Abstract:
The present invention provides a system for detecting and analyzing at least one of an electric field and an electromagnetic field. The system includes a micro/nanomechanical oscillator which oscillates in the presence of at least one of the electric field and the electromagnetic field. The micro/nanomechanical oscillator includes a dense array of cantilevers mounted to a substrate. A charge localized on a tip of each cantilever interacts with and oscillates in the presence of the electric and/or electromagnetic field. The system further includes a subsystem for recording the movement of the cantilever to extract information from the electric and/or electromagnetic field. The system further includes a means of adjusting a stiffness of the cantilever to heterodyne tune an operating frequency of the system over a frequency range.

Description:
GOVERNMENT RIGHTS 
     This invention was made with government support under Contract No. DE-AC05-00OR22725 awarded by the U.S. Department of Energy. The government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a system for sensing an electric field and/or an electromagnetic field. More particularly, the invention relates to a nanomechanical oscillator for sensing an electric field and/or an electromagnetic field, which is tunable over a frequency range. 
     BACKGROUND OF THE INVENTION 
     Known systems for sensing static electric fields and/or time-varying electric fields (electromagnetic fields) utilize an antenna and a receiver. In these known systems, the sensitivity of the system is dependent on the design of the antenna and the receiver electronics. However, these antenna-based systems do not exhibit high sensitivity over a broad frequency or wavelength range. 
     Another drawback of these known systems is their size. The size of the antenna is related to a wavelength of the electric field. As a result, the dimensions of these known systems are relatively large, especially at lower frequencies, thereby preventing the design and creation of a compact electric field sensor. 
     As such, there exists a need for a sensor for detecting electric and/or electromagnetic fields, which is sensitive over a broad frequency range and has dimensions suitable for a compact design. 
     SUMMARY OF THE INVENTION 
     The present invention includes a system for sensing an electric field and/or an electromagnetic field that is capable of high sensitivity over a broad frequency range. The present invention utilizes a micro/nanomechanical system (MNS) to detect very small electric fields (μV/m) over a large frequency range while maintaining substantial power efficiency. As used herein, references to the MNS and the nanomechanical system are to be understood to refer to at least one of the micromechanical system and the nanomechanical system. 
     The present invention is based on the interaction of an electric charge q with at least one of the electric field and the electromagnetic field. The electric charge is preferably localized on a cantilever and the cantilever is mounted generally perpendicular to a substrate. The substrate is preferably manufactured from a semiconductor material, for example silicon. In a preferred embodiment, the cantilever includes a stem and a tip which is positioned on the stem at a position opposite of the substrate. The tip is preferably manufactured from a material capable of maintaining the electric charge q and in a shape that allows for uniform distribution of the charge. In one embodiment, the tip is a glass microsphere. To localize the electric charge and to prevent the loss of charge, the stem is preferably made of an electrically nonconductive material. 
     In operation, as a target electric field passes through the MNS, a positive charge of the tip interacts with the target electric field oscillating from side to side tracing a wave of the target electric field. After the target electric field passes the cantilever returns to the generally perpendicular initial position. 
     The system of this invention may also include a subsystem for measuring and recording the movement of the cantilever in response to the target electric field. The subsystem is also preferably capable of extracting information of the target electric field from the movement of the cantilever. According to a preferred embodiment, the subsystem for measuring and recording the movement of the cantilever is an optical readout system. The optical readout system includes a driver and a light source positioned over and at an angle to the substrate. Light from the light source passes through a projecting optics and onto the substrate, the light reflects off the cantilever and the substrate and into a digital camera. In a preferred embodiment, the reflected light passes through imaging optics and/or spatial filtering before being recorded by the digital camera. The recorded motion of the cantilever is received and processed by a digital signal processor to extract information about the target electric field and/or electromagnetic field including, for example, a frequency of the target electric field. An embodiment of the subsystem for measuring and recording the movement of the cantilever can further include high magnification (diffraction limited) optics, a MHz range voltage source and a stroboscopic video analyzer. 
     In order to achieve both high dynamic range and wide spectral response, the system of this invention should be capable of tuning a cantilever operating frequency. In one embodiment, the cantilever operating frequency is tunable by including a piezoelectric element to a base of the cantilever, which can serve to modify a stiffness of the cantilever. Another embodiment involves the modulation of an applied voltage, V(t)=V 0  cos(ω r t+φ), of the cantilever. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above-mentioned and other features and objects of this invention will be better understood from the following detailed description taken in conjunction with the drawings wherein: 
         FIG. 1  is a perspective view of a system for detecting at least one of an electric field and an electromagnetic field according to one embodiment of this invention; 
         FIG. 2  is a perspective view of a micro/nanomechanical structure according to the embodiment of  FIG. 1 ; 
         FIG. 3  is a magnified photograph of an embodiment of the micro/nanomechanical structure of this invention; 
         FIG. 4  is a side view of the micro/nanomechanical structure and an electric field according to one embodiment of this invention; 
         FIG. 5  is the side view of the micro/nanomechanical structure of  FIG. 4  with an electric field at five discrete periods of time; and 
         FIG. 6  is a representation of a photolithography fabrication steps involved in producing an embodiment of the micro/nanomechanical structure of this invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention utilizes micro/nanomechanical structures (MNS) to detect an electric field and/or an electromagnetic field (a time varying electric field). The invention is based on the interaction of an electric charge, localized on a cantilever, with the electric field and/or the electromagnetic field. As used herein, to ease the description, references to the electric field are to be understood to refer to at least one of the electric field and the electromagnetic field. 
       FIG. 1  shows a preferred embodiment of a system  10  of this invention. In this embodiment, the system  10  includes a MNS  12  and a subsystem  14  for measuring and recording the movement of the MNS  12  in response to a target electric field. The system  10  is capable of detecting electric fields having a frequency from 10 (0.1) to 10 6  (10 9 ) Hz. In a preferred embodiment, the MNS  12  of this invention is disposed in an inert gas atmosphere. 
       FIG. 2  shows the MNS  12 , not necessarily shown to scale, according to one embodiment of this invention. In this embodiment, a 6×6 array of cantilevers  16  are mounted generally perpendicular to a substrate  18 . However, it should be understood that the array of cantilevers  16  can include any number cantilevers  16  and is desirably a dense array that is capable of achieving high spatial resolution as well as high sensitivity. In order to achieve high spatial resolution and high sensitivity, the array of cantilevers  16  preferably comprises a dense array having from 100 to 10 5  cantilevers per millimeter 2 . For example, the array in the photograph of  FIG. 3  has 10 5  cantilevers per millimeter 2 . 
       FIGS. 4 and 5  show an embodiment of this invention with a single cantilever  16  mounted generally perpendicular to the substrate  18  and an external electric field  24 . The substrate  18  is preferably manufactured from a semiconductor material such as, but not limited to, silicon. In an alternative embodiment, the substrate can be manufactured from a variety of materials including, but not limited to, silicon nitride, silicon oxide, aluminum oxide and aluminum nitride. 
     The cantilever  16  includes a stem  20  and a tip  22 . The stem  20  is mounted generally perpendicular to the substrate  18  and the tip  22  is positioned on the stem  20  at a position opposite from the substrate  18 . The stem  20  can be manufactured from any suitable material including, but not limited to, silicon. In a preferred embodiment, the stem  20  is made of an electrically nonconductive material. 
     The tip  22  is made of a conductive or nonconductive material capable of maintaining an electric charge q. In an alternative embodiment, the tip  22  is made of an electret material which is capable of holding an electric charge for long time periods including many years. In a preferred embodiment, the tip  22  comprises glass however, the tip material can be any suitable material including, but not limited to, silicon. The electric charge q can be either a positive charge or a negative charge. In a preferred embodiment, the electric charge q is a positive charge which can be better maintained on the tip  22 . Methods of depositing the charge q on the tip  22  include, but are not limited to, using an electron beam (negative charge), using an ion beam (positive charge), by applying a negative charge and by applying a positive charge. In a preferred embodiment, the tip  22  comprises a spherical shape that allows for a generally uniform distribution of charge, however, the tip  22  may be designed as any other shape. In one embodiment, the tip  22  is a glass microsphere with a positive charge q. 
     In a preferred embodiment, the cantilever  16  has a length ranging from 1 to 10 3  micrometers and a width to length ratio ranging from 0.01 to 0.3. In a preferred embodiment, the cantilever  16  is capable of oscillating with an amplitude greater than 5% of a length of the stem  20 . 
       FIG. 6  shows an embodiment of a method for manufacturing the substrate  18  and the stem  20 . This method uses photolithography fabrication steps to construct the substrate  18  and the stem  20 . The process begins with a silicon (Si) wafer  42 . A sacrificial layer of silicon dioxide  44  (SiO 2 ) is then applied to the Si wafer  42  using plasma-enhanced chemical vapor deposition (PECVD). Next an anchoring point  46  is etched into the sacrificial layer  44  of SiO 2  using reactive ion etching (RIE). A layer of low stress silicon nitride  48  (SiN x ) is then applied to the sacrificial layer  44  of SiO 2  and the anchoring point  46  using PECVD as a structural layer. Next, resonators  50  are patterned using RIE etching. In the next step the sacrificial layer  44  of SiO 2  is removed with a wet etch. The array of vertical cantilevers shown in  FIG. 3  was manufactured using this process. In a preferred embodiment, the tip can be applied to the stem with a deposition technique, for example PECVD, that creates a nonconformal coating. In an alternative embodiment, the above process can be adapted to use single crystal Si, amorphous Si or low stress silicon nitride (SiN x ) as a structural layer. These materials are known for their excellent chemical stability, mechanical properties and compatibility with a variety of patterning/etching techniques. 
     Using the method described above, the cantilever  16  is capable of oscillating with large amplitudes and with a resonance frequency in the MHz. In a preferred embodiment, the cantilever  16  is capable of oscillating with an amplitude greater than 5% of a length of the stem  20 . 
       FIG. 5  shows an interaction of the cantilever  16  with an incoming sinusoidal electric field  26  at five discrete moments for one period, time t=t 0  to t=t 4 . At time t=t 0 , the sinusoidal electric field  26  approaches the cantilever  16  while the cantilever is centered and/or at rest in a generally perpendicular state. As the sinusoidal electric field  26  propagates, the cantilever  16  traces the sinusoidal electric field  26  to an apex, at t=t 1 , back to the initial state, at t=t 2 , down to a trough, at t=t 3 , and back to the initial state, at t=t 4 . After the sinusoidal electric field  26  passes the MNS  12 , the cantilever  16  stops responding. 
       FIG. 1  shows an embodiment of a subsystem  14  for measuring and recording the movement of the cantilever  16  in response to the sinusoidal electric field  26 . This subsystem  14  is an optical readout system. The optical readout system includes a driver  28  and a light source  30  positioned over and at an angle to the MNS  12 . In a preferred embodiment, the light source  30  is a light emitting diode (LED). Light from the light source  30  passes through projecting optics  32  and onto the MNS  12 . The light then reflects off the cantilever  16  and the substrate  18  and into a digital camera  34 . In a preferred embodiment, the reflected light passes through at least one of imaging optics  36  and a spatial filter  38  before being recorded by the digital camera  34 , preferably a charge coupled device (CCD). A recorded motion of the cantilever  16  is received and processed by a digital signal processor  40  to extract information about the sinusoidal electric field  26 . In an embodiment of this invention, the subsystem  14  includes a signal generator  52  which produces a potential oscillating with a reference frequency ω r  that can be used for heterodyning to detect the electromagnetic field with frequency ω=ω r +ω o . 
     Another embodiment of the subsystem for measuring and recording the movement of the cantilever can further include high magnification diffraction limited optics, a MHz range voltage source and a stroboscopic video analyzer with a frequency modulated phase-locked loop. 
     By extracting information about the movement of the cantilevers  16 , including an amplitude response, Δx, and a resonance frequency of the cantilever  16 , information about the sinusoidal electric field  26  can be calculated including a frequency of the sinusoidal electric field  26 , ω. For example, assuming the cantilever  16  comprises an electrically nonconductive stem  20  and the tip  22  comprises a conductive microsphere, an amplitude response, as a function of frequency ω, of the cantilever is: 
                     Δ   ⁢           ⁢     x   ⁡     (   ω   )         =     qE     m   ⁢           (       ω   2     -     ω   0   2       )     2     +       (     ω   ⁢       ω   0     Q       )     2                     (   1   )               
where q is the charge on the tip  22 , ω 0  is a resonance frequency of the cantilever  16 , E is the external electric field  26 , m is the mass of the system and Q is the quality factor of the cantilever  16 .
 
     As with every mechanical system at a finite temperature there will be a component of noise, which is described as thermomechanical noise. This invention limits the impact of thermomechanical noise by operating in regime where the signal to be detected produces cantilever oscillations which are greater than the thermomechanical noise. In this invention, the thermomechanical noise for the cantilever at a temperature T and a bandwidth B is given by: 
     
       
         
           
             
               
                 
                   
                     
                       〈 
                       
                         δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             x 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                           TM 
                           2 
                         
                       
                       〉 
                     
                     
                       1 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             k 
                             B 
                           
                           ⁢ 
                           TB 
                         
                         Qk 
                       
                       ⁢ 
                       
                         
                           ω 
                           0 
                           3 
                         
                         
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 - 
                                 
                                   ω 
                                   0 
                                   2 
                                 
                               
                               ) 
                             
                             2 
                           
                           - 
                           
                             
                               ω 
                               0 
                               4 
                             
                             
                               Q 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     At low frequencies (ω&lt;&lt;ω 0 ) this noise becomes: 
     
       
         
           
             
               
                 
                   
                     
                       〈 
                       
                         δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             x 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                           TM 
                           2 
                         
                       
                       〉 
                     
                     
                       1 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             4 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               k 
                               B 
                             
                             ⁢ 
                             TB 
                           
                           Qk 
                         
                         ⁢ 
                         
                           
                             ω 
                             0 
                             3 
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   - 
                                   
                                     ω 
                                     0 
                                     2 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 0 
                                 4 
                               
                               
                                 Q 
                                 2 
                               
                             
                           
                         
                       
                     
                     → 
                     
                       
                         
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             k 
                             B 
                           
                           ⁢ 
                           TB 
                         
                         
                           Qk 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In order to obtain analytical expressions for a fundamentally limited detector performance, a signal-to-noise ratio, Δx/&lt;δx 2 &gt; 1/2 , must be calculated: 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       x 
                     
                     
                       
                         〈 
                         
                           δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             x 
                             TM 
                             2 
                           
                         
                         〉 
                       
                       
                         1 
                         2 
                       
                     
                   
                   = 
                   
                     
                       q 
                       m 
                     
                     ⁢ 
                     
                       1 
                       
                         
                           
                             
                               4 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 k 
                                 B 
                               
                               ⁢ 
                               TB 
                             
                             
                               Qk 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                         
                         ⁢ 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   - 
                                   
                                     ω 
                                     0 
                                     2 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 
                                   ω 
                                   0 
                                   2 
                                 
                               
                               
                                 Q 
                                 2 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     E 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Defining, a Noise Equivalent Electric Field Difference (NEEFD) as the electric field for which the signal to noise ratio equals unity, leads to: 
     
       
         
           
             
               
                 
                   NEEFD 
                   = 
                   
                     
                       m 
                       q 
                     
                     ⁢ 
                     
                       
                         
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             k 
                             B 
                           
                           ⁢ 
                           TB 
                         
                         
                           Qk 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             0 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             ( 
                             
                               
                                 ω 
                                 2 
                               
                               - 
                               
                                 ω 
                                 0 
                                 2 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             
                               ω 
                               2 
                             
                             ⁢ 
                             
                               ω 
                               0 
                               2 
                             
                           
                           
                             Q 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Using the expressions derived above, estimates of both the NEEFD and the thermomechanical noise, as a function of frequency, can be calculated. Note that for a low frequency limit condition, the frequency dependent term in Eqn. (1) becomes unity and the following expression can be used to estimate static responses, Δx=q E/k. Assuming values for the parameters shown in Table 1, then for frequencies much smaller that the cantilever resonance frequency, NEEFD=3.98×10 −6  V/m. This corresponds to a mechanical response Δx=(10 −12  C×3.98×10 −6  V/m)/(10 −5  N/m)=6.37×10 −14  m. Which corresponds to an electric field sensitivity of ΔE=k Δx/q=10 −5  N/m×10 −12  m)/(10 −12  C)=10 −5  V/m. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Parameter Values 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 mass, m 
                 10 −15   
                 kg 
               
               
                   
                   
               
               
                   
                 spring constant, k 
                 10 −5   
                 
                   
                     
                       
                         N 
                         m 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 charge, q 
                 10 −15   
                 C 
               
               
                   
                 Bandwidth, B 
                 10 
                 Hz 
               
               
                   
                   
               
             
          
         
       
     
     In a preferred embodiment, in order to achieve a high dynamic range and a wide spectral response, the cantilever resonance frequency is preferably tunable. In one embodiment, the cantilever resonance frequency can be tuned, during a microfabrication process, by including a piezoelectric element, not shown, at a base of the cantilever  16  to modify a stiffness of the cantilever. 
     In another embodiment of this invention, the cantilever resonance frequency is tunable by modulating an applied voltage V(t)=V 0  cos(ω r t+φ) of the cantilever, which serves as the source of the electric charge on the cantilever, given by q(t)=V(t) R=q 0  cos(ω r t+φ). Assuming the oscillation is directed along the x-axis, then at large distances r&gt;&gt;R a time varying electric field component is given by 
     
       
         
           
             
               
                 E 
                 r 
               
               ⁡ 
               
                 ( 
                 
                   r 
                   , 
                   θ 
                   , 
                   t 
                 
                 ) 
               
             
             = 
             
               
                 
                   2 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     q 
                     0 
                   
                   ⁢ 
                   L 
                 
                 
                   r 
                   3 
                 
               
               ⁢ 
               cos 
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 ϑ 
                 ) 
               
               ⁢ 
               
                 sin 
                 ⁡ 
                 
                   ( 
                   
                     
                       ω 
                       0 
                     
                     ⁢ 
                     t 
                   
                   ) 
                 
               
               ⁢ 
               
                 sin 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         ω 
                         r 
                       
                       ⁢ 
                       t 
                     
                     + 
                     φ 
                   
                   ) 
                 
               
             
           
         
       
     
     A frequency ω r  will serve as a reference heterodyning frequency that can be varied to achieve a wide dynamic range. An additional advantage of this embodiment is that it is possible to cancel a local electric field of a local oscillator if devices are made in pairs and the applied voltage is out of phase by π. Furthermore, fabricating the devices in pairs is equivalent to micro-tuning forks. A mechanical Q of tuning forks can be extremely high which can be very beneficial to the present application. There is also the possibility of having the tuning forks charged in phase with each other, thereby creating a micro AC electric field emitter for signal transmission as well as for detection. 
     While there has been shown and described what are at present considered the preferred embodiments of the invention, it will be obvious to those skilled in the art that various changes and modifications can be prepared therein without departing from the scope of the inventions defined by the appended claims.