Abstract: This computational research study analyzes the increase of the specific charge capacity that comes with the reduction of the anisotropic volume expansion during lithium ion insertion within silicon nanowires. This research paper is a continuation from previous work that studied the expansion rate and volume increase. It has been determined that when the lithium ion concentration is decreased by regulating the amount of Li ion flux, the lithium ions to silicon atoms ratio, represented x, decreases within the amorphous lithiated silicon (a-LixSi) material. This results in a decrease in the volumetric strain of the lithiated silicon nanowire as well as a reduction in Maxwell stress that was calculated and Young’s elastic module that was measured experimentally using nanoindentation. The conclusion as will be seen is that as there is a decrease in lithium ion concentration there is a corresponding decrease in anisotropic volume and a resulting increase in specific charge capacity. In fact the amplification of the electromagnetic field due to the electron flux that created detrimental effects for a fully lithiated silicon nanowire at x=3.75 which resulted in over a 300% volume expansion becomes beneficial with the decrease in lithium ion flux as x approaches 0.75 which leads to a marginal volume increase of ~25 percent. This could lead to the use of crystalline silicon, c-Si, as an anode material that has been demonstrated in many previous research work to be ten times greater charge capacity than carbon base anode material for lithium ion batteries.

Power semiconductor devices are essential from the operation point of view, size, efficiency and cost, these components are used in a myriad of applications, providing features that make them an important part of the system in which they are operating. This document analyzes and compares the basic structure, properties, design aspects, as well as temperature performance, stability and switching losses, present in devices on silicon (Si), silicon carbide (SiC) and new generation devices fabricated in gallium nitride (GaN) applied in renewable energy systems. The main objective is determinate the viability of the new generation components, which present a superior performance in view of an increase in efficiency, conductivity, decreases in switching losses, lower resistances and parasitic capacitances as well as higher operating frequency range. Therefore demonstrating the GaN components are a strong and viable candidate to solve some of the problems present in renewable energy systems.

The NA61/SHINE experiment studies hadron production in hadron-hadron, hadron-nucleus and nucleus-nucleus collisions. The physics programme includes the study of the onset of deconfinement and search for the critical point as well as reference measurements for neutrino and cosmic ray experiments. For strong interactions, future plans are to extend the programme of study of the onset of deconfinement by measurements of open-charm and possibly other short-lived, exotic particle production in nucleus-nucleus collisions. This new programme is planned to start after 2020 and requires upgrades to the present NA61/SHINE detector setup. Besides the construction of a large acceptance silicon detector, a 10-fold increase of the event recording rate is foreseen, which will necessitate a general upgrade of most detectors.

By means of density functional theory (DFT) calculations, we have investigated the effect of hydrostatic pressure on the structural, electronic and elastic properties of the barium-doped silicon clathrate Ba8Si46 in the type-VIII structure (α phase). Physical properties are calculated under different conditions of pressure (0 GPa to 45 GPa) using the GGA-PBE functional, those calculations have been performed using the Cambridge serial total energy package CASTEP code within the Materials Studio package. Electronic properties have shown that the type-VIII Ba8Si46 has metal-like properties with a fundamental bandgap of 1 eV. Under pressure the fundamental bandgap increases slightly and the positions of the valence band maximum VBM and the conduction band minimum CBM remain unchanged. We found that the compound is mechanically stable under the pressure range, but this needs to be confirmed experimentally through synthesis, a comparison with the type-I and the guest-free counterparts has exhibited promising features for the type-VIII Ba8Si46.

We describe the direct formation of mixed-phase (1T and 2H) MoS2 layers on Si as a photocathode via atomic layer deposition (ALD) for application in the photoelectrochemical (PEC) reduction of water to hydrogen. Without typical series-metal interfaces between Si and MoS2, our p-Si/SiOx/MoS2 photocathode showed efficient and stable operation in hydrogen evolution reactions (HERs). The resulting performance could be explained by spatially genuine device architectures in three dimensions (that is, laterally homo and vertically heterojunction structures). The ALD-grown MoS2 overlayer with the mixed-phase 1T and 2H homojunction passivates light absorber and surface states and functions as a monolithic structure for effective charge transport within MoS2. It is also beneficial in the operation of p-i-n heterojunctions with inhomogeneous barrier heights due to the presence of mixed-phase cocatalysts. The effective barrier heights reached up to 0.8 eV with optimized MoS2 thicknesses, leading to a 670 mV photovoltage enhancement without employing buried Si p-n junctions. The fast-transient behaviors via light illumination show that the mixed-phase layered chalcogenides can serve as efficient cocatalysts by depinning the Fermi levels at the interfaces. A long-term operation of ~ 70 h was also demonstrated in a 0.5 M H2SO4 solution.

Compressive residual stresses in thin films can inhibit crack propagation under normal or sliding contact loading, with associated enhancement of the coating apparent toughness, load bearing capacity and wear resistance. This study investigates the influence of residual stress distributions on the thin film/substrate adhesion using a nanoindenter coupled with scanning electron microscope (SEM) investigations of indentation induced failure modes. Reactive and un-reactive magnetron sputtering with ion plating was used to coat a (100) silicon substrate with aluminum nitride (AlN) with and without an aluminum (Al) adhesion layer. The presence of an Al bond layer gives additional interfacial tensile stress because of the difference in thermal expansion coefficient. Additionally, a different magnitude of residual stresses in the AlN coating was achieved by changing the applied bias voltage onto the substrate. Wafer curvature method and incremental focused ion beam (FIB) milling, combined with high-resolution in situ scanning electron microscopy (SEM) imaging and full field strain analysis by digital image correlation (DIC), were used to measure the average and in-depth stress residual stress distribution in the produced coatings. The adhesion energy was then quantified by using a nanoindentation based model. Results demonstrate that the additional tensile residual stress in the aluminum adhesion layer decrease significantly the coating adhesion, even in presence of a higher compressive stress state in the AlN top-layer. Therefore, the coatings without Al-layer showed better adhesion because of a more homogeneous compressive residual stress in comparison with the coating having Al layer, even though both groups of coatings are produced under same bias voltage. Results are discussed, and some general suggestions are made on the correlation between coating/substrate property combination and the adhesion energy of multilayer stacks. The results suggested that Al bond-layer and inhomogeneous residual stresses affected the adhesion of AlN negatively to a substrate like silicon.

Thanks to advanced semiconductor microfabrication technology, chip-scale integration and miniaturization of lab-on-a-chip components, silicon-based optical biosensors have made significant progress for the purpose of point-of-care diagnosis. In this review, we provide an overview of the state-of-the-art in evanescent field biosensing technologies including interferometer, microcavity, photonic crystal, and Bragg grating waveguide-based sensors. Their sensing mechanisms and sensor performances, as well as real biomarkers for label-free detection, are exhibited and compared. We also review the development of chip-level integration for lab-on-a-chip photonic sensing platforms, which consist of the optical sensing device, flow delivery system, optical input and readout equipment. At last, some advanced system-level CMOS-chip packaging examples are presented, indicating the commercialization potential for the low cost, high yield, portable biosensing platform leveraging CMOS processes.

This paper presents the design, fabrication and characterization of Schottky erbium/silicon photodetectors working at 1.55 µm. These erbium/silicon junctions are carefully characterized using both electric and optical measurements at room temperature. A Schottky barrier ΦB of ~673 meV is extrapolated; the photodetectors show external responsivity of 0.55 mA/W at room temperature under a 8 V of reverse bias applied. In addition, the device performance is discussed in terms of normalized noise and noise equivalent power. To the best of our knowledge, these are the first Er/Si photodetectors designed for operation in free space at 1.55 µm. The proposed devices will pave the way towards development of Er-based photodetectors and light sources to be monolithically integrated in the same silicon substrate and both operating at 1.55 µm.

Silicon-based photoelectrochemical (PEC) conversion system has recently gained attention with its ability to provide cost-efficient and superior photoresponsive behavior in regard to other various semiconductor photoelectrodes. Carbon-based co-catalysts have always shared the spotlight for being rendered as alternative metal-free electrocatalysts intended for hydrogen evolution reaction (HER). In particular, a representative carbon-derived material, reduced Graphene Oxide (rGO) has attracted much attention as a non-metal catalyst for efficient and durable HER. Herein, we have deposited rGO on silicon nanowire (SiNW) structure which shows the highest reduction in the overpotential for HER up to date. This could be attributed to the synergistic effects of rGO and SiNW with unique anisotropic morphology, facile tuning capabilities, and scalable fabrication methods. Combined with nanostructured photocathode, rGO deposited SiNW showed better applied bias photon to current conversion efficiency of 3.16%, which is 158 times higher than that of bare planar Si system. In regard to this development we believe that rGO-SiNW photoelectrodes would pave the way for state-of-the-art highly efficient non-metal catalysts for energy conversion technologies.

Integrated ultra-low-loss waveguides are highly desired for integrated photonics to enable applications that require long delay lines, high-Q resonators, narrow filters, etc. Here we present an ultra-low-loss silicon waveguide on 500 nm thick SOI platform. Meter-scale delay lines, million-Q resonators and tens of picometer bandwidth grating filters are experimentally demonstrated. We design a low-loss low-reflection taper to seamlessly integrate the ultra-low-loss waveguide with standard heterogeneous Si/III-V integrated photonics platform to allow realization of high-performance photonic devices such as ultra-low-noise lasers and optical gyroscopes.

In this paper, we present a study of various ZnO/SiO2-stacked thin film structures for flexible micro-energy harvesting devices. Two groups of micro-energy harvesting devices, SiO2/ZnO/SiO2 micro-energy generators (SZS-MGs) and ZnO/SiO2/ZnO micro-energy generators (ZSZ-MGs), were fabricated by stacking both SiO2 and ZnO thin films, and the resulting devices were characterized. With a particular interest in the fabrication of flexible devices, all the ZnO and SiO2 thin films were deposited on ITO-coated PEN substrates using an RF magnetron sputtering technique. The effects of the thickness and/or position of the SiO2 films on the device performance were investigated by observing the variations of output voltage in comparison with that of a control sample. As a result, compared to the ZnO single-layer device, all the ZSZ-MGs showed much better output voltages, while all the SZS-MG showed only slightly better output voltages. Among the ZSZ-MGs, the highest output voltages were obtained from the ZSZ-MGs where the SiO2 thin films were deposited using a deposition power of 150 W. Overall, the device performance seems to depend significantly on the position as well as the thickness of the SiO2 thin films in the ZnO/ SiO2-stacked multilayer structures, in addition to the processing conditions.

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q].

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q]. We compute several Zagreb polynomials and Redefined Zagreb indices of these silicon-carbons.

Three-dimensional nanocomposite networks consisting of percolated Si nanowires in a SiO₂ matrix, Si:SiO₂, were studied. The structures were obtained by reactive ion beam sputter deposition of SiO_x (x ≈ 0.6) thin films at 450 °C and subsequent crystallization using conventional oven as well as millisecond line focus laser annealing. Rutherford backscattering spectrometry, Raman spectroscopy, X-ray diffraction, cross-sectional and energy-filtered transmission electron microscopy were applied for sample characterization. While oven annealing resulted in a mean Si wire diameter of 10 nm and a crystallinity of 72 % within the Si volume, almost single-domain Si structures with 30 nm in diameter and almost free of amorphous Si were obtained by millisecond laser application. The structural differences are attributed to the different crystallization processes: Conventional oven tempering proceeds via solid state, millisecond laser application via liquid phase crystallization of Si. The 5 orders of magnitude larger diffusion constant in the liquid phase is responsible for the three times larger Si nanostructure diameter. In conclusion, laser annealing offers not only significantly shorter process times but moreover a superior structural order of nano-Si compared to conventional heating.

This article reports a novel and efficient method to synthesize graphene by thermal decomposition process. In this method, silicon carbide (SiC) thin films grown on Si(100) wafers with an AlN buffer layer were used as substrates. A CO₂ laser beam heating without vacuum or controlled atmosphere was applied for SiC thermal decomposition. The physical, chemical, morphological, and electrical properties of the laser-produced graphene were investigated for different laser energy densities. The results demonstrate that graphene was produced in form of small islands with quality, density and properties depending on the applied laser energy density. Furthermore, the produced graphene exhibits a sheet resistance characteristic similar to graphene grown on mono-crystalline SiC wafer, which indicates its potential for electronic device applications.

Band-gap alignment engineering has now been extensively studied due to its high potential application. Here we demonstrate a simple route to synthesize two metal oxide layers and align them together according to their bandgaps on surface of crystalline silicon (c-Si) solar cells. The metal oxide layers can not only extend absorption spectrum to generate extra carriers but also serve to separate electron-hole pairs more efficiently. As a consequence, the photovoltaic performance of SnO₂/CdO /Si double-layer solar cell (DLSC) is highly improved compared to CdO/Si and SnO₂/Si single-layer solar cells(SLSCs) and SnO₂/CdO/Si double-layer solar cell (DLSC). By the alignment engineering, the SnO₂/CdO/Si DLSC produces a short circuit photocurrent (J_sc) of 38.20 mA/cm², an open circuit photovoltage (V_oc) of 0.575 V and a fill factor (FF) of 68.7%, corresponding to a light to electric power conversion efficiency (η) of 15.09% under AM1.5 illumination. These results suggest that with the use of metal oxide layers by band-gap alignment engineering, new avenues have been opened for developing high-efficiency and cost-effective c-Si solar cells.

A simple fabrication method in the surface modification of electroosmotic silicon microchannel using thermal dry oxidation is presented. The surface modification is done by coating the silicon surface with a silicon dioxide (SiO₂) layer using thermal oxidation process. The process is aimed not only to improve the surface quality of the channel to be suitable for electroosmotic fluid transport but also to reduce the channel width using a simple technique. Initially, the parallel microchannel array with dimensions of 0.5 mm length and width ranging from 1.8 µm to 2 µm are created using plasma etching on the 2x2 cm <100> silicon substrate. The oxidation of silicon channel in a thermal chamber is then conducted to create the SiO₂ layer. The layer properties and the quality of the surface are analyzed using SEM and surface profiler, respectively. The results show that the maximum oxidation growth rate occurs in the first 4 hours of oxidation time and the rate decreases by time as the oxide layer becomes thicker. It is also found that the surface roughness is reduced with the increase of process temperature and oxide thickness. The scallop effect on the vertical wall due to plasma etching process also improved with the presence of the oxide layer. After the oxidation, the channel width is reduced by ~40%. The demonstrated method is suggested for the fabrication of a uniform channel cross section with high aspect ratio in sub-micro and nanometer scale that will be useful for the electroosmotic flow (EOF) manipulation of the biomedical fluid sample.

Cycling reliability is crucial for Si-based materials due to severe volume change during cycles that results in the fast capacity fading. Though the binder only occupies a very low amount of the total mass of anodes, it is proved to perform a key parameter to improve the cycle performance of Si-based anodes. Because they are eco-friendly and cost saving, water-based binders styrene-butadiene rubber (SBR) and carboxymethyl cellulose (CMC) are regarded as the better binder to substitute Poly (vinylidene difluoride) (PVDF) as the binder for Si-based anode. In this study, the anodes are fabricated by simply mixing the active materials (naso Si, graphite and conductive additive) together and using the mixture of SBR and CMC as a binder. The results showed that the retention capacities of the anodes are more than 440 mAh/g after 400 cycles. It indicates that it is an easy and simple way to make high performance anodes.

Hybrid carbon-silicon, carbon-nitrogen, and carbon-boron clathrates are new classes of Type I carbon-based clathrates that have been identified by first-principles computational methods by substituting atoms on the carbon clathrate framework with Si, N, and/or B atoms. The hybrid framework is further stabilized by embedding appropriate guest atoms within the cavities of the cage structure. Series of hybrid carbon-silicon, carbon-boron, carbon-nitrogen, and carbon-silicon-nitrogen clathrates have been shown to exhibit small positive values of the energy of formation, indicating that they may be metastable compounds and amenable to fabrication. In this overview article, the energy of formation, elastic properties, and electronic properties of selected hybrid carbon-based clathrates are summarized. Theoretical calculations that explore the potential applications of hybrid carbon-based clathrates as energy storage materials, electronic materials, or hard materials are presented. The computational results identify compositions of hybrid carbon-silicon and carbon-nitrogen clathrates that may be considered candidate materials for use as either electrode materials for Li-ion batteries or as hydrogen storage materials. Prior processing routes for fabricating selected hybrid carbon-based clathrates are highlighted and difficulties encountered are discussed.

Neural microprobes represent an important component of neural prosthetic systems where implanted microprobes record the electro-potentials generated by specific thoughts in the brain and convey the signals to algorithms trained to interpret these thoughts. Here, we present novel elongated multi-site neural probe that can reach depths greater than 10mm. We hypothesize that reaching such depth allows the recording of cognitive signals required to drive cognitive prosthetics. The impedance of the recording sites on the probes was on the order of 500 kΩ at 1 kHz, which is consistent with probes used for neurophysiological recordings. The probes were made porous using Xenon Difluoride (XeF₂) dry etching to improve the biocompatibility and their adherence to the surrounding neural tissue. Numerical studies were performed to determine the reliability of the porous probes. We implanted the elongated probe in rats and show that the elongated probes are capable of simultaneously recording both spikes and local field potentials (LFPs) from various recording sites.

Effect of abrasive shape on the three-body abrasion behaviors of monocrystalline silicon was investigated by Molecular dynamics modelling. The axial ratio of abrasive particle was varied from 1.00, i.e., a complete sphere, to 0.40 to mimic abrasive shape. The particle’s movement turns toward sliding from rolling when the axial ratio becomes less than a critical value 0.46. In the abrasion process, the friction force and normal force showed an approximately sinusoid-like fluctuation for the rolling ellipsoidal particles, while the front cutting of particle caused that friction force increased and became larger than normal force for sliding particles. The phase transformation process was tracked under different particle’ movement patterns. The Si-II and Bct5 phase producing in loading process can partially transform to Si-III/Si-XII phase and backtrack to original crystal silicon under pressure release, which also occurred in the abrasion process. The secondary phase transformation showed difference for particles’ rolling and sliding movements after three-body abrasion. The rolling of particle induced the periodical and inhomogeneous deformation of substrates, while the sliding benefited producing high-quality surface in CMP process. This study aiming to construct more precise model to understand the wear mechanism benefits evaluating the MEMS wear and CMP process of crystal materials.

Sputtered reactive multilayers applied as a heat source in electronic joining processes are an emerging technology. Their use promises low-stress assembly of components while improving the thermal contact and reducing the thermal resistance. Nanostructured surface modifications can significantly enhance adhesion and reliability of joints between different materials. This work examines reactive multilayer of nickel and aluminum, directly sputtered on nanostructured black silicon surfaces and compares their phase transformation with reference samples deposited on pristine silicon surface. The investigation of the quenched self-propagating reaction reveals a clear influence of the nanostructured surface on the prolongation of the phase transition. Rapid thermal annealing tests result in the formation of Al_1.1Ni_0.9 phase. The nanostructured interface seems to hinder the full transformation of the parent material. The surface modification improves the adhesion of the formed alloy on silicon surfaces and can possibly increase the reliability of joints based on reactive aluminum/nickel multilayer. The use of black silicon, a nanostructured surface modification, is thus a promising approach to realize reliable multi-material joints in complex systems.

In this study, a graphene-doped porous silicon (G-doped/p-Si) substrate for low ppm H₂ gas detection by an inexpensive synthesis route was proposed as a potential noble graphene-based gas sensor material and to understand the sensing mechanism. The G-doped/p-Si gas sensor was synthesized by a simple capillary force-assisted solution dropping method on p-Si substrates, whose porosity was generated through an electrochemical etching process. G-doped/p-Si was fabricated with various graphene concentrations and exploited as a H₂ sensor operated at room temperature. The sensing mechanism of the sensor with/without graphene decoration on p-Si was proposed to elucidate the synergetic gas sensing effect generated from the interface between the graphene and p-type silicon.

Clock Network Design (CDN) is a critical step while designing any Integrated-Circuits (ICs). It holds vital importance in the performance of entire circuit. Due to continuous scaling, 3D ICs stacked with TSV are gaining importance, with an objective to continue with the Moore's law. Through-Silicon-Via (TSV) provides the vertical interconnection between two die, which allows the electrical signal to flow through it. 3D ICs has many advantages over conventional 2D planar ICs like reduced power, area, cost, wire-length etc. The proposed work is mainly focused on power reduction and obstacle avoidance for 3D ICs. Various techniques have already been introduced for minimizing clock power within specified clock constraints of the 3D CND network. Proposed 3D Clock Tree Synthesis (CTS) is a combination of various algorithms with an objective to meet reduction in power as well as avoidance of obstacle or blockages while routing the clock signal from one sink to other sink. These blockages like RAM, ROM, PLL etc. are fixed during the placement process. The work is carried out mainly in three steps- first is Generation of 3D Clock tree avoiding the blockages, then Buffering and Embedding and finally validating the results by SPICE simulation. The experimental result shows that our CTS approach results in significant 9% reduction in power as compare to the existing work.

Functional Near Infrared Spectroscopy (fNIRS) systems for e-health applications usually suffer of poor signal detection mainly due to a low end-to-end signal to noise ratio of the electronics chain. Lock-In Amplifiers (LIA) historically represent a powerful technique helping to improve performances in such circumstances. In this work it has been designed and implemented a digital LIA system, based on a Zynq® Field Programmable Gate Array (FPGA), trying to explore if this technique might improve fNIRS system performances. More broadly, FPGA based solution flexibility has been investigated, with particular emphasis applied to digital filter parameters, needed in the digital LIA, and it has been evaluated its impact on the final signal detection and noise rejection capability. The realized architecture was a mixed solution between VHDL hardware modules and software ones, running within a softcore microprocessor. Experimental results have shown the goodness of the proposed solutions and comparative details among different implementation will be detailed. Finally a key aspect taken into account throughout the design was its modularity, allowing an ease increase of the input channels while avoiding the growth of the design cost of the electronics system.

A compact Mach-zehnder interferometer with a novel design of directional couplers and a phase shifter has been presented as a thermo-optical sensor. With the aim of reducing device size to micro and nano dimension silicon-on-insulator technology was employed. That allowed miniaturization of device size through the reduction of its cross sectional area to 0.066 µm² and the radius of curvature of both the arms of the directional coupler and S-bends of the phase shifter to 5 µm and C-bends to 3 µm. These nano size device dimensions made it possible to reduce the coupling gap to 0.2 µm, which resulted in a significant reduction in the coupling length. The device geometry and its performance characteristics were analyzed and optimized using coupled mode analysis and finite difference time domain simulation tools, respectively. The wavelength dependent transmission loss of the device was measured at different temperature to verify and validate its performance characteristics. Tested devices showed a remarkable temperature dependent transmission characteristic offering significant changes in transmission loss band – with as low as 0.45 ⁰C change in substrate temperature. The extinction ratio and the free spectral range of the device were 26 dB and 0.26 nm respectively in the wavelength range of 1549.5 nm – 1550.5 nm. These results imply that the devices presented here can be used as compact and highly sensitive thermal sensors and optical switches.

This paper presents a piezoresistive pressure sensor with a shield layer for improved stability. Compared with the conventional piezoresistive pressure sensors, p-type piezoresistors are covered by an n-type shield layer, which is formed by ion implantation. The proposed pressure sensors have been successfully fabricated by bulk micromachining techniques. The impact of electrical field on piezoresistors is studied by simulation. The temperature drift of the pressure sensor has been investigated by both simulation and experimental measurement. Characteristics of developed pressure sensors are tested from -40 C to 125 C. A sensitivity of 0.022 mV/V/KPa and a maximum non-linearity of 0.085% FS are measured for the fabricated sensor in a pressure range of 1 MPa. The temperature coefficients of resistance of shielded piezoresistors are found to be smaller than those of un-shielded ones. It is demonstrated that the shield layer is able to reduce the drift caused by electrical field and ambient temperature variation.

A single mode waveguide grating coupler based on multiple Si-SiO₂ pairs onto Si substrate has been designed. Numerical analysis has been carried out to calculate optimum thickness of the layers of Si-SiO₂ that ensures the constructive interference between reflected waves and actual guided wave for high coupling efficiency. Based on the results, an optimal design is developed and modeled by using a 2-D finite difference time domain (2-D FDTD) simulator that dictates a coupling efficiency of as much as 78% (-1.07 dB) at the wavelength of 1550 nm, and a 1-dB bandwidth of 77 nm. The numerical method will be useful to calculate the optimum thicknesses of the layers for any reflector based grating coupler of different materials.