Patent Description:
Inorganic nanotubes (INT's), first reported in <NUM> increasingly attract interest as the rolled-up version of non-carbon 2D materials, and as potential building blocks for nanotechnology. In <NPL>et al. describe a procedure for the synthesis of various inorganic nanotubes. A metallic (Pb) catalyst is used in the synthesis. Carbon nanotubes (CNTs) have long been regarded as attractive building blocks for nano-electromechanical systems (NEMS) owing to their outstanding mechanical and electrical properties, as well as their unique electromechanical coupling. In particular, torsional electromechanical systems could be used as the basis for gyroscopes for navigation of ultra-miniaturized unmanned aerial vehicles (UAVs), and for various chemical and biological sensors. Extensive work has been done with respect to CNT-based torsional devices: fabrication, characterization of torsional and electromechanical properties in single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs), and creation of MWCNT and SWCNT torsional resonators. For example, <CIT> discloses an electromechanical oscillator comprising carbon nanotube that is provided with inertial clamps in the form of metal beads. The metal beads serve to clamp the nanotube so that the fundamental resonance frequency is in the microwave range. In <NPL>et al. describe the characteristic structure of metal chalcogenide nanotubes and the stability of such nanotubes. The stability of multi-walled nanotubes is addressed. In <NPL>et al. provides a theoretical analysis of the performance of transition metal dichalcogenide (MX<NUM>) single wall nanotube (SWNT) surround gate MOSFET. The analysis shows that tungsten dichalcogenide nanotubes offer superior device output characteristics compared to the molybdenum dichalcogenide nanotubes. It is also theoretically found that increase in SWNT diameter provides higher ON currents. In <NPL>et al. provides a study of IF-Mo(<NUM>-x)NbxS<NUM> nanoparticles. The study describes the organization of the Nb atoms in the particles. The nanostructures are found to be metallic, independent of the substitution pattern of the Nb atoms in the lattice of MoS<NUM>. <CIT> discloses a tunable nanomechanical oscillator device. The device comprises at least one nanoresonator, such as a suspended nanotube, designed such that injecting charge density into the tube, for example, by applying a capacitively-coupled voltage bias, changes the resonant frequency of the nanotube, and where exposing the resonator to an RF bias induces oscillatory movement in the suspended portion of the nanotube, forming a nanoscale resonator, as well as a force sensor when operated in an inverse mode. <CIT> discloses a method for controlled deposition and orientation of molecular sized nanoelectromechanical systems (NEMS) on substrates, wherein the method comprises: forming a thin layer of polymer coating on a substrate; exposing a selected portion of the thin layer of polymer to alter a selected portion of the thin layer of polymer; forming a suspension of nanostructures in a solvent, wherein the solvent suspends the nanostructures and activates the nanostructures in the solvent for deposition; and flowing a suspension of nanostructures across the layer of polymer in a flow direction; thereby: depositing a nanostructure in the suspension of nanostructures only to the selected portion of the thin layer of polymer coating on the substrate to form a deposited nanostructure oriented in the flow direction. <CIT> discloses the use of a high-quality factor torsional resonator of microscale dimensions. The resonator has a paddle that is supported by two nanoscale torsion rods made of a very low thermal conductivity material. The paddle is coated by an infrared absorbing material providing sufficient IR absorption. Sensing of the response of the paddle to applied electromagnetic radiation provides a measure of the intensity of the radiation as detected by absorption, and the resulting temperature change, in the paddle. One of the most critical factors determining the sensitivity of resonant NEMS is their quality factor - a dimensionless parameter corresponding to the ratio between the stored and dissipated energy per cycle. Namely, the higher the quality factor, the less energy gets dissipated during one oscillation cycle. Internal friction, interlayer coupling, crystallographic structure and chemical composition can play a critical role in determining the torsional behavior of nanotubes, and specifically their quality factor (Q).

As mentioned above, one of the most critical factors determining the sensitivity of resonant NEMS is their quality factor. The higher the quality factor, the less energy gets dissipated during one oscillation cycle. Internal friction, interlayer coupling, crystallographic structure and chemical composition can play a critical role in determining the torsional behavior of nanotubes, and specifically their quality factor (Q).

These aspects influencing the quality factor have motivated the examination of metal chalcogenide nanotubes as potential building blocks for torsional devices. To this end, WS<NUM> nanotubes (WS<NUM> NTs) were found to be a promising material owing to their significant electromechanical response, stick-slip torsional behavior, and high current-carrying capacity.

The present invention provides an electromechanical resonator, said resonator comprising:.

In one embodiment, electromechanical resonators of the present invention are torsional resonators based on metal chalcogenide nanotubes. The electromechanical properties of the resonators are compared with CNT-based torsional resonators, in ambient conditions and in vacuum. It was found that metal chalcogenide nanotubes exhibit higher torsional resonance frequencies and quality factors, extending the available material toolbox for torsional NEMS devices. This invention further demonstrates that metal chalcogenide nanotubes are promising building blocks for NEMS in general and torsional NEMS in particular.

The torsional resonators disclosed in this invention exhibit an intentional broken symmetry that enables their electrostatic actuation.

An embodiment of a torsional resonator (<FIG>) consists of a suspended nanotube (MWCNT, WS<NUM>NT) clamped between metallic pads at its ends, with a suspended pedal attached to its top. The pedal is off-centered with respect to the nanotube, so that each end of the pedal stands at a different distance from the nanotube (<FIG>, the right-hand side of the pedal is longer than the left-hand side of the pedal with respect to the nanotube; and in <FIG>, the far side of the pedal is shorter than the near side with respect to the nanotube line). The resonators were fabricated using electron-beam lithography, followed by wet etching and critical point drying (see Examples). In order to measure the oscillatory behavior of the torsional resonators, a DC bias voltage and a smaller AC drive voltage were applied between the substrate and the pedal using a network analyzer. The frequency of the AC component was swept from <NUM> to <NUM> (the upper limit of the detection system according to this embodiment). The alternating voltage between the substrate and the pedal combined with the offset of the center of the pedal with respect to the nanotube created an oscillatory net torque on the pedal, thus periodically twisting the nanotube. The amplitude of the pedal was detected using a laser Doppler vibrometer (LDV), and is presented as a function of the drive AC voltage frequency, in order to capture the resonant response of each nanotube-based resonator (<FIG>).

In summary, for the first time the resonance spectrum of torsional NEMS based on metal chalcogenide nanotubes, namely WS<NUM> NTs and BNNTs, was measured and compared to that of similar devices based on MWCNTs. It was found that under atmospheric pressure WS<NUM> NTs exhibit the highest quality factor and resonance frequency, followed by BNNTs and MWCNTs. Without being bound to any theory, these results can be attributed to three main differences between the carbon, BN and WS<NUM> NTs: (i) diameter (which strongly affects the torsional spring constant), (ii) shear modulus (which linearly affects the spring constant), and (iii) the intershell coupling, which affects the effective number of layers contributing to the overall torsional behavior. The quality factor has a systematic dependence on the torsional spring constant in air, which is expected to change significantly in higher vacuum, where the intrinsic material properties dominate.

It was found that for INT when compared to CNT has higher coupling between the layers. The higher inter-layer coupling increases their stiffness, and this increases the resonant frequency. The higher inter-layer coupling also reduces the energy dissipation, and this increases the quality factor. The electrical response to torsion/twist (i.e. the change in electrical conductance as a result of being twisted) of WS<NUM> NTs is higher than that of CNTs. Having a higher resonant frequency, a higher quality factor and a higher electrical response to torsion all bring to an increase of the sensitivity of a torsional resonator to inertial changes. Therefore, resonators provided by this invention, based on INT's, are advantageous when compared with resonators based on CNT's.

Dynamic torsional spring constants were extracted from the torsional resonance peaks and compared to the static spring constants measured by AFM. It was found that while for CNTs and BNNTs the dynamic torsional spring constant is slightly higher than the static one, the dynamic κ of WS<NUM> NTs is significantly larger than its static one. This difference between the constants might stem from a velocity-dependent intershell friction, though further study is needed in order to fully understand this interesting behavior. The resonance spectra of the various NTs were measured under vacuum conditions as well. It is believed that despite observing an expected increase in the quality factors of all NTs due to reduction of air damping, a sufficient vacuum level to enable observing the true intrinsic behavior of the NTs has not yet been reached. Future experiments at higher vacuum will provide more accurate values for the torsional mechanical properties of metal chalcogenide nanotubes. Nevertheless, the available data provide a significant estimation of their unique torsional resonant characteristics, showing that metal chalcogenide nanotubes have higher resonance frequencies and quality factors than carbon nanotubes, thus demonstrating the high potential of metal chalcogenide nanotubes to serve as building blocks for functional NEMS devices. The electromechanical coupling during the torsional motion of WS<NUM> NTs and BCNNTs (BCNNT=boron carbon nitride nanotube) could in principle enable electrical detection of the torsional motion, further contributing to the potential of metal chalcogenide nanotubes as building blocks for NEMS.

In some embodiments, the pedal is not just for analysis of electromechanical offset, but is part of the device. The pedal provides mass which has an inertial behavior and modulates the resonant frequency. In examples not forming part of the present invention where the device does not comprise a pedal, other resonant electromechanical functions are enabled. For example, devices that are based on the vibrations of the nanotube as a string are encompassed by embodiments of the present invention. According to this aspect and in one embodiment, the nanotube portion suspended over a substrate, in between two anchors or pads, does not comprise any additional structure attached to the nanotube. In one embodiment, electrical activation of devices of this invention generates a mechanical response. In one embodiment, electrical activation of devices of this invention generates resonance response. In one embodiment, electrical activation at a certain resonance frequency, causes the nanotube to rotate or vibrate. In one embodiment, electrical activation at a certain resonance frequency, causes the nanotube to rotate or vibrate such that the rotation/vibration can be detected. In one embodiment, electrical activation at a certain resonance frequency, causes the nanotube to rotate or vibrate such that the rotation/vibration is used for further activation of other devices/systems. In one embodiment, movement of the nanotube in devices of this invention causes an electrical response. In one embodiment, the electrical response is detected or recorded. In one embodiment, the electrical response is used to activate other devices/systems. The devices described herein above are further characterized as described herein below.

The term "nanostructure" is meant to encompass any three-dimensional structure having at least one dimension in the nanometer range (i.e. between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM> according to certain embodiments). According to the present invention a nanostructure in the form of a nanotube comprises rolled-up sheet(s) of at least one metal-chalcogenide compound of a general formula MpXq, wherein M is a metal and X is a chalcogenide atom (ion), and p and q are any number between <NUM> and <NUM>. In one embodiment, p, q or a combination thereof are integers. In one embodiment, a nanotube (NT) is a nanostructure as described herein above, in the form of a tube.

According to other embodiments, a nanostructure in the form of a nanotube comprises rolled-up sheet(s) of at least one metal-chalcogenide compound of a general formula M<NUM>p<NUM>M<NUM>p<NUM>X<NUM>q<NUM>X<NUM>q<NUM>, wherein M<NUM> is a first metal, M<NUM> is a second metal, X<NUM> is a first chalcogenide and X<NUM> is a second chalcogenide atom (ion), and p and q are between <NUM> and <NUM>. In one embodiment, p1, p2, q1, q2, or a combination thereof are integers. In some embodiments, p1, p2, q1, q2, or a combination thereof are not integers. In one embodiment, p1 is zero and p2, q1 and q2 are not zero. In one embodiment, q1 is zero and p1, p2 and q2 are not zero. In one embodiment, the metal-chalcogenide compound comprises one metal and one chalcogenide. In one embodiment, the metal-chalcogenide compound comprises two metals and one chalcogenide. In one embodiment, the metal-chalcogenide compound comprises one metal and two chalcogenides. In one embodiment, the metal-chalcogenide compound comprises two metals and two chalcogenides.

The description above is an example for the possible metal chalcogenides from which nanotubes of this invention are made. It is noted that any metal-chalcogenide composition is included in nanotubes of this invention, including a metal chalcogenide comprising one type of metal only (e.g. W only) and only one type of chalcogenide (e.g. S only), a metal chalcogenide comprising more than one metal and only one chalcogenide, a metal chalcogenide comprising one metal only and more than one chalcogenide, a metal chalcogenide comprising more than one metal and more than one chalcogenide. Combinations of nanotubes as described herein above can be used in devices where more than one nanotube is used. In a specific embodiment, the nanotube is of the formula MXn wherein M is a metal, X is a chalcogenide and n ranges between <NUM> and <NUM>. In another specific embodiment, the nanotube is of the formula MXn wherein M is a metal, X is a chalcogenide and n is an integer with a value of <NUM>, <NUM> or <NUM>.

For example, the nanostructure is selected from a nanotube, a nanoscroll, a nanocage, or any combination thereof.

The term metal-chalcogenide nanotube is meant to encompass nanotubes comprising metal-chalcogenide compounds (which do not consist of carbon atoms in some embodiments). The nanotubes are formed from two-dimensional sheet(s) (i.e. sheet of a metal-chalcogenide compound) the sheets are rolled up to form a tube. The atoms within the sheet are held by strong chemical bonds.

In one embodiment, inorganic nanotubes (INT's) refer to nanotubes that do not comprise carbon. In one embodiment, the term 'inorganic nanotube' excludes carbon nanotubes. In one embodiment, inorganic nanotubes consist of inorganic elements only, excluding carbon.

Nanotubes of this invention can be single-walled in one embodiment. In some embodiments, nanotubes of this invention are multi-walled nanotubes. In some devices of this invention, single-wall nanotubes and multi-walled nanotubes are both present. In some embodiments, the nanotube is a single-walled closed tube comprising one layer of material. In one embodiment, multiwalled nanotube comprises more than one closed hollow tube, wherein the smaller diameter tubes(s) are positioned within the larger diameter tube(s). In other embodiment, the tube is a helical tube. In one embodiment, the tube is a spiral tube.

In metal chalcogenides of this invention of the formula MXn as described herein above, in some embodiments, M is any metal. In some embodiments, Metal M can be alkali metal, alkaline earth metal, transition metal or semi-metal.

In some embodiments, the metal M is selected from Li, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu, Ca, Sr, Ba, Sn, Pb, Sb, Bi, rare earths, Ti, V, Cr, Mn, Fe, Co, Ni, Nb, Ta, W, and Mo. Re, Zr, Hf, Pt, Ru, Rh, In, Ga, and alloys like WMo, TiW, WzMo<NUM>-z,. In some embodiments, these metals are present in the metal chalcogenides of this invention of the formula M<NUM>p<NUM>M<NUM>p<NUM>X<NUM>q<NUM>X<NUM>q<NUM> as described herein above.

Chalcogenide (X) or (X<NUM>)/(X<NUM>), is selected from S, Se, Te, in some embodiments.

In some embodiments, the diameter of the nanotube ranges between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM>. In some embodiments, the diameter of the nanotube ranges between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM>. In some embodiments, the diameter of the nanotube ranges between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM>, or even between <NUM> and <NUM>. In some embodiments, the diameter of the tubular nanostructure is between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, or even between about <NUM> and about <NUM>. In an additional embodiment, the diameter of the tubular nanostructure is between about <NUM> and about <NUM>, between about <NUM> and about <NUM>, or between about <NUM> and about <NUM>.

Nanoscroll is a wire-shaped structure, wherein the layer of metal-chalcogenide material is scrolled and wherein the diameter of the wire-shaped scroll is within the nanometer range. In some embodiments not part of the invention, the nano-scroll comprises no hollow center. In other embodiments not part of the invention, the nanoscroll comprises a hollow center. In embodiments of this invention, where reference is made to a nanotube, the same is applicable to a nanoscroll.

In multiwalled nanotube that comprises layers of <NUM>-D rolled up material, the number of layers ranges between <NUM>-<NUM> or between <NUM>-<NUM>.

For nanotubes comprising layers that are each formed into a closed tube, the cross section of the nanotube exhibit <NUM>-<NUM> or <NUM>-<NUM> concentric circles one inside of the other.

In (multiwalled) nanoscrolls as described herein above, the number of layers can be counted from the inner layer or from the center of the cross-section of the scroll, going outwardly to the outermost layer.

In some embodiments, nanotubes or nanoscrolls of this invention are coated. The coating layer may comprise inorganic or organic material.

In some embodiments, electromechanical devices/resonators of this invention are combined with optical actuating/sensing. In some embodiments, electromechanical devices of this invention are combined with magnetic actuating/sensing. In some embodiments, electromechanical devices of this invention are combined with electrical actuating/sensing. In one embodiment, electromechanical devices of this invention are used as sensors for sensing the presence of chemical/biological materials. In one embodiment, the material sensed is water. In one embodiment, sensors/detectors based on devices of this invention comprise humidity sensors (water sensor), material detectors, chemical sensors/detectors, biological sensor/detectors, density detectors, geological detectors. In one embodiment, electromechanical devices of this invention are used as sensors for evaluating the dynamics of reactions of chemical/biological materials.

In one embodiment, the spacing (distance) between the pads in device of this invention ranges between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM>.

In one embodiment, the length of nanotubes of this invention ranges between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>, or between <NUM> and <NUM>. In one embodiment, the length of the nanotube ranges between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM>.

A Chalcogenide is a chemical compound consisting of at least one chalcogen anion and at least one cation. The chalcogenide anion is formed from an atom from group <NUM> of the periodic table. Metal chalcogenides are compounds comprising metal cation(s) and chalcogenide anion(s). In some embodiments, the term "chalcogenide" refers to the anion only while in other embodiments the term "chalcogenide" refers to the compound comprising the chalcogenide anion and a metal cation.

The production of devices of the invention may involve one or more of the following methods: deposition from solution (e.g. electrode position or electroless deposition, saturation, centrifugation), vapor phase deposition/evaporation methods such as PVD, CVD, e-beam evaporation or resistive heating evaporation. Methods used to form portions of devices of this invention may include methods utilizing a movable tip and a surface such as STM, AFM or methods related to STM and AFM devices and systems. In one embodiment, structures of this invention utilize self-assembly of atoms/molecules from solution or from a vapor phase onto a surface. E-beam lithography involving various exposure parameters may be used to form structures in devices of this invention. Methods involving stamping, molding, soft lithography, UV and e-beam lithography and related methods may be used to pattern/form structures and components in devices of this invention. Methods involving wet etching, dry etching, resist application and lift-off, spin-coating, drop casting and relevant methods can be used to pattern/form components and structures in devices of this invention. Combinations of techniques from the techniques described above may be useful to construct devices of this invention. Any other method can be used to form structures of this invention as known to the skilled artisan.

In one embodiment, the nanotubes are doped. In one embodiment, the dopant material is non-metal. According to this aspect and in one embodiment the dopant in the nanotube/nanoscroll is hydrogen, oxygen, fluorine or sodium. Any other element in the form of neutral atom or ion can be used as a dopant in embodiments of the invention.

In another embodiment, the dopant is metal. According to this aspect and in one embodiment, the general structural formula of a doped metal-chalcogenide nanotube is A(<NUM>-x)-Bx-chalcogenides. Atom (ion) B is incorporated into the lattice of the A-chalcogenide altering its characteristics as a function of the nature of A and B, and the amount of incorporated B, i.e. the value of x in the A-B-chalcogenide lattice. In some embodiments, the incorporation of Bx into the lattice of the A-chalcogenide produces changes in the electronic properties leading to the formation of high conductivity semiconductors or even to metal and metal-like nanotubes obtained from a previously known semiconductor (i.e. the selected A-chalcogenide).

Thus, in some embodiments, the nanotubes of this invention comprise inorganic metal-chalcogenide nanotubes of the formula A(<NUM>-x)-Bx-chalcogenide, wherein A is either a metal/transition metal or an alloy of such metals/transition metals, B is a metal or transition metal, and x being smaller or equal to <NUM> provided that A≠B.

The metal A may be a metal or transition metal or an alloy of metals or transition metals selected from the following: Mo, W, Re, Ti, Zr, Hf, Nb, Ta, Pt, Ru, Rh, In, Ga, and alloys like WMo, TiW, WzMo<NUM>-z. The metal A can also be selected from any metal or any metal alloy that forms metal-chalcogenide nanotubes.

In some embodiments, metal B is selected from the following: Si, Nb, Ta, W, Mo, Sc, Y, La, Hf, Ir, Mn, Ru, Re, Os, V, Au, Rh, Pd, Cr, Co, Fe, Ni, and alloys like WzMo<NUM>-z.

Within the nanotube, B and/or B-chalcogenide are incorporated within the A-chalcogenide. In some embodiments, the chalcogenide is selected from S, Se, Te. For example, a nanotube of the invention may be Mo<NUM>-xNbxS<NUM>, Mo(W)<NUM>-xRexS<NUM>, or can comprise or consist of alloys of WMoS<NUM>, WMoSe<NUM>, TiWS<NUM>, TiWSe<NUM>, where Nb or Re are doped therein. Within the alloys of the invention, taking WMo, TiW for example, the ratio between W and Mo or Ti and W may be <NUM>-<NUM> of one metal or transition metal and <NUM>-<NUM> of the other metal or transition metal, e.g. W<NUM>Mo<NUM>Nb<NUM>S<NUM> (given with the percentage of the Nb dopant). The metal B can be selected from any metal that can be used as dopant in metal-chalcogenide nanotubes.

By incorporated it is meant that the B and/or B-chalcogenide are doped or alloyed uniformly within the A-chalcogenide lattice. The B and/or B-chalcogenide substitute the A atom within the lattice. Such substitution may be continuous or alternate substitutions.

In one embodiment, the concentration of the dopant ranges between <NUM>% and <NUM>% of the total metal content of the nanotube. In one embodiment, in the A(<NUM>-x)-Bx-chalcogenide formula, x is less than <NUM>. In one embodiment, x is less than <NUM>. In one embodiment, x is between <NUM> and <NUM>.

In one embodiment, the dopant is between <NUM>% and <NUM>% of the total metal content of the nanotube. In one embodiment, the chalcogenide is selected from S, Se, and Te. In one embodiment, the nanotube comprises or is consisting of a material selected from the following: Mo<NUM>-xNbxS<NUM>, Mo<NUM>-xNbxSe<NUM>, W<NUM>-xTaxS<NUM>, W<NUM>-xTaxSe<NUM>, MoxWyNb<NUM>-x-yS<NUM>, MoxWyNb<NUM>-x-ySe<NUM>, Re<NUM>-xWxS<NUM>, Ti<NUM>-xScxS<NUM>, Zr<NUM>-xYxS<NUM>, Hf<NUM>-xLaxS<NUM>, Ta<NUM>-xHfxS<NUM>, Pt<NUM>-xIrxS<NUM>, Ru<NUM>-xMnxS<NUM>, Rh<NUM>-xRuxS<NUM>, Mo<NUM>-xRexS<NUM>, W<NUM>-xRexS<NUM>, Re<NUM>-xOsxS<NUM>, Ti<NUM>-xVxS<NUM>, Zr<NUM>-xNbxS<NUM>, Hf<NUM>-xTaxS<NUM>, Ta<NUM>-xWxS<NUM>, Pt<NUM>-xAuxS<NUM>, Ru<NUM>-xRhxS<NUM>, Rh<NUM>-xPdxS<NUM> wherein <NUM><x<<NUM> and <NUM><y<<NUM> or wherein <NUM><x<<NUM> and <NUM><y<<NUM>, or wherein <NUM><x<<NUM> or wherein <NUM><x<<NUM> or wherein <NUM><x<<NUM> or wherein <NUM><x<<NUM> and <NUM><y<<NUM>.

A mixture of chalcogenides in one compound is also an embodiment of this invention as described herein above. According to this aspect and in one embodiment, the nanotube comprises or consists of WS<NUM>-xSeX, Mo<NUM>-xWxS<NUM>-ySey, WS<NUM>-x-ySexTey, etc..

In one embodiment, the metal chalcogenide nanotubes of this invention comprise misfit compounds. In one embodiment, the metal chalcogenide nanotube comprises or consists of Bi<NUM>Se<NUM>.

Electromechanical device is a device wherein electrical energy is converted to mechanical energy or vice versa. For example, in an electromechanical device, motion is generated in response to electrical stimulation.

In embodiments of this invention, a pedal is a piece of material that is attached to the nanotube and is used to detect the mechanical properties (e.g. motion/rotation/bending/oscillations) of the nanotube in response to electrical stimulation. In embodiments of the invention the pedal modifies, enables, balances, augments, reduces, transfers, absorbs, exhibit, sense, detect, and/or control the mechanical actions performed by the nanotube in devices of this invention.

In one embodiment, the nanotube does not comprise carbon nanotubes. In one embodiment, the nanotube does not comprise carbon. In one embodiment, devices of this invention do not comprise carbon nanotubes.

Critical point drying (CPD) is a method that involves drying a sample without suffering the destructive effects of surface tension of solvents, by rinsing with a supercritical liquid CO<NUM>, which smoothly goes from liquid to gas without a liquid-gas interface.

A system or an apparatus not forming part of the invention may comprise one or more devices/resonators of this invention. Systems and apparatuses not forming part of this invention further comprise probes, monitors, controllers, measurement devices, computerized elements, electrical contacts, optical instruments, current/voltage generators, shock absorbers, electrical components, optical components, and other elements that enable/facilitate the operation and function of the electromechanical devices, systems and apparatuses of this invention. In one embodiment not forming part of the invention, device is a microelectromechanical (MEM) device, nanoelectromechanical (NEM) device or a combination thereof.

In one embodiment, the metal chalcogenide nanotube comprises WS<NUM>, MoS<NUM>, WSe<NUM>, MoSe<NUM>. In one embodiment, the metal chalcogenide nanotube comprises Mo<NUM>-xNbxS<NUM>, Mo<NUM>-xNbxSe<NUM>, W<NUM>-xTaxS<NUM>, W<NUM>-xTaxSe<NUM>, MoxWyNb<NUM>-x-yS<NUM>, MoxWyNb<NUM>-x-ySe<NUM>, Re<NUM>-xWxS<NUM>, Ti<NUM>-xScxS<NUM>, Zr<NUM>-xYxS<NUM>, Hf<NUM>-xLaxS<NUM>, Ta<NUM>-xHfxS<NUM>, Pt<NUM>-xIrxS<NUM>, Ru<NUM>-xMnxS<NUM>, Rh<NUM>-xRuxS<NUM>, Mo<NUM>-xRexS<NUM>, W<NUM>-xRexS<NUM>, Re<NUM>-xOsxS<NUM>, Ti<NUM>-xVxS<NUM>, Zr<NUM>-xNbxS<NUM>, Hf<NUM>-xTaxS<NUM>, Ta<NUM>-xWxS<NUM>, Pt<NUM>-xAuxS<NUM>, Ru<NUM>-xRhxS<NUM>, Rh<NUM>-xPdxS<NUM>, WS<NUM>-xSeX, Mo<NUM>-xWxS<NUM>-ySey, WS<NUM>-x-ySexTey. In one embodiment, the nanotube is doped by another material. In one embodiment, the nanotube is doped by a metal. In one embodiment, the metal is Nb or Re. In one embodiment, the doping material comprises hydrogen, oxygen, fluorine or sodium.

The present invention also provides a gyroscope, accelerometer, mass sensor, magnetometer, moving mirror comprising the resonator of the present invention.

In one embodiment, the diameter of the nanotube ranges between <NUM> and <NUM>. In one embodiment, the diameter of the nanotube ranges between <NUM> and <NUM>. In one embodiment, the diameter of the nanotube ranges between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM> or between <NUM> and <NUM>.

In one embodiment, for a single nanotube, the nanotube is single-walled or multi-walled nanotube. In one embodiment, for more than one nanotube, the nanotubes are single-walled, multi-walled or a combination thereof. In one embodiment, the nanotube is at least partially hollow. In one embodiment, the nanotube is not hollow.

In one embodiment, devices/resonators of this invention further comprise:.

In one embodiment, each of the first pad and the second pad is in contact with the substrate. In one embodiment, the substrate is coated. In one embodiment, the substrate comprises Si and the coating comprise SiO<NUM>. In one embodiment, the substrate is doped Si. In one embodiment, the substrate is electrically conducting. In one embodiment, the coating on the substrate is electrically insulating.

In one embodiment, the suspended portion of the nanotube is located between the two pads. In one embodiment, the suspended portion of the nanotube bridges between the two pads and is suspended over a surface of the substrate (or over the coated substrate). In one embodiment, the electrical contacts are connected to the pads. In one embodiment, at least one electrical contact is connected to each pad. In one embodiment, the electrical contacts connect the pads to an electrical instrument, to a measurement instrument, to an instrument that applies current/voltage to the pad(s) or a combination thereof. In one embodiment, the substrate is a material with low electrical resistance. In one embodiment, electrical contact(s) is/are connected to the substrate. In one embodiment, the electrical contact(s) that are connected to the substrate, connect the substrate to an electrical instrument, to a measurement instrument, to an instrument that applies current/voltage to the substrate or a combination thereof.

In one embodiment, the pedal is of a rectangular shape and is attached to the nanotube such that the longer dimension of the rectangle is positioned perpendicular to the longer dimension of the nanotube. In one embodiment, the nanotube is suspended over the substrate. In one embodiment, the device further comprises or is connected to electronic instrument(s). In one embodiment, the instrument(s) comprise network analyzer, oscilloscope, lock-in amplifier, spectrum analyzer, RF signal generator, power supply, AC power generator, DC power generator, signal generator, pulse generator, function generator, waveform generator, digital pattern generator, frequency generator or a combination thereof. In one embodiment, voltage applied to the device generates mechanical response in the nanotube.

In one embodiment, the device further comprises electronic components.

In one embodiment, the pads and the substrate are connected by the electrical contacts to the network analyzer (or to any other instrument(s) from the list provided herein above), and the network analyzer (or any other instrument(s) from the list provided herein above), applies voltage between the pads and between the substrate, utilizing the electrical contacts.

In one embodiment, the applied voltage generates mechanical response in said nanotube. In one embodiment, the applied voltage comprises DC voltage and AC voltage. In one embodiment, the Q factor of the device ranges between <NUM> and <NUM>. In one embodiment, the Q factor of the device ranges between <NUM> and <NUM>. In one embodiment, the Q factor of the device ranges between <NUM> and <NUM>. In one embodiment, the Q factor of the device ranges between <NUM> and <NUM>. In one embodiment, the Q factor of the device ranges between <NUM> and <NUM>.

In one embodiment, the device/resonator further comprising an electrode fabricated on the substrate. According to this aspect and in one embodiment, voltage is applied to the device by connecting the pads to one pole of the voltage generator, and connecting the electrode on the substrate to another pole of the voltage generator. According to this aspect and in one embodiment, instead of connecting the substrate underneath an insulating coating to the voltage generator, the electrode is connected to the voltage generator. In one embodiment, such connection allows to generate voltage between the electrode and the pads such that the nanotube will exhibit a mechanical response. According to this aspect and in one embodiment, the electrode is connected to the voltage generator (or to any other voltage source as described herein) through electrical contact(s).

An electromechanical device of the present invention may be provided by a method of fabrication, the method comprising:.

In one embodiment, the substrate comprises Si coated by SiO<NUM>. In one embodiment, removing a substrate surface layer comprises removing a layer of the coating of the substrate. In one embodiment, removing a substrate surface layer means removing a layer of the SiO<NUM> coating of the substrate. According to this aspect and in one embodiment, the coated substrate is referred to as the "substrate". According to this aspect, the coating is a portion of the substrate. In other embodiments, the coating layer on the substrate is referred to as the coating or the coating layer and it does not include the substrate.

In one embodiment, the pads comprise chromium layer coated by gold layer. In one embodiment, the step of applying the pads comprises photolithography and metal deposition. In one embodiment, the step of applying at least one metal-chalcogenide nanotube, comprises dry dispersion of said nanotube. In one embodiment, the step of removing a substrate surface layer underneath the nanotube comprises etching the substrate layer using hydrofluoric acid (HF). In one embodiment, etching is followed by critical point drying (CPD). Other etching techniques and other etching materials can be used for etching substrates of this invention. Longer or shorter etching times can be used to control the etching profile/etching depth of the substrate/coated substrate of this invention. Other etching parameters such as etching material, etching temperature and etchant solution concentration can be modified to control the etching process. Such modifications are known to the skilled artisan.

The method may further comprise fabricating an electrode on the substrate. The electrode can be fabricated using lithography in one embodiment. Any other known fabrication technique can be utilized to fabricate an electrode on the substrate. The electrode can be fabricated before or after the fabrication of the pads. The electrode can be fabricated before or after application of the nanotube onto the pads in some embodiments. More than one electrode can be fabricated on the substrate as needed in embodiments of this invention.

An electrochemical device/resonator may be operated by a method not forming part of the present invention, the method comprising:.

In one embodiment not part of the invention, the resonator is activated by DC voltage. In one embodiment not part of the invention, the resonator is activated by AC voltage. The resonator may be activated by a combination of DC and AC voltages. The resonator may be activated by an RF signal generator. The resonator may be activated by a function generator. The activation of the resonator may be conducted using one or more of the following instruments: a network analyzer, oscilloscope, lock-in amplifier, spectrum analyzer, RF signal generator, AC power generator, DC power generator, signal generator, pulse generator, power supply, function generator, waveform generator, digital pattern generator, frequency generator or a combination thereof. The voltage applied to the device may be applied using any one or more of the instruments described herein above.

The mechanical response of the device may be detected. The mechanical response of the device may be detected optically or electrically. The mechanical response of the device comprises resonance at a certain frequency or at certain frequencies. The resonance frequency of the device may be detected as noted herein above. The resonance behavior of the device may be used to generate a signal.

The mechanical response of the device may be detected electrically, by measuring the electrical response of the inorganic nanotube to mechanical deformation as noted above.

The optical detection of the mechanical response may be performed by laser doppler vibrometer, laser interferometer, optical microscope, or other methods as known in the art. In some embodiments, electrical detection is performed using a lock in amplifier, network analyzer, spectrum analyzer, and/or using any generic electrical circuit. Some electrical instruments described herein above for applying voltage to the resonator can be used to detect the mechanical response of the nanotube.

The mechanical response of the device may be detected electrically, by measuring the electrical response of the inorganic nanotube to mechanical deformation as noted herein above.

The detection of the mechanical response may be performed by measuring changes in the conductance of the nanotube upon deformation or by measuring changes in the capacitance of the resonator upon deformation. (capacitance between the nanotube and the substrate, or between the nanotube and the electrode, changes as the nanotube moves).

The substrate may be coated. The coated substrate may comprise silicon and said coating comprises silicon oxide.

In one embodiment, the region of the nanotube that is suspended over the substrate is located between the first pad and the second pad. In one embodiment, at least one region of the nanotube that is suspended over the substrate is located between the first pad and the second pad.

In one embodiment, the mechanical response comprises torsion, in-plane rotation, in-plane bending, out of phase bending or a combination thereof.

In one embodiment, the electromechanical device is used as a gyroscope for navigation of miniaturized unmanned aerial vehicles (UAVs), as a chemical sensor, or as a biological sensor. In one embodiment, the device further comprises a pedal, the pedal is in contact with the suspended nanotube, such that the pedal is suspended over said substrate. <FIG> shows an embodiment not part of the invention of a device wherein the pedal and the nanotube are suspended over the substrate.

In one embodiment, the pedal is of a rectangular shape and is attached to said nanotube such that the longer dimension of said rectangle is positioned substantially perpendicular to the longer dimension of said nanotube. In one embodiment, symmetrically and asymmetrically refers to the orientation of the pedal with respect to the longer dimension of the nanotube. For example, in a symmetric orientation, the portion of the pedal on one side of the nanotube is of the same shape and size as the portion of the pedal on the other side of the nanotube. In some embodiments, in an asymmetric orientation, the portion of the pedal on one side of the nanotube is smaller or larger than the portion of the pedal on the other side of the nanotube. In some embodiments, such asymmetry results in certain electromechanical properties which are different from the electromechanical properties of a device wherein the pedal is symmetrically oriented with respect to the nanotube.

In one embodiment, perpendicular or substantially perpendicular orientation of the longer dimension of the pedal with respect to the longer dimension of the nanotube means at an angle of <NUM> degrees or at any angle between <NUM> and <NUM>, between <NUM> and <NUM>, or between <NUM> and <NUM> degrees with respect to the longer dimension of the nanotube. Other angular orientations of the pedal with respect to the nanotube are used in embodiments of this invention. In some embodiments, the pedal has non-rectangular shape. Other pedal shapes and other pedal orientations with respect to the nanotubes are possible. For example, round or circular pedals, tear drop, wire, oval, or completely non-symmetric pedal geometries are used in embodiments of this invention. For each pedal shape used, any non-symmetric orientation with respect to the long dimension of the nanotube is included in embodiments of this invention. In embodiments of this invention, the size of the pedal portion present on one side of the nanotube is different from the size of the pedal portion present on the other side of the pedal. Pedal size can also be modified and fitted to various applications of devices of this invention.

The application of a voltage may comprise applying AC voltage, or a combination of AC and DC voltages. The frequency of the AC voltage may be in the RF range.

A method of operating the device not forming part of the present invention further comprises detecting the mechanical response of the nanotube. The response may be detected optically or electrically. Electrical detection may comprise a conductivity measurement. Electrical detection may comprise a capacitance measurement.

Resonators of this invention may be devices. The devices may be electromechanical devices. The resonators of this invention may comprise electromechanical devices. The description of a resonator may refer to description of a device.

The terms RF, AC and DC are the electronics terms known in the art.

A nanotube suspended over a substrate means that a portion of the nanotube is suspended over the substrate while at least two anchor portions of the nanotube are attached to pads (each portion to a separate pad) such that the suspended portion of the nanotube is located between the two portions of the nanotube that are attached to the pads.

A resonance frequency of resonators of this invention may range between <NUM> and <NUM>, between <NUM> and <NUM>, between <NUM> and <NUM> or between <NUM> and <NUM>. The resonance frequency is a torsional resonance frequency. The resonance frequency may be in the MHz range or in the KHz range.

The voltage may be applied to the resonator in order to activate the resonator. An RF generator may be used to apply voltage to the resonator. An AC power generator may be used to apply voltage to the device/resonator. The frequency of the AC voltage applied may be in the RF (radio frequency) range or in the MHz range.

Self-sensing means that activating the device and detecting the response of the device is done using the same or similar technique, or by the same apparatus, or according to the same or similar principles, or by using the same or similar physical property/parameter.

In one embodiment, the term "a" or "one" or "an" refers to at least one. In one embodiment the phrase "two or more" may be of any denomination, which will suit a particular purpose. In one embodiment, "about" or "approximately" or "substantially" may comprise a deviance from the indicated term of + <NUM> %, or in some embodiments, - <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %, or in some embodiments, ± <NUM> %.

<FIG> shows representative resonance spectra of CNT-, BNNT- and WS<NUM> NT-based torsional resonators under atmospheric pressure. The resonance frequency and quality factor were extracted for each peak in the spectrum by fitting the results to a classical driven damped oscillator, Equation <NUM>, where θmax is the amplitude of the pedal, κ is the torsional spring constant, τ<NUM> is the maximal electrostatic torque on the pedal, v is the driving frequency, v<NUM> is the natural resonance frequency ( <MAT>, ) where I is the pedal mass moment of inertia, and Q is the quality factor. Results for all the CNT-, BNNT- and WS<NUM> NT-based resonators are summarized in Tables <NUM>, <NUM> and <NUM> respectively. A total of <NUM> devices were measured: <NUM> of CNTs, <NUM> of BNNTs and <NUM> of WS<NUM> NTs. While CNT-based resonators exhibited <NUM>-<NUM> peaks in the measured frequency range, WS<NUM> NTs exhibited <NUM>-<NUM> peaks, and BNNTs displayed only one distinct peak.

In order to assign the different peaks to their corresponding oscillation mode, and in particular, to identify the torsional mode, a finite element analysis (FEA) using COMSOL MULTIPHYSICS™ has been conducted. The numerical convergence of our FEA simulations was verified through refining of the mesh. A variety of simulations comprising the wide range of parameters that can exist in these systems have been performed, namely: (i) NT diameters between <NUM> and <NUM>; (ii) Young's modulus between <NUM> GPa (for WS<NUM> NTs) and <NUM>-<NUM> TPa (for CNTs and BNNTs); (iii) Poisson's ratios between <NUM> and <NUM>; (iv) densities between <NUM>/m<NUM> (for BNNTs) and <NUM>/m<NUM> (bulk density of WS<NUM>); and (v) extents of intershell coupling ranging from the extreme case of a hollow cylinder (only the outermost shell carrying the load) to the other extreme case of a solid rod (all the shells coupled). In all these simulations, the lowest-frequency natural (eigen) mode was always the torsion, followed by significantly higher frequencies related to the other modes (in-plane rotation, in-plane bending and out-of-plane bending). Following this detailed analysis, the first peak (i.e. lowest-frequency) of all our measured spectra can be safely assigned to the torsional mode of the nanotube-based resonators. <FIG> shows an example for such an analysis for the resonator whose resonance spectrum is depicted in <FIG>. Comparing the FEA simulations to the experiments, it can be seen that the torsional mode is consistent with a hollow cylinder case, while the in-plane and out-of-plane bending modes are consistent with a solid rod case. This result is consistent with the torsional behavior of MWCNTs, which is known to involve only the outer shell of the nanotube, and the intuitive assumption that the bending motion will have to involve all the shells. Discrepancies between measured peak positions and calculated resonance frequencies can be explained by the simplicity of the model, which does not take into account the complexity of the inner structure of the nanotubes and its anisotropy, as well as defects and imperfections appearing during the fabrication process. Also, the normal mode designated as "torsion" does in fact contain a small component of bending motion, and likewise, the normal mode designated as "out-of-plane" in fact contains a small component of torsional motion, each mode having a different contribution from all the walls (solid rod case) or only from the outer wall (hollow cylinder case). In principle, the experimental setup is not designed to actuate nor detect in-plane motion, so these modes are ideally not expected to appear in the spectra. Nonetheless, due to misalignment of the resonator with respect to the laser beam, and the offset of the pedal with respect to the nanotube, x-y-z cross-talk and parasitic actuation is expected to a certain degree. This could explain the appearance of the in-plane bending mode and the absence of the in-plane rotation mode in the spectrum.

FEA simulations of BNNT- and WS<NUM> NT-based torsional resonators are qualitatively similar to those of CNTs (<FIG>), and are summarized in <FIG> and <FIG>, respectively. Comparing the measured resonance frequency of BNNT-based resonators to the simulation suggests that the resonant torsional motion of BNNTs is an intermediate case between the solid rod and hollow cylinder cases, i.e. there is some degree of intershell coupling during the torsional motion. The FEA simulation for WS<NUM> NT-based resonators seemingly points out to a discrepancy: the measured torsional resonance frequency appears to be higher than the extreme case of solid rod, as if the number of shells twisting together was larger than the number of existing shells in the nanotube. This discrepancy can be related to the fact that the Young's modulus used for the simulation was the most widely accepted value (<NUM> GPa), but WS<NUM> NTs are known to exhibit a large variance in their Young's modulus (between ~<NUM> GPa and ~<NUM> GPa).

<FIG> shows a comparison of the torsional resonance spectrum for a typical torsional device from each material under atmospheric pressure and in vacuum (values in parenthesis represent the values measured in vacuum). Comparing the torsional resonance spectra of all the measured torsional resonators, WS<NUM> NTs exhibit the highest average torsional resonance frequency (<NUM> ± <NUM>), followed by BNNTs (<NUM> ± <NUM>) and CNTs (<NUM> ± <NUM>). The same trend applies for the average quality factors as well: <NUM> ± <NUM> for WS<NUM> NTs, <NUM> ± <NUM> for BNNTs, and <NUM> ± <NUM> for CNTs. Note that the numbers in the inset of <FIG> are results for certain devices and therefore differ from the average values noted herein above. Dynamic κ, namely the torsional spring constants extracted from the resonance spectra measured in air using the relation: <MAT>, is plotted as a function of nanotube diameter d in <FIG> (for our devices, the effective κ takes into consideration the two segments of the suspended nanotube, which are simultaneously twisted in opposite directions). WS<NUM> NTs exhibit the highest dynamic κ, followed by BNNTs and CNTs. This trend is consistent with the expected strong dependence of κ on the diameter of the nanotube (~d<NUM> assuming a solid rod case, and ~d<NUM> assuming a hollow cylinder case). The power law of κ in the diameter can thus provide a measure of the intershell coupling: it should be closer to <NUM> if the shells are more coupled and closer to <NUM> if only the outermost shell carries the torsional load. It can be seen that the BNNTs exhibit a power law of ~d<NUM>, which suggests a more significant intershell coupling than CNTs (~d<NUM>). The power law of BNNTs is consistent with an intermediate case between the two extreme cases suggested by the FEA simulations. WS<NUM> NTs could not be fitted to any such power law, probably due to the high variance in the intershell coupling between the individual nanotubes constituting the resonators and the large variance in their Young's moduli mentioned earlier.

<FIG> shows that the measured quality factors under atmospheric pressure increase with the dynamical torsional spring constant. This relationship can be attributed to the dominant effect of air drag. When viscous losses (i.e. damping by the air) are the dominant energy dissipation mechanism, as in ambient conditions, then <MAT>, where κ is the dynamic torsional spring constant, I is the pedal mass moment of inertia, and b is the damping coefficient due to air friction. The mass moment of inertia depends mainly on the geometry and density of the pedal, since the nanotube material and diameter have a negligible influence, and thus I should be quite similar for all resonators (except for small differences in the offset of the pedal position with respect to the nanotube due to nanofabrication inaccuracies). A calculated squeeze number of <NUM> and <NUM> (see Example <NUM>) for CNT- and BNNT-based resonators, respectively, indicates that for these resonators, the damping coefficient b of the system is expected to be mainly contributed by pure drag-force damping (drag caused by a moving object in a fluid far away from other surfaces), as opposed to squeeze-film damping (increased damping caused by squeezing of the gas confined between two nearby surfaces). A common approach to estimate pure drag-forces is to substitute the oscillating object by a superposition of spheres. The damping coefficient of each sphere is given by Equation <NUM>, where µ is the air viscosity, r is the radius of the sphere, ρ is the air density, and ω is the oscillation frequency. Since at resonance <MAT>, the expected damping coefficient of our system should be b~κ<NUM>-<NUM>, and thus Q~κ<NUM>-<NUM> is expected. As seen in <FIG>, our result of Q~κ<NUM>±<NUM> is consistent with this prediction. Due to their higher resonance frequency, the squeeze number of torsional resonators based on WS<NUM> NT is higher (<NUM>), indicating a higher contribution of squeeze-film damping. The squeeze-film damping coefficient for torsional resonators at high frequencies is of the form of a converging series and thus does not have a simple power law dependence on the resonance frequency.

In order to observe the intrinsic behavior of the nanotube, i.e. the internal friction which is induced by the nanotube material and structure, the air damping has to be reduced down to the point where it is negligible compared to the internal friction of the NT. The air pressure range in which the intrinsic behavior is dominant can be referred to as the intrinsic region. Measurements of the torsional devices frequency response were thus conducted in vacuum and are summarized in Table <NUM>. As expected due to reduction of the interaction of the pedal with the air molecules, the vacuum caused an increase in the quality factor of all nanotubes. Averaging the ratios of the quality factors in vacuum with respect to the quality factors in air, it appears that all the quality factors have changed approximately by the same factor (<NUM> ± <NUM> for CNT devices, <NUM> ± <NUM> for BNNTs and <NUM> ± <NUM> for WS<NUM> NTs). This suggests that, although the quality factor that was measured was closer to the intrinsic Q, the vacuum level that was reached did not completely eliminate air damping. If the intrinsic region would have been reached, it would have been expected to see the quality factor of each material change by a different factor under vacuum, since the intrinsic Q of each material should be independent of the Q in air. Nonetheless, the intrinsic component of the Q measured in vacuum was more significant when compared to the measurement in air.

By comparing the quality factor Q that was measured in air for MWCNT torsional devices with the Q that was measured in sufficient vacuum for similar devices as previously performed, it is possible to roughly estimate the expected intrinsic Q for BNNTs and WS<NUM> NTs (see Example <NUM>). According to the rough estimates, the quality factors of BNNTs and WS<NUM> are quite similar (<NUM> and <NUM> respectively), and both are larger than CNTs, which have an average quality factor of <NUM> in vacuum, according to previous measurements. While the change in the Q factors is apparent for all devices of all materials when comparing the behavior under atmospheric pressure and in vacuum, the resonance frequency remains the same within the range of error, despite the seemingly expected shift to higher frequency predicted by Equation <NUM>. Because the change in Q is by a factor of ~<NUM>, the expected shift in frequency should be ~<NUM>%, which is within the margin of error of the measurement.

Following our calculation of the dynamic κ, the static torsional spring constant (static κ) of the various nanotubes was also determined using the established method of pressing an atomic force microscope (AFM) tip against the pedal in various positions along the pedal, and measuring the force while twisting the nanotube (<FIG>). The linear stiffness K of the system was calculated for each position across the pedal. The static κ was extracted by fitting the plot of K as a function of the tip position (<FIG>) to Equation <NUM>, where x and a are the positions of the tip and the nanotube with respect to an arbitrary origin, respectively, κ is the static torsional spring constant and KB is the bending spring constant.

In Table <NUM> the torsional spring constants that were extracted from the resonance spectrum measurements (dynamic κ, <FIG>) are compared to the static ones that were extracted from the AFM measurements. All measured devices exhibit a higher dynamic torsional spring constant than the static one. While for the CNT-based device the difference between the constants is within the range of error, for BNNT- and WS<NUM> NT- based devices this difference is significant.

The resonance spectrum measurements, from which the dynamic κ is extracted, involve twisting the nanotube at an average speed that is <NUM>-<NUM> orders of magnitude higher than in the static AFM-pressing measurement. It has been found during pullout experiments in double-wall carbon nanotubes (DWCNTs) that the intershell friction between the outer- and inner-shell increases linearly with increasing pullout velocity. Although the measured pullout velocities were axial rather than torsional, and they were significantly smaller than in the dynamic experiments presented herein, these findings are consistent with the present results, since the higher the intershell friction, the higher the coupling between shells should be, and thus more shells share the load and contribute to the overall torsion - i.e. the dynamic κ should be higher than the static one. The increased dynamic κ with respect to the static one does not seem to stem from squeeze-film effect, because, as seen in Table <NUM>, there is no apparent difference between the resonance frequencies and thus dynamic torsional spring constants in air and in vacuum. The only comparison between static and dynamic κ of a CNT-based torsional device, based on a single MWCNT device measurement, had found the dynamic κ to be slightly smaller than the static one. The discrepancy between that and the present results is not yet understood.

BNNTs show an increase in the dynamic κ with respect to the static one. Similar to the CNT case, a velocity-dependent intershell friction mechanism might explain the higher dynamic κ. The fact that the dynamic/static ratio for BNNTs is higher than the dynamic/static ratio for CNTs could be explained by the different chemical composition and structure of the two types of nanotubes, and by the difference in diameters between the two types of nanotubes (since intershell friction is contact area dependent, the larger the diameter the larger the contact area). An additional factor leading to the higher dynamic κ should be considered for BNNTs and is related to their facets. It has been shown that BNNTs of large diameters (><NUM>) are faceted but undergo unfaceting when twisted using an AFM. It is possible that the time it takes for the BNNT to undergo unfaceting is longer than the time of oscillation, so the BNNT stays faceted through the whole oscillation. If this is indeed the case, the dynamic κ should be larger than the static one due to the intershell coupling of the faceted BNNT compared to the unfaceted one.

Compared to CNTs and BNNTs, WS<NUM> NTs exhibit the highest dynamic/static ratio. WS<NUM> NTs are known to exhibit torsional stick-slip behavior. This behavior, in which energy is dissipated due to irreversible jumps between neighboring equilibrium positions, is known to be responsible for velocity dependent friction on the atomic scale. As described earlier for CNTs, the high torsional velocity during dynamic measurements might cause increased intershell friction which may lead to higher coupling between shells. This means that more shells are involved in the torsional movement thus increasing κ. It has been suggested before that during the "stick regime" the different shells of the WS<NUM> NT are not necessarily locked or unlocked in an all-or-nothing situation. There is a possibility that the dynamic actuation causes the shells to have an increased degree of locking compared to the static AFM-pressing measurements. The high dynamic/static ratio might be explained by the difference in the mechanical and structural properties of WS<NUM> NTs with respect to CNTs and BNNTs. Although these are all different materials with different mechanical properties and dynamic behaviors, the difference in diameters also needs to be considered, since intershell friction is contact-area dependent. Further experiments with nanotubes of similar diameters could help in distinguishing between the effects of nanotube material and dimensions.

Highly doped silicon wafers (Si<<NUM>>, P/B doped, resistivity of <NUM>-<NUM>Ω·cm) with <NUM> oxide layer were cut to approximately <NUM> x <NUM>. The cut silicon wafer was then cleaned by sonication in acetone, followed by sonication in IPA and blow drying by N<NUM>. The clean silicon wafers underwent photolithography of pads (to serve later for wire bonding contacts) and alignment marks (to be used for electron-beam lithography later on), followed by electron beam evaporation of <NUM> Cr and <NUM> of Au and lift off in acetone. The nanotubes were later dispersed on the silicon wafer in the following manner:.

Nanotubes were mapped by SEM and their diameter was measured by AFM imaging. Pedal devices and electrodes were patterned on top of the selected nanotubes using electron beam lithography (EBL). In the case of CNTs, mild plasma ashing was carried out. To complete the patterning of the pedal devices and electrodes, evaporation of <NUM> Cr and <NUM> Au was carried out followed by acetone lift off. All torsional devices were then imaged by AFM in order to measure the dimensions of all the pedal devices. The wafer was glued by conductive epoxy glue to a chip-carrier and wire-bonding was carried out between the electrodes of the torsional devices and the chip-carrier. In order to make the NTs suspended and finalize the fabrication process HF (<NUM>:<NUM> BOE) was used for <NUM> minutes in order to etch ~<NUM> of the SiO<NUM> layer. The etching was followed by critical point drying (CPD) to allow drying while avoiding surface tension damages.

A network analyzer (Keysight E5061B network analyzer) was connected to a torsional device fabricated using the methods described herein above. The electrostatic actuation signal generated by the network analyzer, which was comprised of a DC and an AC component, was connected to the highly doped silicon (the substrate) while the ground was connected to the two electrodes clamping the suspended nanotube and pedal. Detection of the displacement of the pedal was achieved by a laser Doppler vibrometer (Polytec LDV OFV5000 with a DD-<NUM> displacement decoder) with a magnification lens of x100. The laser was aimed at the torsional device which was being actuated using a camera connected to the LDV, as seen in <FIG>. The output of the LDV was fed back to the network analyzer, which in addition to actuation was also used to filter out only the relevant frequency, reduce noise, and display the results - a spectrum of pedal displacement as a function of driving frequency (the excitation frequency of the pedal). In a standard experiment a DC voltage of <NUM> V and an AC voltage of <NUM> V were applied (although in high driving frequencies the voltage reaching the device was lower due to attenuation from the cables used). A frequency sweep of the actuation voltage was carried out from <NUM> to <NUM> (the upper limit of the LDV detection range) in order to get the full resonance spectrum. After measuring the full resonance spectrum high resolution measurements were made by narrowing the frequency sweep to include only one peak at a time in order to increase the accuracy of the measurement. In order to increase signal to noise ratio, averaging has been used - each frequency sweep was in fact an average of at least <NUM> measurements. The resonance frequency and quality factor were extracted by fitting each peak to Equation <NUM>.

AFM imaging and static κ measurements were performed on Veeco Multimode/Nanoscope V with a closed-loop scanner. Measurement procedure is described in depth in <NPL>.

First, the contribution of air damping to the total Q of CNT devices (Q viscous) was estimated by comparing Q in air (QCNT,air) from our measurements and Q in vacuum in the intrinsic region (Q intrinsic) measured by <NPL>. <MAT> In order to roughly estimate the intrinsic Q of the nanotubes it was assumed that the friction coefficient and moment of inertia are the same for all materials. Using the following equation: <MAT> where κ is the dynamic torsional spring constant, I is the mass moment of inertia and b is the damping coefficient, Qviscous, is scaled, (the Q due to viscous damping that was found earlier for CNTs), to find its equivalent for BNNTs and WS<NUM> NTs: <MAT> <MAT> These estimated values were used to estimate the intrinsic Q factor of BNNTs and WS<NUM>: <MAT> <MAT>.

The squeeze number is a dimensionless parameter indicating the significance of squeeze-film damping in the system, and defined as follows: <MAT> where µ is the dynamic viscosity, ω is the frequency, l is the length of the pedal, P is the pressure, and h is the gap size. Substituting all the parameters a value of ~<NUM> is obtained for CNTs, <NUM> for BNNTs and ~<NUM> for WS<NUM> NTs.

An electromechanical device was constructed. The device is based on an inorganic nanotube (e.g. WS<NUM>), either single wall or multi-wall, that was placed on a substrate composed of a conducting material (e.g. doped Si wafer). The conducting material was coated by a highly insulating dielectric layer, such as silicon oxide. The nanotube was clamped at the ends by two metallic pads (source and drain) which are patterned on the insulating layer, and on top of the nanotube, a flat metallic plate (pedal) has been placed asymmetrically. The center part of the nanotube, including the pedal, is suspended above a trench that is etched in the insulating layer. The suspended part of nanotube, clamped by the pads, together with the pedal, constitute the resonator.

The pads were connected by a metallic pattern to an external circuit. The source pad is connected to an RF signal generator, and the drain is fed to a lock-in amplifier. The conducting layer of the substrate, which constitutes a gate electrode, was connected to another signal generator. The gate is applied with an RF signal (ω), which is offset by some DC voltage that is higher than the amplitude of the signal. The source was applied with a signal at double the frequency and a small shift of an intermediate frequency (2ω-Δω). Mechanical oscillation of the device at the resonant frequency leads to modulation of the conductivity due to either piezoresistivity or charge modulation on the nanotube. The resonator device acts as a signal mixer, and the detection of mechanical resonance is obtained by measuring a signal at an intermediate frequency (Δω) that is detected with lock-in techniques. The signal has distinct behavior when the device is at resonance.

The device was similarly actuated with an RF signal which is applied to the gate, and detected optically using a laser Doppler vibrometer. The two spectra, obtained by sweeping the frequency of actuation and measure manifestations (optical and electrical) of the mechanical resonances, were compared in order to characterize the device.

<FIG> is a comparison of resonance spectra for a WS<NUM> nanotube based torsional device. The spectra were obtained with a laser Doppler vibrometer (lower line), and an electrical signal mixing measurement (upper line). There is a correlation between the resonance features obtained in each measurement. The peak at <NUM> (obtained in both optical and electrical measurements), is postulated to belong to the torsion mode of the resonator. Another resonant feature at <NUM> is possibly a bending mode, such as out-of-plane bending.

Claim 1:
An electromechanical resonator, said resonator comprising:
• at least one nanotube;
• a substrate;
• a first pad and a second pad;
• a pedal, said pedal being in contact with said nanotube;
wherein at least a portion of said nanotube is suspended over said substrate and wherein a first region of said nanotube is in contact with said first pad and wherein a second region of said nanotube is in contact with said second pad, characterized in that said at least one nanotube is at least one metal-chalcogenide nanotube and said pedal is positioned asymmetrically with respect to said nanotube.