a “top-...

In situ analysis was performed on the graphene growth in ultrahigh vacuum chemical vapor deposition by exposing the epitaxial Ni(111) thin film to benzene vapor at 873 K. It is shown that the highly uniform single- and bi-layer graphenes can be synthesized by the control of benzene exposure in the range of 10–105 langmuirs, reflecting a change in the graphene growth-rate by three orders of magnitude in between the first and second layer. Electron energy loss spectroscopy measurements of single- and bi-layer graphenes indicates that the interface interaction between bi-layer graphene and Ni(111) is weakened in comparison with that between single-layer graphene and Ni(111). It is also clarified from the micro-Raman analysis that the structural and electrical uniformities of the graphene film transformed on a SiO2 substrate are improved remarkably under the specific exposure conditions at which the growths of single- and bi-layer graphenes are completed.

We mechanically clean graphene devices using an atomic force microscope (AFM). By scanning an AFM tip in contact mode in a broom-like way over the sample, resist residues are pushed away from the desired area. We obtain atomically flat graphene with a root mean square (rms) roughness as low as 0.12 nm after this procedure. The cleaning also results in a shift of the charge-neutrality point toward zero gate voltage, as well as an increase in charge carrier mobility.

Metal-catalyst-free chemical vapor deposition (CVD) of large area uniform nanocrystalline graphene on oxidized silicon substrates is demonstrated. The material grows slowly, allowing for thickness control down to monolayer graphene. The as-grown thin films are continuous with no observable pinholes, and are smooth and uniform across whole wafers, as inspected by optical-, scanning electron-, and atomic force microscopy. The sp 2 hybridized carbon structure is confirmed by Raman spectroscopy. Room temperature electrical measurements show ohmic behavior (sheet resistance similar to exfoliated graphene) and up to 13 of electric-field effect. The Hall mobility is ∼40 cm 2/Vs, which is an order of magnitude higher than previously reported values for nanocrystalline graphene. Transmission electron microscopy, Raman spectroscopy, and transport measurements indicate a graphene crystalline domain size ∼10 nm. The absence of transfer to another substrate allows avoidance of wrinkles, holes, and etching residues which are usually detrimental to device performance. This work provides a broader perspective of graphene CVD and shows a viable route toward applications involving transparent electrodes.

This paper describes a pulse technique for measuring the properties and charge‐transfer characteristics of electrographic receptors. This method has the unique capability, as compared with electrometer methods or ac bridge methods, of separately measuring the charge deposited on the surface of the dielectric layer, the displacement charge, and the charge passing through the dielectric. The technique is used to obtain a detailed analysis of the electrographic properties of a dielectric coated paper, including the relaxation of the paper substrate, the capacitances of the virtual air gap and the dielectric layer, and the threshold voltage for charge transfer.

Due to the exciting physical mechano-bactericidal approach developed in recent years using nanopatterned surfaces with its potential applications in biomedical engineering, now it becomes crucially important to fabricate optimal surface structures so as to achieve the best bactericidal ability. In this paper, the bactericidal efficacy of the cylindrical nanopillar-patterned surface and the sinusoidal nanopillar-patterned surface is presented via minimizing total free energy for a bacterial cell adhered on these two kinds of surfaces. Our theoretical analyses show that the adhesion depth at equilibrium along the nanopillar shafts and the corresponding stretching degree is related to the the nanopillar density and nanopillar radius. The bactericidal efficacy on the nanopillar-patterned surface is determined by the combination of nanopillar density and naopillar radius, which is also supported by the phase diagrams obtained, showing that at large internanopillar spacing and nanopillar radius, the sinusoidal nanopillar-patterned surface is more advantageous in bactericidal efficacy, while in small interspacing and nanopillar radius, the cylindrical nanopillar-patterned surface structure is more powerful. The conclusions obtained in this paper unveil how the mechano-bactericidal effect is achieved by tuning the topography of the nanopatterned surface, a technique helpful to the optimal design and fabrication of bio-mimicking nanotextured surfaces.

InGaN-based light-emitting diodes (LEDs) have higher luminescence efficiency than other materials used for the blue and green LEDs in spite of their relatively high dislocation density. Localization theory has been used to explain this phenomenon, but the direct observation of localization states in the InGaN active region has been rarely reported. In this paper, we propose an LED structure to obtain higher luminescence efficiency in the yellow-green LEDs and directly observe the transition of carriers between different localization states. The localization states were investigated and confirmed by temperature-dependent photoluminescence and excitation power-dependent photoluminescence. The value of the external quantum efficiency also exhibited a higher radiative efficiency of the quantum well with a higher degree of localization states. These results offer a promising means of realizing high-luminescence LEDs.InGaN-based light-emitting diodes (LEDs) have higher luminescence efficiency than other materials used for the blue and green LEDs in spite of their relatively high dislocation density. Localization theory has been used to explain this phenomenon, but the direct observation of localization states in the InGaN active region has been rarely reported. In this paper, we propose an LED structure to obtain higher luminescence efficiency in the yellow-green LEDs and directly observe the transition of carriers between different localization states. The localization states were investigated and confirmed by temperature-dependent photoluminescence and excitation power-dependent photoluminescence. The value of the external quantum efficiency also exhibited a higher radiative efficiency of the quantum well with a higher degree of localization states. These results offer a promising means of realizing high-luminescence LEDs.

This paper presents a novel thermochromic induced transmittance filter (ITF) based on VO2 films. The ITF structure enables high transmittance in the short wavelength range with wide rejection at longer wavelengths, which meets the requirements of thermochromic VO2 for the metal-insulator transition. Thus, the VO2-based ITFs are designed and fabricated based on the induced transmittance effect, and a graded-index material TiO2 is initially adopted for the simplified structure of VO2-based ITF comparing standard ITFs. The VO2-based ITF's properties are characterized systematically and compared with those of VO2 films. Favorable results of crystallinity, surface roughness, hydrophobicity, the thermal hysteresis width, and pleasant appearance color are achieved in these VO2-based ITFs. Moreover, luminous transmittance Tlum (380–780 nm) of 48.8% and a solar modulation ability ΔTsol of 6.2% are achieved with an ideal spectrum shape in the VO2-based ITF, which provides a highly efficient solution to improve thermochromic VO2 films and related field.This paper presents a novel thermochromic induced transmittance filter (ITF) based on VO2 films. The ITF structure enables high transmittance in the short wavelength range with wide rejection at longer wavelengths, which meets the requirements of thermochromic VO2 for the metal-insulator transition. Thus, the VO2-based ITFs are designed and fabricated based on the induced transmittance effect, and a graded-index material TiO2 is initially adopted for the simplified structure of VO2-based ITF comparing standard ITFs. The VO2-based ITF's properties are characterized systematically and compared with those of VO2 films. Favorable results of crystallinity, surface roughness, hydrophobicity, the thermal hysteresis width, and pleasant appearance color are achieved in these VO2-based ITFs. Moreover, luminous transmittance Tlum (380–780 nm) of 48.8% and a solar modulation ability ΔTsol of 6.2% are achieved with an ideal spectrum shape in the VO2-based ITF, which provides a highly efficient solution to improve ther...

This paper reports the fabrication of InN layers on the epitaxial graphene (EG) using radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). Prior to the fabrication of InN, single crystalline EG with step and terrace structure was formed on 6H-SiC (0001) substrate in an Ar ambient by the Si sublimation method. Single crystalline epitaxial layers of InN with smooth surfaces are successfully fabricated on the EG using RF-MBE. InN layers with terrace and step structure are grown on the graphene surface up to 2MLs, and InN are grown in a layer by layer 2D growth mode. If the number of layers is increased above 3 MLs, the terrace and steps disappear, and the growth mode changes to 3D mode. The Raman spectroscopy analysis shows that the interfacial stress is reduced for the InN layer grown on the EG surface. The quality of the grown InN layer on the EG surface achieved at present is comparable to the InN film grown on sapphire. This work opens the possibility of growing high-quality InN layers on the EG surface in the near future.This paper reports the fabrication of InN layers on the epitaxial graphene (EG) using radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). Prior to the fabrication of InN, single crystalline EG with step and terrace structure was formed on 6H-SiC (0001) substrate in an Ar ambient by the Si sublimation method. Single crystalline epitaxial layers of InN with smooth surfaces are successfully fabricated on the EG using RF-MBE. InN layers with terrace and step structure are grown on the graphene surface up to 2MLs, and InN are grown in a layer by layer 2D growth mode. If the number of layers is increased above 3 MLs, the terrace and steps disappear, and the growth mode changes to 3D mode. The Raman spectroscopy analysis shows that the interfacial stress is reduced for the InN layer grown on the EG surface. The quality of the grown InN layer on the EG surface achieved at present is comparable to the InN film grown on sapphire. This work opens the possibility of growing high-quality InN layers on the...

III-V optoelectronics grown epitaxially on Si substrates have large networks of dislocations due to a lattice constant mismatch between the device layers and the substrate. Recombination-enhanced dislocation glide (REDG) allows these dislocations to move and increase in length during device operation, which degrades performance. In this paper, we study REDG dynamics of threading dislocations in situ in (In)AlGaAs double heterostructures grown on Si substrates using scanning electron microscopy cathodoluminescence. The driving force for REDG arises due to the coefficient of thermal expansion differences between Si and the III-V layers leading to large residual strains in the films. Tracking of threading dislocations as moving dark spot defects reveals glide characteristics that vary based on the nature of the dislocation. Remarkably, the alloying of a few atom percent of indium using metamorphic structures arrests threading dislocation glide by more than two orders of magnitude. Finally, we present REDG-based filtering as a pathway to reducing the threading dislocation density in select areas, removing a large fraction of the mobile dislocations. Together, these techniques will enable the understanding of dislocation–dislocation and carrier–dislocation interactions that have so far remained elusive during device operation, leading to reliable III-V integrated optoelectronics on silicon.III-V optoelectronics grown epitaxially on Si substrates have large networks of dislocations due to a lattice constant mismatch between the device layers and the substrate. Recombination-enhanced dislocation glide (REDG) allows these dislocations to move and increase in length during device operation, which degrades performance. In this paper, we study REDG dynamics of threading dislocations in situ in (In)AlGaAs double heterostructures grown on Si substrates using scanning electron microscopy cathodoluminescence. The driving force for REDG arises due to the coefficient of thermal expansion differences between Si and the III-V layers leading to large residual strains in the films. Tracking of threading dislocations as moving dark spot defects reveals glide characteristics that vary based on the nature of the dislocation. Remarkably, the alloying of a few atom percent of indium using metamorphic structures arrests threading dislocation glide by more than two orders of magnitude. Finally, we present REDG-ba...

In this paper, we propose a simple and effective method to manipulate photonic spin accumulation with an applied magnetic field. When a linearly polarized Gaussian light beam is reflected from the prism-air interface at the Brewster angle, the magnitude and direction of the photonic spin accumulation can be flexibly modulated by adjusting the applied magnetic field. Importantly, the maximum displacement of photonic spin accumulation can reach about 39.14 μ m, which provides the opportunity to directly observe photonic spin accumulation without weak measurements. These findings may hold potential applications for manipulating and detecting the electron spin current, leading to the development of a new spintronic device.In this paper, we propose a simple and effective method to manipulate photonic spin accumulation with an applied magnetic field. When a linearly polarized Gaussian light beam is reflected from the prism-air interface at the Brewster angle, the magnitude and direction of the photonic spin accumulation can be flexibly modulated by adjusting the applied magnetic field. Importantly, the maximum displacement of photonic spin accumulation can reach about 39.14 μ m, which provides the opportunity to directly observe photonic spin accumulation without weak measurements. These findings may hold potential applications for manipulating and detecting the electron spin current, leading to the development of a new spintronic device.

Plasmonic structure (PS) has recently been demonstrated to provide full control of dispersion characteristics by virtue of spoof surface plasmonic polariton (SSPP). In this paper, a comprehensive scheme is proposed, which develops the non-planar PS as a covering on the absorber to enhance the k-vector matching absorption in a wider frequency band. Owing to the dispersion engineering of SSPP, our theoretical investigation shows that the PS covering based on a straight wire array can not only enhance the k-vector matching absorption of the ground absorber at low frequency, but also achieve the broadband absorption at high frequency. As a proof, two hybrid plasmonic metamaterial absorbers (PMAs) based on the combinations of PS covering and various absorbers are proposed here. Simulations and experimental measurements demonstrate that two kinds of hybrid PMAs can simultaneously achieve broadband absorption enhancement, especially for the lower-frequency absorption. Our proposed strategy succeeds in the comprehensive utilization of dispersion engineering for broadband absorption enhancement, and a wide range of applications is expected to emerge from our design concept ranging from microwave to optical frequencies.Plasmonic structure (PS) has recently been demonstrated to provide full control of dispersion characteristics by virtue of spoof surface plasmonic polariton (SSPP). In this paper, a comprehensive scheme is proposed, which develops the non-planar PS as a covering on the absorber to enhance the k-vector matching absorption in a wider frequency band. Owing to the dispersion engineering of SSPP, our theoretical investigation shows that the PS covering based on a straight wire array can not only enhance the k-vector matching absorption of the ground absorber at low frequency, but also achieve the broadband absorption at high frequency. As a proof, two hybrid plasmonic metamaterial absorbers (PMAs) based on the combinations of PS covering and various absorbers are proposed here. Simulations and experimental measurements demonstrate that two kinds of hybrid PMAs can simultaneously achieve broadband absorption enhancement, especially for the lower-frequency absorption. Our proposed strategy succeeds in the compre...

In this paper, the design, fabrication, and measurement of a high-performance metamaterial absorber (MMA) have been presented. The three major concerns of MMA's are narrow bandwidth, angle sensitivity, and uncontrollable polarization. By smartly controlling the proposed design, the solutions to these three concerns of MMA are given in this paper. By integrating the design with varactor diodes, we make the MMA tunable to wide frequency ranges. Frequency tunability ranges from 4.2 to 7 GHz. By using circular sectors in the resonator, wide incident angle insensitivity has been achieved. The presented MMA exhibits more than 80% absorptivity up to 70° incident angles. With the proposed design, it is possible to control either TM or TE polarization resonant frequency by fixing the resonant frequency of other polarization. Also, a biasing technique which is simple and effective to control both TM and TE resonant frequencies simultaneously is given in this paper. Moreover, all these advantages have been achieved by using a single layer low cost FR4 material having thickness 0.6 mm as a substrate. By using a standard parameter retrieval technique, the real and imaginary parts of both permittivity and permeability of the presented MMA are calculated. It is expected that the presented work improves the state-of-the-art in the smart metamaterial absorber domain.

This paper investigates energy filtering in silicon nanowires and nanosheets by resonant electron tunneling through a geometric superlattice. A geometric superlattice is any kind of periodic geometric feature along the transport direction of the nanowire or nanosheet. Multivalley quantum-transport simulations are used to demonstrate the manifestation of minibands and minibandgaps in the transmission spectra of such a superlattice. We find that the presence of different valleys in the conduction band of silicon favors a nanowire with a rectangular cross section for effective energy filtering. The obtained energy filter can consequently be used in the source extension of a field-effect transistor to prevent high-energy electrons from contributing to the leakage current. Self-consistent Schrodinger-Poisson simulations in the ballistic limit show minimum subthreshold swings of 6 mV/decade for geometric superlattices with indentations. The obtained theoretical performance metrics for the simulated devices are compared with conventional III-V superlatticeFETs and TunnelFETs. The adaptation of the quantum transmitting boundary method to the finite-element simulation of 3-D structures with anisotropic effective mass is presented in Appendixes A and B. Our results bare relevance in the search for steep-slope transistor alternatives which are compatible with the silicon industry and can overcome the power-consumption bottleneck inherent to standard CMOS technologies.This paper investigates energy filtering in silicon nanowires and nanosheets by resonant electron tunneling through a geometric superlattice. A geometric superlattice is any kind of periodic geometric feature along the transport direction of the nanowire or nanosheet. Multivalley quantum-transport simulations are used to demonstrate the manifestation of minibands and minibandgaps in the transmission spectra of such a superlattice. We find that the presence of different valleys in the conduction band of silicon favors a nanowire with a rectangular cross section for effective energy filtering. The obtained energy filter can consequently be used in the source extension of a field-effect transistor to prevent high-energy electrons from contributing to the leakage current. Self-consistent Schrodinger-Poisson simulations in the ballistic limit show minimum subthreshold swings of 6 mV/decade for geometric superlattices with indentations. The obtained theoretical performance metrics for the simulated devices are ...

An all-solid-state AlGaN/GaN based ion-sensitive heterostructure field effect transistor (ISHFET) pH sensor was fabricated by integrating a noble metal (Au) quasi-reference electrode to improve the device stability when measuring the pH value of a small aqueous volume. In this paper, the influence of the size of the quasi-reference electrode against the stability of the pH readings was investigated. Through optimizing the size of the integrated quasi-reference electrode, the all-solid-state ISHFET pH sensor can sustain stable pH measurements for aqueous solutions of micro-litre size. A sensitivity of 55 mV/pH was achieved by the pH sensor at room temperature. Thus, the device may have potential uses in biomedical applications which require small volume pH measurements.An all-solid-state AlGaN/GaN based ion-sensitive heterostructure field effect transistor (ISHFET) pH sensor was fabricated by integrating a noble metal (Au) quasi-reference electrode to improve the device stability when measuring the pH value of a small aqueous volume. In this paper, the influence of the size of the quasi-reference electrode against the stability of the pH readings was investigated. Through optimizing the size of the integrated quasi-reference electrode, the all-solid-state ISHFET pH sensor can sustain stable pH measurements for aqueous solutions of micro-litre size. A sensitivity of 55 mV/pH was achieved by the pH sensor at room temperature. Thus, the device may have potential uses in biomedical applications which require small volume pH measurements.

Silicon nanocrystals embedded in silicon oxide that show room temperature photoluminescence (PL) have great potential in silicon light emission applications. Nanocrystalline silicon particle formation by laser irradiation has the unique advantage of spatially controlled heating, which is compatible with modern silicon micro-fabrication technology. In this paper, we employ continuous wave laser irradiation to decompose substrate-bound silicon-rich silicon oxide films into crystalline silicon particles and silicon dioxide. The resulting microstructure is studied using transmission electron microscopy techniques with considerable emphasis on the formation and properties of laser damaged regions which typically quench room temperature PL from the nanoparticles. It is shown that such regions consist of an amorphous matrix with a composition similar to silicon dioxide which contains some nanometric silicon particles in addition to pores. A mechanism referred to as “selective silicon ablation” is proposed which consistently explains the experimental observations. Implications for the damage-free laser decomposition of silicon-rich silicon oxides and also for controlled production of porous silicon dioxide films are discussed.Silicon nanocrystals embedded in silicon oxide that show room temperature photoluminescence (PL) have great potential in silicon light emission applications. Nanocrystalline silicon particle formation by laser irradiation has the unique advantage of spatially controlled heating, which is compatible with modern silicon micro-fabrication technology. In this paper, we employ continuous wave laser irradiation to decompose substrate-bound silicon-rich silicon oxide films into crystalline silicon particles and silicon dioxide. The resulting microstructure is studied using transmission electron microscopy techniques with considerable emphasis on the formation and properties of laser damaged regions which typically quench room temperature PL from the nanoparticles. It is shown that such regions consist of an amorphous matrix with a composition similar to silicon dioxide which contains some nanometric silicon particles in addition to pores. A mechanism referred to as “selective silicon ablation” is proposed which ...

In this paper, we proposed a novel nano-gap thermophotovoltaic (TPV) device made up of thin-films including the radiator. The optical, electrical, and thermal responses and performance of the device were assessed using coupled opto-electro-thermal numerical simulation. The device design consists of a thin-film tungsten radiator which is paired with a thin-film silicon TPV cell across a nanometric vacuum gap. Results were simulated based on experimental properties available in the current literature database. It is discovered that the maximum electrical power output of the thin-film nano-gap TPV device increases with cell temperature up to a certain threshold value due to improvements in generated photocurrent. Thin-film tungsten as a radiator is shown to improve radiative heat transfer above the bandgap compared to conventional bulk tungsten. The effect of cell thickness on responses and performance was also analysed. A 1-μm cell produces better performance over thinner thicknesses at the cost of greater cooling requirements. However, the improvements in output power offset the cooling costs, allowing for consistently favourable efficiencies. Finally, it is shown that the temperature profile in silicon thin-films under convective cooling can be approximated as uniform, simplifying the heat transport modelling process.In this paper, we proposed a novel nano-gap thermophotovoltaic (TPV) device made up of thin-films including the radiator. The optical, electrical, and thermal responses and performance of the device were assessed using coupled opto-electro-thermal numerical simulation. The device design consists of a thin-film tungsten radiator which is paired with a thin-film silicon TPV cell across a nanometric vacuum gap. Results were simulated based on experimental properties available in the current literature database. It is discovered that the maximum electrical power output of the thin-film nano-gap TPV device increases with cell temperature up to a certain threshold value due to improvements in generated photocurrent. Thin-film tungsten as a radiator is shown to improve radiative heat transfer above the bandgap compared to conventional bulk tungsten. The effect of cell thickness on responses and performance was also analysed. A 1-μm cell produces better performance over thinner thicknesses at the cost of greater ...

Ferroelectric hafnium oxide is a promising candidate for logic and memory applications as it maintains excellent ferroelectric properties at nm-size ensuring compatibility with state of the art semiconductor manufacturing. Most of the published papers report on the study of this material through Metal-Insulator-Metal capacitors or Metal-Insulator-Silicon transistors. However, for 3D vertical transistors in which both the channel and gate are polysilicon, the case of silicon-based electrodes cannot be ignored. In this paper, we report the fabrication of various ferroelectric capacitors with silicon (S) based conductive layers and titanium nitride metal (M) electrodes using aluminum doped hafnium oxide (I). The ferroelectric device with silicon-based electrodes shows superior polarization and steeper switching. These results pave the way toward 3D integration for potential 3D NAND replacement.

Fano resonances usually arise when a narrow resonance or discrete state and a broad resonance or continuum state are coupled. In this paper, we theoretically and numerically study asymmetric Fano line shape realized in a photonic crystal nanobeam (PCN) side-coupled with a photonic crystal nanobeam cavity (PCNC). Asymmetric transmission profiles with a transmission peak and a transmission valley are obtained for a low index concentrated cavity mode. The transmission valley, associated with the destructive interference, of our PCN-PCNC structures is deeper than that of a waveguide or Fabry-Perot resonator side-coupled with a PCNC structure. Through changing the position of the photonic band gap (PBG) of the PCN, we can utilize the high or low frequency band edge modes and the Fano transmission profiles can be further controlled. The transmission spectra of our PCN-PCNC structures can be well fitted by the Fano resonance formula and agree qualitatively with the prediction made by the temporal coupled mode theory. By using the band edge modes of the PCN as the continuum state instead of a usual broad resonance, we have demonstrated a new way to generate a prominent Fano resonance. Our PCN-PCNC structures are compact and feasible to achieve large-scale high-performance integrated photonic devices, such as optical modulators or switches.Fano resonances usually arise when a narrow resonance or discrete state and a broad resonance or continuum state are coupled. In this paper, we theoretically and numerically study asymmetric Fano line shape realized in a photonic crystal nanobeam (PCN) side-coupled with a photonic crystal nanobeam cavity (PCNC). Asymmetric transmission profiles with a transmission peak and a transmission valley are obtained for a low index concentrated cavity mode. The transmission valley, associated with the destructive interference, of our PCN-PCNC structures is deeper than that of a waveguide or Fabry-Perot resonator side-coupled with a PCNC structure. Through changing the position of the photonic band gap (PBG) of the PCN, we can utilize the high or low frequency band edge modes and the Fano transmission profiles can be further controlled. The transmission spectra of our PCN-PCNC structures can be well fitted by the Fano resonance formula and agree qualitatively with the prediction made by the temporal coupled mode th...

The paper compares the achievements of quantum well infrared photodetector (QWIP) technology with those of competitive technologies, with the emphasis on the material properties, device structure, and their impact on focal plane array (FPA) performance. Special attention is paid to two competitive technologies, QWIP and HgCdTe, in the long-wavelength IR (LWIR) and very-long-wavelength IR (VLWIR) spectral ranges. Because so far, the dialogue between the QWIP and HgCdTe communities is limited, the paper attempts to settle the main issues of both technologies. Such an approach, however, requires the presentation of fundamental limits to the different types of detectors, which is made at the beginning. To write the paper more clearly for readers, many details are included in the Appendix. In comparative studies both photon and thermal detectors are considered. Emphasis is placed on photon detectors. In this group one may distinguish HgCdTe photodiodes, InSb photodiodes, and doped silicon detectors. The potential performance of different materials as infrared detectors is examined utilizing the α/G ratio, where α is the absorption coefficient and G is the thermal generation rate. It is demonstrated that LWIR QWIP’s cannot compete with HgCdTe photodiodes as single devices, especially at higher operating temperatures (>70 K). This is due to the fundamental limitations associated with intersubband transitions. The advantage of HgCdTe is, however, less distinct at temperatures lower than 50 K due to problems inherent in the HgCdTe material (p-type doping, Shockley–Read recombination, trap-assisted tunneling, surface and interface instabilities). Even though QWIP is a photoconductor, several of its properties, such as high impedance, fast response time, long integration time, and low power consumption, comply well with the requirements imposed on the fabrication of large FPA’s. Due to a high material quality at low temperatures, QWIP has potential advantages over HgCdTe in the area of VLWIR FPA applications in terms of array size, uniformity, yield, and cost of the systems. The performance figures of merit of state-of-the-art QWIP and HgCdTe FPA’s are similar because the main limitations come from the readout circuits. Performance is, however, achieved with very different integration times. The choice of the best technology is therefore driven by the specific needs of a system. In the case of readout-limited detectors a low photoconductive gain increases the signal-to-noise ratio and a QWIP FPA can have a better noise equivalent difference temperature than an HgCdTe FPA with a charge well of similar size. Both HgCdTe photodiodes and QWIP’s offer multicolor capability in the MWIR and LWIR range. Powerful possibilities offered by QWIP technology are associated with VLWIR FPA applications and with multicolor detection. The intrinsic advantage of QWIP’s in this niche is due to the relative ease of growing multicolor structures with a very low defect density.

Vertical stacking of organic light emitting devices (OLEDs) that emit the three primary colors is a means for achieving full-color flat panel displays. The physics, performance, and applications of stacked OLEDs (SOLEDs) are discussed in this and the following paper (Papers I and II, respectively). In Paper I, we analyze optical microcavity effects that can distort the emission colors of SOLEDs if not properly controlled, and describe design principles to minimize these parasitic effects. We also describe the fabrication and operating characteristics of transparent contacts that are an integral part of SOLEDs. We demonstrate that both metal-containing and metal-free transparent electrodes can serve as efficient electron and hole injectors into the stacked organic semiconductor layers. Two different transparent SOLED structures (metal-containing and metal-free) that exhibit sufficient performance for many full-color display applications will be discussed in Paper II.

This paper describes a simple microwave apparatus to measure the Hall effect in semiconductor wafers. The advantage of this technique is that it does not require contacts on the sample or the use of a resonant cavity. Our method consists of placing the semiconductor wafer into a slot cut in an X-band (8–12 GHz) waveguide series tee, injecting microwave power into the two opposite arms of the tee, and measuring the microwave output at the third arm. A magnetic field applied perpendicular to the wafer gives a microwave Hall signal that is linear in the magnetic field and which reverses phase when the magnetic field is reversed. The microwave Hall signal is proportional to the semiconductor mobility, which we compare for calibration purposes with d.c. mobility measurements obtained using the van der Pauw method. We obtain the resistivity by measuring the microwave reflection coefficient of the sample. This paper presents data for silicon and germanium samples doped with boron or phosphorus. The measured mobi...

Molecular electronics studies how the molecular nature affects the probability of charge carriers to tunnel through the molecules. Nevertheless, transport is also critically affected by the contacts to the molecules, an aspect that is often overlooked. Specifically, the limited ability of non-metallic contacts to maintain the required charge balance across the fairly insulating molecule often have dramatic effects. This paper shows that in the case of lead/organic monolayer-silicon junctions, a charge balance is responsible for an unusual current scaling, with the junction diameter (perimeter), rather than its area. This is attributed to the balance between the 2D charging at the metal/insulator interface and the 3D charging of the semiconductor space-charge region. A derivative method is developed to quantify transport across tunneling metal-insulator-semiconductor junctions; this enables separating the tunneling barrier from the space-charge barrier for a given current-voltage curve, without complementary measurements. The paper provides practical tools to analyze specific molecular junctions compatible with existing silicon technology, and demonstrates the importance of contacts' physics in modeling charge transport across molecular junctions.

The development and optimization of sputtering techniques for the deposition of refractory metal thin films for very large scale integration (VLSI) barrier and encapsulation layers is of significant concern for the microelectronic fabrication industry. A number of directed sputtering techniques such as collimation and low pressure longthrow configurations have been applied to this problem. This paper addresses a number of issues present in the understanding and simulation of the growth of films deposited by directed sputtering techniques over VLSI topography. In particular the role of high energy neutral gas atoms reflected from the target is investigated as a source of resputtering. Also addressed is the creation of a low density porous film on the sidewalls of vias/contacts due to oblique incident fluxes on these areas. Experimentally Ti and W films are deposited at pressures varying from 0.2 to 12.0 mTorr with and without collimators present. A number of re-emission/resputtering mechanisms were investigated using a Monte Carlo growth simulator and it was found that the model most consistent with the experimental films was an assumption of resputtering due to reflected neutrals. A significant result is a dramatic increase in the resputtering rate when a collimator was present due to a relative increase in the reflected neutral flux. Finally, the paper presents an analysis of the effect of pressure on bottom and step coverage in high aspect topography.The development and optimization of sputtering techniques for the deposition of refractory metal thin films for very large scale integration (VLSI) barrier and encapsulation layers is of significant concern for the microelectronic fabrication industry. A number of directed sputtering techniques such as collimation and low pressure longthrow configurations have been applied to this problem. This paper addresses a number of issues present in the understanding and simulation of the growth of films deposited by directed sputtering techniques over VLSI topography. In particular the role of high energy neutral gas atoms reflected from the target is investigated as a source of resputtering. Also addressed is the creation of a low density porous film on the sidewalls of vias/contacts due to oblique incident fluxes on these areas. Experimentally Ti and W films are deposited at pressures varying from 0.2 to 12.0 mTorr with and without collimators present. A number of re-emission/resputtering mechanisms were investi...

The gated polysilicon field emitter arrays coated with diamondlike carbon (DLC) were fabricated by a transfer mold method using anisotropic etching of Si and the deposition of DLC using methane ion beam. This paper describes significant enhancement in electron emission and considerable reduction in turn-on voltage for the emitter arrays by the DLC coating. In addition, the paper discusses the emission mechanism from the energy band diagram of a field emitter coated with a sufficiently thin dielectric material having a low electron affinity, and shows that an effective work function of the DLC coated polysilicon field emitter is about 2.9 eV.

Thin film transistors (TFTs) on elastomers promise flexible electronics with stretching and bending. Recently, there have been several experimental studies reporting the behavior of TFTs under bending and buckling. In the presence of stress, the insulator capacitance is influenced due to two reasons. The first is the variation in insulator thickness depending on the Poisson ratio and strain. The second is the geometric influence of the curvature of the insulator-semiconductor interface during bending or buckling. This paper models the role of curvature on TFT performance and brings to light an elegant result wherein the TFT characteristics is dependent on the area under the capacitance-distance curve. The paper compares models with simulations and explains several experimental findings reported in literature. (C) 2014 AIP Publishing LLC.

Optical transport behavior of organic photo-voltaic devices with nano-pillar transparent electrodes is investigated in this paper in order to understand possible enhancement of their charge-collection efficiency. Modeling and simulations of optical transport due to this architecture show an interesting regime of length-scale dependent optical characteristics. An electromagnetic wave propagation model is employed with simulation objectives toward understanding the mechanism of optical scattering and waveguide effects due to the nano-pillars and effective transmission through the active layer. Partial filling of gaps between the nano-pillars due to the nano-fabrication process is taken into consideration. Observations made in this paper will facilitate appropriate design rules for nano-pillar electrodes. (C) 2014 AIP Publishing LLC.

In this paper piezoelectric stress transducers are proposed on the base of GaAs and AlxGa(1−x)As. These materials exhibit reasonable piezoelectric properties and since GaAs based integrated circuits have reached a high maturity they are a promising choice for integrated stress transducers. An additional feature of the high band‐gap material GaAs is its superior high‐temperature performance in comparison with Si. In this paper the piezoelectric and related properties of GaAs and AlxGa(1−x) are discussed. Therefore the piezoelectric tensors for the commonly used (100) and (111) oriented substrates are derived. These calculations are verified by measurements of some realized sensors using different substrate orientations.

Current balance factor (CBF) value, the ratio of the recombination current density and the total current density of a device, has an important function in fluorescence-based organic light-emitting diodes (OLEDs), as well as in the performance of the organic electrophosphorescent devices. This paper investigates the influence of the applied voltage of a device on the CBF value of single layer OLED based on the numerical model of a bipolar single layer OLED with organic layer trap free and without doping. Results show that the largest CBF value can be achieved when the electron injection barrier ( ϕ n ) is equal to the hole injection barrier ( ϕ p ) in the lower voltage region at any instance. The largest CBF in the higher voltage region can be achieved in the case of ϕ n > ϕ p under the condition of electron mobility ( μ 0 n ) > hole mobility ( μ 0 p ), whereas the result for the case of μ 0 n μ 0 p , is opposite. The largest CBF when μ 0 n = μ 0 p can be achieved in the case of ϕ n = ϕ p in the entire region of the applied voltage. In addition, the CBF value of the device increases with increasing applied voltage. The results obtained in this paper can present an in-depth understanding of the OLED working mechanism and help in the future fabrication of high efficiency OLEDs.

In this paper, we modeled a quantum dot at near proximity to a gap plasmon waveguide to study the quantum dot-plasmon interactions. Assuming that the waveguide is single mode, this paper is concerned about the dependence of spontaneous emission rate of the quantum dot on waveguide dimensions such as width and height. We compare coupling efficiency of a gap waveguide with symmetric configuration and asymmetric configuration illustrating that symmetric waveguide has a better coupling efficiency to the quantum dot. We also demonstrate that optimally placed quantum dot near a symmetric waveguide with 50 nm × 50 nm cross section can capture 80% of the spontaneous emission into a guided plasmon mode.

Theoretical studies and numerical simulations on design, performance, and improvements of terahertz quantum-well photodetector (THz QWP) are presented. In the first part of this paper, we discuss the device band structure resulting from a self-consistent solution and simulation results. First, the temperature dependence of device characteristics is analyzed. Next, we deduce the condition of optimal doping concentration for maximizing dark current limited detectivity Ddet* when QWP is lightly doped. Accordingly, unlike in previously published reports, doping concentration is not fixed and is selected by the above condition. In the second part of this paper, we propose two schemes for improving operation temperature. The first is to incorporate an optical antenna which focuses incident THz wave. Numerical results show that the QWP with peak frequency higher than 5.5 THz is expected to achieve background-noise-limited performance at 77 K or above when employing a 106 times enhancement antenna. The second sch...

This paper presents the findings of investigating core-shell multiple quantum well nanowire light-emitting diodes (LEDs). A fully self-consistent three dimensional model that solves Poisson and drift-diffusion equations was employed to investigate the current flow and quantum-confined stark effect. The core-shell nanowire LED showed a weaker droop effect than that of conventional planar LEDs because of a larger active area and stronger recombination in nonpolar quantum wells (QWs). The current spreading effect was examined to determine the carrier distribution at the sidewall of core-shell nanowire LEDs. The results revealed that a larger aspect ratio by increasing the nanowire height could increase the nonpolar-active area volume and reduce the droop effect at the same current density. Making the current spreading length exceed a greater nanowire height is critical for using the enhancement of nonpolar QWs effectively, when an appropriate transparent conducting layer might be necessary. In addition, this paper presents a discussion on the influences of the spacing between each nanowire on corresponding nanowire diameters.

This paper analyzes the optical polarization characteristics and internal quantum efficiency (IQE) of an AlGaN based polar, nonpolar, and semipolar deep ultra-violet (UV) light emitting diode (LED). A one dimensional model is used to solve drift-diffusion, Poisson equations, and 6 × 6 k·p Schrodinger equations to investigate band structure and emission characteristics. The light emission polarization ratios of c-plane, nonpolar, and semipolar AlGaN based deep UV LEDs with different Al compositions and injection current were studied. The study shows that the optical polarization of the c-plane AlGaN based deep UV LED is dominated by the out-plane polarization as the Al composition increases. For nonpolar and semipolar structures, the light polarization direction is mainly dominated by the in-plane polarized light which is good for the surface emitting. Finally, influences of the IQE by changing the p-type activation energy, growth orientation, and nonradiatve lifetime are studied in this paper.

In recent years, GaN nanorods are emerging as a very promising novel route toward devices for nano-optoelectronics and nano-photonics. In particular, core-shell light emitting devices are thought to be a breakthrough development in solid state lighting, nanorod based LEDs have many potential advantages as compared to their 2 D thin film counterparts. In this paper, we review the recent developments of GaN nanorod growth, characterization, and related device applications based on GaN nanorods. The initial work on GaN nanorod growth focused on catalyst-assisted and catalyst-free statistical growth. The growth condition and growth mechanisms were extensively investigated and discussed. Doping of GaN nanorods, especially p-doping, was found to significantly influence the morphology of GaN nanorods. The large surface of 3 D GaN nanorods induces new optical and electrical properties, which normally can be neglected in layered structures. Recently, more controlled selective area growth of GaN nanorods was realized using patterned substrates both by metalorganic chemical vapor deposition (MOCVD) and by molecular beam epitaxy (MBE). Advanced structures, for example, photonic crystals and DBRs are meanwhile integrated in GaN nanorod structures. Based on the work of growth and characterization of GaN nanorods, GaN nanoLEDs were reported by several groups with different growth and processing methods. Core/shell nanoLED structures were also demonstrated, which could be potentially useful for future high efficient LED structures. In this paper, we will discuss recent developments in GaN nanorod technology, focusing on the potential advantages, but also discussing problems and open questions, which may impose obstacles during the future development of a GaN nanorod based LED technology.

This paper proposes an integrated micro-chip for the manipulation and detection of magnetic particles (MPs). A conducting ring structure is used to manipulate MPs toward giant magnetoresistance (GMR) sensing elements for rapid detection. The GMR sensor is fabricated in a horseshoe shape in order to detect the majority of MPs that are trapped around the conducting structure. The GMR sensing elements are connected in a Wheatstone bridge circuit topology for optimum noise suppression. Full fabrication details of the micro-chip, characterization of the GMR sensors, and experimental results with MPs are presented in this paper. Experimental results showed that the micro-chip can detect MPs from low concentration samples after they were guided toward the GMR sensors by applying current to the conducting ring structure.

Quantum dot–plasmon waveguide systems are of interest for the active control of plasmon propagation, and consequently, the development of active nanophotonic devices such as nano-sized optical transistors. This paper is concerned with how varying aspect ratio of the waveguide cross-section affects the quantum dot–plasmon coupling. We compare a stripe waveguide with an equivalent nanowire, illustrating that both waveguides have a similar coupling strength to a nearby quantum dot for small waveguide cross-section, thereby indicating that stripe lithographic waveguides have strong potential use in quantum dot–plasmon waveguide systems. We also demonstrate that changing the aspect ratio of both stripe and wire waveguides can increase the spontaneous emission rate of the quantum dot into the plasmon mode, by up to a factor of five. The results of this paper will contribute to the optimisation of quantum dot–plasmon waveguide systems and help pave the way for the development of active nanophotonics devices.

In this paper, an analytical model for the estimation of threshold voltage shift, mobility, drain current and subthreshold leakage current in virgin as well as irradiated nanoscale fin-shaped field effect transistor (FinFET) device has been presented. The generation of traps in the buried oxide (BOX) and the interface traps at the sidewall influence the characteristics of an irradiated FinFET device. A mobility model considering the influence of quantum mechanical structural confinement and the contribution of interface traps due to all the interfaces is reported in this paper. The modified definition of effective field is adopted to account for nonzero electric field at the back oxide interface of SOI (Silicon-on-Insulator) FinFET device. The results obtained on the basis of our models were compared and contrasted with reported experimental results. A close match was found that validate our analytical modeling approach.