Table of contents

We report on a detailed characterization and analysis of thermal crosstalk in a heated microcantilever array. The fabricated heated cantilever array consists of five identical independently controlled heated cantilevers. The temperature of each cantilever can be controlled over a large temperature range, up to 900 °C, by means of an integrated solid-state resistive heater. We analyze thermal crosstalk in steady and transient operating conditions when the heated cantilever array is either in contact with a substrate or freely suspended in air. The thermal conductance between neighboring cantilevers is as high as 0.61 µW °C⁻¹, resulting in non-negligible temperature increases in neighboring cantilevers, depending upon the operating conditions. By understanding and accounting for thermal crosstalk, it is possible to improve temperature control and temperature measurements with heated microcantilever arrays.

A large-aperture and large-angle MEMS-based 2D pointing mirror is presented. The device is electromagnetically actuated by a moving-magnet/stationary-coil pair and potentially suited for high power laser beam shaping and beam pointing applications, such as LIDAR. The 4×4 mm² mirror, the radially symmetric compliant membrane, and the off-the-shelf permanent magnet are manually assembled, with the planar coil kept at a well-defined vertical distance from the permanent magnet by simple alignment pins. The mirror and the compliant membrane structures are separately microfabricated on bulk silicon and SOI wafers, respectively. The hybrid integration of microfabricated and off-the-shelf components enable low-risk/high-yield fabrication, while limiting the throughput. The device features minimum inter-axis cross coupling and good linearity and is highly immune to alignment and assembly imperfections, thanks to the robust actuation principle. All the components including the bi-axial electromagnetic actuator provide a device footprint as small as the top mirror, allowing the design to be used in compact and high-fill-factor mirror arrays. With a drive coil of 400 mA and 5.12 W drive power, the total uniaxial dc rotation exceeds ±16° (optical) for both axes with good decoupling. At maximum measured angle (biaxial 10° (mechanical)), a position stability better than 0.05° over 7 h, and a position repeatability of 0.04° over 5000 switching cycles is reported. Thermally, the simulated mirror temperature increases to 64 K above the heat sink temperature with a thermal in-flux of 1 kW m⁻², under absolute vacuum.

We have explored the use of mold coatings and optimized processing conditions to injection mold high aspect ratio nanostructures (height-to-width >1) in cyclic olefin copolymer (COC). Optimizing the molding parameters on uncoated nickel molds resulted in slight improvements in replication quality as described by height, width and uniformity of the nanoscopic features. Use of a mold temperature transiently above the polymer glass transition temperature (T_g) was the most important factor in increasing the replication fidelity. Surface coating of the nickel molds with a fluorocarbon-containing thin film (FDTS) greatly enhanced the quality of replicated features, in particular at transient mold temperatures above T_g. Injection molding using the latter mold temperature regime resulted in a bimodal distribution of pillar heights, corresponding to either full or very poor replication of the individual pillars. The poorly replicated structures on nickel molds with or without FDTS coatings all appeared fractured. We investigated the underlying mechanism in a macroscopic model system and found reduced wetting and strongly decreased adhesion of solidified COC droplets on nickel surfaces after coating with FDTS. Reduced adhesion forces are consistent with lowered friction that reduces the risk of fracturing the nanoscopic pillars during demolding. Optimized mold surface chemistry and associated injection molding conditions permitted the fabrication of square arrays of 40 nm wide and 107 nm high (aspect ratio >2.5) pillars on a 200 nm pitch.

Surfaces that repel both water and oil effectively (contact angles > 150°) are rare. Here we detail the microfabrication method of silicon surfaces with such properties. The method is based on careful tuning of the process conditions in a reactive etching protocol. We investigate the influence of SF₆, O₂ and CHF₃ gases during the etching process using the same pitch of a photolithographic mask. Varying the loading conditions during etching, we optimized the conditions to fabricate homogeneous pedestal-like structures. The roughness of the microstructures could also effectively be controlled by tuning the dry plasma etching conditions. The wetting behavior of the resulting microstructures was evaluated in terms of the water and oil contact angles. Excitingly, the surfaces can be engineered from superhydrophobic to omniphobic by variation of the aforementioned predefined parameters.

This paper presents a film transfer process to integrate barium strontium titanate (BST) metal–insulator–metal (MIM) structures with surface acoustic wave (SAW) devices on a lithium niobate (LN) substrate. A high-quality BST film grown on a Si substrate above 650 °C was patterned into the MIM structures, and transferred to a LN substrate below 130 °C by Ar-plasma-activated Au–Au bonding and the Si lost wafer process. Simple test SAW devices with the transferred BST variable capacitors (VCs) were fabricated and characterized. The resonance frequency of a one-port SAW resonator with the VC connected in series changed from 999 to 1018 MHz, when a dc bias voltage of 3 V was applied to the VC. Although the observed frequency tuning range was smaller than expected due to the degradation of BST in the process, the experimental result demonstrated that a tunable SAW filter with the transferred BST VCs was feasible.

In this paper, we present the design, fabrication and testing of novel micromachined silicon-based acoustic delay lines. The acoustic properties of different silicon delay-line structures have been characterized. Based on the experiment results, two different acoustic delay line systems (parallel and serial) have been successfully demonstrated to create controlled time delays in multiple channels of ultrasound signals. The time-delayed ultrasound signals are received with a single-element ultrasound transducer in a time-serial manner. This unique capability could be used to merge multiple signal channels, thereby enabling new ultrasound receiver designs with potentially less complexity and lower cost.

Nanotechnological advancements have made a great contribution in developing label-free and highly sensitive biosensors. The detection of ultrasmall adsorbed masses has been enabled by such sensors which transduce molecular interaction into detectable physical quantities. More specifically, microcantilever-based biosensors have caught widespread attention for offering a label-free, highly sensitive and inexpensive platform for biodetection. Although there are a lot of studies investigating microcantilever-based sensors and their biological applications, a comprehensive mathematical modeling and experimental validation of such devices providing a closed form mathematical framework is still lacking. In almost all of the studies, a simple lumped-parameters model has been proposed. However, in order to have a precise biomechanical sensor, a comprehensive model is required being capable of describing all phenomena and dynamics of the biosensor. Therefore, in this study, an extensive distributed-parameters modeling framework is proposed for the piezoelectric microcantilever-based biosensor using different methodologies for the purpose of detecting an ultrasmall adsorbed mass over the microcantilever surface. An optimum modeling methodology is concluded and verified with the experiment. This study includes three main parts. In the first part, the Euler–Bernoulli beam theory is used to model the nonuniform piezoelectric microcantilever. Simulation results are obtained and presented. The same system is then modeled as a nonuniform rectangular plate. The simulation results are presented describing model's capability in the detection of an ultrasmall mass. Finally the last part presents the experimental validation verifying the modeling results. It was shown that plate modeling predicts the real situation with a degree of precision of 99.57% whereas modeling the system as an Euler–Bernoulli beam provides a 94.45% degree of precision. The detection of ultrasmall immobilized enzyme molecules over the cantilever surface was achieved using a self-exciting piezoelectric-based microcantilever in the dynamic mode.

The method used by SolMateS to determine the effective piezoelectric coefficient d_31,eff of Pb(Zr,Ti)O₃ (PZT) thin films from cantilever displacement measurements is described. An example from a 48 cantilever dataset using different cantilever widths, lengths and crystal alignments is presented. It is shown that for the layer stack of our cantilevers, the multimorph model is more accurate compared to the bimorph model for the d_31,eff determination. Corrections to the input parameters of the model are further applied in order to reduce the geometrical error of the cantilever that is caused by its design and processing, as well as correction to the measured tip displacement caused by resonance amplification. It is shown that after these corrections, the obtained d_31,eff values are still up to 10% uncertain as the plate behavior and the non-constant radius of curvature of the cantilevers lead to inconsistent results. We conclude that quantitative determination of d_31,eff from the cantilevers is highly subjective to misinterpretation of the models used and the measurement data. The true value of d_31,eff was determined as −118.9 pm V⁻¹.

Photoresists are light-sensitive resins used in a variety of technological applications. In most applications, however, photoresists are generally used as sacrificial layers or a structural layer that remains on the fabrication substrate. Thin layers of patterned 1002F photoresist were fabricated and released to form a freestanding film. Films of thickness in the range of 4.5–250 µm were patterned with through-holes to a resolution of 5 µm and an aspect ratio of up to 6:1. Photoresist films could be reliably released from the substrate after a 12 h immersion in water. The Young's modulus of a 50 µm-thick film was 1.43 ± 0.20 GPa. Use of the films as stencils for patterning sputtered metal onto a surface was demonstrated. These 1002F stencils were used multiple times without deterioration in feature quality. Furthermore, the films provided biocompatible, transparent surfaces of low autofluorescence on which cells could be grown. Culture of cells on a film with an isolated small pore enabled a single cell to be accessed through the underlying channel and loaded with exogenous molecules independently of nearby cells. Thus 1002F photoresist was patterned into thin, flexible, free-standing films that will have numerous applications in the biological and MEMS fields.

This paper presents the design and evaluation of magnetoelastic sensors intended for wireless monitoring of tissue accumulation in peripheral artery stents. The sensors are fabricated from 28 µm thick foils of magnetoelastic 2826MB Metglas™, an amorphous Ni–Fe alloy. The sensor layer consists of a frame and an active resonator portion. The frame consists of 150 µm wide struts that are patterned in the same wishbone array pattern as a 12 mm × 1.46 mm Elgiloy stent cell. The active portion is a 10 mm long symmetric leaf shape and is anchored to the frame at mid length. The active portion nests within the stent cell, with a uniform gap separating the two. A gold-indium eutectic bonding process is used to bond Metglas™ and Elgiloy foils, which are subsequently patterned to form bi-layer resonators. The response of the sensor to viscosity changes and mass loading that precede and accompany artery occlusion is tested in vitro. The typical sensitivity to viscosity of the fundamental, longitudinal resonant frequency at 361 kHz is 427 ppm cP⁻¹ over a 1.1–8.6 cP range. The sensitivity to mass loading is typically between 63000 and 65000 ppm mg⁻¹ with the resonant frequency showing a reduction of 8.1% for an applied mass that is 15% of the unloaded mass of the sensor. This is in good agreement with the theoretical response.

A novel piezoresistive sensing method is presented herein for the detection of nanobeam resonator based on a monolithically integrated MOS (metal–oxide–semiconductor) capacitor structure. The bottom layer of the nanobeam located beneath the MOS capacitor is utilized as a piezoresistor for the detection of internal stress resulting from nanobeam deformation, and therefore the challenging process of ultra-shallow junction doping is avoided. When a bias voltage applied on the MOS gate exceeds the threshold, the depletion layer width is built up to the maximum, and the piezoresistive cancellation effect beside the neutral plane is eliminated. Based on a conventional microelectromechanical (MEMS) process, an MOS capacitor is fabricated at the terminal of a double-clamped nanobeam with dimensions of 46 µm × 7 µm × 149 nm. The measured R–V curve of this MOS structure presents a 64.7 nm thick piezoresistor which closely agrees with the design. This double-clamped nanobeam is excited into mechanical resonance by mounting it on a piezoelectric ceramic, and the amplitude–frequency response is measured by a network analyzer. The measured resonant frequency is 3.97 MHz and the quality (Q)-factor is 82 in atmosphere environment. Besides, this piezoresistive sensing method is verified by a laser-Doppler vibrometry.

This work presents the simultaneous fabrication of ambient relative humidity (RH) and temperature sensors arrays, inkjet-printed on flexible substrates and subsequently encapsulated at foil level. These sensors are based on planar interdigitated capacitors with an inkjet-printed sensing layer and meander-shaped resistors. Their combination allows the compensation of the RH signals variations at different temperatures. The whole fabrication of the system is carried out at foil level and involves the utilization of additive methods such as inkjet-printing and electrodeposition. Electrodeposition of the printed lines resulted in an improvement of the thermoresistors. The sensors have been characterized and their performances analyzed. The encapsulation layer does not modify the performances of the sensors in terms of sensitivity or response time. This work demonstrates the potential of inkjet-printing in the large-area fabrication of light-weight and cost-efficient gas sensors on flexible substrates.

We present the development of a technological platform dedicated to 3D capacitive inertial sensors. The proof of concept will be made on a 3D gyroscope. The mobile structure is made within a 30 µm thick Si top layer of a SOI substrate, while poly-Si deposited on top of a sacrificial PSG layer serves as suspended top electrodes and connection wires. This technology enables us to maintain low parasitic capacitance, which is of paramount significance for capacitive detection. After packaging and association with an analogue electronic board, functionality of the sensor is demonstrated.

Cryogenic temperatures are required for improving the performance of electronic devices and for operating superconducting sensors and circuits. The broad implementation of cooling these devices has long been constrained by the availability of reliable and low cost cryocoolers. After the successful development of single-stage micromachined coolers able to cool to 100 K, we now present a micromachined two-stage microcooler that cools down to 30 K from an ambient temperature of 295 K. The first stage of the microcooler operates at about 94 K with nitrogen gas and pre-cools the second stage operating with hydrogen gas. The microcooler is made from just three glass wafers and operates with modest high-pressure gases and without moving parts facilitating high yield fabrication of these microcoolers. We have successfully cooled a YBCO film through its superconducting transition state to demonstrate a load on the microcooler at cryogenic temperatures. This work could expedite the application of superconducting and electronic sensors and detectors among others in medical and space applications.

This paper describes the design, fabrication, and electromechanical characteristics of inductive stents developed for intelligent stent applications. The stents, fabricated out of 316L stainless-steel tubes using laser machining, are patterned to have zigzag loops without bridge struts, and when expanded, become a helix-like structure. Highly conductive metals such as copper and gold are coated on the stents to improve their inductive/antenna function. The Q-factor of the stent is shown to increase by a factor of 7 at 150 MHz with copper coating. The expansion of the stent from 2 to 4 mm diameter results in a 3.2× increase in the inductance, obtaining ∼1 µH at a similar frequency. The stent passivated by Parylene-C film is used to characterize its resonance in different media including saline. The copper-coated inductive stent exhibits a 2.4× radial stiffness for 1 mm strain as well as a 16× bending compliance compared with a commercial stent, each of which is potentially beneficial in preventing/mitigating stent failures such as recoil as well as enabling easier navigation through intricate blood vessels. The mechanical stiffness may be tailored by adjusting stent-wire thickness while maintaining necessary coating thickness to achieve particular mechanical requirements and high inductive performance simultaneously.

This paper describes maskless lithography as a rapid and cost-effective technique for fabricating high-quality microfluidic devices in laboratories. The detailed effects of exposure parameters on microstructure features are explored. A quantitative analysis of these effects provides insights into the device design and the selection of optimum processing parameters. To overcome the limitation of small exposure area, subregion stitching and sequential exposure are adopted for fabricating larger patterns. Seamless stitching between adjacent exposure subregions is achieved by optimizing the grayscale values of the stitching side/corner. These data are also valuable for exploring grayscale and multi-step lithography. Various hydrodynamic microdevices are then fabricated and characterized to validate the optimized parameters.

This paper presents the direct three-dimensional (3D) fabrication of polymer scaffolds with sub-10 µm structures using electrohydrodynamic jet (EHD-jet) plotting of melted thermoplastic polymers. Traditional extrusion-based fabrication approaches of 3D periodic porous structures are very limited in their resolution, due to the excessive pressure requirement for extruding highly viscous thermoplastic polymers. EHD-jet printing has become a high-resolution alternative to other forms of nozzle deposition-based fabrication approaches by generating micro-scale liquid droplets or a fine jet through the application of a large electrical voltage between the nozzle and the substrate. In this study, we successfully apply EHD-jet plotting technology with melted biodegradable polymer (polycaprolactone, or PCL) for the fabrication of 2D patterns and 3D periodic porous scaffold structures in potential tissue engineering applications. Process conditions (e.g. electrical voltage, pressure, plotting speed) have been thoroughly investigated to achieve reliable jet printing of fine filaments. We have demonstrated for the first time that the EHD-jet plotting process is capable of the fabrication of 3D periodic structures with sub-10 µm resolution, which has great potential in advanced biomedical applications, such as cell alignment and guidance.

This paper presents different low-temperature and high-throughput LIGA-like processes for the batch fabrication of metal micro systems that use long nano- or microwires perpendicularly rising from a substrate. First, circuit paths and seed layers are fabricated applying standard UV lithography and PVD. Second, three lithography techniques are used, namely ion track lithography, enhanced UV lithography and aligned x-ray lithography, to structure 20–400 µm thick polymer films. Ion track lithography is only used to fabricate extremely high aspect ratio cylindrical pores with 0.1–1 µm diameter and 20–100 µm length. The aligned UV and x-ray lithographies are employed to structure templates for various micro system components. Third, these polymer templates are filled using low-temperature electroplating processes transferring the polymer openings into metal structures. Finally, the polymer is dry etched to release all metal structures. These structures are applicable in future accelerometers and gas flow sensors. Using five configurations to define five different functional structures, we demonstrate fabrication processes applying the three different types of lithography. The main aspects concern the combination of both standard lithography techniques and especially developed lithography techniques. Furthermore, these aspects comprise the use of structures created by lithography for high aspect ratio polymer templates and multilayer electroplating with varying aspect ratios. The growth in place of nanowire arrays and micropillars along with surrounding structures is the key feature for low-temperature large-scale micro-nano integration technology without harmful transfer technologies.

Surface acoustic wave (SAW) propagation characteristics in a multilayer structure including a piezoelectric aluminum nitride (AlN) thin film and an epitaxial cubic silicon carbide (3C–SiC) layer on a silicon (Si) substrate are investigated by theoretical calculation in this work. Alternating current (ac) reactive magnetron sputtering was used to deposit highly c-axis-oriented AlN thin films, showing the full width at half maximum (FWHM) of the rocking curve of 1.36° on epitaxial 3C–SiC layers on Si substrates. In addition, conventional two-port SAW devices were fabricated on the AlN/3C–SiC/Si multilayer structure and SAW propagation properties in the multilayer structure were experimentally investigated. The surface wave in the AlN/3C–SiC/Si multilayer structure exhibits a phase velocity of 5528 m s⁻¹ and an electromechanical coupling coefficient of 0.42%. The results demonstrate the potential of AlN thin films grown on epitaxial 3C–SiC layers to create layered SAW devices with higher phase velocities and larger electromechanical coupling coefficients than SAW devices on an AlN/Si multilayer structure. Moreover, the FWHM values of rocking curves of the AlN thin film and 3C–SiC layer remained constant after annealing for 500 h at 540 °C in air atmosphere. Accordingly, the layered SAW devices based on AlN thin films and 3C–SiC layers are applicable to timing and sensing applications in harsh environments.

A high-performance thermal management method for three-dimensional integrated circuit (IC) integration has been developed for use in conjunction with a three-dimensional (3D) large-scale integration (LSI) technology. By depositing a 10 µm thick high thermal conductivity (HTC) film consisting of 1680 alternating layers of silicon and graphite nano-films directly onto the backside of a Si substrate via an automatic sequencing sputtering method, reduction in the transient hotspot temperature in a thin-substrate CMOS IC chip is achieved. It is shown that this novel HTC film is able to overcome the thermal problems associated with thin substrates and allow the cooling of stacked ICs. In the work described in this paper, we demonstrated the performance of the HTC using a 100 µm thick substrate IC chip consisting of a complementary metal-oxide semiconductor (CMOS) ring oscillator circuit film. Our experimental results, which were confirmed in simulation, reveal a 28% reduction in the hotspot temperature rise owing to the presence of the HTC film. This technology is applicable to future developments in the 3D ultrathin substrate LSI chip stacking technology utilizing through-silicon vias (TSVs) and micro-bumps.

We present two transfer bonding schemes for incorporating fragile nanoporous inorganic membranes into microdevices. Such membranes are finding increasing use in microfluidics, due to their precisely controllable nanostructure. Both schemes rely on a novel dual-cure dry adhesive bonding method, enabled by a new polymer formulation: OSTE(+), which can form bonds at room temperature. OSTE(+) is a novel dual-cure ternary monomer system containing epoxy. After the first cure, the OSTE(+) is soft and suitable for bonding, while during the second cure it stiffens and obtains a Young's modulus of 1.2 GPa. The ability of the epoxy to react with almost any dry surface provides a very versatile fabrication method. We demonstrate the transfer bonding of porous silicon and porous alumina membranes to polymeric microfluidic chips molded into OSTE(+), and of porous alumina membranes to microstructured silicon wafers, by using the OSTE(+) as a thin bonding layer. We discuss the OSTE(+) dual-cure mechanism, describe the device fabrication and evaluate the bond strength and membrane flow properties after bonding. The membranes bonded to OSTE(+) chips delaminate at 520 kPa, and the membranes bonded to silicon delaminate at 750 kPa, well above typical maximum pressures applied to microfluidic circuits. Furthermore, no change in the membrane flow resistance was observed after bonding.

We report on the fabrication and characterization of a highly sensitive pressure sensor using a Au film patterned on a polydimethylsiloxane (PDMS) membrane. The strain-induced change in the film resistance was utilized to perform the quantitative measurement of absolute pressure. The highest sensitivity obtained for a 200 µm thick PDMS film sensor was 0.23/KPa with a range of 50 mm Hg, which is the best result reported so far, over that range, for any pressure sensor on a flexible membrane. The noise-limited pressure resolution was found to be 0.9 Pa (0.007 mm Hg), and a response time of ∼200 ms, are the best reported results for these sensors. The ultrahigh sensitivity is attributed to the strain-induced formation of microcracks, the effect of which on the resistance change was found to be highly reversible within a certain pressure range. A physical model correlating the sensitivity with the sensor parameters and crack geometry has been proposed.

Glass substrates functionalized by biochemical substances and/or metal thin films have been used in a number of micro-total analysis systems (µTAS) and microelectromechanical systems (MEMS) devices. We propose a dry patterning process for glass nanoparticles (NPs) using an electrospray of the sol of tetraethyl orthosilicate (TEOS) containing hydrochloric acid as a catalyst. We experimentally found that the size of the glass NPs was controlled by the viscosity and feed rate of the TEOS sol, and the applied voltage. In order to verify the usefulness of these glass NPs, we deposited silver NPs on the glass NPs using a modified silver mirror reaction. Silver NPs are reported to enhance the Raman scattering, which is required for ultrasensitive biochemical sensing. Silver NPs on the glass NPs were experimentally found to exhibit greater surface-enhanced Raman scattering than those on a flat glass substrate. Silver NPs can be used in chemical sensors, such as surface-enhanced Raman scattering (SERS) and fluorescence spectroscopy, due to the enhanced electromagnetic field on the surface. Silver NPs are deposited on the glass NPs by the silver mirror reaction with dispersants, for application as ultrasensitive sensors. When silver NPs are formed sterically congested, the enhanced Raman spectrum from the silver NPs on the electrosprayed glass NPs shows an intensity three times that from silver NPs on a flat glass plate substrate. The glass NPs formed by electrospraying are thus proving to yield high performance substrates for chemical sensors.

A curved design for in-plane micro- and nano-electromechanical switches based on a single clamped cantilever is proposed, optimized with finite-element simulations and demonstrated experimentally. The design enables precise control of the switch motion and of the closed-state air gap, resulting in a uniform electrostatic field and increased robustness. The switch size and curvature are optimized for actuation voltage, actuation energy and the electrostatic field strength. These optimizations and the proposed fabrication process are amenable to micro- and nano-electromechanical switches. The scalability of the concept is demonstrated with simulations of nanoscale relays in terms of force and energy, showing that the concept is suitable for sub-100 aJ switching energy. Experimental results on microscale devices demonstrate the advantages of the curved MEM switches, namely a fabrication process with a single sacrificial layer for a switch with a low actuation voltage and excellent robustness. The designed as well as the experimentally observed breakdown voltage is four times higher than the contact voltage, thus enabling a large operating window for electromechanical switches.

This paper presents an analytical method to calculate residual stress and Young's modulus in clamped–clamped beams. These types of structures are a typical building block of many MEMS devices, and this guarantees accurate transferability of the measured parameters. The method is based on the determination of beam bending as a function of applied load by means of a surface profiler, and as a function of beam length. By modeling analytically both the elastic and the stress contribution to beam bending, it is possible to obtain both the stress value and Young's modulus by a simple fitting of the experimental data. Results are presented for electrodeposited gold beam arrays of different widths, but the method is in principle exploitable for every type of suspended film where the residual stress strongly influences the material properties. Accuracy and limitations of the method are also discussed.

This paper presents a theoretical and experimental strategy for thermal de-isolation of silicon microstructures during a plasma etching process. Heat sinking blocks and thin metal layers are implemented around a thermally isolated mass to avoid severe spring width losses by a steep temperature rise. Thermal de-isolation significantly reduces the fabrication errors from −51.0% to −9.0% and from −39.5% to −6.7% for spring widths and resonant frequencies, respectively. Thermal de-isolation also reduces the standard deviation of resonant frequencies from 8.7% to 1.5% across a wafer, which clearly demonstrates the proposed method.