Abstract:
Various aspects as described herein are directed to piezoelectric materials. As consistent with one or more embodiments, an apparatus includes a nanomaterial and structures coupled to the nanomaterial. This nanomaterial-structure combination manifests piezoelectric characteristics, via the combination. In certain implementations, neither the nanomaterial nor the coupled structures independently exhibit piezoelectric characteristics, yet do so in combination.

Description:
RELATED PATENT DOCUMENT 
       [0001]    This patent document claims benefit of U.S. Provisional Application Ser. No. 61/605,656 filed on Mar. 1, 2012; this provisional patent document and its accompanying Appendix are fully incorporated herein by reference. 
     
    
     FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT 
       [0002]    This invention was made with Government support under contract W911NF-07-0027 awarded by the U.S. Army Research Laboratory. The Government has certain rights in this invention. 
     
    
     FIELD 
       [0003]    The aspects of the present disclosure relate to apparatuses, systems and methods involving piezoelectricity, and in manifesting piezoelectric characteristics. 
       BACKGROUND AND OVERVIEW 
       [0004]    Advances in nanoscale fabrication are leading to remarkably innovative devices for electronics, photonics, energy harvesting, and other applications. Microelectromechanical systems (MEMS) are being extended to the nanoscale (NEMS) in the context of nanosized actuators, motors, robots, and locomotive devices. 
         [0005]    A challenge with these technologies relates to dynamically controlling motion and deformation at the nanoscale level. Piezoelectric materials have been used for dynamical control of material deformation by the application of an external electromagnetic field, in a wide variety of applications from pressure sensors to acoustic transducers to high voltage generators. Piezoelectricity is traditionally thought to be an intrinsic property of a particular material phase, for example, wurtzite structure. 
         [0006]    However, many piezoelectric materials are limited in application due to one or more of composition, size and relatively limited interactivity variation. 
       SUMMARY 
       [0007]    Aspects of the present disclosure relate generally to piezoelectric apparatuses, systems and methods, as may address challenges including those discussed above. 
         [0008]    In accordance with various embodiments, an apparatus includes a nanomaterial and structures coupled to the nanomaterial, with the structures and nanomaterial manifesting piezoelectric characteristics therein. In some embodiments, dopants or other structures are added to a non-piezoelectric nanomaterial such as graphene to manifest piezoelectric characteristics therein via the combination of materials. The dopants or other structures may also be of a non-piezoelectric material. The respective structures may be combined with the nanomaterial uniformly or with a location-based approach to respectively set uniform or site-specific piezoelectric characteristics. 
         [0009]    A variety of apparatuses can be implemented using manifested piezoelectricity as discussed herein. One embodiment is directed to a NEMS relay having a nanomaterial and structures coupled thereto that, together, manifest piezoelectric characteristics for operation of the relay. Another embodiment is directed to a pressure sensor having a nanomaterial and structures coupled thereto that manifest pressure-responsive piezoelectric characteristics. Another embodiment is directed to a cantilever-type structure including a nanomaterial and structures coupled thereto, with the nanomaterial and structures manifesting electromagnetic field-responsive piezoelectric characteristics. 
         [0010]    Other embodiments are directed to manufacturing an apparatus by coupling structures to a nanomaterial and therein manifesting piezoelectric characteristics. This approach may be carried out to effect structures as above, such as by uniformly doping a nanomaterial to manifest generally uniform piezoelectric characteristics, or by doping different regions of a nanomaterial with different concentrations of dopants and/or different types of dopants to manifest varying piezoelectric characteristics that are different in different regions of the nanomaterial. 
         [0011]    Another example embodiment is directed to a method of using an apparatus having a nanomaterial and structures that are coupled to and configured and arranged with the nanomaterial to manifest piezoelectric characteristics. Interaction with the nanomaterial, such as a pressure interaction or electric interaction, is effected to manifest a piezoelectric response in the nanomaterial. This approach may be implemented, for example, to cause a deflection of the nanomaterial and/or to effect an electrical characteristic in the nanomaterial. 
         [0012]    In another example embodiment, an apparatus having a nanomaterial and structures that are coupled to and configured and arranged with the nanomaterial is used to induce piezoelectric characteristics. Specifically, the structures are used to strain the nanomaterial and therein manifest piezoelectric characteristics. For instance, atoms can be adsorbed and patterned to engineer strain in the nanomaterial. This strain can be used to set and/or alter characteristics such as those relating to electronic, optical and chemical properties. 
         [0013]    Other embodiments are directed to a method in which a nanomaterial is provided, and piezoelectric characteristics are manifested in the nanomaterial via structures coupled to the nanomaterial and causation of interaction of the structures with the nanomaterial. 
         [0014]    In another embodiment, an apparatus includes a piezoelectric material having a monolayer of nanomaterial with strain-induced piezoelectric characteristics, and a circuit structure including the piezoelectric material and respective circuit nodes coupled via the piezoelectric material. The piezoelectric material passes current between the circuit nodes in response to a bias applied to the piezoelectric material, via the strain-induced piezoelectric characteristics. 
         [0015]    The above summary is not intended to describe each embodiment or every implementation of the present disclosure. The figures, detailed description and claims that follow more particularly exemplify various embodiments. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]    Aspects of the present disclosure may be more completely understood in consideration of the detailed description of various embodiments of the present disclosure that follows in connection with the accompanying drawings, in which: 
           [0017]      FIG. 1  shows a nanomaterial with structures coupled thereto in a generally uniform manner, and exhibiting manifested piezoelectric characteristics in accordance with an example embodiment of the present disclosure; 
           [0018]      FIG. 2  shows a nanomaterial with structures coupled thereto in a region-specific manner, and exhibiting manifested piezoelectric characteristics in accordance with another example embodiment of the present disclosure; 
           [0019]      FIGS. 3A-3B  show a nanomaterial with structures doped therein, the nanomaterial and structures manifesting piezoelectric characteristics in accordance with example embodiments of the present disclosure; 
           [0020]      FIG. 4  shows a NEMS relay apparatus, in accordance with another example embodiment of the present invention; 
           [0021]      FIG. 5  shows a pressure sensor apparatus, in accordance with another example embodiment of the present invention; 
           [0022]      FIG. 6  shows a bilayer piezoelectric structure, in accordance with another example embodiment of the present invention; 
           [0023]      FIG. 7  shows a cantilever apparatus, in accordance with another example embodiment of the present invention; 
           [0024]      FIG. 8  shows a planar device having static strain set via adsorption and/or doping of atoms on a nanomaterial, in accordance with another example embodiment of the present invention; and 
           [0025]      FIG. 9 , shows a planar device having static strain set via adsorption and/or doping of atoms on a nanomaterial, in accordance with another example embodiment of the present invention. 
       
    
    
       [0026]    While the disclosure is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the disclosure to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure including aspects defined in the claims. 
       DETAILED DESCRIPTION 
       [0027]    The present disclosure relates to piezoelectric materials, apparatuses, systems and related methods, with various aspects directed to manifesting piezoelectric characteristics such as by combining (e.g., non-piezoelectric) materials to form a material exhibiting piezoelectric characteristics. While the present disclosure is not necessarily limited to such devices and applications, various aspects of the disclosure may be appreciated through a discussion of examples using these and other contexts. 
         [0028]    In accordance with various embodiments, an apparatus includes a nanomaterial and structures coupled to the nanomaterial, with the structures and nanomaterial manifesting piezoelectric characteristics therein. In one embodiment, dopants or other structures such as atoms, molecules and other nanomaterials are added to a non-piezoelectric nanomaterial such as graphene to manifest piezoelectric characteristics therein via the combination of materials. Such manifestation may, for example, involve inducing in-plane and/or out-of-plane piezoelectricity. Various embodiments are also directed to the manipulation and dynamic control of the optical, chemical, electronic, and other properties of nanoscale devices. Such embodiments may be implemented as a method of using a device, or embodied in an apparatus that exhibits characteristics amenable to implementation for effecting such dynamic control (e.g., having adsorbants that interact with a nanomaterial to manifest piezoelectric characteristics for manifesting the control). 
         [0029]    As described herein, manifesting piezoelectric characteristics involves a combination of materials that, when the materials are combined/interacting, exhibits piezoelectric properties. For instance, two materials having little or no intrinsic piezoelectric characteristics may be combined to form a structure that is piezoelectrically responsive. Such an approach may involve adding structures to a monolayer to strain the monolayer, which may be piezoelectrically responsive to mechanical deformation and/or an electromagnetic field (and in some instances, an electric field). Using such strain approaches, static piezoelectric characteristics can be imparted to the monolayer. Other approaches may involve combining materials in which one material exhibits at least some piezoelectric characteristics, with the combination and interaction exhibiting resulting piezoelectric characteristics that are different than either one of the materials. 
         [0030]    Piezoelectric characteristics are manifested in one or more of a variety of manners, to suit different applications. In some embodiments, dopants or other structures are used to engineer uniform or site-specific piezoelectricity in the resulting combination of materials, to set piezoelectric characteristics of the nanomaterial and/or to form piezoelectric circuits therein. For instance, structures can be uniformly added to a nanomaterial in order to manifest generally uniform piezoelectric characteristics across the nanomaterial. Structures can also be added to specific regions, or with different concentrations in different regions, to induce region-specific or site-specific piezoelectric characteristics. In addition, different types of structures or dopants can be added in different regions of a monolayer, to manifest different piezoelectric characteristics in the different regions. The different regions or sites can be controlled independently from one another for manifesting piezoelectric characteristics therein. In certain embodiments, site-specific operation of a nanomaterial can be similarly effected with a uniformly-doped sheet, by applying an electromagnetic field to specific sites in the nanomaterial. 
         [0031]    One or more mechanisms can be used to manifest piezoelectric characteristics, and can be implemented to suit particular applications, available materials or manufacturing conditions. For example, certain embodiments are directed to manifesting piezoelectric characteristics by using dopants or other structures to induce strain in a nanomaterial. The strained regions are rendered piezoelectrically responsive, and may render or otherwise set one or more characteristics such as those relating to one or more of electronic, optical and chemical properties. 
         [0032]    In connection with various example embodiments, it has been discovered that piezoelectric effects can be engineered into non-piezoelectric graphene through the selective surface adsorption or doping of atoms. In some implementations, a single sheet of graphene is doped with atoms (e.g., on one side) to generate piezoelectricity by breaking inversion symmetry in the graphene. Piezoelectric magnitudes can be achieved with a two-dimensional sheet (e.g., a monolayer) in a manner that is comparable to magnitudes achieved in three-dimensional piezoelectric materials. Such three-dimensional materials may include, for example, bilayer materials or materials having a few layers. Using these approaches, designer piezoelectric characteristics are manifested in nanoscale materials, and can be used to dynamically control nanoscale electromechanical devices. 
         [0033]    As may be related to the above, various example embodiments are directed to the patterned adsorption of atoms in a nanomaterial sheet to selectively control which spatial regions on the sheet are endowed with piezoelectricity. One embodiment is directed to one-sided doping of graphene and spatial control of adatom distribution. Such chemical doping of graphene with adatoms may include, for example, using one-sided hydrogen and/or fluorine covering of graphene. Another embodiment is directed to two-sided graphene doping, with different structures on each side being configured and arranged to break inversion symmetry in the graphene. 
         [0034]    Other embodiments are directed to coadsorption of both hydrogen and fluorine, which can be used to obtain an e 11  type of piezoelectric response. In connection with various embodiments, it has been discovered that the e 11  type of piezoelectric response can be engineered into monolayer graphene. In some embodiments, this engineered piezoelectric effect is used for monolithic integration of electronic and electromechanical devices in graphene monolayers for resonators, sensors, and NEMS. One or more implementations are directed to a structure having hydrogen and fluorine as structures adsorbed on alternating carbon sites of a nanomaterial to manifest piezoelectricity. Such implementations may be effected with a change in point group symmetry from hexagonal 6/mmm to trigonal 3 m, removing an inversion center and introducing piezoelectricity (e.g., in grapheme), using a formation energy is defined, e.g., as: 
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         [0000]    As may be implemented with such approaches, configurations for C 2 HF and C 4 HF can be used with a nanomaterial, with all carbon sites being occupied with alternating hydrogen atoms above the surface and fluorine atoms below the surface. This configuration may be obtained, for example, using an annealing process to reduce/minimize the number of grains in the sample and maximize the piezoelectric effect. Such configurations that exhibit in-plane (e 11 ) piezoelectricity can be implemented, with both a non-zero e 11  and e 31  piezoelectric effect. Such configurations can be used with nanoelectromechanical devices such as FETs, relays and sensors, which utilize this engineered piezoelectric effect in graphene to dynamically control mechanical motion at the nanoscale level. In some embodiments, such piezoelectric devices are monolithically integrated with other electronic devices on a single piece of graphene by controlling the spatial regions that are chemically modified and endowed with piezoelectricity. For general information regarding piezoelectric structures, and for specific information regarding such structures as may be implemented in accordance with one or more example embodiments herein, reference may be made to Ong, et al., “The Effect of Hydrogen and Fluorine Coadsorption on the Piezoelectric Properties of Graphene,”  J. Phys. Chem , Jan. 18, 2013, which is fully incorporated herein by reference. 
         [0035]    Still other embodiments are directed to approaches as described herein using nanomaterials with some intrinsic piezoelectricity. For example, coupling adatoms or other materials to such nanomaterials, and/or straining such nanomaterials, can be effected to induce or set other piezoelectric characteristics. In connection with various embodiments, it has been discovered that materials such as thin sheet metals, and two-dimensional monolayer transition metal dichalcogenide (TMDC) nanoscale materials are piezoelectric, unlike their bulk parent crystals. Further, these materials can be tuned with piezoelectric characteristics in accordance with one or more approaches discussed herein, and can be used with nanoelectromechanical systems and piezotronics. For general information regarding piezoelectricity, and for specific information regarding such nanomaterials and to such nanomaterials having strain-induced piezoelectric characteristics as may be implemented with one or more embodiments (e.g., as strain-gauge type devices), reference may be made to Duerloo, et al., “Intrinsic Piezoelectricity in Two-Dimensional Materials,  J. Phys. Chem. Lett ., pp. 2871-2876 (2012) (e.g., as indicated in Table 1 therein), which is fully incorporated herein by reference. 
         [0036]    Other example embodiments are directed to a method of using an apparatus having a nanomaterial and structures coupled to the nanomaterial in order to manifest piezoelectric characteristics. In one embodiment, an electromagnetic field is applied to the nanomaterial-coupled structures to manifest piezoelectric characteristics in regions (e.g., portions) of the nanomaterial at which the structures are coupled and/or at which the field is applied. The field may, for example, be dynamically applied to modify the manifested piezoelectric characteristics (e.g., to control piezoelectric deflection and/or piezoelectric electrical characteristics). Certain embodiments involve applying strain to a material via structure-nanomaterial combinations as discussed herein, such as by applying static strain in the formation of the combination or by applying dynamic strain via the application of an electromagnetic field. 
         [0037]    Other embodiments are directed to manufacturing an apparatus with manifested piezoelectric characteristics. Structures are coupled to a nanomaterial to manifest the piezoelectric characteristics, such as by coupling non-piezoelectric structures to a non-piezoelectric nanomaterial to form a piezoelectric structure-nanomaterial combination. Certain approaches involve patterning atoms on a surface of a nanomaterial to manifest piezoelectric characteristics at the patterned portions of the nanomaterial. 
         [0038]    A variety of different materials are used in connection with various example embodiments. Example nanomaterials (e.g., as two-dimensional sheets) that can be used include Graphene, Boron Nitride (2D-hBN), Cobalt Oxide (CoO 2   − ) Molybdenum disulfide (MoS 2 ), Manganese Oxide (MnO 2 ), Niobium diselenide (NbSe 2 ), Bi 2 Sr 2 CaCu 2 O x , Bi 2 SrTa 2 O 9  Tungsten disulfide (WS 2 ), Bismuth telluride (Bi 2 Te 3 ), Molybdenum ditelluride (MoTe 2 ), Molybdenum diselenide (MoSe 2 ), Tantalum diselendie (TaSe 2 ) and Nickel ditelluride (NiTe 2 ). For general information regarding two-dimensional materials, and for more specific information regarding two-dimensional materials that may be implemented in connection with one or more example embodiments, reference may be made to Novoselov et al., Two-Dimensional Atomic Crystals, PNAS, 102, 10451 (2005), and to Coleman et al., Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials,  Science,  331, 568 (2011), both of which are fully incorporated herein by reference. 
         [0039]    Various other embodiments may be implemented in connection with Appendix A which was filed in the underlying provisional application, and the related publication entitled “Engineered Piezoelectricity in Graphene,” ACS Nano January 2012, each of which is fully incorporated herein by reference. For instance, the various materials and structures as shown in and described in the Appendix can be implemented in one or more apparatuses, devices, systems and methods as described herein. In addition, the various graphical representations of piezoelectric and other characteristics as shown in the Appendix may be manifested in connection with various embodiments. 
         [0040]    Turning now to the figures,  FIGS. 1-3B  show various apparatuses having a nanomaterial and structures coupled thereto, which manifest piezoelectric characteristics in accordance with various example embodiments. These apparatuses are exemplary of various approaches to adsorbing, doping or otherwise combining structures with a nanomaterial for the manifestation of the piezoelectric characteristics. Accordingly, a variety of different types of structures can be combined with a variety of different nanomaterials, in different manners and in different locations. Moreover, as exemplified in  FIGS. 3A and 3B , the approaches herein are amenable to implementation with monolayers of material as well as with other materials, such as two or more monolayers, laminated materials and others. 
         [0041]    Beginning with  FIG. 1 , an apparatus  100  includes a nanomaterial  110  with structures coupled thereto in a generally uniform manner. The structures, including structures  120  as labeled by way of example, are arranged on or at a surface of the nanomaterial  110  in a generally uniform manner. The apparatus  100  exhibits manifested piezoelectric characteristics, via the combination of the structures  120  with the nanomaterial. 
         [0042]    Referring to  FIG. 2 , an apparatus  200  similarly includes a nanomaterial  210  with structures that exhibit region-specific piezoelectricity. The structures include structure  220  labeled by way of example, and are arranged in groups  230 ,  232  and  234  to manifest piezoelectric characteristics in respective regions of the nanomaterial  210  at which the groups are located. The groupings are shown by way of example, and may include similar densities of structures, or disparate densities of structures to effect differing degrees of piezoelectric characteristics. 
         [0043]      FIGS. 3A-3B  show apparatuses  300  and  305  including nanomaterials having structures doped therein that manifest piezoelectric characteristics. In  FIG. 3A , a nanomaterial  310  is doped with various dopants ( 320  labeled by way of example) in different regions  330 ,  332  and  334 . In  FIG. 3B , a nanomaterial  340 , which may be implemented in layers  342  and  344  as represented by the dashed line, is also doped in different regions  360 ,  362  and  364 , with similar or different dopants ( 350  labeled by way of example). Accordingly, the respective layers  342  and  344  in  FIG. 3B  may include a laminated layer or two layers arranged to effect certain piezoelectric reactions (e.g., as described in connection with  FIGS. 6 and 7 ). By way of example, circuit nodes  372  and  374  are shown coupled via region  332 , for detecting a current-based response of the region (such an approach may be implemented with some or all piezoelectric regions as shown in the figures). In some embodiments, the nanomaterial  340  is a three-dimensional material (e.g., greater than one atom thick), with dopants therein to manifest piezoelectric characteristics as described herein. 
         [0044]    In some embodiments, one or both of the apparatuses  300  and  305  in  FIGS. 3A-3B  are apparatuses having strain-induced piezoelectric characteristics that are site specific, with the structures shown as dopants instead being implemented as strained regions of the nanomaterial  310  (e.g., where the nanomaterial is undoped). In this context, the nanomaterial  310  may also include an intrinsically piezoelectric material, with strain-induced piezoelectric characteristics at the respective regions shown as dopants (e.g., via an applied bias). 
         [0045]      FIG. 4  shows a NEMS relay apparatus  400 , in accordance with another example embodiment of the present invention. The apparatus  400  includes a NEMS relay utilizing a graphene sheet  410  having structures  412  that manifest piezoelectric characteristics. The NEMS relay includes a source  420 , drain  430  and gate  440 , with a channel region between the source and drain including n-type doped silicon dioxide (SiO 2 ) regions  450  and  452  separated by an undoped region  460  of SiO 2 . The sheet  410  is above the silicon dioxide and is configured and arranged to contract in response to an externally applied field, causing an overlap with an insulating region and turning off current flow through the relay (e.g., by selectively coupling the n-type doped regions  450  and  452 ). 
         [0046]    In one implementation, the NEMS relay apparatus  400  is operated as follows. A gate voltage is applied over the relay at the gate  440 , which applies an external electromagnetic field to the sheet  410  and which is about perpendicular to the surface of the sheet ( FIG. 4  being shown in cross-section). This applied field strains the graphene sheet in-plane, and can be applied such that the sheet contracts and no longer overlaps the n-type region  452 , for switching current off. Correspondingly, the field can be removed and in response to which the sheet  410  expands again, connecting the n-doped regions  450  and  452  and switching the relay on. This type of dynamic control is effected via the manifestation of piezoelectric characteristics in the sheet  410 , via the coupling of structures  412  thereto. 
         [0047]    In some embodiments, a plurality of NEMS relays as shown in  FIG. 6  is implemented using a single sheet  410 , with different regions of the sheet being manipulated via respective gates ( 440 ) to control the relay operation. In some implementations, different regions of the sheet are doped differently to effect relay operation at different threshold levels of voltage applied to create a field necessary to switch the relay. 
         [0048]      FIG. 5  shows a pressure sensor apparatus  500 , in accordance with another example embodiment of the present invention. The apparatus  500  includes an array  510  of pressure sensors, with one sensor shown in greater detail in inset  512 . Each pressure sensor includes a sheet such as graphene or other two-dimensional material as referenced herein, and extending between electrodes  540  and  542 . The sheet includes a plurality of structures/dopants  520  coupled to respective portions/molecules  530  within the sheet. The electrodes transfer an electrical signal to an external circuit when pressure is applied to the sheet, with the sheet being piezoelectrically responsive via the structure-molecule ( 520 - 530 ) interaction. The respective sensors in the array can be used, for example, to map out pressure patterns, or conversely, to generate pressure patterns. 
         [0049]    A 2D piezoelectric material such as boron nitride or piezoelectric graphene can be used as a pressure sensor by connecting the sheet to two electrodes that transfer an electrical signal to an external circuit when pressure is applied to the system. Multiple units of this system can be arranged in a rectangular array where each unit feels a different pressure and hence transmits different electrical signals. This facilitates mapping of pressure gradients across the sensor. 
         [0050]    In another example embodiment, an apparatus includes first and second monolayers of nanomaterial, the second monolayer being configured and arranged with the first monolayer to manifest strain characteristics via piezoelectric strain mismatch. In some implementations, the first and second monolayers include boron nitride and are oppositely aligned relative to one another. In such implementations, the first and second monolayers are responsive to an electromagnetic field by elongating in the first monolayer and contracting in the second monolayer in a direction determined by the applied electromagnetic field. 
         [0051]      FIG. 6  shows a bilayer piezoelectric structure  600 , in accordance with another example embodiment of the present invention. The structure  600  includes first and second monolayers  610  and  620  of boron nitride, respectively including alternating boron and nitrogen ( 630  and  640 , labeled by way of example). Boron nitride exhibits a honeycomb structure, such as in graphene, and exhibits in-plane linear piezoelectricity (i.e., in-plane fields generate proportional in-plane strains) as its planar form lacks inversion symmetry. When an electromagnetic field is applied along an x (armchair) direction as shown in inset  602 , a contraction or an elongation in the bilayer material is effected, depending on the relative orientations of the electromagnetic field and the relevant B-&gt;N axis. In some embodiments, two boron nitride sheets are oppositely aligned to form a bilayer that is responsive to an in-plane field along the x-direction by elongating in one sheet and contracting in the other sheet. 
         [0052]    The boron nitride interlayer bonding is such that there is an energetic preference for the boron sites to be on top of the nitrogen sites and vice versa, as shown in  FIG. 6 . This arrangement is implemented such that the bilayer as a whole will bend slightly to accommodate piezoelectric strain mismatch while preserving the relative position of the two honeycomb structures. This can be used in a variety of applications, including cantilever applications as described in connection with  FIG. 7  below. 
         [0053]      FIG. 7  shows a cantilever apparatus  700 , in accordance with another example embodiment of the present invention. The apparatus  700  includes a bilayer structure cantilever including layers  710  and  720 , respectively anchored at  712  and  722 . This bilayer structure may, for example, be implemented using a non-centrosymmetric material as shown in  FIG. 6 . The end  730  of the cantilever deflects as shown in response to an in-plane field, accommodating a mismatch in the piezoelectric equilibrium strain between the respective materials. Correspondingly, the layers  710  and  720  generate a piezoelectric response when the layers are moved as shown, facilitating the detection of such bending. 
         [0054]    The position of the tip of the bilayer cantilever can be tuned with sub-Angstrom accuracy using an applied in-plane voltage. In some implementations, a molecule is attached to the tip area  730  and carefully manipulated or even deposited on a substrate. As the cantilever is largely insensitive to vertical fields, a vertical field pulse can be used to transfer molecules on and off of the tip, giving very high versatility in addition to fine control for bottom-up nanoscale applications. 
         [0055]    In various embodiments, the respective layers  710  and  720  are made of non-piezoelectric materials such as graphene, with piezoelectric characteristics manifested therein via the addition of structures such as dopants and others described hereinabove. 
         [0056]    In another example embodiment, a sound or ultrasound generator includes a bilayer piezoelectric structure as discussed herein. The generator includes a large rectangular array of bilayer columns on a substrate in a fluid medium, and the array is subdivided into pixels respectively having a set of electrodes supplying an alternating field. Using this approach, the amplitude, frequency and phase of the (ultra)sound generated by each pixel can be spatially controlled. This facilitates the engineering of sound fields to fit a specific purpose (e.g., killing tumor cells at a predetermined location using ultrasound from a ‘sticker’ with such a BN array attached to the body). 
         [0057]    In another embodiment, a hydrocarbon vapor sensor includes a bilayer piezoelectric material. The bilayer structure deflects when molecules having sufficient momentum hit it, and this deflection is sensed. For example, heavy molecules in the air can include hydrocarbons from unwanted pipeline and engine leaks. Accordingly, the bilayer structure can be implemented as a sensor and used to detect such leaks, with the detected molecules being registered as a voltage pulse coming from the bilayer structure. 
         [0058]    Another example embodiment involving a bilayer structure includes a molecular gate. A cantilever as shown in  FIG. 7  is used to open or close an aperture through which small molecules pass. In some embodiments, the molecules passing through the aperture are counted as they bump into the cantilever. This facilitates fine control over impurity concentrations in a medium. 
         [0059]    Referring to  FIG. 8 , a planar device  800  is shown with static strain set (e.g., engineered) by selectively adsorbing or doping atoms on a graphene nanomaterial  810 . Doped region  820  (e.g., doped with hydrogen) sets a specific strain pattern. Region-specific in-plane strain and out-of-plane ripples are achieved at the boundaries between doped and undoped regions of the graphene nanomaterial  810 . Using this approach, one or more of electronic, optical and chemical properties of the graphene nanomaterial  810  can be set or manipulated, via the application of strain. For example, engineering strain in this manner can create channels, which can bias chemical reactivity for atoms or molecules on a surface of the graphene nanomaterial  810 . In some embodiments, strain is set in the graphene nanomaterial  810  via atom deposition to change the Fermi energy and density of states around the Fermi energy, which affects the nanomaterial&#39;s ability to absorb light and thus, its optical properties. 
         [0060]      FIG. 9  shows another planar device  900 , also having strain set via adsorbing and/or doping of atoms upon a graphene nanomaterial  910 . A portion  920  of the nanomaterial  910  is doped as shown, and configured to strain the nanomaterial, with ripples extending from an end region of the doped portion  920 . 
         [0061]    In some embodiments, dynamical changes in strain are achieved through a piezoelectric effect, using the dopants as shown in one or both of  FIGS. 8 and 9 . The piezoelectric properties manifested by several varieties of doped nanomaterials can be used for fast mechanical switching of optical properties. In one embodiment, slabs of nanomaterial are controlled by an electromagnetic field and therein moved in and out of an optical path, modulating the amplitude and phase of passing light waves. In another embodiment, several parallel non- or weakly interacting layers are used to develop a periodic Moiré pattern upon application of a field, thereby effectively creating a diffraction grating that can be used for various applications, such as for spectral operations upon an image. In addition, while the approaches shown in  FIGS. 8 and 9  refer to graphene, various embodiments are directed to similar approaches using nanomaterials other than graphene. 
         [0062]    Another embodiment is directed to optical sensing. A sheet of nanomaterial is rendered optically active by selective absorption of atoms on a very specific site on one side of the nanomaterial, and another side of the nanomaterial (e.g., an opposing side of a nanomaterial sheet) is piezoelectrically doped. The piezoelectric effect is configured and arranged to provide an optically active zone on the sheet that can be scanned very finely across a surface, and therein providing a near-field optical sensor. 
         [0063]    While various aspects of the present invention are amenable to modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in further detail. It should be understood that the intention is not to limit the invention and disclosure herein to the particular embodiments and/or applications described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.