Abstract:
This disclosure provides systems, methods, and apparatus associated with an electrostatically driven graphene speaker. In one aspect, a device includes a graphene membrane, a first frame on a first side of the graphene membrane, and a second frame on a second side of the graphene membrane. The first frame and the second frame both include substantially circular open regions that define a substantially circular portion of the graphene membrane. A first electrode is proximate the first side of the circular portion of the graphene membrane. A second electrode proximate the second side of the circular portion of the graphene membrane.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a continuation of International Application No. PCT/US2013/075821, filed Dec. 17, 2013, which claims priority to U.S. Provisional Patent Application No. 61/740,058, filed Dec. 20, 2012, both of which are herein incorporated by reference. 
     
    
     STATEMENT OF GOVERNMENT SUPPORT 
       [0002]    This invention was made with government support under Contract No. DE-AC02-05CH11231 awarded by the U.S. Department of Energy, under Grant No. N00014-09-1066 awarded by the Office of Naval Research, and under Grant No. EEC-083819 awarded by the National Science Foundation. The government has certain rights in this invention. 
     
    
     TECHNICAL FIELD 
       [0003]    This disclosure relates to devices including graphene, and more specifically to a graphene speaker. 
       BACKGROUND 
       [0004]    Efficient audio sound transduction has a history dating back millions of years. Primitive insect singers generated loud and pure-tone sound with high efficiency by exciting resonators inside their bodies. Male crickets generate chirping sounds via stridulation, where the scraper edge of one wing is rubbed against the ribbed edge of the other wing. Advantageous structural properties of the wings (i.e., relatively large, low-mass flexural membranes) allow efficient muscle-to-sound energy transduction. 
         [0005]    In a human context, unnatural (i.e., non-voice) sound production has been explored for millennia, with classic examples being drumheads and whistles for long-range communications and entertainment. In modern society, efficient small-scale audio transduction is ever more important for discrete audio earphones and microphones in portable or wireless electronic communication devices. 
         [0006]    For human audibility, an ideal speaker or earphone should generate a constant sound pressure level (SPL) from 20 Hz to 20 kHz, i.e., it should have a flat frequency response. Currently, most commercial speakers are diaphragm based, and most of the diaphragms are driven by a magnetic coil. Because the coil moves together with the diaphragm, the total effective mass becomes large. As a result, the high frequency response may be poor. 
         [0007]    To overcome poor high frequency response, acoustic engineers manipulate damping, which basically decreases the response at lower frequencies to make the total response curve flat. It is difficult, however, to engineer an arbitrary damping curve at all frequencies. Further, the damping complicates the acoustic design of the speaker and can increase the fabrication cost significantly. Another problem created by a large effective mass is that it stores kinetic energy which can be released later to jeopardize the music transparency (e.g., the diaphragm does not start or stop immediately with the input signal). 
       SUMMARY 
       [0008]    Graphene has extremely low mass density and high mechanical strength, key qualities for an efficient wide-frequency-response electrostatic audio speaker design. Low mass may enable good high frequency response, while high strength may allow for relatively large free-standing diaphragms necessary for effective low frequency response. Disclosed herein are the fabrication and testing of a miniaturized graphene-based electrostatic audio transducer. The speaker/earphone has good frequency response across the entire audio frequency range (20 HZ-20 kHz), with performance matching or surpassing commercially available audio earphones. 
         [0009]    In one aspect, a graphene diaphragm, biased by a DC source, is suspended midway between two perforated electrodes driven at opposite polarity. A varying electrostatic force drives the graphene diaphragm which in turn disturbs air and emits sound through the electrodes. The light mass and low spring constant of the graphene diaphragm, together with strong air damping, allow for high-fidelity broad-band frequency response. Such a speaker also may have a high power efficiency. 
         [0010]    Another innovative aspect of the subject matter described in this disclosure can be implemented in a device including a graphene membrane, a first frame on a first side of the graphene membrane, and a second frame on a second side of the graphene membrane. The first frame and the second frame both include substantially circular open regions that define a substantially circular portion of the graphene membrane. The device further includes a first electrode proximate the first side of the circular portion of the graphene membrane, and a second electrode proximate the second side of the circular portion of the graphene membrane. 
         [0011]    In some embodiments, the device further includes a wire in electrical contact with the graphene membrane. In some embodiments, the wire is a gold wire with a diameter of about 10 microns to 30 microns. 
         [0012]    In some embodiments, the graphene membrane is about 20 nanometers to 40 nanometers thick. In some embodiments, the first electrode and the second electrode define open regions having a dimension of about 200 microns to 300 microns. In some embodiments, the circular portion of the graphene membrane has a diameter of about 5 millimeters to 9 millimeters. In some embodiments, the first frame and the second frame are about 60 microns to 180 microns thick. 
         [0013]    In some embodiments, the first electrode and the second electrode include silicon wafers. In some embodiments, the first electrode and the second electrode further include an oxide layer on surfaces of the silicon wafers. 
         [0014]    In some embodiments, the first electrode is in contact with the first frame and the first electrode is spaced a first distance of about 60 microns to 180 microns from the first side of the circular portion of the graphene membrane. The second electrode is in contact with the second frame, and the second electrode is spaced a second distance of about 60 microns to 180 microns from the second side of the circular portion of the graphene membrane. 
         [0015]    In some embodiments, the first frame and the second frame are a unitary body. 
         [0016]    Another innovative aspect of the subject matter described in this disclosure can be implemented in a method including provide a device. The device includes a graphene membrane, a first frame on a first side of the graphene membrane, and a second frame on a second side of the graphene membrane. The first frame and the second frame both include substantially circular open regions that define a substantially circular portion of the graphene membrane. The device further includes a first electrode proximate the first side of the circular portion of the graphene membrane, and a second electrode proximate the second side of the circular portion of the graphene membrane. The graphene membrane is biased with a direct current voltage. The first electrode and the second electrode are biased with an input signal, causing the graphene membrane to move and generate a sound. 
         [0017]    In some embodiments, the input signal is generated from an audio signal. In some embodiments, the direct current voltage is about 50 volts to 150 volts. In some embodiments, an amplitude of the input signal is about 0 volts to 15 volts. In some embodiments, the first electrode and the second electrode are biased at opposite polarities. 
         [0018]    Details of embodiments of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Note that the relative dimensions of the following figures may not be drawn to scale. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1A  shows an example of a cross-sectional schematic illustration of an electrostatically driven graphene speaker (EDGS). 
           [0020]      FIG. 1B  shows an example of a graphene membrane suspended in a frame. 
           [0021]      FIG. 2  shows an example of a method of use of a device including a graphene membrane. 
           [0022]      FIG. 3A-3C  show examples of the frequency response of various miniature audio speakers. 
           [0023]      FIG. 4  shows the vibration velocity of a graphene diaphragm in the EDGS versus frequency, measured by Laser Doppler Velocimetry (LDV). 
       
    
    
     DETAILED DESCRIPTION 
       [0024]    Reference will now be made in detail to some specific examples of the invention including the best modes contemplated by the inventors for carrying out the invention. Examples of these specific embodiments are illustrated in the accompanying drawings. While the invention is described in conjunction with these specific embodiments, it will be understood that it is not intended to limit the invention to the described embodiments. On the contrary, it is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the invention as defined by the appended claims. 
         [0025]    In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. Particular example embodiments of the present invention may be implemented without some or all of these specific details. In other instances, well known process operations have not been described in detail in order not to unnecessarily obscure the present invention. 
         [0026]    Various techniques and mechanisms of the present invention will sometimes be described in singular form for clarity. However, it should be noted that some embodiments include multiple iterations of a technique or multiple instantiations of a mechanism unless noted otherwise. 
       Introduction 
       [0027]    One approach to response spectrum broadening for speakers is to reduce both the mass and spring constant of the diaphragm so that inherent air damping dominates and flattens the response peaks. Moreover, with ambient air serving as the dominant damping mechanism, most input energy is converted to a sound wave, which makes such speakers highly power efficient. For these reasons, the ideal audio transduction diaphragm should have small mass and a soft spring constant, and be non-perforated to efficiently displace the surrounding air. 
         [0028]    Electrostatically-driven thin-membrane loudspeakers employing an electrically conducting, low mass diaphragm with significant air damping have been under development since the 1920&#39;s (e.g., the first were made of pig intestine covered with gold-leaf), but miniaturized electrostatic earphones are still rare. One reason is that the per-area air damping coefficient significantly decreases when the size of the diaphragm falls below the sound wavelength. Hence, for small speakers, a thinner and lower mass density diaphragm is required to continue the dominance of air damping. Such a diaphragm is difficult to realize. For example, if conventional materials such as metalized Mylar® are made too thin, they may fatigue and break. 
         [0029]    Graphene is an ideal material for small, efficient, high-quality broad-band audio speakers because it satisfies all the above criteria. It is electrically conducting, has a small mass density, and can be configured to have small effective spring constant. The effective spring constant of a thin circular membrane is 
         [0000]        k   eff =4πσ t   (1)
 
         [0000]    where σ is the stress and t is the thickness of the membrane. It is convenient to use per-area values for modeling the diaphragm vibration since for a given membrane, the mass per unit area is constant. The equivalent per area spring constant is therefore 
         [0000]    
       
         
           
             
               
                 
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         [0000]    where R is the radius of the circular membrane. Note that the spring constant k scales proportionally with the thickness of the membrane and inversely with the 2nd power of the radius of the membrane. The exceptional mechanical strength of graphene makes it possible to construct large and thin suspended diaphragms, which effectively reduces k. 
         [0030]    Graphene has been previously used to construct a thermoacoustic loudspeaker. In the thermoacoustic configuration, graphene serves as a stationary heater to alternately heat the surrounding air, thereby producing, via thermal expansion, a time-dependent pressure variation (i.e., a sound wave). The method is effective in the ultrasonic region because of graphene&#39;s small heat capacity; for this reason, carbon nanotube films can also be utilized. However, for thermoacoustic speakers operating at audio frequencies, most of the input energy is dissipated by heat conduction through the air and does not generate sound. For example, the power efficiency for a graphene thermoacoustic speaker is exceedingly small, decreasing from ˜10 −6  at 20 kHz to ˜10 −8  at 3 kHz. The thermoacoustic approach also suffers from sound distortion because the heating power is proportional to the square of the input signal, and the transduction is therefore intrinsically non-linear. 
       Apparatus 
       [0031]    Described herein are embodiments of an electrostatically driven, high-efficiency, mechanically vibrating graphene diaphragm-based audio speaker. Even without optimization of the speaker design, a test speaker was able to produce excellent frequency response across the whole audible region (about 20 Hz to 20 KHz), comparable or superior to the performance of conventional-design commercial counterparts. 
         [0032]      FIG. 1A  shows an example of a cross-sectional schematic diagram of an electrostatically driven graphene speaker (EDGS)  100 . The EDGS  100  includes a graphene membrane  105  suspended in a frame  107  (see  FIG. 1B  for a top-down view) approximately midway between two electrodes  110  and  115 . In some embodiments, the graphene membrane  105  is a monolayer graphene membrane (i.e., a single layer of graphene). In some embodiments, the graphene membrane  105  is a multilayer graphene membrane. For example, the graphene membrane  105  may include about 1 to 100 layers of graphene. In some embodiments, the graphene membrane  105  is about 20 nanometers (nm) to 40 nm thick, or about 30 nm thick. 
         [0033]    The frame  107  allows for a portion of the graphene membrane  105  to be suspended or not in contact with other materials. Suspending the graphene membrane  105  in the frame  107  in this manner may form a graphene diaphragm; a diaphragm is a sheet of a semi-flexible material anchored at its periphery. In some embodiments, the frame is a disk of material defining a substantially circular open region, typically in a central portion of the disk. That is, in some embodiments, the frame is similar to a hardware washer; a washer is a thin plate of material (typically disk-shaped) with a hole (typically circular and in the middle) though it. In some embodiments, the frame is about 120 microns to 360 microns thick, or about 240 microns thick. In some embodiments, the frame has an outer diameter of about 7 millimeters (mm) to 21 mm, or about 14 mm. The open region defined by the frame may have a diameter of about 3 mm to 11 mm, or about 7 mm. 
         [0034]    In some embodiments, the frame may include other configurations. For example, the frame may define an open region having a rectangular, square, or oval shape, with the material of the frame designed to suspend the graphene membrane in this open region. 
         [0035]    In some embodiments, the graphene membrane  105  is mounted about midway along the thickness of the frame  107 . For example, when the frame  107  is about 240 microns thick, the graphene membrane  105  may be mounted to the frame  107  such that about 120 microns of the frame extend from each side of the graphene membrane. In some embodiments, the graphene membrane is offset from the midpoint along the thickness of the frame. 
         [0036]    In some embodiments, the frame  107  is a polymer, metal, or semiconducting material. Many different materials could be used for the frame, as long as the material has sufficient mechanical strength to support the graphene membrane  105  and to allow for incorporation of the frame  107  into the EDGS  100 . 
         [0037]    In some embodiments, the frame  107  includes two parts, such that the graphene membrane  105  is attached to one part of the frame and then the other part of the frame is stacked on top of the graphene membrane, sandwiching the graphene membrane between the two parts of the structure. For example, a graphene membrane could be suspended in a frame by aligning and attaching two hardware washer shaped parts to either side of the graphene membrane. 
         [0038]    In some embodiments, the graphene membrane  105  is in electrical contact with a terminal (not shown). In some embodiments, the terminal is a metal wire. For example, in some embodiments, the terminal is a gold wire that is about 10 microns to 30 microns thick, or about 20 microns thick. In some embodiments, terminals of other materials and of other dimensions may be used. 
         [0039]    The electrodes  110  and  115  are configured to actuate the graphene membrane  105 . In some embodiments, the electrodes  110  and  115  include perforations  117  so that sound may be emitted from the EDGS  100 . The perforations  117  are though-holes in the electrodes  110  and  115 . The perforations  117  may have any cross-section. For example, in some embodiments, the perforations  117  may have a square cross-section. In some embodiments, the perforations  117  may have a dimension of about 200 microns to 300 microns, or about 250 microns. For example, when the perforations  117  have a square cross-section, the side of a perforation may be about 200 microns to 300 microns; when the perforations  117  have a circular cross-section, the diameter of a perforation may be about 200 microns to 300 microns. In some embodiments, the electrodes are about 425 microns to 625 microns thick, or about 525 microns thick. 
         [0040]    In some embodiments, one of the electrodes  110  or  115  includes perforations so that sound may be emitted from the EDGS  100 . The other electrode may define an open region, and not necessarily perforations. The open region may allow the graphene membrane to move; i.e., the open region may allow for air/gas to enter and exit from between the electrode and the membrane, which could hinder the movement of the membrane. 
         [0041]    The electrodes  110  and  115  may be any material that is capable of conducting electricity. In some embodiments, the electrodes  110  and  115  are silicon electrodes. In some embodiments, an oxide layer  120  is deposited or formed on the electrodes  110  and  115  to prevent the graphene membrane  105  from shorting to the electrodes  110  and  115  at large drive amplitudes when the EDGS is in operation. In some embodiments, the oxide layer  120  is about 400 nm to 600 nm thick, or about 500 nm thick. In some embodiments, the oxide layer is a SiO 2  layer. 
         [0042]      FIG. 2  shows an example of a method of use of a device including a graphene membrane. The method  200  may be similar to elements of the prototype demonstration of an EDGS device described below. Starting at block  205 , a device is provided. The device may be an EDGS, similar to a device as described above with respect to  FIGS. 1A and 1B . At block  210 , the graphene membrane of the device is biased with a direct current voltage. At block  215 , the first electrode and the second electrode of the device are biased with an input signal. Biasing the first electrode and the second electrode may cause the graphene membrane of the device to move and generate a sound. 
         [0043]    In some embodiments, the input signal is generated from an audio signal. In some embodiments, an amplitude of the input signal is about 0 volts to 15 volts. In some embodiments, the direct current voltage applied to the graphene membrane is about 50 volts to 150 volts. In some embodiments, the first electrode and the second electrode are biased at opposite polarities. 
       EXAMPLES 
       [0044]    The following examples are intended to be examples of the embodiments disclosed herein, and are not intended to be limiting. 
         [0045]    To fabricate an EDGS device, graphene was first synthesized and then attached to a frame, which was then sandwiched between separately fabricated electrodes. Multilayer graphene was synthesized on an about 25 micron thick nickel foil in a chemical vapor deposition (CVD) furnace at about 1000° C. The nickel foil was first annealed at about 1000° C. for about 1 hour with about 50 sccm hydrogen flow at about 200 mTorr, after which the hydrogen flow was increased to about 100 sccm and methane was introduced at about 5 sccm to start the growth process. The growth pressure was about 2 Torr. After about 20 minutes, the furnace was turned off and the nickel foil was quickly removed from the hot zone to allow the formation of graphene layers. 
         [0046]    After the growth, a self-adhesive circular frame (e.g., 60 microns thick) with an about 7 mm diameter opening was attached to the graphene layer on the nickel foil. The foil was then etched away with an about 0.1 g/ml FeCl 3  solution, so that the graphene membrane was only attached to and supported by the frame. The frame was first transferred to a fresh deionized (DI) water bath several times to clean the etchant residue, and then immersed in acetone. The multilayer graphene diaphragm may be strong enough to be directly dried in air by pulling the frame out from acetone. In one experimental fabrication process, the thickness of a free-standing graphene diaphragm was determined by light transmission measurement to be about 30 nm thick (e.g., about 22% to 25% transmission) using the above-described fabrication process. 
         [0047]    Electrical contact to the graphene membrane was made by attaching an about 20 micron diameter gold wire to the portion of graphene lying on the supporting frame. Another circular frame was attached to the original frame from the opposite side (so that the graphene diaphragm was sandwiched between them) to fix the gold wire. The frames also served as spacers between graphene and the electrodes in the speaker assembly. The gap distance can be increased by stacking multiple (empty) frames on each other. For the EDGS used to generate the results presented below, two frames on each side of the graphene were used, which gave a gap distance d of about 120 microns. 
         [0048]    The electrodes were constructed from silicon (about 525 microns thick, resistivity of about 10 Ohm·cm, test grade). Photolithography and deep-reactive-ion-etching operations were used to construct through-wafer square holes of about 250 microns wide as sound emitting windows. An about 500 nm thick protective wet thermal oxide layer was then grown on the wafer at 1050° C. The wafer was then diced into individual electrodes. Dicing the wafer also exposed the silicon so that electric connections are made by attaching conductive wires to the edges of the electrodes, for example, with silver paste. 
         [0049]    To operate the EDGS, the graphene of the EDGS is DC biased at V DC . With no input signal, the electrostatic forces from the upper electrode and the lower electrode balance. When the two electrodes are driven with opposite polarity at V in , the total electrostatic force applied on graphene is (per unit area) 
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         [0000]    where F 1  and F 2  are force magnitudes due to the respective electrodes, ε is the electric permittivity of air, and d is the nominal distance between graphene and electrodes. Eq. (3) shows that the actuating force is linearly proportional to the input signal, an advantage for low sound distortion. 
         [0050]    For prototype demonstration, two electrodes and one graphene diaphragm were sandwiched together and held by a spring clip. In another implementation, a 7 mm inner-diameter pipe, serving as a wave guide, was perpendicularly attached to the surface of the electrodes to facilitate sound coupling between the speaker and a listener&#39;s ear. A wave guide will improve far-field efficiency for a small speaker operating at wavelength larger than the diaphragm size. 
         [0051]    Described below are prototype demonstration tests for the EDGS. V DC =100 V was used to bias the EDGS device, and the input sound signal was introduced from a signal generator or from a commercial laptop or digital music player. The maximum amplitude of the input signal V in  used in the test was 10 V. The operation current was usually a few nano-amps, indicating very low power consumption (i.e., much less than 1 μW) and high power efficiency. In fact, the power efficiency of an electrostatic speaker can be very high (i.e., close to 1) because the power dissipation path is almost pure air damping, which converts the mechanical vibration of diaphragm to sound. Magnetic coil type earphones, the type used today for virtually all earphone applications, typically have efficiencies less than 0.1. 
         [0052]    The sound generated by the graphene speaker was easily audible by the human ear. The fidelity was qualitatively excellent when listening to music. To quantitatively characterize the speaker, the frequency response curve was measured from 20 Hz to 20 kHz and compared to a commercial earphone of similar size. The sound card in a laptop computer was used to generate equal-amplitude sine waves, and a commercial condenser microphone was used to measure the sound pressure level (SPL) at different frequencies. 
         [0053]    As can be seen in  FIGS. 3A and 3B , the graphene speaker ( FIG. 3A ), with almost no specialized acoustic design, performed comparably to a high quality commercial earphone ( FIG. 3B ). Moreover, the high-frequency performance of the EDGS, both in terms of maintaining high response and avoiding sharp resonances (the slow oscillations in the EDGS curve were due to sound wave interference in the space between the speaker and microphone and they depend on the relative position of the speaker and microphone, but the main trend is consistent), was markedly better than that of the commercial earphone ( FIG. 3B ) due to the low-mass diaphragm. In the low frequency region, the EDGS and commercial earphone response curves both bend downward, likely due to limited capability of the sensing microphone and restricted coupling between the speaker and microphone. Nevertheless, the low-frequency performance of the EDGS was markedly better than that predicted for a thermoacoustic speaker ( FIG. 3C ; points in  FIG. 3C  are experimental data, while the solid line is the theoretically predicted behavior for an ideal thermoacoustic speaker). At very high frequencies (&gt;10 kHz), the thermoacoustic speaker maintained its good high frequency response, but, as noted above, the power efficiency was at least six orders of magnitude lower than that for the EDGS, which makes it impractical for most portable applications. 
         [0054]    The speaker-to-microphone performance test had limited accuracy, because the measured response curve is for the whole system—from the sound card to amplifier, to speaker, to microphone, and finally back to sound card. Every transduction introduces some distortion in the measurement. For example, the response was sensitive to the relative position between the speaker and the microphone. To further demonstrate the capability of the EDGS graphene diaphragm, a laser Doppler velocimetry (LDV) was employed to directly measure the mechanical response limits of the diaphragm. Such a measurement is useful because it eliminates extrinsic effects (e.g., acoustic structural design, sound card, and microphone response), and represents the “pure” response of the graphene diaphragm itself. The measured frequency response is illustrated in  FIG. 4 . Within experimental error, the LDV frequency response curve for the EEGS diaphragm is relatively flat from 20 Hz to 20 kHz, which is the desired response of an ideal speaker diaphragm. 
       CONCLUSION 
       [0055]    In summary, a robust speaker including a graphene diaphragm (e.g., single-layer of multi-layer) is disclosed herein. The diaphragm is driven electrostatically and can reproduce sound with high fidelity. Further, the technique can be scaled to construct larger speakers by arraying the graphene diaphragm. 
         [0056]    An EDGS device as described herein could also serve as a microphone. The microphone should also have outstanding response characteristics due to the graphene&#39;s low mass and the good coupling to ambient air. 
         [0057]    In the foregoing specification, the invention has been described with reference to specific embodiments. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the invention as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of invention.