Abstract:
An apparatus ( 200 ) comprising: a first electrode ( 204 ), wherein the first electrode comprises at least one layer of graphene; a second electrode ( 208 ); and a layer of piezoelectric material ( 206 ) disposed between the first electrode ( 204 ) and the second electrode ( 208 ), wherein the piezoelectric material ( 206 ) is able to resonate at a resonant frequency in response to application of an oscillating electrical signal to the first or second electrode ( 204, 208 ).

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates to a piezoelectric resonator. 
       BACKGROUND TO THE INVENTION 
       [0002]    Many modern devices contain oscillators and filters for producing and isolating high frequency signals. These components find widespread application in devices which receive and transmit radio frequency signals. It is also well known to use quartz crystal oscillators to produce accurate clock signals. 
       SUMMARY OF THE INVENTION 
       [0003]    A first aspect of the invention provides an apparatus comprising:
       a first electrode, wherein the first electrode comprises at least one layer of graphene;   a second electrode; and   a layer of piezoelectric material disposed between the first electrode and the second electrode, wherein the piezoelectric material is able to resonate at a resonant frequency in response to application of an oscillating electrical signal to the first or second electrode.       
 
         [0007]    The apparatus may further be configured to change a voltage bias applied to the first electrode. 
         [0008]    The first electrode may be comprised of a single layer of graphene or of multiple layers of graphene. In addition the second electrode may be comprised of at least one layer of graphene. The resonant frequency may be a radio frequency. 
         [0009]    The apparatus may further comprise a radio frequency signal input and a voltage bias input. 
         [0010]    The apparatus may be incorporated in an integrated circuit. The integrated circuit may be incorporated in a circuit board. The integrated circuit or circuit board may be incorporated in a portable device 
         [0011]    A second aspect of the invention provides a method comprising:
       providing a first electrode, wherein the first electrode comprises at least one layer of graphene;   providing a second electrode; and   providing a layer of piezoelectric material disposed between the first electrode and the second electrode, wherein the piezoelectric material is able to resonate at a resonant frequency in response to application of an oscillating electrical signal to the first or second electrode.       
 
         [0015]    The method may further comprise providing means for changing a voltage bias applied to the first electrode. 
         [0016]    A third aspect of the invention provides a method of operating a device, the method comprising:
       applying an oscillating electrical signal to apparatus comprising a first electrode, the first electrode comprising at least one layer of graphene, a second electrode, and a layer of piezoelectric material disposed between the first electrode and the second electrode, such as to cause the piezoelectric material to resonate at a resonant frequency; and   changing a bias voltage applied to the apparatus.       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]    Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: 
           [0020]      FIG. 1  is a graph showing the dependence of the capacitance of a graphene capacitor on voltage; 
           [0021]      FIG. 2  shows a piezoelectric resonator according to exemplary embodiments of the invention; 
           [0022]      FIG. 3  is a circuit model of the piezoelectric resonator of  FIG. 2 ; 
           [0023]      FIG. 4  is a circuit model showing the piezoelectric resonator of  FIG. 2  in an exemplary implementation; and 
           [0024]      FIG. 5  is a schematic illustration of an exemplary portable device containing the resonator of  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0025]    Graphene is a material formed of a single layer of tightly packed carbon atoms. As graphene is a planar sheet of atomic thickness, it can be considered as a two dimensional or quasi two dimensional material. Graphite and other graphitic materials are formed of many stacked layers of graphene. Although the structure of graphite has been extensively studied, the isolation of individual graphene sheets was only achieved in the last few years. Graphene sheets can be produced by the exfoliation of graphite, either mechanically or by using liquid phase solvents. Graphene can also be produced by epitaxial growth on a wide range of substrates. Early attempts at isolating graphene produced low yields of monolayer graphene, with most of the graphene produced being multilayered. More advanced techniques are being developed and it is now possible to produce graphene films which are predominantly monolayer and to produce bi-layer and tri-layer graphene sheets. Recently, very large (˜0.5 m×0.5 m), predominantly monolayer graphene films have been grown on copper substrates and transferred to flexible target substrates. 
         [0026]    Graphene has been found to have remarkable electronic and mechanical properties, including very high electron mobility levels and very low resistivity at room temperature. If graphene is incorporated into an electrode of a capacitor, a contribution to the total capacitance can be observed due to the electronic compressibility of graphene. This contribution is often referred to as the “quantum capacitance” and is a direct measure of the density of state at the Fermi energy. An expression which is often used to define the quantum capacitance is C q =e 2 D, where e is the electron charge and D is the density of states. The quantum capacitance is inversely proportional to the effective mass of electrons and holes in a material and so materials with a relatively high electron (and hole) mobility will have a relatively large quantum capacitance. Graphene has a Dirac-like electronic spectrum, meaning that electrons and holes have an effective mass close to zero. Because of this, the quantum capacitance of graphene is very high. 
         [0027]    In most two dimensional systems, the quantum capacitance is usually a small, constant value. In graphene however, the density of state is a strong function of the Fermi energy. If a voltage is applied to graphene, a change in the Fermi level results, which in turn produces a change in the density of states. Referring to  FIG. 1 , a graph  100  is shown which illustrates the dependence of the capacitance of a graphene capacitor on the voltage difference applied across the capacitor. The axis scales are shown for illustrative purposes only. The change in total capacitance observed is due to the changing value of the quantum capacitance of the graphene. At zero applied voltage, the capacitor has a capacitance which is a product of the geometric electrostatic capacitance and the quantum capacitance. As the applied voltage is varied, the change in the quantum capacitance contribution produces pronounced changes in the total capacitance. 
         [0028]    As described above, graphene is formally defined as a two dimensional monolayer of carbon atoms. However, in reality a manufactured sheet or film of graphene may contain regions of multilayered graphene. Imperfect graphene sheets may still exhibit the same electronic properties such as quantum capacitance required to put the claimed invention into effect. This is particularly the case with epitaxially grown graphene in which areas of multilayered graphene do not have their lattices aligned and therefore continue to behave as individual layers. As such, use of the term “graphene” is intended to encompass not only perfect monolayer graphene but also imperfect sheets of graphene having a sufficient level of electronic compressibility. 
         [0029]    Resonators are common electrical components used in many modern devices and applications. Resonators are extensively used in radio frequency applications. Electrical resonators may take the form of an LC or RLC circuit. Alternatively, a resonator may comprise a piezoelectric material sandwiched between parallel plate electrodes. A piezoelectric material oscillates when subjected to an electric field and conversely will produce an electric field when a force is applied to it. A resonator including piezoelectric material resonates at an oscillation frequency that depends on a number of aspects of the configuration of the resonator. Crystals such as quartz are commonly used as the piezoelectric material in resonators. 
         [0030]    Electrical tuning of the output frequency of a resonator is possible using a variable capacitor, often termed a varactor or varactor diode. A varactor usually takes the form of a reversed biased diode (possibly coupled with other circuit components) and is connected in parallel or series with the crystal electrodes. A varactor is responsive to a change in a bias voltage to cause a change in the load capacitance. A change in the load capacitance of the varactor causes a change in the resonating frequency of the piezoelectric resonator. Many voltage tunable piezoelectric resonators are “off chip” components due to the difficulty of integrating mono crystal piezoelectric materials in CMOS fabrication processes. These resonators are therefore bulky and expensive. Some techniques are being developed for integrating polycrystalline piezoelectric materials into CMOS processes allowing the fabrication of “on chip” resonators. However these resonators are expensive to produce, only polycrystalline material can be used, and the resulting resonator occupies a relatively large area of the chip. 
         [0031]    Referring now to  FIG. 2 , a structural representation of a resonator  200  embodying aspects of the present invention is shown. The resonator  200  comprises a substrate  202 . Formed on top of the substrate are a lower electrode  204 , a piezoelectric layer  206  and an upper electrode  208 . The resonator  200  may have a number of other standard component parts which are not shown for simplicity and clarity. 
         [0032]    In some embodiments, the lower electrode  204  is formed of graphene and the upper electrode  208  is made of a metallic material. A wide range of metallic materials may be used to form the upper electrode  208 . In some embodiments, the upper electrode  208  is made of Aluminium. 
         [0033]    In some embodiments, the graphene is produced by epitaxial growth on a substrate. The substrate on which the graphene is grown may be the substrate  202 , or the graphene may be transferred to the substrate  202  from a different growth substrate (not shown). 
         [0034]    The piezoelectric layer  206  is disposed between the lower electrode  204  and the upper electrode  208 , which form a parallel plate structure. When an alternating current is applied to one of the electrodes  204 ,  208  an alternating voltage difference across the parallel plate structure is produced and the piezoelectric layer  206  undergoes resonance. The frequency at which the piezoelectric layer  206  resonates depends on the type of piezoelectric material used. Quartz is the most commonly used piezoelectric crystal, however any other suitable substances may instead be used, for example lithium and gallium based crystals. 
         [0035]    Piezoelectric resonators have a dedicated circuit symbol (see item  200  in  FIG. 4 ). However they are often represented by an equivalent circuit so that their function may be better understood. Referring now to  FIG. 3 , a circuit equivalent model  300  of a piezoelectric resonator embodying some aspects of the present invention is shown. The model  300  has a series inductor  302 , a series capacitor  304 , a series resistor  306 , a parallel capacitor  308  and a quantum capacitor  310 . The model also shows an input  312  and an output  314 . The series inductor  302 , the series capacitor  304  and the series resistor  306  are connected in series between the input  312  and the output  314 . The parallel capacitor  308  and quantum capacitor  310  are shown connected in series with each other between the input  312  and the output  314  and are connected in parallel with the three other components. The branch containing the series inductor  302 , the series capacitor  304  and the series resistor  306  is called the series branch and the branch containing the parallel capacitor  308  and the quantum capacitor  310  is called the parallel branch. 
         [0036]    The piezoelectric resonator can be modelled in this way because many piezoelectric materials have two modes of resonance; a series resonance and a parallel resonance relating to the series and parallel branches respectively. In order for this model to be valid, the series capacitor  304  must have a much smaller capacitance than the parallel capacitor  308  and the quantum capacitor  310  combined. The parallel capacitor  308  represents the geometrical electrostatic capacitance of the piezoelectric layer  206 . The quantum capacitor  310  represents the quantum capacitance component due to the electronic compressibility of graphene. The quantum capacitor  310  is shown as a variable capacitor element due to the variable nature of the quantum capacitance of graphene under an external voltage bias. 
         [0037]    The parallel resonant frequency of the piezoelectric resonator  200  exemplified by  FIGS. 2 and 3  can be tuned by changing the value of the capacitance of the system. This is achieved by changing a voltage bias applied to the electrodes of the resonator  200  when operating the resonator  200  at parallel resonance. The piezoelectric resonator  200  has a parallel plate structure as described above with reference to  FIG. 2 . This results in the resonator  200  having an intrinsic load capacitance. However, because one of the electrodes of the resonator  200  is made of graphene, there is a significant contribution to the total capacitance from the quantum capacitance of the graphene such that varying this contribution has a significant effect on the total capacitance. 
         [0038]    An advantage of the resonator  200  exemplified by  FIGS. 2 and 3  is that the function of tunability is built into the resonator itself. The resonator  200  is intrinsically tunable due to the property of quantum capacitance exhibited by graphene. Thus a tunable resonator can be manufactured which occupies a very small area of a chip, and can be said to be highly integratable. Experiments indicate that the resonator  200  has a pulling range and tuning voltage range similar to that of current varactor-coupled tunable resonators, even at normal operating temperatures. These experiments also indicate that the resonator  200  has a comparable level of integration to resonators where a physical constant of the piezoelectric layer is controlled by the application of a voltage, although the pulling range and tuning voltage range of the resonator  200  is far superior. 
         [0039]      FIG. 4  shows an exemplary circuit  400  embodying some aspects of the present invention. The circuit  400  of  FIG. 4  has a first input  402 , a second input  404  and an output  412 . Both the first and second inputs  402 ,  404  are coupled to a first electrode of the piezoelectric resonator  200 . The output  412  is coupled to the second electrode of the piezoelectric resonator  200 . A capacitor  406  is located on the first input  402 . An inductor  408  is located on the second input  404 . A connection to ground  410  is coupled to the output  412 . A grounded inductor  414  is located between the output  412  and the connection to ground  410 . 
         [0040]    The piezoelectric resonator  200  requires an oscillating input signal in order for the piezoelectric layer  206  to resonate. An oscillating signal is applied via the first input  402 . This signal may be generated in any suitable way, for example by a signal generator. The oscillating signal is preferably a radio frequency signal of approximately the same frequency as the resonating frequency of the piezoelectric layer  206 . The capacitor  406  acts as a low frequency block. This results in a cleaner oscillating signal reaching the resonator  200 . The capacitor  406  could instead be replaced or augmented by a more complex high-pass filter arrangement. 
         [0041]    A direct current (DC) signal or low frequency alternating current (AC) signal is applied via the second input  404 . The inductor  408  acts as a high frequency choke. This ensures that the oscillating signal applied to the first input  402  is not passed to components attached to the second input  404 . The inductor  408  could instead be replaced or augmented by a more complex low pass filter arrangement. The voltage bias used to control the quantum capacitance of the graphene electrode is received at the second input  404  signal. 
         [0042]    When the oscillating signal and the DC or low frequency AC signal are applied to the resonator  200  via the first and second inputs  402  and  404  respectively, the piezoelectric layer  206  is caused to resonate. The resonant frequency, which is the frequency at which the piezoelectric layer  206  oscillates, is dependent on the load capacitance of the resonator  200 . If the load capacitance is increased, the resonant frequency is pulled downwards. If the load capacitance is decreased, the resonant frequency is pulled upwards. The resonator  200  therefore produces an oscillating signal which is output through the output  412 . The grounded inductor  414  and connection to ground  410  provides grounding for low frequency or DC signals. The grounded inductor  414  acts as a radio frequency choke, ensuring that the radio frequency signals are output through the output  412 . 
         [0043]    The circuit  400  may also include control electronics (not shown) for receiving instruction to alter the output signal frequency and controlling the voltage bias applied to the resonator  200 . 
         [0044]    The piezoelectric resonator  200  could be considered to operate like a high quality filter. An oscillating signal having a relatively high bandwidth (low Q factor) is input via the first input  402 . The piezoelectric layer  206  resonates with a high Q factor, producing an output signal with a much lower bandwidth. In addition, this high quality output signal is tunable as described above. In some embodiments (not shown), two or more resonators may be used in combination. 
         [0045]    In some embodiments, both the lower and upper electrodes  204 ,  208  of the piezoelectric resonator  200  are made of graphene. This may increase the amount by which the quantum capacitance changes in response to a change in the applied voltage bias and therefore the range over which the resonating frequency can be pulled. In some embodiments, the graphene electrodes may be made of multilayer graphene having, for example, two or three layers of graphene. Such multilayered graphene has some different electronic properties such as an increased conductivity; however it retains many of its original properties. Due to current epitaxial graphene growth techniques, the hexagonal lattices of upper and lower layers are randomly orientated, allowing the layers to behave independently. 
         [0046]      FIG. 5  shows a schematic of an exemplary portable device  500  in which the resonator  200  is utilised. The portable device  500  comprises a controller  502 , a signal generator  504  and a power generator  506 . The controller  502  is connected to the signal generator  504  and the power generator  506  in order to control the outputs thereof. The portable device  500  also comprises a circuit board  508 . The circuit board  508  has disposed thereon a radio frequency integrated circuit  510  and a baseband processor  512 . Located on the radio frequency integrated circuit  510  are the piezoelectric resonator  200  and radio frequency circuits  514 . The portable device  500  may contain many other components which are not shown for reasons of clarity. 
         [0047]    The piezoelectric resonator  200  is configured to produce a radio frequency output signal as described above. This signal is passed to other components on the radio frequency integrated circuit  510 , represented by radio frequency circuits  514 . The radio frequency circuits  514  uses the signal created by the resonator  200  to produce baseband signals, which are passed to the baseband processor  512 . The radio frequency circuits  514  may be any combination of suitable components configured to perform a variety of tasks. 
         [0048]    An oscillating electrical signal input is applied by the signal generator  504  to the resonator  200 . A DC or low frequency AC voltage bias is applied by the power generator  506  to the resonator  200 . The controller  502  is configured to control the power generator  506  to change the applied bias voltage. The controller  502  may also be configured to control the signal generator  504  to change the frequency of the applied oscillating signal. The portable device  500  may have some feedback means (not shown) so that the controller  502  may monitor the voltage bias and oscillating signal being applied to the resonator  200  and to monitor the output from the resonator  200 . 
         [0049]    Resonators  200  as described above are implemented in voltage controlled oscillators in some embodiments and in tunable filters in other embodiments. 
         [0050]    It will be appreciated that the above described embodiments are purely illustrative and are not limiting on the scope of the invention. Other variations and modifications will be apparent to persons skilled in the art upon reading the present application. Moreover, the disclosure of the present application should be understood to include any novel features or any novel combination of features either explicitly or implicitly disclosed herein or any generalization thereof and during the prosecution of the present application or of any application derived therefrom, new claims may be formulated to cover any such features and/or combination of such features.