Abstract:
A device comprising a nanotube configured as a resonator, a source electrode, a gate electrode, a drain electrode and at least one impeding element, wherein the at least one impeding element is configured to minimize energy loss due to a contact resistance between at least the source electrode and the nanotube.

Description:
FIELD OF THE INVENTION 
     The invention relates to a device including a nanotube electrode, and to a method of making such a device. 
     BACKGROUND TO THE INVENTION 
     Nanotube devices are known for use in various electrical applications. Since their operation depends on mechanical movement, nanotube devices can be termed NanoElectroMechanical (NEMS) structures. 
     It is desirable to use carbon nanotubes in tuneable radio frequency (RF) filter technologies, as this could potentially be the main enabler for software-defined and cognitive radio hardware. 
     WO 03/078305 describes a carbon nanotube device which can be used as a filter. 
     SUMMARY 
     A first aspect of the invention provides a device comprising a nanotube configured as a resonator, a source electrode, a gate electrode, a drain electrode and at least one impeding element, wherein the at least one impeding element is configured to minimize energy loss due to a contact resistance between at least the source electrode and the nanotube. 
     A device thus constructed can result in a reduction in Q-factor degradation. 
     The impeding element may be a layer of solid insulating material, and a first end portion of the nanotube may be fixed to the source electrode via the layer of solid insulating material, the layer of solid insulating material being interposed between the nanotube and the source electrode. 
     The nanotube, the source electrode, the gate electrode and the drain electrode may be arranged such that a second end portion of the nanotube extends from the source electrode above the gate electrode and the drain electrode. 
     The nanotube may be in first capacitive contact with the source electrode, in second capacitive contact with the gate electrode and in third capacitive contact with the drain electrode, wherein the capacitance of the first capacitive contact is greater than the capacitance of the second and third capacitive contacts. 
     Alternatively, the at least one impeding element may comprise a first layer of solid insulating material and a second layer of solid insulating material, and wherein a first end portion of the nanotube may be fixed to the source electrode via the first layer of solid insulating material, the first layer of insulating material being interposed between the first end portion of the nanotube and the source electrode, and a second end portion of the nanotube may be fixed to the drain electrode via the second layer of solid insulating material, the second layer of insulating material being interposed between the second end portion of the nanotube and the drain electrode. 
     The nanotube, the source electrode, the gate electrode and the drain electrode may be arranged such that a middle portion of the nanotube, between the first and second end portions, bridges a gap between the source electrode and the drain electrode, the middle portion of the nanotube being positioned generally above the gate electrode. 
     The nanotube may be in first capacitive contact with the source electrode, in second capacitive contact with the gate electrode and in third capacitive contact with the drain electrode, wherein the capacitances of the first capacitive contact and the third capacitive contact are greater than the capacitance of the second capacitive contact. 
     Alternatively, the at least one impeding element may comprise an inductive element, the inductive element being connected in series with the source electrode. 
     The nanotube may be arranged such that a first end portion of the nanotube is in contact with a surface of the source electrode and a second end portion of the nanotube extends from the source electrode generally above the gate electrode and the drain electrode. 
     Alternatively, the at least one impeding element may comprise a first inductive element and a second inductive element, wherein the first inductive element is connected in series with the source electrode, and the second inductive element is connected in series with the drain electrode. 
     The nanotube may be arranged such that a first end portion of the nanotube is in contact with a surface of the source electrode and a second end portion of the nanotube is in contact with a surface of the drain electrode, and a middle portion of the nanotube, between the first and second end portions, bridges a gap between the source electrode and drain electrode, the middle portion of the nanotube being positioned generally above the gate electrode. 
     The source electrode, gate electrode and the drain electrode may be located on a surface of a substrate and the gate electrode may be located generally between the source electrode and the drain electrode. 
     The device may have a resonant frequency, the resonant frequency being changeable by applying a bias voltage to the gate electrode. 
     According to a second aspect of the invention, a device is provided, the device comprising a nanotube configured as a resonator, a source electrode, a gate electrode, and a drain electrode, wherein a first end portion of the nanotube is fixed to the source electrode via an interposed layer of solid insulating material. 
     The nanotube, the source electrode, the gate electrode and the drain electrode may be arranged such that a second end portion of the nanotube extends from the source electrode generally above the gate electrode and the drain electrode. 
     The nanotube may be in first capacitive contact with the source electrode, in second capacitive contact with the gate electrode and in third capacitive contact with the drain electrode, wherein the capacitance of the first capacitive contact is greater than the capacitance of the second and third capacitive contacts. 
     Alternatively, the first end portion of the nanotube may be fixed to source electrode via a first layer of solid insulating material and a second end portion of the nanotube may be fixed to the drain electrode via a second layer of interposed solid insulating material. 
     The nanotube, source electrode, the gate electrode and the drain electrode are arranged such that a middle portion of the nanotube, between the first and second end portions, bridges a gap between the source electrode and the drain electrode, the middle portion of the nanotube being positioned generally above the gate electrode. 
     The nanotube may be in first capacitive contact with the source electrode, in second capacitive contact with the gate electrode and in third capacitive contact with the drain electrode, wherein the capacitances of the first capacitive contact and the third capacitive contact are greater than the capacitance of the second capacitive contact. 
     The source electrode, the gate electrode and the drain electrode may be located on a surface of a substrate. 
     The gate electrode may be located generally between the source electrode and the drain electrode. 
     The device may have a resonant frequency, the resonant frequency being changeable by applying a bias voltage to the gate electrode. 
     According to a third aspect of the invention, a device is provided, the device comprising a nanotube configured as a resonator, a source electrode, a gate electrode and a drain electrode wherein the source electrode is in series connection with an inductive element. 
     A first portion of the nanotube may be in contact with a surface of the source electrode and the source electrode, the gate electrode and the drain electrode are arranged such that a second end portion of the nanotube extends from the source electrode generally above the gate electrode and the drain electrode. 
     Alternatively, the device may further comprise an inductive element in series connection with the drain electrode. 
     The nanotube may be arranged such that a first end portion of the nanotube is in contact with a surface of the source electrode and a second end portion of the nanotube is in contact with a surface of the drain electrode, and a middle portion of the nanotube, between the first and second end portions, bridges a gap between the source electrode and drain electrode. 
     The may further comprise a substrate, wherein the source electrode, the gate electrode and the drain electrode are located on a surface of the substrate. 
     The gate electrode may be located generally between the source electrode and the drain electrode. 
     The device may have a resonant frequency, the resonant frequency being changeable by applying a bias voltage to the gate. 
     Any of the above aspects of the invention may be incorporated into tuneable filtering device, a voltage-controlled oscillator or a mobile terminal. 
     According to a fourth aspect of the invention a method may be provided, the method, comprising providing a substrate, forming, on the substrate, a source electrode, a gate electrode and a drain electrode forming a layer of solid insulating material in contact with a surface of the source electrode and fixing an end portion of a nanotube to an opposite surface, to that in contact with the source electrode, of the layer of solid insulating material. 
     Forming the electrodes may comprise forming the gate electrode generally between the source electrode and the drain electrode. 
     Fixing an end portion of a nanotube, may further comprise fixing a first end portion of the nanotube to the layer of solid insulating material, a second end portion of the nanotube extending generally above the gate electrode and the drain electrode. 
     Alternatively, the method further comprises forming a second layer of solid insulating material in contact with a surface of the drain electrode, and fixing an opposite end portion of the nanotube to an opposite surface, to that in contact with the drain electrode, of the second layer of solid insulating material. 
     Fixing the nanotube may comprise growing the nanotube on the layer of insulating solid material from seed. 
     According to a fifth aspect of the invention, a method is provided, the method comprising providing a substrate, forming, on the substrate, a source electrode, a gate electrode and a drain electrode, connecting an inductive element to the source electrode and fixing an end portion of a nanotube to a surface of the source electrode. 
     Forming the electrodes may comprise forming the gate electrode generally between the source electrode and the drain electrode. 
     Fixing an end portion of a nanotube, may further comprise fixing a first end portion of the nanotube to the source electrode, a second end portion of the nanotube extending generally above the gate and drain electrodes. 
     Alternatively, the method may further comprise connecting a second inductive element to the drain electrode and fixing an opposite end portion of the nanotube to a surface of the drain electrode. 
     Fixing the nanotube comprises growing the nanotube on the source and drain electrodes from seed. 
     According to a sixth aspect of the invention, a method of operating a device according to the third aspect is provided, the method comprising applying a reverse voltage pulse to one of the gate and the drain electrode before the expiration of a time period, the time period being a charge relaxation time of the device. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic side-view of a singly-clamped nanotube device; 
         FIG. 2  is a schematic side-view of a doubly-clamped nanotube device; 
         FIG. 3  is a circuit element to which the device of  FIG. 1  can be approximated; 
         FIG. 4  is a circuit element to which the device of  FIG. 2  can be approximated; 
         FIG. 5  is a schematic side-view of a first embodiment of the invention; 
         FIGS. 6   a  and  6   b  are circuit elements to which the device of  FIG. 5  can be approximated; 
         FIG. 7  is a schematic side-view of a second embodiment of the invention; 
         FIGS. 8   a  and  8   b  are circuit elements to which the device of  FIG. 7  can be approximated; 
         FIG. 9  is a flow chart illustrating a method of producing the devices of  FIGS. 5 and 7 ; 
         FIG. 10  is a schematic side-view of a third embodiment of the invention; 
         FIG. 11  is a circuit element to which the device of  FIG. 10  can be approximated; 
         FIG. 12  is a schematic side-view of a fourth embodiment of the invention; 
         FIG. 13  is a circuit element to which the device of  FIG. 12  can be approximated; 
         FIG. 14  is a flow chart illustrating a method of producing the devices of  FIGS. 10 and 12 ; 
         FIG. 15  is a schematic side-view of the third embodiment of the invention experiencing stiction; 
         FIG. 16  is a schematic side-view of a fourth embodiment of the invention experiencing stiction; 
         FIG. 17  is a diagram illustrating a radio receiver incorporating the devices of either of  FIG. 5 ,  7 ,  10  or  12 ; and 
         FIG. 18  is a diagram illustrating an alternative radio receiver incorporating the devices of either of  FIG. 5 ,  7 ,  10  or  12 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a schematic of a side-view of a singly-clamped nanotube device of the type that may be used in tuneable RF filter technologies. The device comprises a substrate  10 , on which are formed a source electrode  11 , a gate electrode  12  and a drain electrode  13 , the gate electrode  12  being formed generally between the source and drain electrodes  11 ,  13 . Typically, the electrodes are metal. The source electrode  11  has a tall profile compared to those of the gate and drain electrodes. Alternatively, the substrate  10  may comprise an end portion of having a greater thickness than the remainder of the substrate, whereby the source electrode  11  is located on the end portion having greater thickness. Fixed to a surface of the source electrode  11  is a carbon nanotube  14 , the carbon nanotube  14  being in mechanical and electrical contact with the source electrode  11 . The carbon nanotube  14  extends parallel to the substrate  10  and extends generally above the drain and gate electrodes  13 ,  12 . The carbon nanotube  14  is mounted as a supported cantilever generally above the gate and drain electrodes  12 ,  13 . A time-varying voltage applied to the gate electrode  12  causes oscillation of the carbon nanotube  14  in a direction generally parallel to the direction from the nanotube  14  to the substrate  10 , as indicated by arrows A. 
       FIG. 2  is a schematic side-view of a doubly-clamped nanotube device. The device comprises a substrate  20 , upon which are formed a source electrode  21  and a drain electrode  22 , each having the same profile. Also formed on the substrate is a gate electrode  23 . The gate electrode  23  may have a relatively shorter profile than the source and drain electrodes  21 ,  22 , and may be formed generally between the source and drain electrodes  21 ,  22 . Fixed to an uppermost surface of the source electrode  21  is a first end portion of a carbon nanotube  24 , the carbon nanotube  24  being in mechanical and electrical contact with the source electrode  21 . Fixed to an uppermost surface of the drain electrode  22  is a second end portion of the carbon nanotube  24 , the carbon nanotube  24  being in mechanical and electrical contact with the drain electrode  22 . The source, drain and gate electrodes  21 ,  22 ,  23  are arranged on the substrate  20  such that a middle portion of the carbon nanotube  24  is suspended above the gate electrode  23 . When an RF signal is applied to the gate electrode  23 , oscillations of the nanotube  24 , in a direction generally parallel to the direction from the nanotube  24  to the gate electrode  23 , as indicated by arrows A, are induced. The oscillation of the nanotube  24  may be detected using capacitive transduction. Alternatively the nanotube  24  may act as a gate for a field-effect transistor or some other means of displacement detection. 
     It is known that one of the problems with the devices shown in  FIGS. 1 and 2  is that of contact resistance between the metal electrodes in direct contact with the nanotube. The contact resistance between metals and carbon nanotubes is a result of Schottky Barrier behaviour caused by surface van Der Waals interactions which create an effective insulating layer between the surfaces of a metal and a nanotube. The theoretical minimum contact resistance between a single-walled carbon nanotube and a metal is h/4e 2  which is equal to about 6.5 KΩ. This can be reduced if the single-walled nanotube is replaced with a multi-walled nanotube, whereby the theoretical minimum is 6.5 kΩ/N, where N is the number of shells of the multi-walled nanotube in contact with the metal electrode. Currently, the best reported contacts between nanotubes and metals have a resistance in the region of 5 to 10 kΩ. (see. Applied Physics Letters 88 053118). 
     It is possible to approximate the device of  FIG. 1  to a circuit element as shown in  FIG. 3 . The circuit element comprises the source electrode  11  in connection with a resistive element  31 , the resistive element  31  being due to the contact resistance between the source electrode  11  and the nanotube  14 . In connection with the resistive element  31  is the nanotube  14 . In a parallel connection with the nanotube  14  is a first capacitive element  32 , the first capacitive element  32  being due to a capacitive contact between the nanotube  14  and the gate electrode  12 . In a series connection with the nanotube  14  is a second capacitive element  33 , the second capacitive element  33  being due to the capacitive contact between the nanotube  14  and the drain electrode  13 . 
     The capacitive elements  32 ,  33  arise as a result of a capacitive contact, due to the presence of insulating layers, between the nanotube  14  and the gate and drain electrodes  12 ,  13 . The insulating layers result from the separation of the nanotube  14  and the gate and drain electrodes  12 ,  13 . 
     Similarly, it is possible to approximate the device of  FIG. 2  to a circuit element as shown in  FIG. 4 . The circuit element comprises, connected in series, the source electrode  21 , a first contact resistance  41  (due to the contact between the nanotube  24  and the source electrode  21 ), the nanotube  24 , a second contact resistance  42  (due to the contact between the nanotube  24  and the drain electrode  22 ) and the drain electrode  22 . The circuit element further comprises a capacitive element  43 , connected in parallel to the nanotube  24 , which arises from the capacitive contact between the nanotube  24  and the gate  23 . 
     For electronic applications, contact resistances  31 ;  41 ,  42  are a serious drawback as they lead to losses. For resonator structures, such as these, where the tube performs mechanical oscillations at RF-frequencies this loss manifests itself not only as heat but also as mechanical damping, thereby significantly reducing the resonator Q-factor. 
     As the nanotube  14 ;  24  oscillates, in order to maintain charge equilibrium, an accompanying AC current flows through the contact resistance  31  (or resistances  41 ,  42 ). Typically electronic relaxation times of such a device (also known as the RC-time) are much smaller than the characteristic vibration period. Therefore, the electronic relaxation can be thought of as instantaneous on the time scale of mechanical motion. The dissipation caused by the AC current flowing through the contact resistance  31  (or resistances  41 ,  42 ) acts as a damping force on the nanotube  14 ;  24  motion and degrades the resonator Q factor. 
     Until now, efforts have primarily been focused on minimizing the contact resistance between the electrodes and the nanotube. However, as was discussed earlier, there is still a theoretical minimum contact resistance, which is yet to have been achieved, beyond which the contact resistance cannot be reduced. 
       FIG. 5  is a schematic side-view of a singly-clamped nanotube device according to a first embodiment of the invention. The device  5  comprises a substrate  50 , on which are formed a source electrode  51 , a gate electrode  52  and a drain electrode  53 , the gate electrode  52  being formed generally between the source and drain electrodes  51 ,  53 . The substrate may comprise any non-conductive material upon which electrodes can be formed, such as high-resistive silicon. Typically, the electrodes are metal, generally one of aluminium, gold and copper. The heights of the gate and drain electrodes may be of the order of 10 nm, with the widths being approximately 50-100 nm. The source electrode  51  may have a relatively tall profile compared to those of the gate and drain electrodes  52 ,  53 . Alternatively, the substrate  50  may comprise an end portion having a greater thickness than the remainder of the substrate, whereby the source electrode  51  is located on the end portion having greater thickness. Coupled to a surface of the source electrode is a layer of insulating material  55 . Typically, this layer  55  may be a thin layer of solid insulating material, for example glass (SiO 2 ). Coupled to an opposite surface, to that coupled to the source electrode  51 , of the layer of insulating material  55  is an end portion of a carbon nanotube  54 . The carbon nanotube  54  extends parallel to the substrate  50  and extends generally above the drain and gate electrodes  53 ,  52 . The carbon nanotube  54  may be approximately 10 nm above the gate and drain electrodes  52 ,  53 . The carbon nanotube  54  is mounted as a supported cantilever generally above the gate and drain electrodes  52 ,  53 . Typical carbon nanotube lengths are in the range of 0.1 μm-1 μm. Typically the carbon nanotubes are multi-walled nanotubes; however, both single walled nanotubes and clusters of attached nanotubes may also be used. A time-varying voltage applied to the gate electrode  52  causes oscillation of the carbon nanotube  54  in a direction generally parallel to the direction from the nanotube to the substrate, as indicated by arrows A. 
     According to this embodiment, the contact resistance, which usually exists between a metal and a nanotube, has been replaced by the layer of insulating material  55 , thereby forming a capacitive contact between the source electrode  51  and the nanotube  54 . 
     The device  5  of  FIG. 5  may be approximated to a circuit element as shown in  FIG. 6   a . The circuit element comprises the source electrode  51  in connection with a first capacitive element  61 , the first capacitive element  61  being due to the capacitive contact between the source electrode  51  and the nanotube  54 . In series connection with the first capacitive element  61  is the nanotube  54 . In a parallel connection with the nanotube  54  is a second capacitive element  62 , the second capacitive element  62  being due to a capacitive contact between the nanotube  54  and the gate electrode  52 . In a series connection with the nanotube  54  is a third capacitive element  63 , the third capacitive element  63  being due to the capacitive contact between the nanotube  54  and the drain electrode  53 . 
     The first capacitive element  61  is formed as a result of capacitive contact between the source electrode  51  and the nanotube  54  via the thin layer of insulating material  55 . The capacitive elements  62 ,  63  arise as a result of capacitive contact, due to the presence of an insulating layer, between the nanotube  54  and the gate and drain electrodes  52 ,  53 . The insulating layer results from the separation of the nanotube  54  and the gate and drain electrodes  52 ,  53 . 
     According to the first embodiment of the invention, the problems with Q-factor degradation as a result of dissipative loss are eliminated because the layer of insulating material  55 , between the source electrode  51  and the nanotube  54 , prevents dissipative currents from flowing. 
     Ideally, the capacitance of the first capacitive element  61 , resulting from capacitive contact between the source electrode  51  and the nanotube  54  via the layer of insulating material  55 , should be much greater than the capacitance of the second and third capacitive elements  62 ,  63 . This may be achieved relatively easily because the capacitance of a capacitive element is as follows: 
             C   ∝     1   d           
where d is the distance between an electrode  51 ,  52 ,  53  and the nanotube  54 . Therefore, as the nature of the device requires the nanotube  54  to be significantly closer to the source electrode  51  than to the gate or drain electrodes  52 ,  53 , the capacitance of the first capacitive element  61  naturally is significantly greater than the capacitances of the second an third capacitive elements  62 ,  63 . The layer of insulating material may be as thin as possible so as to maximise capacitance, but thick enough so as to prevent electrical breakdown and tunnelling currents between the source electrode  51  and the nanotube  54 . Typically, the thickness of the layer of insulating material is in the region of 5 nm.
 
     If the capacitance of the first capacitive element  61  is significantly greater than capacitances of the second and third capacitive elements  62 ,  63 , which, as has been discussed, is generally the case, then the first capacitive element  61  acts as an effective short circuit for the source electrode  51  to nanotube  54  AC current. Therefore, in this situation, the device of  FIG. 5  can be approximated further to the circuit diagram shown in  FIG. 6   b . The circuit comprises the source electrode  51  connected directly to the nanotube  54 . In a parallel connection with the nanotube  54  is the second capacitive element  62 , the second capacitive element  62  being due to a capacitive contact between the nanotube  54  and the gate electrode  52 . In a series connection with the nanotube  54  is a third capacitive element  63 , the third capacitive element  63  being due to the capacitive contact between the nanotube  54  and the drain electrode  53 . 
       FIG. 7  shows a doubly-clamped nanotube device according to a second embodiment of the invention. The device  7  comprises a substrate  70 , upon which are formed a source electrode  71  and a drain electrode  72 , each having the same profile. Also formed on the substrate is a gate electrode  73 . The gate electrode  73  may have a relatively shorter profile than the source and drain electrodes  71 ,  72 , and may be formed generally between the source and drain electrodes  71 ,  72 . The height of the gate electrode may be of the order of 10 nm, with the width being approximately 50-100 nm. Coupled to a surface of the source electrode  71  is a first layer of insulating material  75  and coupled to a surface of the drain electrode  72  is a second layer of insulating material  76 . Typically, the first and second layers of insulating material  75 ,  76  may be thin layers of solid insulating material, for example glass (SiO 2 ). Coupled to an opposite surface, to that coupled to the source electrode  71 , of the first layer of insulating material  75  is a first end portion of a carbon nanotube  74 . Coupled to an opposite surface, to that coupled to the drain electrode  72 , of the first layer of insulating material  76  is a second end portion of the carbon nanotube  74 . The source, drain and gate electrodes  71 ,  72 ,  73  are arranged on the substrate  70  such that a middle portion of the carbon nanotube  74  is suspended generally above the gate electrode  73 . When an RF signal is applied to the gate electrode  73 , oscillations of the nanotube, in a direction generally parallel to the direction from the nanotube  74  to the gate electrode  73 , as indicated by arrows A, are induced. 
     The device  7  of  FIG. 7  may be approximated to a circuit element as shown in  FIG. 8   a . The circuit element comprises, connected in series, the source electrode  71 , a first capacitive element  81 , the first capacitive element  81  being due to the capacitive contact between the source electrode  71  and the nanotube  74 , the nanotube  74 , a second capacitive element  82 , the second capacitive element  82  being due to the capacitive contact between the drain electrode  72  and the nanotube  74 , and finally the drain electrode  72 . In parallel connection with the nanotube  74  is a third capacitive element  83 , the third capacitive element  83  being due to the capacitive contact between the gate electrode  73  and the nanotube  74 . 
     As with the singly-clamped nanotube device  5  according to the first embodiment of the invention, the doubly-clamped nanotube device  7  of  FIG. 7  can be further approximated from the circuit elements of  FIG. 8   a , if the relative capacitances of the first, second and third capacitive elements  81 ,  82 ,  83  are correct. In this case, if the capacitances of both the first and second capacitive elements  81 ,  82  are significantly greater than the capacitance of the third capacitive element  83 , the first and second capacitive elements  81 ,  82  act as effective short circuits for an AC current. This further approximation of the device  7  of  FIG. 7  can be seen in  FIG. 8   b.    
     The circuit elements shown in  FIG. 8   b  comprise, connected in series, the source electrode  71 , the nanotube  74  and the drain electrode  72 . In a parallel connection with the nanotube  74  is the third capacitive element  83 , the third capacitive element  83  being due to a capacitive contact between the nanotube  74  and the gate electrode  73 . 
     As with the first embodiment, by effectively eliminating the contact resistance between the metal electrodes and the nanotube, the energy loss through dissipation is dramatically reduced. As such the mechanical damping is lower and the Q-factor of the device is very high. 
     The first and second embodiments not only provide the advantage of effectively eliminating the problems associated with contact resistance between metal electrodes and nanotubes, but potentially also enable higher precision during the fabrication of the devices. This is because the contact resistance between a metal and a nanotube is typically a hard parameter to control during fabrication of such a device. With a purely capacitive contact, on the other hand, the main parameters determining the capacitance are the thickness and length of the insulating layer, which generally is easier to control. 
     A method of making the device  5  of  FIG. 5  will now be described with reference to  FIG. 9 . 
     The first step, Step S 1 , is to provide the substrate  50 . At Step S 2 , the metallisation areas  51 ,  52 ,  53  are formed on the substrate  50 . This can be carried out in any suitable manner. This step provides source, gate and drain electrodes  51 ,  52 ,  53  on the substrate  50 . The gate electrode  52  is located between the source and drain electrodes  51 ,  53 . The height of the source electrode  51  from the surface of the substrate  50  may be greater than the heights of the gate and drain electrodes  52 ,  53 . Alternatively, the substrate may comprise an end portion of the substrate having a greater thickness than the remainder of the substrate, whereby the source electrode is located on the end portion having greater thickness. At Step S 3 , a layer of insulating material  55  is formed in contact with a surface of the source electrode  51 . The length and thickness of the insulating layer may be predetermined depending on the capacitance required. At Step S 4 , a carbon nanotube  54  is fixed to the opposite surface of the layer of insulating material  55  to that in contact with the source electrode  51 . The carbon nanotube  54  is fixed such that its length extends generally above the gate and drain electrodes  52 ,  53 . Typically, the nanotubes are grown elsewhere and are floated on a liquid to above the desired fixing site and aligned using an electric field. When they are correctly positioned, the liquid is evaporated away. Alternatively, the nanotubes may be grown in situ. According to one growth process, a seed for the nanotube is provided at the relevant location on the surface of the layer of insulating material  55 . The seeds are catalyst particles. Good catalyst particles are Iron (Fe) particles, although other seeds may also be suitable. The carbon nanotube  54  is then formed from the seeds using chemical vapour deposition (CVD). 
     A method of making the device  7  of  FIG. 7  will now be described, also with reference to  FIG. 9 . 
     The first step, Step S 1 , is to provide the substrate  70 . At Step S 2 , the metallisation areas  71 ,  72 ,  73  are formed on the substrate  70 . This can be carried out in any suitable manner. This step provides source, drain and gate electrodes  71 ,  72 ,  73  on the substrate  70 . The source electrode  71  and the drain electrode  72  may have the same profile, their profile being relatively taller than that of the gate electrode  73 . The gate electrode  73  may be formed generally between the source and drain electrodes  71 ,  72 . At Step S 3 , the first layer of insulating material  75  is formed in contact with a surface of the source electrode  71  and the second layer of insulating material  76  is formed in contact with a surface of the drain electrode  72 . The lengths and thicknesses of the insulating layers may be predetermined depending on the capacitance required. At Step S 4 , a first end portion of a carbon nanotube  74  is fixed to the opposite surface of the first layer of insulating material  75  to that in contact with the source electrode  71  and a second end portion of the carbon nanotube  74  is fixed to the opposite surface of the second layer of insulating material  76  to that in contact with the drain electrode  72 . The carbon nanotube  74  is arranged such that a middle portion, between the first and second end portions is raised above the gate electrode  73  and thus bridges a gap between the locations on the substrate  70  of the source and drain electrodes  71 ,  72 . The carbon nanotube may be grown elsewhere and positioned and fixed using the technique described earlier. Alternatively, they may be grown in situ. 
       FIG. 10  is a schematic side-view of a nanotube device according to a third embodiment of the invention. The device comprises a substrate  100 , on which are formed a source electrode  101 , a gate electrode  102  and a drain electrode  103 , the gate electrode  102  being formed generally between the source and drain electrodes  101 ,  103 . Typically, the electrodes are metal. The source electrode  101  may have a relatively tall profile compared to those of the gate and drain electrodes  102 ,  103 . Alternatively, the substrate  100  may comprise an end portion having a greater thickness than the remainder of the substrate, whereby the source electrode  101  is located on the end portion having greater thickness. Fixed to a surface of the source electrode  101  is a carbon nanotube  104 , the carbon nanotube  104  being in mechanical and electrical contact with the source electrode  101 . The carbon nanotube  104  extends parallel to the substrate  100  and extends generally above the drain and gate electrodes  103 ,  102 . The carbon nanotube  104  is mounted as a supported cantilever generally above the gate and drain electrodes  102 ,  103 . A time-varying voltage applied to the gate electrode  102  causes oscillation of the carbon nanotube  104  in a direction generally parallel to the direction from the nanotube to the substrate  100 , as indicated by arrows A. Connected in series to the source electrode  101  is an inductive element  105 . 
     The device of  FIG. 10  may be approximated to a circuit element as shown in  FIG. 11 . The circuit element comprises, connected in series, the inductive element  105 , the source electrode  101 , a resistive element  111 , the resistive element being due to the contact resistance between the source electrode  101  and the nanotube  104 , and the nanotube  104 . In a parallel connection with the nanotube  104  is a first capacitive element  112 , the first capacitive element  112  being due to a capacitive contact between the nanotube  104  and the gate electrode  102 . In a series connection with the nanotube  104  is a second capacitive element  113 , the second capacitive element  113  being due to the capacitive contact between the nanotube  104  and the drain electrode  103 . 
     When the nanotube oscillates, the AC currents which usually flow in the resistive contact  111 , and therefore dissipate heat, are opposed by the inductive element  105 . This is because the time constant of the inductive element  105  is much greater than the time period of the AC signal. The result, therefore, is that very minimal alternating current flows through the resistive contact  111  and thus the energy dissipation and the Q-factor degradation, due to the presence of the resistive contact  111  between source electrode  101  and the nanotube  104 , are reduced. 
       FIG. 12  shows a nanotube device according to a fourth embodiment of the invention. The device  127  comprises a substrate  120 , upon which are formed a source electrode  121  and a drain electrode  122 , each having the same profile. A gate electrode  123  may also be formed on the substrate  120 . The gate electrode  123  may have a relatively shorter profile than the source and drain electrodes  121 ,  122 , and may be formed generally between the source and drain electrodes  121 ,  122 . Coupled to an uppermost surface of the source electrode  121  is a first end portion of a carbon nanotube  124 . Coupled to an uppermost surface of the drain electrode  122  is a second end portion of the carbon nanotube  124 . The source and drain electrodes  121 ,  122  are arranged on the substrate  120  such that a middle portion of the carbon nanotube  124  is suspended above the gate electrode  123 . In series connection with the source electrode is a first inductive element  125  and in series connection with the drain electrode  122  is a second inductive element  126 . Oscillations of the nanotube  124 , in a direction generally parallel to the direction from the nanotube  124  to the gate electrode  123  as indicated by arrows A, may be detected using capacitive transduction. Alternatively, the nanotube  124  may act as a gate for a field-effect transistor or some other means of displacement detection. 
     A device according to the fourth embodiment may be suitable for use when a DC-component is required through the nanotube device. 
     The device of  FIG. 12  may be approximated to a circuit element as shown in  FIG. 13 . The circuit element of  FIG. 13  comprises, connected in series, the inductive element  125 , the source electrode  121 , a first resistive element  131  (due to the contact resistance between the nanotube  124  and the source electrode  121 ), the nanotube  124 , a second resistive element  132 , (due to the contact resistance between the nanotube  124  and the drain electrode  122 ), the drain electrode  122 , and a second inductive element  126 . The circuit element further comprises a capacitive element  133  and the gate electrode  123 , connected in parallel to the nanotube  124 , the capacitive element  113  arising as a result of the capacitive contact between the nanotube  124  and the gate electrode  123 . 
     As with the third embodiment of the invention, when the nanotube oscillates, the AC currents which usually flow in the resistive contacts  131 ,  132  are opposed by the corresponding inductive elements  125 ,  126 . This is, again, because the time constants of the inductive elements  125 ,  126  are much greater than the time period of the AC signal. The result, therefore, is that the net alternating current that flows through the resistive contacts  131 ,  132  are greatly reduced and thus the energy dissipation and the Q-factor degradation, due to the presence of the resistive contacts between electrodes and the nanotube, are also greatly reduced. 
     It should be understood that many of relevant dimensions and materials specified with reference to the first and second embodiments of the invention are also relevant with regard to the third and fourth embodiments of the invention. 
     A method of making the device  107  of  FIG. 10  will now be described with reference to  FIG. 12 . 
     The first step, Step P 1 , is to provide the substrate  100 . At Step P 2 , the metallisation areas  101 ,  102 ,  103  are formed on the substrate  100 . This can be carried out in any suitable manner. This step provides source, gate and drain electrodes  101 ,  102 ,  103  on the substrate  100 . The gate electrode  102  is located between the source and drain electrodes  101 ,  103 . The height of the source electrode  101  from the surface of the substrate  100  may be greater than the heights of the gate and drain electrodes  102 ,  103 . Alternatively, the substrate may comprise an end portion of the substrate having a greater thickness than the remainder of the substrate, whereby the source electrode is located on the end portion having greater thickness. At Step P 3 , the first inductive element  105  is coupled to the source electrode  101 . The first inductive element  105  may be coupled to the source electrode  101  in series. At Step P 4 , a carbon nanotube  104  is fixed such that an end portion of the carbon nanotube  104  is in mechanical and electrical contact with a surface of the source electrode  101 . The carbon nanotube  104  is fixed such that its length extends generally above the gate and drain electrodes  102 ,  103 . The carbon nanotube may be grown elsewhere and positioned and fixed using the technique described previously. Alternatively, they may be grown in situ. 
     A method of making the device  127  of  FIG. 12  will now be described, also with reference to  FIG. 14 . 
     The first step, Step P 1 , is to provide the substrate  120 . At Step P 2 , the metallisation areas  121 ,  122 ,  123  are formed on the substrate  120 . This can be carried out in any suitable manner. This step provides source, drain and gate electrodes  121 ,  122 ,  123  on the substrate  120 . At Step P 3 , a first inductive element  125  is coupled to the source electrode  121  and a second inductive element  126  is coupled to the drain electrode  122 . The first and second inductive elements  125 ,  126  may be coupled to the source and drain electrodes  121 ,  122  in series. At Step P 4 , a carbon nanotube  124  is fixed such that a first end portion of a carbon nanotube  124  is in mechanical and electrical contact with a surface of the source electrode  121  and an opposite second end of the carbon nanotube  124  is in mechanical and electrical contact with the surface of the drain electrode  122 . The carbon nanotube  124  is arranged such that a middle portion, between the first and second end portions is raised above the gate electrode  123  and thus bridges a gap between the locations on the substrate  120  of the source and drain electrodes  121 ,  122 . The carbon nanotube may be grown elsewhere and positioned and fixed using the technique described previously. Alternatively, they may be grown in situ. 
     According to the third and fourth embodiments of the invention, an advantage of counteracting stiction may also be achieved. Stiction may occur when the oscillation of the nanotube causes it to come within a certain distance of an electrode, the certain distance being the distance at which the surface forces between the nanotube and the electrode override other forces. This may result in the nanotube becoming permanently stuck to the electrode. The devices  107 ,  127  of  FIGS. 10 and 12  are depicted experiencing stiction depicted in  FIGS. 15 and 16  respectively. In  FIG. 15 , the nanotube  104  is stuck to the drain electrode  103 , while in  FIG. 16  the nanotube  124  is stuck to the gate electrode  123 . With a purely resistive contact between the source electrode and the nanotube (i.e. without the series coupled inductive element(s)), the charge relaxation time for the electronic subsystem is typically much shorter than the time scale for mechanical motion. This means that, even if a large positive bias is put on the contacted electrode (the electrode to which the nanotube is stuck), the force between the nanotube and the contacted electrode remains attractive. However, by coupling an inductive element  105 ;  125  in series with the source electrode  101 ;  121 , as is shown in  FIGS. 10 and 12  (and  FIGS. 15 and 16 ), the charge relaxation time can be increased by several orders of magnitude. This results in the positive charge on the nanotube remaining even if the voltage applied to the contacted electrode is raised. Therefore, if a reverse voltage pulse is applied to the contacted electrode in a time shorter than the relaxation time of the electronic subsystem, a repulsive force acting between the contacted electrode and the nanotube may result, and the release of the nanotube from the contacted electrode may be achieved. It should be noted, with reference to  FIG. 16 , that the advantage of counteracting stiction may also be achieved if only one of the first inductive element  125  and the second inductive element  126  was included in the device of  FIG. 11  or  13 , with the other being omitted. 
     As with many electromechanical systems, the devices according to any one of the embodiments of the invention (as depicted in  FIGS. 5 ,  7 ,  10  and  12 ) have a resonant frequency. The resonant frequency varies according to the length and stiffness of the nanotube. Multi-walled nanotubes or clusters of nanotubes are generally stiffer than single-walled nanotubes and can therefore be longer than single nanotubes having the same resonant frequency. Generally, obtainable resonant frequencies are in the range 1 to 5 GHz. The resonant frequency is tuneable using a voltage bias applied to the gate electrode. As such, the devices are usable as tuneable filters, wherein if the gate voltage is modulated with an RF signal containing several frequency components, the frequency components with frequencies out of resonance are suppressed. Therefore, only those components of the signal which match the resonant frequency pass. 
     As shown in  FIG. 17 , the resonator  170 , which may comprise any one of devices  5 ,  7 ,  107 ,  127 , and controllable voltage bias circuitry (not shown) is included as part of filter  171  of an RF front end of a radio receiver, in this example a radio transceiver  172 . 
     A filter incorporating any one of the devices  5 ,  7 ,  107 ,  127  can also be used in a front end of RF transmitter, that is, between the power amplifier and the antenna. 
     By using any of the devices according to any of the embodiments of the invention in the resonator  170 , the resonator  170  can be a very high quality, or high-Q, resonator. These capabilities derive from the physical arrangement of the devices  5 ,  7 ,  107 ,  127  as shown in  FIGS. 5 ,  7 ,  10  and  12 . The resonator  170  is suitable for forming an essential component in software-defined and cognitive radio hardware. 
     The devices  5 ,  7 ,  107 ,  127  of  FIGS. 5 ,  7 ,  10  and  12  have a number of other potential applications. 
     For instance, the devices can also be used as resonators  180  in a voltage-controlled oscillator (VCO)  181 . This is shown in  FIG. 18 . This kind of VCO is an integral part of a radio synthesizer. The potentially wide tuning range and high quality factor of the resonator device of the invention enable low phase noise synthesizers operating at several RF bands with only a single core VCO. 
     The VCO can be tuned by varying the bias voltages applied to the gate electrodes as will be appreciated from the above explanation. 
     As shown in  FIG. 18 , the resonator  180 , which comprises any one of the devices  5 ,  7 ,  107 ,  127  and controllable voltage bias circuitry (not shown) is included as part of VCO  181  of a radio receiver, in this example a radio transceiver  182 .