Patent Publication Number: US-2021180723-A1

Title: Virtual valve in a mems-based cooling system

Description:
BACKGROUND OF THE INVENTION 
     As computing devices grow in speed and computing power, the heat generated by the computing devices also increases. Various mechanisms have been proposed to address the generation of heat. Active devices, such as fans, may be used to drive air through large computing devise, such as laptop computers or desktop computers. Passive cooling devices, such as heat spreaders, may be used in smaller computing devices, such as smartphones. However, such active and passive devices may be unable to adequately cool both mobile devices such as smartphones and larger devices such as laptops and desktop computers. Consequently, additional cooling solutions for computing devices are desired. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various embodiments of the invention are disclosed in the following detailed description and the accompanying drawings. 
         FIGS. 1A-1D  are diagrams depicting an exemplary embodiment of an active cooling system usable with a structure. 
         FIGS. 2A-2C  are graphs depict operation and driving of cooling elements in an embodiment of an active cooling system. 
         FIGS. 3A-3B  are diagrams depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIGS. 4A-4B  are diagrams depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIGS. 5A-5C  are diagrams depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIG. 6  is a diagram depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIG. 7  is a diagram depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIGS. 8A-8C  are diagrams depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIG. 9  is a diagram depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIGS. 10A-10B  are diagrams depicting another exemplary embodiment of an active cooling system usable with a structure. 
         FIG. 11  is a flow chart depicting an exemplary embodiment of a method for driving cooling elements in an embodiment of an active cooling system. 
     
    
    
     DETAILED DESCRIPTION 
     The invention can be implemented in numerous ways, including as a process; an apparatus; a system; a composition of matter; a computer program product embodied on a computer readable storage medium; and/or a processor, such as a processor configured to execute instructions stored on and/or provided by a memory coupled to the processor. In this specification, these implementations, or any other form that the invention may take, may be referred to as techniques. In general, the order of the steps of disclosed processes may be altered within the scope of the invention. Unless stated otherwise, a component such as a processor or a memory described as being configured to perform a task may be implemented as a general component that is temporarily configured to perform the task at a given time or a specific component that is manufactured to perform the task. As used herein, the term ‘processor’ refers to one or more devices, circuits, and/or processing cores configured to process data, such as computer program instructions. 
     A detailed description of one or more embodiments of the invention is provided below along with accompanying figures that illustrate the principles of the invention. The invention is described in connection with such embodiments, but the invention is not limited to any embodiment. The scope of the invention is limited only by the claims and the invention encompasses numerous alternatives, modifications and equivalents. Numerous specific details are set forth in the following description in order to provide a thorough understanding of the invention. These details are provided for the purpose of example and the invention may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the invention has not been described in detail so that the invention is not unnecessarily obscured. 
     As semiconductor devices become increasingly powerful, the heat generated during operations also grows. For example, processors for mobile devices such as smartphones, tablets and notebooks can operate at high clock speeds, but produce a significant amount of heat. Because of the quantity of heat produced, processors may run at full speed only for a relatively short period of time. After this time expires, throttling (e.g. slowing of the processor&#39;s clock speed) occurs. Although throttling can reduce heat generation, it also adversely affects processor speed and, therefore, the performance of devices using the processors. As technology moves to  5 G and beyond, this issue is expected to be exacerbated. 
     Larger devices, such as laptop or desktop computers include electric fans that have rotating blades. The fan that can be energized in response to an increase in temperature of internal components. The fans drive air through the larger devices to cool internal components. However, such fans are typically too large for mobile devices such as smartphones or for thinner devices such as tablets. Fans also may have limited efficacy because of the boundary layer of air existing at the surface of the components, provide a limited airspeed for air flow across the hot surface desired to be cooled and may generate an excessive amount of noise. Passive cooling solutions may include components such as a heat spreader and a heat pipe or vapor chamber to transfer heat to a heat exchanger. Although a heat spreader somewhat mitigates the temperature increase at hot spots, the amount of heat produced in current and future devices may not be adequately addressed. Similarly, a heat pipe or vapor chamber may provide an insufficient amount of heat transfer to remove excessive heat generated. Thus, additional cooling solutions capable of being used with smaller mobile device are desired. 
     An active cooling system is described. The active cooling system includes at least one cooling element that has a vent therein and is in communication with a fluid. The cooling element(s) are actuated to vibrate to drive the fluid toward a heat-generating structure and to alternately open and close at least one virtual valve corresponding to the vent. The virtual valve is open for a low flow resistance and closed for a high flow resistance. The vent remains physically open for the virtual valve being closed. 
     In some embodiments, the at least one cooling element includes a first cooling element and a second cooling element. The first cooling element and/or the second cooling element may be a piezoelectric micro-electrical mechanical system (MEMS) cooling element. The first cooling element has a passive vent therein and is in communication with a fluid. The second cooling element is between the first cooling element and a heat-generating structure. The second cooling element has an active vent therein. The virtual valve(s) include a passive virtual valve corresponding to the passive vent and an active virtual valve corresponding to the active vent. The passive virtual valve is open in a suction arrangement and closed in an expulsion arrangement. The active virtual valve is closed in the suction arrangement and open in the expulsion arrangement. At least one of the first cooling element and the second cooling element uses vibrational motion to provide the suction arrangement and the expulsion arrangement such that the fluid is directed toward the heat-generating structure and such that the active vent and the passive vent remaining physically open throughout the vibrational motion. 
     The first and second cooling elements may be configured such that in the suction arrangement the passive vent has a passive suction flow resistance and the active vent has an active suction flow resistance. The first and second cooling elements may also be configured such that in the expulsion arrangement, the passive vent has a passive expulsion flow resistance and the active vent has an active expulsion flow resistance. The passive expulsion flow resistance is greater than the active expulsion flow resistance. The passive suction flow resistance is less than the active suction flow resistance. Thus, by moderating the dynamic flow resistance through the active and passive vents, virtual valves may be formed at the active and passive vents. The active and passive virtual valves may be alternately opened and closed as described above. 
     In some embodiments, the active cooling system includes an orifice plate having orifice(s) therein. The orifice plate is between the second cooling element and the heat-generating structure. The orifice(s) have an axis oriented at an angle from a normal to a surface of the heat-generating structure. The angle is selected from substantially zero degrees and a nonzero acute angle. 
     In some embodiments, the first and second cooling elements are separated by a gap. The vibrational motion is such that the gap has a first width of not more than ten micrometers in the expulsion arrangement and the gap has a second width of not less than twenty micrometers in the suction arrangement. Thus, the width of the gap may affect the flow resistance of the active and passive vents. The passive vent may be configured such that the passive expulsion flow resistance divided by the passive suction flow resistance is at least three and not more than ten. Thus, the passive virtual valve for the passive vent may be considered open in the suction arrangement and closed in the expulsion arrangement. In some embodiments, the active vent is configured such that the active suction flow resistance divided by the active expulsion flow resistance is at least three and not more than ten. Thus, the active virtual valve for the active vent may be considered to be open in the expulsion arrangement and closed in the suction arrangement. In such embodiments, the ratio of the flow resistance for the virtual valve being closed to the virtual valve being open is at least three and not more than ten. The cooling elements may be configured to direct the fluid toward the heat-generating structure at a speed of at least thirty meters per second. 
     The vibrational motion has a frequency of at least 15 kHz in some embodiments. The vibrational motion may be out-of-phase vibrational motion of the first cooling element and the second cooling element. Both cooling elements vibrate in some embodiments. This out-of-phase vibration, or the vibration of individual cooling element(s), may be at or near the resonance frequency of the cooling element(s). In some embodiments, an elastic device couples the first and second cooling elements. Such an elastic device may aid in maintaining out-of-phase vibration at or near resonance. In some embodiments, the first cooling element has a landing adjacent to the passive vent and the second cooling element includes a plug opposite to the landing the first cooling element. In some embodiments, the plug includes a plug surface facing the passive vent. The plug surface and/or a landing surface of the landing forms tortuous path for the fluid. In some embodiments, the cooling system includes a return path for the fluid to a side of the first cooling element distal from the heat-generating structure. 
     Using the active cooling system, fluid may be drawn in through the passive vent (in the suction arrangement/passive virtual valve open) and driven through the active vent and orifices in the orifice plate (in the expulsion arrangement/active virtual valve open). Because of the vibrational motion, fluid is driven toward the heat-generating structure, may deflect off of the heat-generating structure and travels along the channel between the heat-generating structure and orifice plate. Thus, the fluid may efficiently dissipate heat from the heat-generating structure. Because fluid impinges upon the heat-generating structure with sufficient speed and in some embodiments substantially normal to the heat-generating structure, the boundary layer of fluid at the heat-generating structure may be thinned and/or partially removed. Consequently, heat transfer between the heat-generating structure and the moving fluid is improved. Because the heat-generating structure is more efficiently cooled, the corresponding integrated circuit may be run at higher speed and/or power for longer times. Thus, performance of a device utilizing the active cooling system may be improved. Further, the active cooling system may be a MEMS device. Consequently, the active cooling systems are suitable for use in thinner devices such as mobile devices (e.g. smartphones, virtual reality devices and tablets). Performance of mobile devices may thus be improved. The active cooling system may also be used in other compute devices-both mobile (such as those discussed above and laptop computers) and non-mobile (such as desktop computers or smart televisions). Because the first and second cooling element(s) may be vibrated at frequencies of 15 kHz or more, users may not hear any noise associated with actuation of cooling elements. If driven at or near resonance frequency for the first and second piezoelectric cooling element(s), the power used in operating cooling systems may be significantly reduced. 
     Further, the active and passive vents remain physically open throughout vibration. Instead of physically closing vents, the virtual valves corresponding to the vents are opened and closed. This is accomplished by providing sufficient differences in the flow resistance (or pressure) between the suction and expulsion arrangements, as described above. In lieu of physically closing, a passive virtual valve for the passive vent may be closed while an active virtual valve for the active vent is open and vice versa. Because vents in cooling element(s) need not be physically closed, resonance of the cooling element(s) may be more readily maintained. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating the active cooling system may be improved. 
       FIGS. 1A-1D  are diagrams depicting an exemplary embodiment of active cooling system  100  usable with a heat-generating structure  102 . For clarity, only certain components are shown and  FIGS. 1A-1D  are not to scale.  FIGS. 1A-1C  depict operation of cooling system  100 , while  FIG. 1D  depicts piezoelectric cooling element  110 / 120 . Referring to  FIGS. 1A-1C , the cooling system  100  is used in connection with a heat-generating structure  102 . Although shown as symmetric, cooling system  100  need not be symmetric. 
     Heat-generating structure  102  generates or conducts heat from a nearby heat-generating object during operation and is desired to be cooled. Heat-generating structure  102  may include semiconductor components(s) including individual integrated circuit components such as processors, other integrated circuit(s) and/or chip package(s); sensor(s); optical device(s); one or more batteries; or other component(s) of an electronic device such as a computing device; heat spreaders; heat pipes; other electronic component(s) and/or other device(s) desired to be cooled. The devices may also have limited space in which to place a cooling system. For example, cooling system  100  may be used in computing devices. Such computing devices may include but are not limited to smartphones, tablet computers, laptop computers, two-in-one laptops, hand held gaming systems, digital cameras, virtual reality headsets, augmented reality headsets, mixed reality headsets and other devices. Cooling system  100  may be a micro-electro-mechanical system (MEMS) cooling system capable of residing within mobile computing devices. For example, the total height of cooling system  100  (from the top of heat-generating structure  102  to the top of system  100 /cooling element  110 ) may be less than one millimeter and in some embodiments does not exceed two hundred and fifty micrometers. Although one cooling system  100  is shown (e.g. one cooling cell), multiple cooling systems might be used in connection with heat-generating structure  102 . For example, a one or two-dimensional array of cooling cells might be utilized. 
     Cooling system  100  is in communication with a fluid used to cool heat-generating structure  102 . The fluid may be a gas or a liquid. For example, the fluid may be air. Cooling system  100  includes a first cooling element  110  that is in contact with a fluid and a second cooling element  120 . In some embodiments, cooling system  100  also includes orifice plate  130  and optional chimneys  160 . The fluid used to cool heat-generating structure  102  starts at the side of cooling element  110  distal from heat-generating structure  102 . 
     Cooling element  110  has a first side distal from heat-generating structure  102  and a second side proximate to heat-generating structure  102 . In the embodiment shown in  FIGS. 1A-1C , the first side of cooling element  110  is the top of cooling element  110  and the second side is the bottom of cooling element  110 . Cooling element  110  also has a passive vent  112  therein. In the embodiment shown, passive vent  112  is a centrally located aperture in cooling element  110 . In other embodiments, passive vent  112  may be located elsewhere. For example, passive vent  112  may be closer to one of the edges of cooling element  110 . Passive vent  112  may have a circular, rectangular or other shaped footprint. Although one passive vent  112  is shown, multiple passive vents might be used. 
     Cooling element  120  is between cooling element  110  and heat-generating structure  102 . In the embodiment shown, cooling element  120  is also between cooling element  110  and orifice plate  130 . Cooling elements  110  and  120  are separated by gap  142  and form a top chamber  140 . A bottom chamber  150  is formed between cooling element  120  and orifice plate  130 . Cooling element  120  also has active vents  122  therein. In the embodiment shown, active vents  122  are apertures located away from the central region of cooling element  120 . In other embodiments, active vents  122  may be located elsewhere. For example, an active vent may be centrally located in cooling element  120 . Although two active vents  122  are shown, another number (e.g. one, three, etc.) might be present. In some embodiments, active vents  122  are positioned such that the active vents  122  are not aligned with passive vent  112 . Active vents  122  may have circular, rectangular or other shaped footprints. 
     Cooling elements  110  and/or  120  may be a piezoelectric cooling element. An embodiment of piezoelectric cooling element  110  and/or  120  is shown in  FIG. 1D . Consequently, cooling element(s)  110  and/or  120  and analogous cooling elements are referred to hereinafter as piezoelectric cooling element though it is possible that a mechanism other than a piezoelectric might be used to drive the cooling element. In some embodiments, cooling element(s)  110  and/or  120  includes a piezoelectric layer  174  on a stainless steel and/or Hastelloy substrate  172 . In some embodiments, piezoelectric layer  174  includes multiple sublayers. For example, piezoelectric layer  174  may be a multilayer piezoelectric. Piezoelectric cooling element(s)  110  and/or  120  may also include a top electrode  176 . In some embodiments, a bottom electrode may be formed by stainless steel substrate  172 . In other embodiments, a bottom electrode (not shown) may be provided between substrate  172  and piezoelectric  174 . Other layers (not shown) including but not limited to seed, capping, passivation or other layers might be included in piezoelectric cooling element(s)  110  and/or  120 . In some embodiments, cooling element(s)  110  and/or  120  have a thickness of not more than two hundred micrometers. In some such embodiments, the thickness(es) of cooling element(s)  110  and/or  120  is not more than one hundred micrometers (e.g. may be nominally one hundred nanometers). In some embodiments, the width and/or length (or radius) of piezoelectric cooling element(s)  110  and/or  120  are at least three millimeters. In some embodiments, the width and/or length is at least five millimeters. In some such embodiments, the width and/or length is at least seven millimeters. 
     Orifice plate  130  has orifices  132  therein. Although shown as distributed throughout orifice plate  130 , orifices may be positioned in another manner. A single orifice plate  120  for a single cooling system  100 . In other embodiments, multiple cooling systems  100  may share an orifice plate. Orifices  132  are shown as having an axis oriented normal to a surface of heat-generating structure  102 . In other embodiments, the axis of one or more orifices  132  may be at another angle. For example, the angle of the axis may be selected from substantially zero degrees and a nonzero acute angle. 
     In some embodiments, cooling system  100  includes chimneys  160 . Chimneys  160  provide a return path for heated fluid to flow away from heat-generating structure  102 . In some embodiments, chimneys  160  return fluid to the side of cooling element  110  distal from heat-generating structure  102 . In the embodiment shown, chimneys  160  direct heated fluid substantially perpendicular to heat-generating structure  102  and toward the side of cooling element  110  distal from heat-generating structure  102 . In other embodiments, chimneys  160  may be omitted or configured in another manner. For example, chimneys may instead directed fluid away from heat-generating structure  102  in a direction parallel to heat-generating structure  102  or perpendicular to heat-generating structure  102  but opposite to the direction shown (e.g. toward the bottom of the page). If multiple cooling systems  100  are provided in an array, each cooling system  100  may include chimneys, only cooling systems  100  at the edges may include chimneys, other ducting may be provided at the edges or other locations in the array to provide a path for heated fluid to flow and/or other mechanisms may be used to allow heated fluid to be removed from the region proximate to heat-generating structure  102 . 
     As discussed above, cooling system  100  may be a MEMS device. Thus, the dimensions of cooling system  100  may be small. For example, cooling system  100  may have a rectangular footprint with sides having a length of not more than seven millimeters. In some such embodiments, the length may be at least three millimeters. In some embodiments, cooling system  100  is square. Orifice plate  130  may be located a distance from heat-generating structure  102  that is at least fifty micrometers and not more than five hundred micrometers. In some embodiments, this distance is not more than two hundred micrometers. In some embodiments, this distance between orifice plate  130  and heat-generating structure  102  is at least one hundred micrometers. Orifice plate  130  may have a thickness of at least ten and not more than twenty-five micrometers in some embodiments. The depth of cooling system  100  may be at least forty micrometers and not more than five hundred micrometers. In some embodiments, this depth is at least fifty micrometers and not more than three hundred micrometers. Thus, piezoelectric cooling elements  110  and/or  120  may be at least forty and not more than five hundred micrometers from orifice plate  130 . Piezoelectric cooling elements  110  and/or  130  may be at least fifty and not more than five hundred micrometers from heat-generating structure  102 . In some embodiments, orifice plate  130  is at least fifty and not more than one hundred fifty micrometers thick. For example, orifice plate  130  may be nominally one hundred micrometers thick. In some embodiments, the entire thickness of cooling system  100  is not more than five hundred micrometers. In some embodiments, the entire thickness of cooling system  100  is at least two hundred fifty micrometers. In some embodiments, the diameters of orifices  132  are at least fifty micrometers and not more than two hundred micrometers. In some embodiments, orifices  132  occupy at least two percent and not more than five percent of the portion of the orifice plate  130  below cooling element  120 . In other embodiments, other dimensions may be used. 
       FIG. 1A  depicts cooling system  100  in a neutral position. Thus, cooling elements  110  and  120  are shown as substantially flat. In operation, piezoelectric cooling elements  110  and  120  are actuated to vibrate between positions shown in  FIGS. 1B and 1C . Piezoelectric cooling elements  110  and  120  are, therefore, piezoelectric actuators. Operation of cooling system  100  is described in the context of  FIGS. 1B and 1C . Referring to  FIG. 1B , piezoelectric cooling element  110  has been actuated to move away from (deform to be convex) heat-generating structure  102 , while piezoelectric cooling element  120  has been actuated to move toward (deform to be concave) heat-generating structure  102 . This configuration is referred to as the suction arrangement. Because of the vibrational motion of piezoelectric cooling elements  110  and  120 , gap  142  has increased in size and is shown as gap  142 A. For example, in some embodiments, gap  142  has a height of at least ten and not more than twenty micrometers in the neutral position ( FIG. 1A ). Gap  142 A may have a height of at least twenty and not more than thirty micrometers in the suction arrangement ( FIG. 1B ). Thus, top chamber  140  has increased in volume, while bottom chamber  150  has decreased in volume. In the suction arrangement, the flow resistance of passive vent  112  (passive suction flow resistance) is low. Consequently, the pressure at passive vent  112  is low. In contrast, the flow resistance of active vent  122  (active suction flow resistance) is high. Consequently, the pressure at active vent  122  is high. Because of the low passive suction flow resistance, fluid is drawn into top chamber  140  through passive vent  112 . This is shown by arrows in  FIG. 1B . However, fluid does not flow out of (or flows out to a limited extent) active vent  122  because of the high passive suction flow resistance. However, active vent  122  is not physically closed in this configuration. For example, active vent  122  is not in contact with orifice plate  130  in the suction arrangement. 
       FIG. 1C  depicts an expulsion arrangement. Piezoelectric cooling element  110  has been actuated to move toward (deform to be concave) heat-generating structure  102 , while piezoelectric cooling element  120  has been actuated to move away from (deform to be convex) heat-generating structure  102 . Because of the vibrational motion of piezoelectric cooling elements  110  and  120 , gap  142  has decreased in size and is shown as gap  142 B. For example, in some embodiments, gap  142  has a height of at least ten and not more than twenty micrometers in the neutral position ( FIG. 1A ). Gap  142 B has a height of at least five and not more than ten micrometers in the expulsion arrangement ( FIG. 1C ). Thus, top chamber  140  has decreased in volume, while bottom chamber  150  has increased in volume. In the expulsion arrangement, the flow resistance of passive vent  112  (passive expulsion flow resistance) is high. Consequently, the pressure at passive vent  112  is high. In contrast, the flow resistance of active vent  122  (active expulsion flow resistance) is low. Consequently, the pressure at active vent  122  is low. Because of the low active expulsion flow resistance, fluid is expelled from top chamber  140  through active vent  122 , into bottom chamber  150  and through orifices  132 . This is shown by arrows in  FIG. 1C . However, fluid does not flow out of (or flows out to a limited extent) passive vent  112  because of the high passive expulsion flow resistance. Thus, passive vent  112  is considered closed and active vent  122  is considered open in the expulsion arrangement. However passive vent  112  is not physically closed in this configuration. For example, passive vent  112  is not in contact with cooling element  120  in the expulsion arrangement. Gap  142 B does not have a zero length. 
     Virtual valves may be considered to be formed at or near active vent  122  and passive vent  112 . A virtual valve has a high, but not infinite, flow resistance when closed. Thus, a virtual valve does not physically block flow but instead uses a high flow resistance or high pressure to throttle or prevent flow. A virtual valve has a significantly lower flow resistance or pressure when open, allowing flow. In some embodiments, the ratio of flow resistances or pressures between closed and open for a virtual valve is at least three and not more than ten. Thus, active vent  122  and its virtual valve (“active virtual valve”) are considered closed in the suction arrangement because the flow resistance is sufficiently high that little or no fluid flows through active vent  122  in the suction arrangement. Passive vent  112  and its virtual valve (“passive virtual valve”) are considered open in the suction arrangement because the pressure or flow resistance is sufficiently low to allow fluid to be drawn in to top chamber  140  through passive vent  112 . In contrast, active vent  122  and active virtual valve are considered open in the expulsion arrangement because the pressure or flow resistance is sufficiently low to allow fluid to flow through active vent  122  and be driven out of orifices  132 . Passive vent  112  and passive virtual valve are considered closed in the expulsion arrangement because the pressure or flow resistance is sufficiently high that little to no fluid is drawn through passive vent  112  in the expulsion arrangement. 
     Due to the vibrational motion of cooling elements  110  and  120  (and the attendant decrease in gap  142 A/ 142 B from  FIG. 1B  to  FIG. 1C ), the fluid is drawn in to top chamber  140  and through orifices  132 . The motion of the fluid is shown by arrows through orifices  132 . The fluid may spread as it travels away from orifice plate  120 , as shown by dashed lines and arrows for some orifices  132  in  FIG. 1C . The fluid deflects off of heat-generating structure  102  and travels along the channel between heat-generating structure  102  and orifice plate  130 . 
     The motion between the positions shown in  FIGS. 1B and 1C  may be repeated. Thus, piezoelectric cooling elements  110  and  120  vibrate, drawing fluid through passive vent  112  from the distal side of cooling element  110 , into top chamber  140 , out of chamber  140  through active vent  122  and pushing the fluid through orifices  132  and toward heat-generating structure  102 . In some embodiments the frequency of vibration of piezoelectric cooling element(s)  110  during operation is at least 15 kHz. In some embodiments, the frequency is at least 20 kHz. Thus, piezoelectric cooling elements  110  and  120  may operate in the ultrasonic range. Further, in some embodiments, piezoelectric cooling element(s)  110  and/or  120  may be driven at or near the resonant frequency. In some embodiments, the resonant frequency of piezoelectric cooling element(s)  110  and/or  120  is at least 15 KHz. The resonant frequencies of piezoelectric cooling element(s)  110  and  120  may also be desired to be close. In some embodiments, the resonant frequencies of piezoelectric cooling element(s)  110  and  120  are desired to be within one hundred Hertz. In some embodiments, feedback is used to maintain piezoelectric cooling element(s)  110  and/or  120  at or near resonance. For example, the current used to drive piezoelectric cooling element(s)  110  and/or  120  may be periodically measured and the driving frequency of piezoelectric cooling element(s)  110  and/or  120  adjusted to maintain resonance. In some embodiments, piezoelectric cooling element(s)  110  and/or  120  are driven within a few hundred Hertz of the resonant frequency/frequencies for optimized performance. However, other frequencies are possible. For example, the proximity of the driving frequency to the resonant frequency may be used control flow. The further the driving frequency if from the resonant frequency, the lower the flow. The driving frequency may also be adjusted to maintain cooling element(s)  110  and/or  120  at or near one hundred and eighty degrees out-of-phase. 
     In some embodiments, the speed at which the fluid impinges on heat-generating structure  102  is at least thirty meters per second. In some embodiments, the fluid is driven by piezoelectric cooling elements  110  and  120  toward heat-generating structure  102  at a speed of at least forty meters per second. In some such embodiments, the fluid has a speed of at least forty-five meters per second. In some embodiments, the fluid has a speed of at least fifty-five meters per second. Further, in some embodiments, fluid speeds of at least sixty meters per section and/or seventy-five meters per second may be achieved. However, higher speeds may be possible in some embodiments. Fluid speeds in the range of thirty meters per second or more may be achievable in part due to judicious selection of the diameters of orifices  132 . 
     As indicated in  FIG. 1C , the fluid driven toward heat-generating structure  102  may move substantially normal (perpendicular) to the top surface of heat-generating structure  102 . In other embodiments, the fluid motion may have a nonzero acute angle with respect to the normal to the top surface of heat-generating structure  102 . In either case, the fluid may thin and/or form apertures in the boundary layer of fluid at heat-generating structure  102 . The boundary layer in one case is indicated by the curved dotted lines at the top surface of heat-generating structure  102  in  FIG. 1C . As a result, transfer of heat from heat-generating structure  102  may be improved. The fluid deflects off of heat-generating structure  102 , traveling along the surface of heat-generating structure  102 . In some embodiments, the fluid moves in a direction substantially parallel to the top of heat-generating structure  102 . Thus, heat from heat-generating structure  102  may be extracted by the fluid. The fluid may exit the region between orifice plate  130  and heat-generating structure  102  at the edges of cooling system  100 . In the embodiment shown, chimneys  160  at the edges of cooling system  100  allow fluid to be carried away from heat-generating structure  102 . In other embodiments, heated fluid may be transferred further from heat-generating structure  102  in another manner. The fluid may return to the distal side of cooling elements  110  where the fluid may exchange the heat transferred from heat-generating structure  102  to another structure or to the ambient environment. The fluid may then be circulated through cooling system  100  to extract additional heat. In other embodiments, heated fluid is carried away and replaced by new fluid at the distal side of cooling element  110 . As a result, heat-generating structure  102  may be cooled. 
     Opening and closing of passive vent  112  (passive virtual valve) and active vent  122  (active virtual valve) to draw fluid into chamber  150  and expel fluid through orifices  132  is based upon dynamic changes to flow resistance. In some embodiments, the ratio of active suction flow resistance to active expulsion flow resistance is at least three. In some such embodiments, the ratio of active suction flow resistance to active expulsion flow resistance is not more than ten. In some embodiments, the ratio of passive expulsion flow resistance to passive suction flow resistance is at least three. In some such embodiments, the ratio of passive expulsion flow resistance to passive suction flow resistance is not more than ten. Thus, virtual valves corresponding to vents  110  and/or  120  may be opened and closed. These ratios of pressures may be considered to be due to the change in size of gap  142 / 142 A/ 142 B (e.g. five through thirty micrometers in some embodiments). In some embodiments, the difference in pressure between being open and closed is 0.1 atmosphere through 0.2 atmosphere. For example, the pressure at passive vent  112  in the suction arrangement may be at least 0.1 atmosphere and not more than 0.2 atmosphere less than the pressure at passive vent  112  in the expulsion arrangement. Similarly, the pressure at active vent  122  in the expulsion arrangement may be at least 0.1 atmosphere and not more than 0.2 atmosphere less than the pressure at active vent  122  in the suction arrangement. 
     For example,  FIGS. 2A-2C  are graphs  200 ,  210  and  220  depicting operation and driving of cooling elements in an embodiment of an active cooling system. For simplicity, graphs  200 ,  210  and  220  are described in the context of cooling system  100 .  FIG. 2A  is a graph  200  depicting the driving of cooling element  110 .  FIG. 2C  is a graph  210  depicting driving of cooling element  120 .  FIG. 2C  is a graph  220  depicting the flow resistance during vibration of cooling elements  110  and  120 . As can be seen in  FIGS. 2A-2B , cooling elements  110  and  120  are driven one hundred and eighty degrees out of phase. In the embodiment shown, the amplitude of vibration is also different for the cooling elements  110  and  120 . In other embodiments, the amplitude of vibration may be the same or the amplitude of vibration for cooling element  120  may exceed that of cooling element  110 . Thus, the suction arrangement of  FIG. 1B  and expulsion arrangement of  FIG. 1C  can be obtained. For example, the suction arrangement is shown in the first section of graphs  210  and  220  (with the situation of  FIG. 1B  occurring at the maximum of graph  200  and the minimum of graph  210 ), the expulsion arrangement is shown in the second section of graphs  210  and  220  (with the situation of  FIG. 1C  occurring at the minimum of graph  200  and the maximum of graph  210 ), and the suction arrangement shown again in the third section of graphs  210  and  220  (with the situation of  FIG. 1B  occurring at the maximum of graph  200  and the minimum of graph  210 ). 
     Graph  200  of  FIG. 2C  depicts the corresponding flow resistance  222  of passive vent  112  and flow resistance  224  of active vent  122 . Thus, in suction arrangement, passive vent flow resistance  222  is low (passive virtual valve open), while active vent flow resistance  224  is high (active virtual valve closed). Fluid flows in through passive vent  112  in this suction arrangement. Although the suction arrangement is referred to as a single configuration (e.g. at the maxima/minima of graphs  200 / 210 ), fluid may flow into passive vent  112  throughout at least a portion of the first section of graphs  200  and  210 . As cooling system  100  transitions to the expulsion arrangement, cooling elements  110  and  120  are actuated toward each other. Thus, passive vent flow resistance  222  increases (passive virtual valve closes), while active vent flow resistance  224  decreases (active virtual valve opens). This trend continues through the expulsion arrangement, for which active vent flow resistance  224  is low and passive vent flow resistance  222  is high. Although the expulsion arrangement is referred to as a single configuration (e.g. at the minima/maxima of graphs  200 / 210 ), fluid may flow out of active vent  122  throughout at least a portion of second first section of graphs  200  and  210 . As cooling elements vibrate back toward the suction arrangement, the trend reverses. Thus, fluid is drawn into top chamber  140  and expelled through orifices  132 . 
     Using the cooling system  100 , fluid may be drawn in through passive vent  112  (in the suction arrangement) and driven through active vent  122  and orifices  132  (in the expulsion arrangement). Thus, the fluid may efficiently dissipate heat from heat-generating structure  102 . Because fluid impinges upon the heat-generating structure with sufficient speed (e.g. at least thirty meters per second) and in some embodiments substantially normal to the heat-generating structure, the boundary layer of fluid at the heat-generating structure may be thinned and/or partially removed. Consequently, heat transfer between heat-generating structure  102  and the moving fluid is improved. Because the heat-generating structure is more efficiently cooled, the corresponding integrated circuit may be run at higher speed and/or power for longer times. For example, if the heat-generating structure corresponds to a high-speed processor, such a processor may be run for longer times before throttling. Thus, performance of a device utilizing cooling system  100  may be improved. Further, cooling system  100  may be a MEMS device. Thus, cooling system  100  may small-having a total height not exceeding five hundred micrometers. Consequently, cooling systems  100  may be suitable for use in mobile devices, such as smart phones, other mobile phones, virtual reality headsets, tablets, two-in-one computers, wearables and handheld games, in which limited space is available. Performance of mobile devices may thus be improved. The active cooling system may also be used in other compute devices. Because piezoelectric cooling element(s)  110  and/or  120  may be vibrated at frequencies of 15 kHz or more, users may not hear any noise associated with actuation of cooling elements. If driven at or near resonance frequency for the first and second piezoelectric cooling element(s), the power used in operating cooling systems may be significantly reduced. 
     Further, passive vent  112  and active vent  122  remain physically open throughout vibration. Instead of physically closing, virtual valves for vents  112  and  122  are opened and closed by providing sufficient differences in the flow resistance (or pressure at the vents) between the vents in the suction and expulsion arrangements. Cooling elements  110  and  120  do not physically contact each other to close active vent  122  or passive vent  112  during vibration. Similarly, cooling element  120  does not contact orifice plate  130  to close active vent  122 . Thus, resonance of cooling element(s)  110  and/or  120  may be more readily maintained. More specifically, physical contact between cooling element(s)  110  and/or  120  and other structures disturbs the resonance conditions for cooling element(s)  110  and/or  120 . Disturbing these conditions may drive cooling element(s)  110  and/or  120  out of resonance. Thus, additional power would need to be used to maintain actuation of cooling element(s)  110  and/or  120 . Further, the fluid driven by cooling element(s)  110  and/or  120  may decrease. These, issues are avoided through the use of virtual valves as discussed above. In addition, because cooling elements  110  and  120  are driven out of phase (e.g. one hundred and eighty degrees out-of-phase in some embodiments), sympathetic vibration may be achieved. For sympathetic vibration, additional motion of cooling elements  110  and/or  120  may be achieved. A larger change in the size of gap  142 / 142 A/ 142 B and, therefore, a higher volume of fluid flow may be obtained. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating the cooling system  100  may be improved. 
       FIGS. 3A-3B  are diagrams depicting an exemplary embodiment of active cooling system  300  usable with a heat-generating structure  302 . For clarity, only certain components are shown and  FIGS. 3A-3B  are not to scale.  FIGS. 3A-3B  depict operation of cooling system  300 . Cooling system  300  is used in connection with a heat-generating structure  302 . 
     Cooling system  300  and heat-generating structure  302  are analogous to cooling system  100  and heat-generating structure  102 , respectively. Thus, cooling system  300  includes piezoelectric cooling elements  310  and  320 , orifice plate  330  having orifices  332  therein, top chamber  340  having gap  342 A/ 342 B, bottom chamber  350  and optional chimneys  360 . Piezoelectric cooling system  300  may be a MEMS device and thus may have dimensions analogous to those described above. However, in the embodiment shown, only cooling element  310  is actuated to vibrate between positions shown in  FIGS. 3A and 3B . In the embodiment shown, therefore, cooling element  320  might be omitted or may simply be a stationary plate having vent(s)  422  therein. 
     Referring to  FIG. 3A , piezoelectric cooling element  310  has been actuated to move away from (deform to be convex) heat-generating structure  302 . This configuration is the suction arrangement. Because of the vibrational motion of piezoelectric cooling element  310 , the gap has increased in size from its neutral position and is shown as gap  342 A. For example, gap  342 A may have a height of at least twenty and not more than thirty micrometers in the suction arrangement ( FIG. 3A ). Thus, top chamber  340  has increased in volume. In the suction arrangement, the flow resistance of passive vent  312  (passive suction flow resistance) is low. Consequently, the pressure at passive vent  312  is low and the corresponding passive virtual vent is open. In contrast, the flow resistance of active vent  322  (active suction flow resistance) is relatively high. Consequently, the pressure at active vent  322  is relatively high and the active virtual vent is closed. Because of the low passive suction flow resistance, fluid is drawn into top chamber  340  through passive vent  312 . This is shown by arrows in  FIG. 3A . However, fluid does not flow out of (or flows out to a limited extent) active vent  322 . Thus, active vent  322  and the corresponding active virtual valve are considered closed and passive vent  312  and corresponding passive virtual valve are considered open in the suction arrangement. However, active vent  322  is not physically closed in this configuration. For example, active vent  322  is not in contact with orifice plate  130  in the suction arrangement. In the suction arrangement, therefore, the virtual valve for active vent  322  is closed while the virtual valve for passive vent  312  is open. 
       FIG. 3B  depicts an expulsion arrangement. Piezoelectric cooling element  310  has been actuated to move toward (deform to be concave) heat-generating structure  302 . Because of the vibrational motion of piezoelectric cooling element  310 , the gap decreased in size from its neutral position and is shown as gap  342 B. For example, in some embodiments, gap  342 B has a height of at least five and not more than ten micrometers in the expulsion arrangement. Thus, top chamber  340  has decreased in volume. In the expulsion arrangement, the flow resistance of passive vent  312  (passive expulsion flow resistance) is high. Consequently, the pressure at passive vent  312  is high. The passive virtual valve corresponding to passive vent  312  is considered closed. In contrast, the flow resistance of active vent  322  (active expulsion flow resistance) is relatively low. Consequently, the pressure at active vent  322  is relatively low. Thus, the active virtual valve corresponding to active vent  322  is open. Because of the low active expulsion flow resistance, fluid is expelled from top chamber  340  through active vent  322 , into bottom chamber  350  and through orifices  332 . This is shown by arrows in  FIG. 3B . However, fluid does not flow out of (or flows out to a limited extent) passive vent  312  because of the high passive expulsion flow resistance. Thus, the passive virtual valve for passive vent  312  is considered closed, while the active virtual valve for active vent  322  is considered open in the expulsion arrangement. However passive vent  312  is not physically closed in this configuration. For example, passive vent  312  is not in contact with cooling element  320  in the expulsion arrangement. Gap  342 B does not have a zero length. 
     Cooling system  300  may share the benefits of cooling system  100 . Cooling system  300  may more efficiently dissipate heat from heat-generating structure  302  for the reasons discussed above. Thus, performance of a device utilizing cooling system  300  may be improved. Further, cooling system  300  may be a MEMS device having the dimensions described above. Thus, piezoelectric cooling system  300  is suitable for use in mobile devices, such as smart phones, in which limited space is available. Piezoelectric cooling system  300  may also be used in other compute devices-both mobile and non-mobile. Performance of such devices may thus be improved. Because piezoelectric cooling elements  310  and/or  320  may be vibrated at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  300  may be quieter and consume less power. Because vents  310  and  320  remain physically open, cooling elements  310  and/or  320  may not contact each other (or orifice plate  330 ) during use. Thus, resonance of cooling elements  310  and/or  320  may more easily be maintained. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  300  may be improved. 
       FIGS. 4A-4B  are diagrams depicting an exemplary embodiment of active cooling system  400  usable with a heat-generating structure  402 . For clarity, only certain components are shown and  FIGS. 4A-4B  are not to scale.  FIGS. 4A-4B  depict operation of cooling system  400 . Cooling system  400  is used in connection with a heat-generating structure  402 . 
     Cooling system  400  and heat-generating structure  402  are analogous to cooling system(s)  100  and/or  300  and heat-generating structure(s)  102  and/or  302 , respectively. Thus, cooling system  400  includes piezoelectric cooling elements  410  and  420 , orifice plate  430  having orifices  432  therein, top chamber  440  having gap  442 A/ 442 B, bottom chamber  450  and optional chimneys  460 . Piezoelectric cooling system  400  may be a MEMS device and thus may have dimensions analogous to those described above. However, in the embodiment shown, only cooling element  420  is actuated to vibrate between positions shown in  FIGS. 4A and 4B . In the embodiment shown, therefore, cooling element  410  might be omitted or may simply be a stationary plate having a vent  412  therein. 
     Referring to  FIG. 4A , piezoelectric cooling element  420  has been actuated to move toward (deform to be concave) heat-generating structure  402 . This configuration is the suction arrangement. Because of the vibrational motion of piezoelectric cooling element  420 , the gap has increased in size from its neutral position and is shown as gap  442 A. For example, gap  442 A may have a height of at least twenty and not more than thirty micrometers in the suction arrangement ( FIG. 4A ). Thus, top chamber  440  has increased in volume and bottom chamber  440  has decreased in volume. In the suction arrangement, the flow resistance of passive vent  412  (passive suction flow resistance) is relatively low. Consequently, the pressure at passive vent  412  is relatively low and passive virtual valve is open. In contrast, the flow resistance of active vent  422  (active suction flow resistance) is high. Consequently, the pressure at active vent  422  is high and active virtual valve is closed. Because of the low passive suction flow resistance, fluid is drawn into top chamber  440  through passive vent  412 . This is shown by arrows in  FIG. 4A . However, fluid does not flow out of (or flows out to a limited extent) active vent  422 . The passive virtual valve for passive vent  412  is open, while the active virtual valve for active vent  422  is closed in the suction arrangement. However, active vent  422  is not physically closed in this configuration. For example, active vent  422  is not in contact with orifice plate  430  in the suction arrangement. 
       FIG. 4B  depicts an expulsion arrangement. Piezoelectric cooling element  420  has been actuated to move away from (deform to be convex) heat-generating structure  402 . Because of the vibrational motion of piezoelectric cooling element  420 , the gap decreased in from its neutral position size and is shown as gap  442 B. For example, in some embodiments, gap  442 B has a height of at least five and not more than ten micrometers in the expulsion arrangement. Thus, top chamber  440  has decreased in volume and bottom chamber  450  has increased in volume. In the expulsion arrangement, the flow resistance of passive vent  412  (passive expulsion flow resistance) is relatively high. Consequently, the pressure at passive vent  412  is relatively high and the passive virtual valve is closed. In contrast, the flow resistance of active vent  422  (active expulsion flow resistance) is low. Consequently, the pressure at active vent  422  is low and the active virtual valve is open. Because of the low active expulsion flow resistance, fluid is expelled from top chamber  440  through active vent  422 , into bottom chamber  450  and through orifices  432 . This is shown by arrows in  FIG. 4B . However, fluid does not flow out of (or flows out to a limited extent) passive vent  412  because of the relatively high passive expulsion flow resistance. Thus, the virtual valve for passive vent  412  is considered closed and the virtual valve for active vent  422  is considered open in the expulsion arrangement. However passive vent  412  is not physically closed in this configuration. For example, passive vent  412  is not in contact with cooling element  420  in the expulsion arrangement. Gap  442 B does not have a zero length. 
     Cooling system  400  may share the benefits of cooling system  100  and/or  300 . Cooling system  400  may more efficiently dissipate heat from heat-generating structure  402  for the reasons discussed above. Further, cooling system  400  may be a MEMS device having the dimensions described above. Thus, piezoelectric cooling system  400  is suitable for use in mobile devices, such as smart phones, in which limited space is available. Piezoelectric cooling system  400  may also be used in other compute devices-both mobile and non-mobile. Performance of such devices may thus be improved. Because piezoelectric cooling elements  410  and/or  420  may be vibrated at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  400  may be quieter and consume less power. Because vents  410  and  420  remain physically open, cooling elements  410  and/or  420  may not contact each other (or orifice plate  430 ) during use. Thus, resonance of cooling elements  410  and/or  420  may more easily be maintained. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  400  may be improved. 
       FIGS. 5A-5C  are diagrams depicting an exemplary embodiment of active cooling system  500  usable with a heat-generating structure  502 . For clarity, only certain components are shown and  FIGS. 5A-5C  are not to scale.  FIGS. 5A, 5B and 5C  depict neutral, suction and expulsion arrangements of cooling system  500 . Cooling system  500  is used in connection with a heat-generating structure  502 . Cooling system  500  and heat-generating structure  502  are analogous to cooling system(s)  100 ,  300  and/or  400  and heat-generating structure(s)  102 ,  302  and/or  402 , respectively. Thus, cooling system  500  includes piezoelectric cooling elements  510  and  520 , orifice plate  530  having orifices  532  therein, top chamber  540  having gap  542 / 542 A/ 542 B, bottom chamber  550  and optional chimneys  560 . Piezoelectric cooling system  500  may be a MEMS device and thus may have dimensions analogous to those described above. 
       FIG. 5A  depicts cooling system  500  in a neutral configuration. Thus, cooling elements  510  and  120  are shown as substantially flat. Cooling element  510  includes not only passive vent  514 , but also a landing  514  adjacent to passive vent  514 . In some embodiments, landing  514  extends around the perimeter of passive vent  514 . Similarly, cooling element  520  includes plug  524  opposite to and aligned with passive vent  514 . In some embodiments, either landing  514  or plug  524  might be omitted. In some embodiments, cooling element  510  might include plug(s) opposite to and aligned with active vents  522 . Similarly, cooling element  520  might include landing(s) adjoining active vent(s)  522 . In some embodiments, such landing(s) may extend around the perimeter of active vent(s)  522 . Landing  514  and/or plug  524  may be used to reduce the size of gap  542  and provide an impediment to fluid flow. The dynamic resistances of the passive vent  512  and/or active vents  522  may be configured by the size (area and/or height perpendicular to heat-generating structure  502 ) of landing  514  and/or plug  524 . For example, the open and closed pressures may be varied from at least four kiloPascals to not more than forty kiloPascals in some embodiments. Thus, landing  514  and/or plug  524  allow for the resistances to flow for vents  512  and  522  in the virtual valve opened and virtual valve closed positions (e.g. the suction and expulsion arrangements) to be better tailored. 
     In  FIG. 5B , piezoelectric cooling element  510  has been actuated to move away from heat-generating structure  502  (deform to be convex), while piezoelectric cooling element  520  has been actuated to move toward (deform to be concave) heat-generating structure  502 . This configuration is the suction arrangement. In the embodiment shown, cooling system  500  is driven such that cooling elements  510  and  520  are one hundred eighty degrees out of phase. Because of the vibrational motion of piezoelectric cooling elements  510  and  520 , the gap  542  has increased in size from its neutral position and is shown as gap  542 A. For example, gap  542 A may have a height of at least twenty and not more than thirty micrometers in the suction arrangement ( FIG. 5B ). Thus, top chamber  540  has increased in volume and bottom chamber  540  has decreased in volume. In the suction arrangement, the flow resistance of passive vent  512  (passive suction flow resistance) is low. Consequently, the pressure at passive vent  512  is low and the passive virtual valve is open. In contrast, the flow resistance of active vent  522  (active suction flow resistance) is high. Consequently, the pressure at active vent  522  is high and active virtual vent is closed. Because of the low passive suction flow resistance, fluid is drawn into top chamber  540  through passive vent  512 . This is shown by arrows in  FIG. 5A . However, fluid does not flow out of (or flows out to a limited extent) active vent  522 . Thus, the active virtual valve for active vent  522  is considered closed and the passive virtual valve for passive vent  512  is considered open in the suction arrangement. However, active vent  522  is not physically closed in this configuration. For example, active vent  522  is not in contact with orifice plate  530  in the suction arrangement. 
       FIG. 5C  depicts an expulsion arrangement. Piezoelectric cooling element  510  is actuated to move toward (deform to be concave) heat-generating structure  502 , while piezoelectric cooling element  520  has been actuated to move away from (deform to be convex) heat-generating structure  502 . Because of the vibrational motion of piezoelectric cooling elements  510  and  520 , the gap decreased in from its neutral position size and is shown as gap  542 B. For example, in some embodiments, gap  542 B has a height of at least five and not more than ten micrometers in the expulsion arrangement. Thus, top chamber  540  has decreased in volume and bottom chamber  550  has increased in volume. In the expulsion arrangement, the flow resistance of passive vent  512  (passive expulsion flow resistance) is high. Consequently, the pressure at passive vent  512  is high. In contrast, the flow resistance of active vent  522  (active expulsion flow resistance) is low. Consequently, the pressure at active vent  522  is low. Because of the low active expulsion flow resistance, fluid is expelled from top chamber  540  through active vent  522 , into bottom chamber  550  and through orifices  532 . This is shown by arrows in  FIG. 5C . However, fluid does not flow out of (or flows out to a limited extent) passive vent  512  because of the high passive expulsion flow resistance. Thus, the passive virtual valve for passive vent  512  is considered closed and the active virtual valve for active vent  522  is considered open in the expulsion arrangement. Because of the presence of plug  524  and landing  514 , the length of gap  542 B is further reduced and the pressure (flow resistance) for passive vent  512  is further increased in the expulsion arrangement. However passive vent  512  is not physically closed in this configuration. For example, passive vent  512  is not in contact with cooling element  520  in the expulsion arrangement. Thus, although landing  514  and plug  524  may be very close, landing  514  and plug  524  are not in physical contact. Gap  542 B does not have a zero length. 
     Cooling system  500  may share the benefits of cooling system  100 ,  300  and/or  400 . Cooling system  500  may more efficiently dissipate heat from heat-generating structure  502  for the reasons discussed above. Because piezoelectric cooling elements  510  and/or  520  may be vibrated at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  500  may be quieter and consume less power. Because vents  510  and  520  remain physically open, cooling elements  510  and/or  520  may not contact each other (or orifice plate  530 ) during use. Thus, resonance of cooling elements  510  and/or  520  may more easily be maintained. Use of landing  514  and/or plug  524  may further increase the resistance to flow in the expulsion arrangement. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  500  may be improved. 
       FIG. 6  is a diagram depicting an exemplary embodiment of active cooling system  600  usable with a heat-generating structure  602 . For clarity, only certain components are shown and  FIG. 6  is not to scale.  FIG. 6  depicts a neutral configuration of cooling system  600 . Cooling system  600  is used in connection with a heat-generating structure  602 . Cooling system  600  and heat-generating structure  602  are analogous to cooling system(s)  100 ,  300 ,  400  and/or  500  and heat-generating structure(s)  102 ,  302 ,  402  and/or  502 , respectively. Thus, cooling system  600  includes piezoelectric cooling elements  610  and  620 , passive vent  612 , active vent  622 , landing  614 , plug  624 , orifice plate  630  having orifices  632  therein, top chamber  640  having gap  642 , bottom chamber  650  and optional chimneys  660 . Cooling elements  610  and/or  620  are actuated to vibrate, opening and closing the virtual valves for active vent  622  and passive vent  612  in a manner analogous to that described above. Consequently, suction and expulsion arrangements analogous to those described above are also provided. Piezoelectric cooling system  600  may be a MEMS device and thus may have dimensions analogous to those described above. 
       FIG. 6  depicts cooling system  600  in a neutral configuration. Cooling elements  610  and/or  620  may be driven to be actuated in a manner analogous to cooling systems  100 ,  300 ,  400  and/or  500 . Thus, fluid is drawn in through passive vent  612  (passive valve open) and flows into top chamber  640  in the suction arrangement. Fluid is expelled out of top chamber  640  through active vents  622  (active valves open) and through orifices  632  in the expulsion arrangement. In some embodiments, the fluid speeds and cooling power described above man be achieved. Fluid flows along heat-generating structure  602  toward chimneys  660 . Heat is transferred from heat-generating structure  602  to the fluid. The fluid flows to chimneys  660  and is carried away from heat-generating structure  602 . In addition, ducting  670  carries heated fluid away from passive vent  612 , for example to edges of cooling system  600  or the device employing cooling system  600 . As a result, the heated fluid is less likely to be rapidly drawn back into passive vent  612  in a suction arrangement. In some embodiments, chimneys  660  may be omitted. In such embodiments, ducting  670  may receive heated fluid directly from the region between orifice plate  630  and heat-generating structure  602 . In some embodiments, ducting  670  may provide a path for heated fluid in other and/or additional direction(s) to that shown. In addition, ducting  670  may provide additional mechanical stability to cooling system  600  and cooling elements  610  and  620 . 
     Cooling system  600  may share the benefits of cooling system  100 ,  300  and/or  400 . Cooling system  600  may more efficiently dissipate heat from heat-generating structure  602  for the reasons discussed above. In addition, because of the presence of ducting  670 , cooling system  600  may more efficiently cool heat-generating structure  602 . Because piezoelectric cooling elements  610  and/or  620  may be actuated to vibrate at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  600  may be quieter and consume less power. Because vents  610  and  620  remain physically open (e.g. virtual valves are used), cooling elements  610  and/or  620  may not contact each other (or orifice plate  630 ) during use. Thus, resonance of cooling elements  610  and/or  620  may more easily be maintained. Use of landing  614  and/or plug  624  may further increase the resistance to flow in the expulsion arrangement. Ducting  670  may also improve the mechanical stability of cooling system  600 . For example, if cooling system  600  is used in an array of multiple cooling elements, the presence of ducting  670  may better isolate the vibration of cooling elements  610  and/or  620  in each cooling system  600  from vibrations in another cooling system  600 . The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  600  may be improved. 
       FIG. 7  is a diagram depicting an exemplary embodiment of active cooling system  700  usable with a heat-generating structure  702 . For clarity, only certain components are shown and  FIG. 7  is not to scale.  FIG. 7  depicts a neutral configuration of cooling system  700 . Cooling system  700  is used in connection with a heat-generating structure  702 . Cooling system  700  and heat-generating structure  702  are analogous to cooling system(s)  100 ,  300 ,  400 ,  500  and/or  600  and heat-generating structure(s)  102 ,  302 ,  402 ,  502  and/or  602 , respectively. Thus, cooling system  700  includes piezoelectric cooling elements  710  and  720 , passive vent  712 , active vent  722 , landing  714 , plug  724 , orifice plate  730  having orifices  732  therein, top chamber  740  having gap  742 , bottom chamber  750 , optional chimneys  760  and ducting  770 . Cooling elements  710  and/or  720  are actuated to vibrate as described above. Consequently, suction and expulsion arrangements analogous to those described above are also provided. Piezoelectric cooling system  700  may be a MEMS device and thus may have dimensions analogous to those described above. 
       FIG. 7  depicts cooling system  700  in a neutral configuration. Cooling elements  710  and/or  720  may be driven to be actuated in a manner analogous to cooling systems  100 ,  300 ,  400 ,  500  and/or  600 . Thus, fluid is drawn in through passive vent  712  (passive valve open) and flows into top chamber  740  in the suction arrangement. Fluid is expelled out of top chamber  740  through active vents  722  (active valves open) and through orifices  732  in the expulsion arrangement. In some embodiments, the fluid speeds and cooling power described above man be achieved. Fluid flows along heat-generating structure  702  toward optional chimneys  760 . Heat is transferred from heat-generating structure  702  to the fluid. The fluid flows away from heat-generating structure  702  through optional chimneys  760  or via another mechanism. Optional ducting  770  carries heated fluid away from passive vent  712 . As a result, the heated fluid is less likely to be rapidly drawn back into passive vent  712  in a suction arrangement. Ducting  770  may provide additional mechanical stability to cooling system  700  and cooling elements  710  and  720 . In some embodiments, ducting  770  and/or chimneys  760  may be omitted or configured differently. 
     Also in  FIG. 7 , plug  724  and landing  714  are shown as having variations in the facing surfaces (e.g. the surfaces of plug  724  and landing  714  are not flat). Although both plug  724  and landing  714  are shown as having surface variations, in other embodiments, only one of plug  724  and landing  714  include such variations. In some embodiments, the variations may extend only across a portion of the surface of plug  724  and/or landing  714 . Thus, the surface of plug  724  and the surface of landing  714  form a tortuous path for fluid traveling through gap  742 . Consequently, fluid entering or exiting top chamber  742  through passive vent  712  is slowed by the variations in the facing surfaces. For example, within manufacturing tolerances, the pitch of the variations (or corrugations) may be at least fifty and not more than two hundred micrometers. Thus, the number of corrugations may be from one to as many fit on a particular geometric surface, with the height of corrugations varying from at least fifty to not more than two hundred micrometers. The initial gap between the top and bottom variations on cooling elements  710  and  720  can be positive, zero or negative, depending on the resistance, pressure and flow requirements dictated by the design. Further, the corrugations of the may be configured to tune flow and pressure in chamber  740 . Thus, the difference in pressure between the open and closed states of passive vent  712  and/or active vent  722  may be increased by the use of the tortuous path. Stated differently, the pressure difference between a large gap  742  (suction arrangement) and a small gap  742  (expulsion arrangement) can be increased. However, gap  742  still has a nonzero height throughout operation of cooling system  700 . 
     Cooling system  700  may share the benefits of cooling system  100 ,  300 ,  400 ,  500  and/or  600 . Cooling system  700  may more efficiently dissipate heat from heat-generating structure  702  for the reasons discussed above. In addition, because of the presence of ducting  770 , cooling system  700  may more efficiently cool heat-generating structure  702 . Because piezoelectric cooling elements  710  and/or  720  may be actuated to vibrate at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  700  may be quieter and consume less power. Because vents  710  and  720  remain physically open, cooling elements  710  and/or  720  may not contact each other (or orifice plate  730 ) during use. Thus, resonance of cooling elements  710  and/or  720  may more easily be maintained. Use of landing  714  and/or plug  724  having surface variations may further increase the resistance to flow in the expulsion arrangement. Ducting  770  may also improve the mechanical stability of cooling system  700 . For example, if cooling system  700  is used in an array of multiple cooling elements, the presence of ducting  770  may better isolate the vibration of cooling elements  710  and/or  720  in each cooling system  700  from vibrations in another cooling system  700 . The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  700  may be improved. 
       FIGS. 8A-8C  are diagrams depicting an exemplary embodiment of active cooling system  800  usable with a heat-generating structure  802  and elastic structures usable in such a cooling system.  FIG. 8A  depicts cooling system  800 .  FIGS. 8B and 8C  depict embodiments  880 A and  880 B of elastic devices usable in cooling system  800 . For clarity, only certain components are shown and  FIGS. 8A and 8B  are not to scale. Cooling system  800  is used in connection with a heat-generating structure  802 . Cooling system  800  and heat-generating structure  902  are analogous to cooling system(s)  100 ,  300 ,  400 ,  500 ,  600  and/or  700  and heat-generating structure(s)  102 ,  302 ,  402 ,  502 ,  602  and/or  702 , respectively. Thus, cooling system  800  includes piezoelectric cooling elements  810  and  820 , passive vent  812 , active vent  822 , landing  814 , plug  824 , orifice plate  830  having orifices  832  therein, top chamber  840  having gap  842 , bottom chamber  850  and optional chimneys  860 . Ducting (not shown) may also be included. Cooling elements  810  and/or  820  are actuated to vibrate as described above. Consequently, suction and expulsion arrangements analogous to those described above are also provided. Piezoelectric cooling system  800  may be a MEMS device and thus may have dimensions analogous to those described above. 
       FIG. 8A  depicts cooling system  800  in a neutral configuration. Cooling elements  810  and/or  820  may be driven to be actuated in a manner analogous to cooling systems  100 ,  300 ,  400 ,  500 ,  600  and/or  700 . Thus, fluid is drawn in through passive vent  812  and flows into top chamber  840  in the suction arrangement. Fluid is expelled out of top chamber  840  through active vents  822  and through orifices  832  in the expulsion arrangement. In some embodiments, the fluid speeds and cooling power described above man be achieved. Fluid flows along heat-generating structure  802  toward optional chimneys  860 . Heat is transferred from heat-generating structure  802  to the fluid. The fluid flows away from heat-generating structure  802  through optional chimneys  860  or via another mechanism. 
     Also shown in cooling system  800  is elastic device  880 . Elastic device  880  is affixed to cooling element  810  and  820  via structures  890  and  892 . Note that only some structures are labeled in  FIG. 8A . In some embodiments, elastic device  880  is formed of the same material(s) as cooling element(s)  810  and/or  820 . For example, elastic device  880  may be formed of stainless steel or a Ni alloy. In other embodiments, other material(s) might be used. The spring constant for elastic device  880  may be selected to be at least five percent and not more than twenty-five percent of the stiffness of cooling element(s)  810  and/or  820 . This selection provides a balance between the variations and the magnitude of deflection of cooling elements  810  and  820 . In other embodiments, another stiffness for the elastic device  880  may be selected. Structures  890  and  892  may be epoxy, adhesive, PSA, solder, brazed joints or some other mechanism for bonding elastic device  880  to cooling elements  810  and  820 . Elastic device  880  couples cooling elements  810  and  820 , but does not prevent fluid flow through cooling system  800 . Thus, portions of elastic device  880  that may include apertures are depicted with a dashed line. Elastic device  880  is used to link the vibrations of cooling elements  810  and  820 . Because of the present of elastic device  880 , small variations in the vibrations of cooling element(s)  810  and/or  820  may not make substantially one hundred and eighty degree out-of-phase resonant vibration unstable. Stated differently, elastic device  880  may stabilize the frequency mode between cooling element  810  and  820 . The natural frequency of the cooling elements  810  and  820  may be chosen to be similar. The elastic device  880  stabilizes the frequency and the mode to be the out-of-phase mode. Without elastic device  880 , it may be very difficult to maintain the operation of cooling elements  810  and  820  in the appropriate mode. In some cases, maintaining operation of system  800  at resonance without elastic device  880  is challenging because the coupled mechanics of fluid pressures and structural mechanics tend to drive cooling elements  810  and  820  at different peak resonances. With the elastic device, system  800  may be more easily operated at resonance. For example, use of elastic device  880  may allow resonant frequencies of cooling elements  810  and  820  may differ by five to ten percent of the base frequency. For example, the resonant frequencies of cooling elements  810  and  820  may differ by up to one kHz but still be operated at resonance if elastic device  880  is incorporated. Consequently, cooling elements  810  and  820  may be more easily controlled to remain both at frequencies of vibration near resonance and out-of-phase. Thus, efficiency of cooling system  800  in driving fluid may be maintained or improved. 
       FIGS. 8B and 8C  depict portions of embodiments  880 A and  880 B of elastic device  880 . Elastic devices  880 A and  880 B are affixed to cooling elements  810  and  820  at locations  882  and  884 , respectively. In some embodiments, elastic devices  880 A and  880 B include additional portions that are affixed to the edges of cooling system  800 . Elastic device  880  in  FIG. 8A  is depicted as including such portions. Elastic device  880 A includes concentric rings connected by radial members. The outer ring is coupled to cooling element  820 , while the inner may be coupled to cooling element  810 . Similarly, elastic device  880 B includes an inner ring and outer ring segments coupled to the inner ring by radial members. The inner ring is coupled to cooling element  810 , while the outer ring segments are coupled to cooling element  820 . 
     Cooling system  800  may share the benefits of cooling system  100 ,  300 ,  400 ,  500 ,  600  and/or  700 . Cooling system  800  may more efficiently dissipate heat from heat-generating structure  802  for the reasons discussed above. Because piezoelectric cooling elements  810  and/or  820  may be actuated to vibrate at ultrasonic frequencies and/or at or near resonance, piezoelectric cooling system  800  may be quieter and consume less power. Because vents  810  and  820  remain physically open, cooling elements  810  and/or  820  may not contact each other (or orifice plate  830 ) during use. Use of elastic device  880  allows the out-of-phase resonant vibration to be significantly more stable. Thus, resonance of cooling elements  810  and/or  820  may more easily be maintained. Use of landing  814  and/or plug  824  may further increase the resistance to flow in the expulsion arrangement. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  800  may be improved. 
       FIG. 9  is a diagram depicting an exemplary embodiment of active cooling system  900  usable with a heat-generating structure  902  and elastic structures usable in such a cooling system. For clarity, only certain components are shown and  FIG. 9  is not to scale. Cooling system  900  is used in connection with a heat-generating structure  902 . Cooling system  900  and heat-generating structure  902  are analogous to cooling system(s)  100 ,  300 ,  400 ,  500 ,  600 ,  700  and/or  800  and heat-generating structure(s)  102 ,  302 ,  402 ,  502 ,  602 ,  702  and/or  802 , respectively. Thus, cooling system  900  includes piezoelectric cooling elements  910  and  920 , passive vent  912 , active vent  922 , landing  914 , plug  924 , orifice plate  930  having orifices  932  therein, top chamber  940  having gap  942  and bottom chamber  950 . Although not shown, chimneys and ducting may also be included. Cooling elements  910  and/or  920  are actuated to vibrate as described above. Consequently, suction and expulsion arrangements analogous to those described above are also provided. Piezoelectric cooling system  900  may be a MEMS device and thus may have dimensions analogous to those described above. 
       FIG. 9  depicts cooling system  900  in a neutral configuration. Cooling elements  910  and/or  920  may be driven to be actuated in a manner analogous to cooling systems  100 ,  300 ,  400 ,  500 ,  600 ,  700  and/or  800 . Thus, fluid is drawn in through passive vent  912  and flows into top chamber  940  in the suction arrangement. Fluid is expelled out of top chamber  940  through active vents  922  and through orifices  932  in the expulsion arrangement. In some embodiments, the fluid speeds and cooling power described above man be achieved. Fluid flows along heat-generating structure  902  and receives heat from heat-generating structure  802 . The fluid flows away from heat-generating structure  802  through optional chimneys (not shown) or via another mechanism. 
     Also shown in cooling system  900  are elastic devices  980 A and  980 B. Elastic devices  980 A and  980 B are analogous to elastic device  880 . Elastic device  980 A is affixed to cooling element  910  via structures  990  (of which only one is labeled). Elastic device  980 B is affixed to cooling element  920  via structure  992  (of which only one is labeled). Elastic devices  980 A and  980 B are affixed to each other using structures  996  (of which only one is labeled). Structures  990 ,  992  and  994  may be epoxy, adhesive or some other mechanism for bonding elastic devices  980 A and  980 B to cooling elements  910  and  920  and to each other. Elastic devices  980 A and  980 B couple cooling elements  910  and  920 , but do not prevent fluid flow through cooling system  900 . Thus, portions of each elastic device  980 A and  980 B that may include apertures are depicted with a dashed line. Elastic devices  980 A and/or  980 B may have portions analogous to elastic devices  880 A and  880 B depicted in  FIGS. 8B and 8C . Referring back to  FIG. 9 , elastic devices  980 A and  980 B are used to link the vibrations of cooling elements  910  and  920 . Because of the present of elastic devices  980 A and  980 B, small variations in the vibrations of cooling element(s)  910  and/or  920  may not make substantially one hundred and eighty degree out-of-phase resonant vibration unstable. Thus, elastic devices  980 A and  980 B may stabilize the frequency mode between cooling element  910  and  920 . Consequently, cooling elements  910  and  920  may be more easily controlled to remain both at frequencies of vibration near resonance and out-of-phase. Thus, efficiency of cooling system  900  in driving fluid may be maintained or improved. 
     Cooling system  900  may share the benefits of cooling system  100 ,  300 ,  400 ,  500 ,  600 ,  700  and/or  800 . Cooling system  900  may more efficiently dissipate heat from heat-generating structure  902  for the reasons discussed above. Cooling system  900  may be quieter and consume less power. Because vents  910  and  920  are closed using virtual valves (e.g. remain physically open), resonance is more readily maintained. Elastic devices  980 A and  980 B allow the out-of-phase resonant vibration to be significantly more stable. Use of landing  914  and/or plug  924  may allow for further tailoring of the flow resistances of the virtual valves. The benefits of improved, quiet cooling may be achieved with limited additional power. Consequently, performance of devices incorporating cooling system  900  may be improved. 
       FIGS. 10A-10B  depict an array  1000  of cooling systems  1001  used to cool heat-generating structure  1002 .  FIG. 10A  is a side view of array  1000 , while  FIG. 10B  is a plan view of array  1000 . Cooling system  1001  may be analogous to one or more of cooling systems  100 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  and/or  900 . Each cooling system  1001  may be considered a cell in array  1000 . Heat-generating structure  1002  may be analogous to one or more of and heat-generating structure(s)  102 ,  302 ,  402 ,  502 ,  602 ,  702 ,  802  and/or  902 . For clarity, the components of each cell  1001  are not labeled. Further, some components that may be included in cells  1001  are not shown. For example, cell(s)  1001  may include elastic devices analogous to elastic devices  880 ,  980 A and/or  980 B. Piezoelectric cells  1001  may be a MEMS device and thus may have dimensions analogous to those described above. Although shown as identical, cells  1001  may differ. Also shown at edges of the array  1000  are chimneys  1060  and ducting  1070  for directing flow of heated fluid. Thus, chimneys  1060  and/or ducting  1070  can, but need not be present at the edges of each cooling system  1001 . In other embodiments, chimneys  1060  and/or ducting  1070  may be removed. Although a rectangular array with aligned cells  1001  are shown, in other embodiments, the array need not be rectangular and cells  1001  need not be aligned. Further, in some embodiments, not all cells  1001  need be activated together. For example, in some embodiments, cells  1001  may be individually driven. Thus, cooling systems described herein may be combined. Further, although various features are described for various embodiments, the features may be combined in manners not explicitly described herein. 
       FIG. 11  is a flow chart depicting an exemplary embodiment of method  1100  for operating a cooling system. Method  1100  may include steps that are not depicted for simplicity. Method  1100  is described in the context of piezoelectric cooling system  100 . However, method  1100  may be used with other cooling systems including but not limited to systems and cells described herein. Method  1100  is also described in the context of driving a 
     One or more of the piezoelectric cooling element(s) in a cooling system is actuated to vibrate, at  1102 . At  1102 , an electrical signal having the desired frequency is used to drive the cooling element(s). In some embodiments, the cooling elements are driven at or near resonance at  1102 . The driving frequency may be 15 kHz or higher. If multiple piezoelectric cooling elements are driven at  1102 , the cooling elements may be driven out-of-phase. In some embodiments, the cooling elements are driven substantially at one hundred and eighty degrees out of phase. 
     Feedback from the piezoelectric cooling element(s) is used to adjust the driving current, at  1104 . In some embodiments, the adjustment is used to maintain the frequency at or near the resonant frequency/frequencies of the cooling element(s). Resonant frequency of a particular cooling element may drift, for example due to changes in temperature. Adjustments made at  1104  allow the drift in resonant frequency to be accounted for. 
     For example, piezoelectric cooling elements  110  and  120  may be driven at their resonant frequency/frequencies, at  1102 . Although the resonant frequencies of cooling elements  110  and  120  may be selected to be similar, there may be small differences in the resonant frequencies. Thus, cooling elements  110  and  120  may not be driven at identical frequencies in some embodiments. Further, as shown in  FIGS. 1B-1C , cooling elements  110  and  120  may be driven at one hundred and eighty degrees out-of-phase. 
     At  1104 , feedback is used to maintain piezoelectric cooling elements  110  and  120  at resonance and, in some embodiments, one hundred and eighty degrees out of phase. Thus, the efficiency of cooling elements  110  and  120  in driving fluid flow through cooling system  100  and onto heat-generating structure  102  may be maintained. In some embodiments,  1104  includes sampling the current through piezoelectric cooling elements and adjusting the current to maintain resonance and low input power. 
     Consequently, piezoelectric cooling elements, such as elements  110  and  120 , may operate as described above. Method  1100  thus provides for use of piezoelectric cooling systems described herein. Thus, piezoelectric cooling systems may more efficiently and quietly cool semiconductor devices at lower power. 
     Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed embodiments are illustrative and not restrictive.