Patent Publication Number: US-2017357325-A1

Title: Localized Deflection Using a Bending Haptic Actuator

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     The application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Patent Application No. 62/349,799, filed on Jun. 14, 2016, and entitled “Reduced Cost Piezoelectric Wafer for Localizing Haptic Output For An Electronic Device;” U.S. Provisional Patent Application No. 62/354,089, filed on Jun. 23, 2016, and entitled “Localized Deflection of a Surface in an Electronic Device;” U.S. Provisional Patent Application No. 62/395,967, filed on Sep. 16, 2016, and entitled “Displacement Amplification in Bending Haptic Actuator;” and U.S. Provisional Patent Application No. 62/398,469, filed on Sep. 22, 2016, and entitled “Pre-Stressed Haptic Actuator in an Electronic Device,” each of which is incorporated by reference as if fully disclosed herein. 
    
    
     FIELD 
     The described embodiments relate generally to haptic output devices in electronic devices. More particularly, the present embodiments relate to a haptic output device that is configured to provide localized deflection of a surface of an electronic device. 
     BACKGROUND 
     Electronic devices are commonplace in today&#39;s society. Some of these electronic devices can incorporate a haptic output system. A haptic output system uses the sense of touch to convey information to a user. An electronic device activates the haptic output system to solicit a user&#39;s attention, enhance the user&#39;s interaction experience with the electronic device, displace the electronic device or a component of the electronic device, or for any other suitable notification or user experience purpose. Typically, the haptic output system generates the haptic output through the production of forces, vibrations, and/or motions. In many situations, the haptic output is perceived by a user as haptic feedback. 
     SUMMARY 
     Embodiments described herein relate to an electronic device that is configured to provide localized haptic feedback to a user on one or more surfaces of the electronic device. In one aspect, an electronic device can include an intermediate layer positioned below a surface and a support structure positioned below the intermediate layer. A haptic actuator is coupled to the support structure, and the support structure is shaped or configured to amplify a haptic response at the surface. Actuation of the haptic actuator causes the support structure to deflect, which in turn causes the intermediate layer to deflect and the surface to deflect. Deflection of the support structure produces a deflection in the surface of the electronic device at a location that corresponds to a location of the haptic actuator on the support structure. In some embodiments, a circuit layer is attached to a surface of the support structure and the haptic actuator is attached and electrically connected to the circuit layer. In other embodiments, one or more signal lines or conductive traces may be included in the support structure and electrically connected to the haptic actuator. The circuit layer or the signal lines can be used to activate the haptic actuator. 
     In an example embodiment, an electronic device is provided. The electronic device includes a cover sheet defining a surface, a haptic actuator positioned below the cover sheet, and a support structure coupled to the haptic actuator. Actuation of the actuator causes a deflection in the surface at a location that substantially corresponds to a location of the haptic actuator. The support structure amplifies the deflection in the surface. 
     In another embodiment, the support structure includes a cavity within a side of the support structure opposite the cover sheet. The cavity is substantially centered over the haptic actuator. In another embodiment, the support structure includes a force concentration region positioned over the haptic actuator. Actuation of the haptic actuator causes an amplified deflection within the force concentration region. 
     In another embodiment, the support structure is curved away from the cover sheet at a location coupled to the haptic actuator. In another embodiment, the support structure has an arm, and an end of the arm displaces upward in response to actuation of the haptic actuator. In another embodiment, the electronic device includes an upper support structure positioned below the cover sheet and curved toward the cover sheet, a lower support structure positioned below the upper support structure and curved away from the cover sheet, and a haptic actuator positioned between and coupled to the upper support structure and the lower support structure. 
     One or more haptic actuators may be placed in a pre-stressed state prior to providing the haptic feedback. The pre-stressed state positions the haptic actuators closer to the surface to be deflected. In this manner, the time lag between actuation of the haptic actuator(s) and providing the haptic output in the surface may be reduced. Additionally, the actuation performances of the haptic actuators can be more uniform, which results in a more uniform haptic output on the surface. 
     In one aspect, an electronic device includes a support structure positioned below a surface to be deflected, a haptic actuator coupled to the support structure, and a processing unit coupled to the haptic actuator. The processing unit is configured to cause a pre-stress signal to be transmitted to the haptic actuator to cause the haptic actuator to be placed in a pre-stressed state. The pre-stressed state causes the support structure to deflect and position the haptic actuator closer to the surface. The processing unit is further configured to cause an actuation signal to be transmitted to the haptic actuator to cause the haptic actuator to be placed in a haptic output state. The haptic output state causes the deflection of the support structure to increase locally and produce a deflection in the surface at a location that substantially corresponds to a location of the haptic actuator on the support structure. 
     In another aspect, an electronic device includes a support structure that is connected to a surface to be deflected. The support structure includes a support plate and sides extending from the support plate to the surface. In some embodiments, a haptic actuator is attached to the support plate and a circuit layer is attached and electrically connected to the haptic actuator. In other embodiments, a circuit layer is attached to the support plate and the haptic actuator is attached and electrically connected to the circuit layer. When the haptic actuator is in a rest or non-actuated state, the support plate is positioned a first distance from the surface to define a gap between the surface and the support plate. A processing unit is configured to cause a pre-stress signal to be transmitted to the haptic actuator to cause the haptic actuator to be placed in a pre-stressed state. In one embodiment, the pre-stressed state causes the support structure to deflect and positions the support plate within the gap at a second distance below the surface, where the second distance is less than the first distance. In some situations, the deflection of the support plate can close the gap. Closure of the gap occurs when the support plate contacts the surface without producing a deflection in the surface. The processing unit is also configured to cause an actuation signal to be transmitted to the haptic actuator to cause the support structure to further deflect and position the support structure at a third distance below the surface. The third distance is less than the second distance and produces a deflection in the surface at a location that substantially corresponds to a location of the haptic actuator on the support structure. 
     In another embodiment, the pre-stressed state causes the support structure to deflect to expand or enlarge the gap, which positions the support structure at a fourth distance below the surface. The fourth distance is greater than the first distance associated with the non-actuated state. When the processing unit causes an actuation signal to be transmitted to the haptic actuator, the support structure deflects and positions the support structure at the third distance below the surface. The third distance is less than the fourth distance and produces a deflection in the surface at a location that substantially corresponds to a location of the haptic actuator on the support structure. 
     In some embodiments, an intermediate layer (e.g., one or more layers) can be attached to the surface. In such embodiments, the gap is defined between the support plate and the intermediate layer. In a non-limiting example, the surface is a cover sheet that is positioned over a display layer, a backlight assembly, and a first force-sensing component. In one embodiment, the first force-sensing component is positioned between the display layer and the backlight assembly. In another embodiment, the first force-sensing component is disposed below the backlight assembly. Thus, the intermediate layer includes the display layer, the backlight assembly, and the first force-sensing component. A second force-sensing component may be attached to a top surface of the support plate. When the haptic actuator is placed in the pre-stressed state, the support plate can deflect toward the bottom surface of the intermediate layer to position the support plate within the gap. In some situations, pre-stressing the haptic actuator can cause the gap between the intermediate layer and the second force-sensing component to be closed. Closure of the gap occurs when the second force-sensing component contacts the intermediate layer without producing a deflection in the cover sheet. 
     In some embodiments, the closure of the gap can be detected when the haptic actuator is in the pre-stressed state. In a first non-limiting example, the haptic actuator can include a piezoelectric material. A processing unit can be configured to receive an output signal from the piezoelectric material that indicates the gap is closed. In a second non-limiting example, the haptic actuator can be attached to the bottom surface of the support plate and another haptic actuator may be positioned over, or attached to, the top surface of the support plate. A processing unit can be configured to receive an output signal from the second haptic actuator that indicates the gap is closed. In a third non-limiting example, the haptic actuator can be attached to the bottom surface of the support plate and a strain sensor may be positioned over, or attached to, the top surface of the support plate. A processing unit can be configured to receive a strain signal from the strain sensor that indicates the gap is closed. Techniques other than these three representative methods can be used to detect the closure of the gap. 
     In other embodiments, the expansion of the gap can be detected when the haptic actuator is in the pre-stressed state. At least one of the first, the second, and/or the third force-sensing components can be configured to detect the displacement of the support structure. For example, expansion of the gap may be detected through capacitance changes between the first and the second force-sensing components and/or through capacitance changes between the third force-sensing component and the support structure. A processing unit can be configured to receive a sense signal from a respective force-sensing component and to associate the sense signal to the enlargement of the gap. 
     In yet another aspect, an electronic device can include a support plate, a surface, a gap between the support plate and the surface, and a haptic actuator attached to the support plate. A method of operating the electronic device includes transmitting a pre-stress signal to the haptic actuator to place the haptic actuator in a pre-stressed state. The pre-stress signal causes the support plate to deflect toward the surface and position the haptic actuator closer to the surface without deflecting the surface. A determination may be made as to whether to place the haptic actuator in a haptic output state that causes the deflection in the support plate to increase locally and deflect the surface. If the haptic actuator is to be placed in the haptic output state, an actuation signal is transmitted to the haptic actuator to place the haptic actuator in the haptic output state. When the haptic output state ends, another pre-stress signal may be transmitted to the haptic actuator to place the haptic actuator in a second pre-stressed state. 
     In yet another aspect, an electronic device can include a surface; an intermediate layer formed with one or more layers attached to the surface; a support plate; a gap between the support plate and the intermediate layer; and a haptic actuator attached to the support plate. A method of operating the electronic device includes transmitting a pre-stress signal to the haptic actuator to place the haptic actuator in a pre-stressed state. The pre-stress signal causes the support plate to deflect toward the intermediate layer and position the haptic actuator closer to the surface without producing a deflection in the surface. A determination may be made as to whether to place the haptic actuator in a haptic output state that causes the deflection in the support plate to increase locally and produce the deflection in the surface. If the haptic actuator is to be placed in the haptic output state, an actuation signal is transmitted to the haptic actuator to place the haptic actuator in the haptic output state. When the haptic output state ends, another pre-stress signal may be transmitted to the haptic actuator to place the haptic actuator in a second pre-stressed state. 
     In some embodiments, if the haptic actuator will not be placed in the haptic output state, the transmission of the pre-stress signal to the haptic actuator can cease to place the haptic actuator in a rest state. Alternatively, if the haptic actuator will not be placed in the haptic output state, the transmission of the pre-stress signal to the haptic actuator may continue to maintain the pre-stressed state. In some embodiments, the method can also include detecting a closure of the gap while the pre-stress signal is transmitted to the haptic actuator. 
     In another aspect, an electronic device includes a surface to be deflected and a support plate. The support plate is positioned a first distance below the surface to define a gap between the surface and the support plate. A haptic actuator is attached to the support plate. A processing unit is configured to cause a pre-stress signal to be transmitted to the haptic actuator to cause the haptic actuator to be placed in a pre-stressed state. In one embodiment, the pre-stressed state can cause the support structure to deflect and position the support structure within the gap at a second distance below the surface, where the second distance is less than the first distance. In another embodiment, the pre-stressed state can cause the support structure to deflect and position the support structure at a third distance below the surface, where the third distance is greater than the first distance. 
     In yet another aspect, an electronic device can include an intermediate layer positioned below a surface and a support structure positioned below the intermediate layer. A haptic actuator is coupled to the support structure, and the support structure includes one or more openings formed through the support structure adjacent at least one side of the haptic actuator. For example, an opening can be formed through the support structure adjacent two opposing sides of the haptic actuator. Actuation of the haptic actuator causes the support structure to deflect, which in turn causes the intermediate layer to deflect and the surface to deflect. Deflection of the support structure produces a deflection in the surface of the electronic device at a location that corresponds to a location of the haptic actuator on the support structure. In some embodiments, a circuit layer is attached to a surface of the support structure and the haptic actuator is attached and electrically connected to the circuit layer. In other embodiments, one or more signal lines or conductive traces may be included in the support structure and electrically connected to the haptic actuator. The circuit layer or the signal line(s) can be used to activate the haptic actuator. 
     In one non-limiting example, a support structure is attached to a cover sheet in an electronic device. A display layer (intermediate layer) is positioned between the cover sheet and the support structure. A circuit layer is attached to a bottom surface of the support structure, and one or more haptic actuators are attached and electrically connected to the circuit layer. When at least one haptic actuator is activated, the support structure deflects upwards toward the cover sheet, and the deflection transmits through the display layer and the cover sheet to produce a deflection in a top surface of the cover sheet. A user may perceive the deflection in the cover sheet as haptic feedback. 
     In some embodiments, one or more additional layers or elements can be positioned between the cover sheet and the support structure. For example, in one embodiment a backlight assembly can be positioned below the display layer. Additionally or alternatively, one or more touch and/or force-sensing components can be positioned between the cover sheet and the support structure. For example, in one embodiment a first force-sensing component may be attached to a backlight assembly and a second force-sensing component can be attached to the support structure (e.g., on a top surface of the support structure). In such embodiments, the support structure can be spaced apart from the first force-sensing component such that a gap is defined between the first force-sensing component and the second force-sensing component. 
     In another aspect, an electronic device can include an intermediate layer positioned below a surface and a support structure positioned below the intermediate layer. A circuit layer is selectively attached (e.g., rigidly affixed) to a surface of the support structure, and a haptic actuator is attached and electrically connected to the circuit layer. In particular, one or more first sections of the circuit layer are affixed to the surface of the support structure and one or more second sections of the circuit layer are not affixed to the surface of the support structure. Actuation of the haptic actuator causes the support structure to deflect and produce a deflection in the surface of the electronic device at a location that corresponds to a location of the haptic actuator on the circuit layer and the support structure. 
     In another aspect, a haptic or deflection module is configured to produce one or more localized deflections in a surface in an electronic device. The haptic or deflection module includes a support structure positioned below the surface and a circuit layer positioned on a bottom surface of the support structure. A haptic actuator is attached and electrically connected to the circuit layer. The support structure includes a first opening and a second opening formed through the support structure, the first opening positioned along a first side of the haptic actuator and the second opening positioned along a second side of the haptic actuator. Actuation of the haptic actuator causes the support structure to deflect and produce a deflection in the surface at a location in the surface that corresponds to a location of the haptic actuator on the circuit layer. 
     In yet another aspect, a haptic or deflection module is configured to produce one or more localized deflections in a surface of an electronic device. The deflection module includes a support structure positioned below the surface, and a circuit layer positioned on a bottom surface of the support structure. One or more first sections of the circuit layer are rigidly affixed to the bottom surface of the support structure and one or more second sections of the circuit layer are not affixed to the bottom surface of the support structure. A haptic actuator is attached and electrically connected to the circuit layer. Actuation of the haptic actuator causes the support structure to deflect and produce a deflection in the surface at a location in the surface that corresponds to a location of the haptic actuator on the circuit layer. 
     A method for producing a haptic or deflection module includes providing a support structure for an electronic device. One or more openings can be formed through the support structure adjacent a location of a haptic actuator. Additionally or alternatively, a circuit layer is selectively attached to the support structure. In particular, one or more first sections of the circuit layer are rigidly attached to a surface of the electronic device, while one or more second sections of the circuit layer are not attached to the surface of the support structure. One or more haptic actuators are attached and electrically connected to the circuit layer. The deflection module may then be attached to a component in the electronic device. Example components include, but are not limited to, an enclosure, a frame, an input surface, or a cover sheet of the electronic device. 
     In another aspect, due to the cost of the materials in the haptic structure, the embodiments described herein are directed to using materials, shapes and configurations that reduce the overall cost of the haptic structure. 
     More specifically, described herein is a haptic structure for an electronic device. The haptic structure comprises a piezoelectric material, a first electrode coupled to a first side of the piezoelectric material and a second electrode coupled to a second side of the piezoelectric material. The haptic structure also includes a first electrical contact formed from a first material and coupled to the first electrode and a second electrical contact formed from a second material that is different than the first material. The second electrical contact is coupled to the second electrode and has a width that is less than a width of the first electrical contact. 
     Other embodiments described herein may generally relate to a haptic structure for providing localized haptic output for an electronic device. The haptic structure includes a cross-shaped piezoelectric material operative to deflect and provide haptic output in response to a received stimulus. The haptic structure also includes a first flex comprising a ground electrical contact coupled to a first side of the cross-shaped piezoelectric material and a second flex comprising a drive electrical contact coupled to a second side of the cross-shaped piezoelectric material. The second flex and the drive electrical contact have a width that is less than a width of the first flex. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure will be readily understood by the following detailed description in conjunction with the accompanying drawings, wherein like reference numerals designate like structural elements. 
         FIG. 1  depicts an example of an electronic device that can provide localized deflection of a surface. 
         FIG. 2A  depicts a cross-sectional view of an example of the electronic device, taken along line A-A of  FIG. 1 . 
         FIG. 2B  depicts the example electronic device of  FIG. 2A , illustrating a haptic actuator being actuated. 
         FIG. 2C  depicts a cross-sectional view of another example of the electronic device, taken along line A-A of  FIG. 1 . 
         FIG. 2D  depicts the example electronic device of  FIG. 2C , illustrating a haptic actuator being actuated. 
         FIG. 3A  depicts a first example haptic actuator, in the form of a piezoelectric transducer. 
         FIG. 3B  depicts a second example haptic actuator, which may be a piezoelectric transducer. 
         FIG. 3C  depicts a third example haptic actuator, which may include reduced cost circuit and ground layers. 
         FIG. 3D  depicts a fourth example haptic actuator, which may include reduced cost and increased performance circuit and ground layers. 
         FIG. 4  depicts a plan view of one example of the deflection module shown in  FIGS. 2A and 2B , as viewed from below. 
         FIG. 5A  depicts a first example of a deflection module having a support structure shaped to amplify the output of a haptic actuator 
         FIG. 5B  depicts the example deflection module of  FIG. 5A , illustrating a haptic actuator being actuated. 
         FIG. 6A  depicts a second example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 6B  depicts the example deflection module of  FIG. 6A , illustrating a haptic actuator being actuated. 
         FIG. 7A  depicts a third example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 7B  depicts the example deflection module of  FIG. 7A , illustrating a haptic actuator being actuated. 
         FIG. 8A  depicts a fourth example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 8B  depicts the example deflection module of  FIG. 8A , illustrating a haptic actuator being actuated. 
         FIG. 9A  depicts a fifth example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 9B  depicts the example deflection module of  FIG. 9A , illustrating a haptic actuator being actuated. 
         FIG. 9C  depicts another embodiment of the fifth example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 9D  depicts the example deflection module of  FIG. 9C , illustrating a haptic actuator being actuated. 
         FIG. 10A  depicts a sixth example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 10B  depicts the example deflection module of  FIG. 10A , illustrating a haptic actuator being actuated. 
         FIG. 11A  depicts a seventh example of a deflection module having a support structure shaped to amplify the output of a haptic actuator. 
         FIG. 11B  depicts the example deflection module of  FIG. 11A , illustrating a haptic actuator being actuated. 
         FIG. 11C  depicts an example linking mechanism of the seventh example deflection module. 
         FIG. 11D  depicts the example linking mechanism of  FIG. 11C , illustrating a haptic actuator being actuated. 
         FIG. 11E  depicts another example linking mechanism of the seventh example deflection module. 
         FIG. 11F  depicts the example linking mechanism of  FIG. 11E , illustrating a haptic actuator being actuated. 
         FIG. 11G  depicts another example linking mechanism of the seventh example deflection module. 
         FIG. 11H  depicts the example linking mechanism of  FIG. 11G , illustrating a haptic actuator being actuated. 
         FIG. 12  depicts a cross-sectional view of the electronic device taken along line A-A in  FIG. 1 . 
         FIG. 13A  depicts a cross-sectional view of another example electronic device with the haptic actuators in a non-actuated state. 
         FIG. 13B  depicts the electronic device shown in  FIG. 13A  with the haptic actuators in a pre-stressed state. 
         FIG. 13C  depicts the electronic device shown in  FIG. 13B  with one haptic actuator in a haptic output state. 
         FIG. 14  depicts an example graph representing the deflection of a cover sheet in response to the application of a signal to a haptic actuator. 
         FIG. 15A  depicts an example graph illustrating an example pre-stress signal that can be applied to a haptic actuator. 
         FIG. 15B  depicts an example graph of an output signal produced by the haptic actuator based on the input signal shown in  FIG. 15A . 
         FIG. 16A  depicts a top view of a haptic actuator that can be used to sense the closure of a gap. 
         FIG. 16B  depicts a side view of the haptic actuator shown in  FIG. 16A . 
         FIG. 17  depicts a second technique for pre-stressing a haptic actuator and sensing the closure of a gap. 
         FIG. 18A  depicts a third technique for pre-stressing a haptic actuator and sensing the closure of a gap. 
         FIG. 18B  depicts a third technique for pre-stressing a haptic actuator and sensing the closure of a gap. 
         FIG. 19  depicts a fourth technique for pre-stressing a haptic actuator and sensing the closure of a gap. 
         FIG. 20  depicts a cross-sectional view of another example of the electronic device taken along line A-A in  FIG. 1 . 
         FIG. 21  depicts a cross-sectional view of another example of the electronic device taken along line A-A in  FIG. 1 , where the haptic actuators are in a pre-stressed state. 
         FIG. 22  depicts a flowchart of a method of calibrating the pre-stress signals for an array of haptic actuators. 
         FIG. 23  depicts a flowchart of a method of operating an electronic device. 
         FIG. 24  depicts one example of a first deflection module that is configured to produce increased deflection. 
         FIG. 25  depicts one example of a second deflection module that is configured to produce increased deflection. 
         FIG. 26  depicts one example of a third deflection module that is configured to produce increased deflection. 
         FIG. 27  depicts one example of a fourth deflection module that is configured to produce increased deflection. 
         FIG. 28  depicts a flowchart of a method of producing a deflection module that provides localized deflection in a surface of an electronic device that is positioned over the deflection module. 
         FIG. 29  illustrates an arrangement of haptic structures that may be used to provide localized haptic output for an electronic device. 
         FIG. 30A  illustrates an example shape of a piezoelectric wafer that may be incorporated in the haptic structures described herein. 
         FIG. 30B  illustrates another example shape of a piezoelectric wafer that may be incorporated in the haptic structures described herein. 
         FIG. 30C  illustrates a third example shape of a piezoelectric wafer that may be incorporated in the haptic structures described herein. 
         FIG. 31  illustrates an example piezoelectric sheet for cutting cross-shaped piezoelectric wafers that may be integrated with a haptic structure. 
         FIG. 32  illustrates an example piezoelectric sheet for cutting wafers of piezoelectric material into cross-shaped sections that may be integrated with a haptic structure. 
         FIG. 33  depicts a system diagram including example components of an electronic device in accordance with the embodiments described herein. 
     
    
    
     The use of cross-hatching or shading in the accompanying figures is generally provided to clarify the boundaries between adjacent elements and also to facilitate legibility of the figures. Accordingly, neither the presence nor the absence of cross-hatching or shading conveys or indicates any preference or requirement for particular materials, material properties, element proportions, element dimensions, commonalities of similarly illustrated elements, or any other characteristic, attribute, or property for any element illustrated in the accompanying figures. 
     Additionally, it should be understood that the proportions and dimensions (either relative or absolute) of the various features and elements (and collections and groupings thereof) and the boundaries, separations, and positional relationships presented therebetween, are provided in the accompanying figures merely to facilitate an understanding of the various embodiments described herein and, accordingly, may not necessarily be presented or illustrated to scale, and are not intended to indicate any preference or requirement for an illustrated embodiment to the exclusion of embodiments described with reference thereto. 
     DETAILED DESCRIPTION 
     Reference will now be made in detail to representative embodiments illustrated in the accompanying drawings. It should be understood that the following descriptions are not intended to limit the embodiments to one preferred embodiment. To the contrary, they are intended to cover alternatives, modifications, and equivalents as can be included within the spirit and scope of the described embodiments as defined by the appended claims. 
     The following disclosure relates to an electronic device that is configured to provide localized haptic feedback to a user on one or more surfaces of the electronic device. The surface that receives the haptic output can be a surface of an input device, a cover sheet disposed over a component of the input device, a cover sheet disposed over a component of the electronic device, and/or at least a portion of the enclosure of the electronic device. Haptic output is generated through the production of mechanical movement, vibrations, and/or force. In some embodiments, the haptic output can be created based on an input command (e.g., one or more touch and/or force inputs), a simulation, an application, or a system state. When the haptic output is applied to a surface (or surfaces), a user can detect or feel the haptic output and perceive the haptic output as localized haptic feedback. 
     The localized haptic output can be produced based on a user interacting with one or more regions of a surface of an electronic device. For example, a user can be providing touch and/or force inputs on a cover sheet positioned over a display in an electronic device. A user can provide the touch and/or force inputs based on an application or a user interface rendered on the display. Localized haptic output may be provided to a region of the cover sheet in response to at least one touch and/or force input. 
     Additionally or alternatively, localized haptic feedback can be applied to one or more regions of a surface of an electronic device that the user is touching. For example, localized haptic output may be applied to one or more regions of an enclosure of the electronic device when the user is touching the region and/or touching the enclosure. 
     In a particular embodiment, a haptic or deflection module is positioned below a surface of the electronic device. The haptic or deflection module includes one or more haptic actuators that are coupled to at least one surface of a support structure. In some embodiments, the haptic actuator is coupled to at least one surface of a support structure. In some embodiments, the haptic actuator(s) is coupled to the support structure through a circuit layer. The circuit layer is operatively (e.g., electrically) connected to a signal generator that produces one or more electrical signals. The circuit layer is configured to provide the electrical signal(s) to each individual haptic actuator to selectively actuate one or more haptic actuators concurrently, with some overlap in time, or sequentially. When actuated, the surface bends or deflects at a location that substantially corresponds to the location of the haptic actuator on the support structure. 
     In some embodiments, one or more intermediate layers are positioned between the surface and the haptic or deflection module. For example, in one embodiment the surface is a cover sheet and the intermediate layer includes a display layer disposed between the cover sheet and the haptic or deflection module. Deflection of the support structure transmits through the display layer to the top surface of the cover sheet and causes a region or section of the cover sheet to bend or deflect. 
     The support structure may be designed to amplify a haptic response at the surface in response to actuation of the haptic actuator. In an example embodiment, the support structure may be designed to be more flexible at a location above the haptic actuator. In some examples, the support structure includes a cavity above the haptic actuator to increase the flexibility directly above the haptic actuator and amplify deflection of the support structure. In other examples, the support structure includes a force concentration region above the haptic actuator. The force concentration region may be formed from a material with a lower modulus of elasticity than surrounding regions, increasing flexibility and deflection in response to the haptic actuator. 
     In another example embodiment, the support structure may be pre-curved and/or pre-strained into a curve. The curved shape of the support structure may act as a spring which “pops” from a downward curve into an upward curve when the haptic actuator is actuated. The support structure is mechanically unstable at an intermediate position, so that when it moves past a midpoint it “pops” and transfers a distinctive haptic response to the surface. 
     In another example embodiment, the support structure includes a movable arm. The arm moves upward in response to actuation of the haptic actuator, causing a corresponding deflection on the surface. In some examples, a pair of arms are connected by a hinge to form a scissor mechanism. In other examples, a pair of arms are connected by a flexure that bends upwards in response to actuation of the haptic actuator. 
     In another example embodiment, an upper support structure and lower support structure surround the haptic actuator. Both support structures respond to actuation of the haptic actuator by deflecting vertically. The lower support structure is in contact with a rigid lower layer such that when it deflects, it causes the upper support structure to be moved upward. The upper support structure simultaneously deflects upward. This adds the deflection of the upper support structure to the response of the lower support structure to amplify the haptic response at the surface. 
     In some embodiments, the support structure may extend along a length and a width of the display layer. An array of haptic actuators may be coupled to the support structure to provide localized feedback across the surface. In other embodiments, the support structure may extend more or less than the length and width of the display. In still other embodiments, the support structure may be an array of support structures, corresponding to an array of haptic actuators. 
     In another particular embodiment, the haptic actuator(s) can operate in three states: a rest state, a pre-stressed state, and an actuation state. The rest state occurs when the haptic actuators are not activated. The pre-stressed state occurs when the haptic actuators receive a pre-stress signal. The pre-stress signal actuates the haptic actuators and causes the support structure to deflect and position the haptic actuators closer to a surface to be deflected without deflecting (or substantially deflecting) the surface. The actuation state occurs when one or more of the pre-stressed haptic actuators receive an actuation signal. The actuation signal further activates the haptic actuator(s), which causes the deflection in the support structure to increase locally and deflect the surface at a location that substantially corresponds to the location of the haptic actuator(s) on the support structure. 
     Thus, a deflection module and/or a haptic output device is arranged to operate in three configurations: a rest configuration where the haptic actuators are not actuated, a pre-stressed configuration where the haptic actuators are actuated and positioned either closer to or farther from the surface without deflecting (or substantially deflecting) the surface, and a haptic output configuration where one or more haptic actuators are further actuated to produce a deflection or deflections in the surface. 
     In some implementations, a haptic or deflection module may be configured to produce increased deflection. In an example, a haptic actuator may be rigidly affixed to a support structure through a circuit layer. However, only shorter sides of a rectangular support structure are rigidly attached to a component in an electronic device. This may relax strain in the support structure, facilitating a greater amount of deflection in response to actuation of the haptic actuator. 
     In another example, an array of haptic actuators may be attached to a support structure through a circuit layer. Only two sides of each haptic actuator may be rigidly attached to the circuit layer, which may similarly facilitate greater deflection in response to actuation of one or more haptic actuators. In other examples, the support structure may additionally or alternatively incorporate openings in order to further relieve strain in the support structure, further facilitating deflection in response to actuation of a haptic actuator. 
     In some implementations, the size of the piezoelectric material (e.g., piezoelectric element) may be related to the amount of deflection of the haptic structure and, as a result, the amount of haptic output that is perceivable by a user. Thus, the larger the piezoelectric material, the higher the amount of deflection. However, the cost of the piezoelectric material also scales by size. The larger the piezoelectric material, the greater the cost to produce the haptic structure. 
     In order to address the high cost of producing haptic structures, some embodiments described herein are directed to piezoelectric elements having a cross-shaped configuration. These cross-shaped piezoelectric elements include areas that are most contributive to providing the haptic output. As such, performance between a cross-shaped piezoelectric element and a square-shaped piezoelectric element is largely maintained while saving approximately 4/9 of the material. Although a cross-shaped piezoelectric element is mentioned, the embodiments described herein may have other shapes, such as, for example, a “T” shape, an “X” shape and so on. 
     Other components of the haptic structure described herein may also be reduced such that additional cost savings are realized. For example, different materials may be used in conjunction with flex circuits that make up the haptic structure. In another embodiment, one or more dimensions of the flex circuits that make up the haptic structure may be reduced. 
     As briefly described above, the haptic structure may include a piezoelectric material. The piezoelectric material may have any suitable shape including, but not limited to, the cross-shape described above. Two electrodes may be positioned on opposite faces of the piezoelectric material. For example, a top electrode can be formed on a top face of the piezoelectric material and a bottom electrode can be formed on a bottom face of the piezoelectric material. 
     In some cases, the bottom electrode can wrap around a sidewall of the piezoelectric material. In such a configuration, the top electrode and the bottom electrode both occupy a portion of the top face of the piezoelectric material. 
     The piezoelectric material and its corresponding electrodes may be coupled to a top flex and a bottom flex. A first electrical connection can be made between the top electrode and the top flex, and a second electrical connection can be made between the bottom electrode and the bottom flex. The first electrical connection may be made from a first material while the second electrical connection is made from a second material. For example, the first electrical connection may be a silver trace while the second electrical connection is a copper trace. In other implementations, the first and second connections may be made from the same material. 
     The first and second electrical connections can be established using any number of suitable techniques including, but not limited to, soldering, welding, bonding with electrically conductive adhesive, bonding with electrically conductive tape, placing electrically conductive surfaces in contact, and so on. 
     In some embodiments, the bottom flex may have a width that is less than the top flex. More specifically, in order to decrease costs but maintain reliability, when a copper trace is used with the bottom flex and a silver trace is used with the top flex, the bottom flex may have a width that is less than the top flex. 
     As used herein, the terms “connected” and “coupled” are generally intended to be construed broadly to cover direct connections and indirect connections. In the context of electrical or circuit operations, the terms “connected” and “coupled” are intended to cover circuits, components, and/or devices that are connected such that an electrical parameter passes from one to another. Example electrical parameters include, but are not limited to, voltages, currents, magnetic fields, control signals, and/or communication signals. Thus, the terms “coupled” and “connected” include circuits, components, and/or devices that are coupled directly together or through one or more intermediate circuits, components, and/or devices. 
     Additionally, the terms “connected”, “affixed”, “attached”, “over”, “overlying”, and “on” are intended to be construed broadly, and therefore should not be interpreted to preclude the presence of one or more intervening layers or other intervening components or elements. Thus, a given layer or element that is described herein as being a layer overlying another layer or element, a layer/element or positioned on or positioned over another layer/element, may be separated from the latter layer (or element) by one or more additional layers (or elements). Similarly, a given layer or element that is described herein as being attached, affixed, and connected to another layer or element may be separated from the latter layer (or element) by one or more additional layers (or elements). 
     Directional terminology, such as “top”, “bottom”, “front”, “back”, “leading”, “trailing”, etc., is used with reference to the orientation of the Figure(s) being described. Because components in various embodiments can be positioned in a number of different orientations, the directional terminology is used for purposes of illustration only and is in no way limiting. 
     These and other embodiments are discussed below with reference to  FIGS. 1-33 . However, those skilled in the art will readily appreciate that the detailed description given herein with respect to these Figures is for explanatory purposes only and should not be construed as limiting. 
       FIG. 1  depicts an example of an electronic device that can provide localized deflection of a surface. In the illustrated embodiment, the electronic device  100  is implemented as a tablet computing device. Other embodiments can implement the electronic device differently. For example, an electronic device can be a smart phone, a laptop computer, a wearable computing device, a digital music player, a kiosk, a stand-alone touch screen display, a mouse, a keyboard, and other types of electronic devices that are configured to provide haptic feedback to a user. 
     The electronic device  100  includes an enclosure  102  at least partially surrounding a display  104  and one or more input/output (I/O) devices  106 . The enclosure  102  can form an outer surface or partial outer surface for the internal components of the electronic device  100 . The enclosure  102  can be formed of one or more components operably connected together, such as a front piece and a back piece. Alternatively, the enclosure  102  can be formed of a single piece operably connected to the display  104 . 
     The display  104  can provide a visual output to the user. The display  104  can be implemented with any suitable technology, including, but not limited to, a liquid crystal display (LCD) element, a light emitting diode (LED) element, an organic light-emitting display (OLED) element, an organic electroluminescence (OEL) element, and the like. In some embodiments, the display  104  can function as an input device that allows the user to interact with the electronic device  100 . For example, the display  104  can be a multi-touch and/or multi-force sensing touchscreen LED display. 
     In some embodiments, the I/O device  106  can take the form of a home button, which may be a mechanical button, a soft button (e.g., a button that does not physically move but still accepts inputs), an icon or image on a display, and so on. Further, in some embodiments, the I/O device  106  can be integrated as part of a cover sheet  108  and/or the enclosure  102  of the electronic device  100 . Although not shown in  FIG. 1 , the electronic device  100  can include other types of I/O devices, such as a microphone, a speaker, a camera, a biometric sensor, and one or more ports, such as a network communication port and/or a power cord port. 
     A cover sheet  108  may be positioned over the front surface (or a portion of the front surface) of the electronic device  100 . At least a portion of the cover sheet  108  can function as an input surface that receives touch and/or force inputs. The cover sheet  108  can be formed with any suitable material, such as glass, plastic, sapphire, or combinations thereof. In one embodiment, the cover sheet  108  covers the display  104  and the I/O device  106 . Touch and force inputs can be received by the portion of the cover sheet  108  that covers the display  104  and by the portion of the cover sheet  108  that covers the I/O device  106 . 
     In another embodiment, the cover sheet  108  covers the display  104  but not the I/O device  106 . Touch and force inputs can be received by the portion of the cover sheet  108  that covers the display  104 . In some embodiments, touch and force inputs can be received on other portions of the cover sheet  108 , or on the entire cover sheet  108 . The I/O device  106  may be disposed in an opening or aperture formed in the cover sheet  108 . In some embodiments, the aperture extends through the enclosure  102  and one or more components of the I/O device  106  are positioned in the enclosure. 
     At least one haptic or deflection module (see  FIGS. 2A-2D ) can be included in the electronic device  100 . For example, one or more haptic or deflection modules may be positioned below the cover sheet  108  and/or at least a portion of the enclosure  102 . The haptic or deflection modules can be configured to provide localized haptic feedback to a user. 
     Embodiments are described herein in conjunction with providing haptic output on the cover sheet  108  positioned over the display  104 . However, the present invention can be used to deflect or provide haptic output to any suitable surface of an electronic device. For example, the surface can be an input surface of an input device, such as a trackpad, a mouse, and a button. Additionally or alternatively, the surface may be a portion of the enclosure of an electronic device. 
       FIGS. 2A and 2B  depict a cross-sectional view of an example of the electronic device illustrated in  FIG. 1 , taken along line A-A.  FIG. 2A  depicts the electronic device  200   a  when the haptic actuators are not actuated, while  FIG. 2B  portrays the electronic device  200   a  when a haptic actuator is actuated. In the illustrated embodiments, a display layer  204   a  is positioned below the cover sheet  208   a . The electronic device  200   a  may include a touch sensor layer  210  positioned between a display layer  204   a  and the cover sheet  208   a.    
     The touch sensor layer  210  may include an array of touch sensors that are configured to detect the location of a finger or object on or near the cover sheet  208   a . The touch sensors may operate in accordance with a number of different sensing schemes. In some implementations, the touch sensors may operate in accordance with a mutual-capacitance sensing scheme. Under this scheme, the touch sensor layer  210  may include two layers of intersecting transparent traces (e.g., sensing nodes) that are configured to detect the location of a touch by monitoring a change in capacitive or charge coupling between pairs of intersecting traces. In another implementation, the touch sensor layer  210  may operate in accordance with a self-capacitive sensing scheme. Under this scheme, the touch sensor layer  210  may include an array of capacitive electrodes or pads (e.g., sensing nodes) that are configured to detect the location of a touch by monitoring a change in self-capacitance of a small field generated by each electrode. In other implementations, a resistive, inductive, or other sensing scheme could also be used. 
     The display layer  204   a  includes the display  104 , and may include additional layers such as one or more polarizers, one or more conductive layers, and one or more adhesive layers. In some embodiments, a backlight assembly (not shown) is positioned below the display layer  204   a . The display layer  204   a , along with the backlight assembly, is used to output images on the display. In other embodiments, the backlight assembly may be omitted. 
     The electronic device  200   a  may further include a force sensor layer  212   a , which may be positioned below the display layer  204   a , and may further be positioned above a support structure  220   a . The support structure  220   a  may be substantially rigid, and may provide support for a circuit layer  222   a  and one or more haptic actuators  224   a . In some embodiments, the support structure  220   a  may form a chassis to support components of the electronic device  200   a , such as the display layer  204   a . The support structure  220   a  may further be positioned above the enclosure  202   a . However, the relative position of the various layers described above may change depending on the embodiment. Some layers, such as the touch sensor layer  210  and the force sensor layer  212   a , may be omitted in other embodiments. The electronic device  200   a  may include additional layers and components, such as control circuitry, a processing unit, a battery, etc., which have been omitted from  FIGS. 2A and 2B  for clarity. 
     Localized haptic feedback may be provided by means of the one or more haptic actuators  224   a  coupled to the support structure  220   a . The support structure  220   a  may be made from a rigid material, such as a metal or metal alloy (e.g., stainless steel, aluminum, and so on), plastic, silicone, glass, ceramic, fiber composite, or other suitable materials, or a combination of these materials. The support structure  220   a  may extend along a length and a width of the display layer  204   a , although this is not required. The support structure  220   a  can have any shape and/or dimensions in other embodiments. In some embodiments, the support structure  220   a  may be a single structure, while in other embodiments the support structure  220   a  may be an array of support structures  220   a.    
     The support structure  220   a  may be coupled to another component of the electronic device  200   a . For example, the support structure  220   a  can be coupled to the cover sheet  208   a  such that the support structure  220   a  is suspended from the cover sheet  208   a . In other embodiments, the support structure  220   a  may be coupled to a component other than the cover sheet  208   a . For example, the support structure  220   a  can be attached to the enclosure  202   a  of the electronic device  200   a  or to a frame or other support component in the enclosure  202   a . For example, the support structure  220   a  can be attached to a support component positioned below the support structure  220   a . In such embodiments, the support structure  220   a  can include one or more legs that contact the support component and position the support structure  220   a  below the display layer  204   a.    
     The support structure  220   a  may further be shaped to amplify the effect of a haptic actuator  224   a . Example embodiments of the support structure  220   a  are further illustrated below with respect to  FIGS. 5A-11H . In the illustrated embodiment, the haptic actuators  224   a  are coupled to a bottom surface of the support structure  220   a . However, in other implementations, one or more haptic actuators  224   a  may be coupled to a top surface and/or a side of the support structure  220   a . In yet other implementations, one or more haptic actuators  224   a  may be coupled to the top surface and/or the bottom surface of the support structure  220   a.    
     In some embodiments, one or more haptic actuators  224   a  may be affixed or coupled to the support structure  220   a  through a circuit layer  222   a  attached to a bottom surface of the support structure  220   a . In the illustrated embodiment, each haptic actuator  224   a  is further attached and electrically connected to the circuit layer  222   a . The circuit layer  222   a  includes signal lines that are electrically connected to the haptic actuators  224   a . The signal lines can be used to transmit electrical signals to each haptic actuator  224   a  to selectively actuate one or more haptic actuators  224   a . A ground layer  238  may be attached and electrically connected to a bottom surface of each haptic actuator  224   a . The ground layer  238  provides a common reference voltage to the haptic actuators  224   a.    
     In other embodiments, the circuit layer  222   a  may be omitted and the one or more haptic actuators  224   a  attached to the support structure  220   a . Signal lines or electrical traces may be included in the support structure  220   a  and electrically connected to the haptic actuators  224   a . Additionally or alternatively, signal lines or electrical traces can be formed on at least one surface of the support structure  220   a  and electrically connected to the haptic actuators  224   a . The signal lines can be used to transmit electrical signals to each haptic actuator  224   a  to selectively actuate one or more haptic actuators  224   a.    
     Any suitable circuit layer  222   a  and ground layer  238  can be used. For example, in one embodiment the circuit layer  222   a  and ground layer  238  may be a flexible printed circuit or a flexible printed circuit board. The circuit layer  222   a  and the ground layer  238  can be made from any number of suitable materials, such as polyimide or polyethylene terephthalate, with conductive traces formed from materials such as copper, silver, aluminum, and so on. 
     Each haptic actuator  224   a  can be selectively activated in the embodiment shown in  FIGS. 2A and 2B . In particular, the ground layer  238  can provide a common reference voltage to the haptic actuators  224   a , while the circuit layer  222   a  can apply an electrical signal across each individual haptic actuator  224   a  independently of the other haptic actuators  224   a . The haptic output produced by one or more haptic actuators  224   a  can cause the support structure  220   a  to deflect or otherwise move. As illustrated in  FIG. 2B , when the support structure  220   a  deflects, it moves into the force sensor layer  212   a , causing a corresponding deflection in the force sensor layer  212   a . The deflection in the force sensor layer  212   a  in turn moves into and causes a corresponding deflection in the display layer  204   a , the touch sensor layer  210 , and the cover sheet  208   a . The transmitted deflection causes one or more sections of the cover sheet  208   a  to deflect or move to provide localized haptic feedback to the user. In particular, the cover sheet  208   a  bends or deflects at a location  226   a  that substantially corresponds to the location of the haptic actuator  224   a  on the support structure  220   a.    
     Any suitable type of haptic actuator can be used. For example, in one embodiment each haptic actuator  224   a  is a piezoelectric transducer. The piezoelectric transducer may be formed from an appropriate piezoelectric material, such as sodium potassium niobate, lead zirconate titanate (PZT), quartz, and other ceramic or non-ceramic materials. A piezoelectric transducer is actuated with an electrical signal. When activated, the piezoelectric transducer converts the electrical signal into mechanical movement, vibrations, and/or force. The mechanical movement, vibrations, and/or force generated by the actuated haptic actuator is known as haptic output. When the haptic output is applied to a surface, a user can detect or feel the haptic output and perceive the haptic output as haptic feedback. 
     Different types of haptic actuators  224   a  can be used in other embodiments. For example, in one embodiment one or more electromagnetic actuators can be disposed on the support structure  220   a  and used to produce localized deflection of the cover sheet  208   a . Alternatively, one or more piston actuators may be disposed on the support structure  220   a  and used to produce localized deflection of the cover sheet  208   a.    
     An example haptic actuator  224   a  and circuit layer  222   a  are further illustrated below with respect to  FIG. 3 . An electronic device  200   a  implementing an array  240  of haptic actuators  224   a  is depicted below with respect to  FIG. 4 . 
     The layer or layers between the cover sheet  208   a  and the support structure  220   a  are referred to herein as intermediate layer(s). In the illustrated embodiment, the display layer  204   a , the optional touch sensor layer  210 , and the optional force sensor layer  212   a  are intermediate layers. 
     In the illustrated embodiment, the force sensor layer  212   a  is formed between the support structure  220   a  and an intermediate layer (e.g., the display layer  204   a ). The support structure  220   a  is positioned to define a gap  218   a  between the support structure  220   a  and the display layer  204   a . A first force-sensing component  214   a  and a second force-sensing component  216   a  may be positioned within the gap  218   a . For example, the first force-sensing component  214   a  can be affixed to the bottom surface of the display layer  204   a  and the second force-sensing component  216   a  to the top surface of the support structure  220   a . Together, the first and second force-sensing components  214   a ,  216   a  form the force sensor layer  212   a . The force sensor layer  212   a  can be used to measure an amount of force that is applied to the cover sheet  208   a.    
     In some implementations, the first force-sensing component  214   a  represents a first array of electrodes and the second force-sensing component  216   a  a second array of electrodes. The first and second arrays of electrodes can each include one or more electrodes. Each electrode in the first array of electrodes is aligned in at least one direction (e.g., vertically) with a respective electrode in the second array of electrodes to form an array of capacitive sensors. The capacitive sensors are used to measure a force applied to the cover sheet  208   a  through measured capacitances or measured changes in capacitances. For example, as the cover sheet  208   a  deflects in response to a received amount of force, a distance between the electrodes in at least one capacitive sensor changes, which varies the capacitance of that capacitive sensor. Drive and sense circuitry can be operatively (e.g., electrically) connected to each capacitive sensor and configured to sense or measure the capacitance of each capacitive sensor. A processing unit may be operatively (e.g., electrically) connected to the drive and sense circuitry and configured to receive signals representing the measured capacitance of each capacitive sensor. The processing unit can be configured to correlate the measured capacitances into an amount of force. 
     In other embodiments the force sensor layer  212   a  can employ a different type of sensor to measure force or the deflection of the first force-sensing component  214   a  relative to the second force-sensing component  216   a . In some representative examples, the force sensor layer  212   a  can operate with optical displacement sensors, magnetic displacement sensors, or inductive displacement sensors. In other embodiments, the force sensor layer  212   a  may be formed from a strain-sensitive material, such as a piezoresistive, piezoelectric, or similar material having an electrical property that changes in response to stress, strain, and/or deflection. Example strain-sensitive materials include carbon nanotube materials, graphene-based materials, piezoresistive semiconductors, piezoresistive metals, metal nanowire material, and the like. 
     In other embodiments, the force sensor layer  212   a  can be positioned at a different location within the electronic device  200   a . For example, the force sensor layer  212   a  may be positioned between the display layer  204   a  and the cover sheet  208   a . In some embodiments, the force sensor layer  212   a  may be combined with the touch sensor layer  210  to form a single force- and touch-sensing layer. In further examples, the first and second force-sensing components  214   a ,  216   a  may be separated by another layer rather than a gap  218   a , such as being separated by the display layer  204   a.    
     In some embodiments, the haptic actuators  224   a , the touch sensor layer  210 , and/or the force sensor layer  212   a  may work together to enhance a user&#39;s experience. In one non-limiting example, at least one haptic actuator  224   a  may provide localized haptic or tactile output at a location of a touch in response to a touch input. Alternatively, at least one haptic actuator  224   a  can provide haptic or tactile output in response to a force input having an amount of force that exceeds a given threshold. Additionally or alternatively, in some implementations, at least one haptic actuator  224   a  may provide a first type of haptic output or a haptic output at a first location in response to a first amount of detected force, and may provide a second type of haptic output or a haptic output at a second location in response to a second amount of detected force. 
     In addition to the above, the haptic actuators  224   a , the touch sensor layer  210 , and/or the force sensor layer  212   a  may also work in conjunction to determine a location of a received touch input and/or force input. When such a location is determined, actuation of at least one haptic actuator  224   a  and any associated haptic output may be localized at the determined position. 
     In another implementation, at least one haptic actuator  224   a  may provide haptic output in an area surrounding or adjacent the determined location. To achieve this, one or more haptic actuators  224   a  may be actuated at different times and at different locations to effectively cancel out (or alternatively enhance) the haptic output. 
       FIG. 2B  depicts a cross-sectional view of the electronic device  200   a  shown in  FIG. 2A  when a haptic actuator  224   a  is actuated and produces a localized deflection in the cover sheet  208   a . In the illustrated embodiment, the haptic actuator  224   a  has been activated with an electrical signal. The haptic actuator  224   a  moves (e.g., contracts) in response to the electrical signal, which causes the support structure  220   a  to deflect. While being deflected, the support structure  220   a , the circuit layer  222   a , and the second force-sensing component  216   a  move into the gap  218   a  and contact the first force-sensing component  214   a . The deflection of the support structure  220   a  propagates through the first force-sensing component  214   a , the display layer  204   a , the touch sensor layer  210 , and the cover sheet  208   a . In response to the transmitted deflection, the cover sheet  208   a  bends or deflects at a location  226   a  that substantially corresponds to the location of the haptic actuator  224   a  on the support structure  220   a . The cover sheet  208   a  around the deflected location  226   a  is substantially unaffected by the haptic output produced by the haptic actuator  224   a . A user can detect the local deflection of the cover sheet  208   a  and perceive the deflection as localized haptic feedback. 
     In the embodiments shown in  FIGS. 2A and 2B , the haptic actuators  224   a , the circuit layer  222   a , and the support structure  220   a  collectively form a haptic or deflection module  201   a . In embodiments that omit the circuit layer  222   a , the haptic or deflection module  201   a  includes the haptic actuators  224   a  and the support structure  220   a.    
       FIGS. 2C and 2D  depict a cross-sectional view of another example of the electronic device, taken along line A-A of  FIG. 1 .  FIG. 2C  depicts the electronic device  200   b  when the haptic actuators are not actuated, while  FIG. 2D  portrays the electronic device  200   b  when a haptic actuator is actuated.  FIGS. 2C and 2D  include layers arranged differently from  FIGS. 2A and 2B . For example, a display layer  204   b  is positioned below the cover sheet  208   b . The display layer  204   b  includes the display  104 , and may include additional layers such as one or more polarizers, one or more conductive layers, and one or more adhesive layers. 
     In some embodiments, a backlight assembly  205  is positioned below the display layer  204   b . The display layer  204   b , along with the backlight assembly  205 , is used to output images on the display. A gap  218   c  may be present between the display layer  204   b  and the backlight assembly  205 . Additionally or alternatively, one or more gaps may exist between the elements or layers in the backlight assembly  205 . The backlight assembly  205  may be omitted in other embodiments. 
     The electronic device  200   b  can also include a support structure  220   b . In the illustrated embodiment, the support structure  220   b  is a U-shaped support structure that includes a support plate  223  and sides  225  that extend from the support plate  223  to the cover sheet  208   b . The support plate  223  is depicted as a substantially horizontal support plate, although this is not required. 
     The support structure  220   b  can be made of any suitable material or materials, such as the materials described above with respect to  FIG. 2A . Some embodiments can form the support structure  220   b , the support plate  223 , and/or the sides  225  with a different material or combination of materials (e.g., a metal support plate  223  and plastic or ceramic sides  225 ). In the illustrated embodiment, the support plate  223  extends along a length and a width of the display layer  204   b , although this is not required. The support structure  220   b  and/or the support plate  223  can have any given shape and/or dimensions in other embodiments. 
     The sides  225  of the support structure  220   b  can be connected to the cover sheet  208   b  such that the support structure  220   b  is suspended from the cover sheet  208   b . In other embodiments, the support structure  220   b  may be connected to the cover sheet  208   b  through one or more intermediate layers, or the support structure  220   b  can be connected to a component other than the cover sheet  208   b . For example, the support structure  220   b  can be attached to an enclosure  202   b  of the electronic device  200   b  (e.g.,  102  in  FIG. 1 ) or to a frame or other support component in the enclosure  202   b . For example, the support structure  220   b  can be attached to a support component positioned below the support structure  220   b . In such embodiments, the sides  225  of the support structure  220   b  can contact the support component and position the support plate  223  below the display layer  204   b  (or below the backlight assembly  205  when the backlight assembly  205  is present). 
     An array  240  of haptic actuators  224   b  may be affixed, through a circuit layer  222   b , to a surface of the support structure  220   b  (e.g., to the support plate  223 ). Any suitable circuit layer  222   b  can be used, such as described above with respect to  FIG. 2A . In other embodiments, the circuit layer  222   b  can be attached to the opposite side of the array  240  of haptic actuators  224   b  (the side opposite the support plate  223 ; see  FIG. 21 ). In still other embodiments, the circuit layer  222   b  may be omitted and signal lines or electrical traces may be included in the support structure  220   b  and electrically connected to the haptic actuators  224   b.    
     In the illustrated embodiment, the array  240  of haptic actuators  224   b  is coupled to a bottom surface of the support plate  223 . However, in other implementations, one or more haptic actuators  224   b  may be coupled to a top surface of the support plate  223  and/or to one or more sides  225  of the support structure  220   b . In yet other implementations, one or more haptic actuators  224   b  may be coupled to the top and bottom surfaces of the support plate  223  or to one or more sides  225  as well as to the top and bottom surfaces of the support plate  223 . Although the array  240  is depicted with three haptic actuators  224   b , other embodiments are not limited to this number. The array  240  can include one or more haptic actuators  224   b.    
     Any suitable type of haptic actuator can be used, such as described above with respect to  FIG. 2A . The haptic actuators  224   b  may similarly be selectively activated in the embodiment shown in  FIGS. 2C and 2D . In particular, each individual haptic actuator  224   b  can receive an electrical signal via the circuit layer  222   b  independent of the other haptic actuators  224   b . The haptic output produced by one or more haptic actuators  224   b  can cause the support structure  220   b  to deflect or otherwise move. In the illustrated embodiment, the deflection(s) of the support structure  220   b  can cause the support plate  223  to move upward such that the deflection transmits through the backlight assembly  205  and the display layer  204   b  to the cover sheet  208   b  (see  FIG. 2D ). The transmitted deflection(s) cause one or more sections of the cover sheet  208   b  to deflect or move and provide localized haptic output on the surface of the cover sheet  208   b . In particular, the cover sheet  208   b  moves or deflects at a location  226   b  that substantially corresponds to the location of the haptic actuator(s)  224   b  on the support structure  220   b.    
     The intermediate layer(s) illustrated in  FIGS. 2C and 2D  include the display layer  204   b , the backlight assembly  205 , and the optional force sensor layer  212   b . The support structure  220   b  is constructed and attached to the cover sheet  208   b  to define a gap  218   b  between the top surface of the support plate  223  and a bottom surface of the intermediate layer (e.g., the bottom surface of the backlight assembly  205 ). In some embodiments, a force sensor layer  212   b  is formed across the gap  218   b . The force sensor layer  212   b  may include a first force-sensing component  214   b  affixed to the bottom surface of the backlight assembly  205  and a second force-sensing component  216   b  affixed to the top surface of the support plate  223 . The force sensor layer  212   b  may be similar to the force sensor layer  212   a  described above with respect to  FIG. 2A . 
     In some embodiments, a battery  203  is positioned below the support structure  220   b . The battery  203  provides power to the various components of the electronic device  200   b . The battery  203  can be positioned such that a gap  218   d  is defined between the array  240  of haptic actuators  224   b  and a top surface of the battery  203 . The gap  218   d  allows the battery  203  to expand due at least in part to heat or temperature. 
     As shown in  FIG. 2C , an additional force sensor  213  can be disposed on a top surface of the battery  203 . The additional force sensor  213  may be used to detect a second amount of force. In some embodiments, the amount of force applied to the cover sheet  208   b  may be sufficient to cause the intermediate layer to deflect such that the first force-sensing component  214   b  traverses into the gap  218   b  and contacts the second force-sensing component  216   b . When the intermediate layer is deflected to a point where the first force-sensing component  214   b  contacts the second force-sensing component  216   b , the amount of force detected by the force-sensing device reaches a maximum level (e.g., a first amount of force). The force-sensing device cannot detect force amounts that exceed that maximum level. In such embodiments, the additional force sensor  213  can detect the amount of force that exceeds the maximum level of the force-sensing device (e.g., a second amount of force) by associating an amount of deflection between the support plate  223  and the additional force sensor  213 . For example, in some embodiments, the additional force sensor  213  represents one or more electrodes that can be used to measure a change in capacitance between the support plate  223  and the additional force sensor  213 . 
       FIG. 2D  depicts a cross-sectional view of the electronic device  200   b  shown in  FIG. 2C  when a haptic actuator is actuated and produces a localized deflection in the cover sheet  208   b . In the illustrated embodiment, the haptic actuator  224   b  in the array  240  has been activated with an electrical signal. The haptic actuator  224   b  moves (e.g., contracts) in response to the electrical signal (e.g., a received stimulus), which causes the support structure  220   b  to deflect. When the support structure  220   b  deflects, the support plate  223 , the circuit layer  222   b , the second force-sensing component  216   b , and the haptic actuator  224   b  can move upward toward the cover sheet  208   b . In particular, the second force-sensing component  216   b  and the support plate  223  (and possibly the circuit layer  222   b  and the haptic actuator  224   b ) move into the gap  218   b  and contact the first force-sensing component  214   b . The deflection of the support structure  220   b  propagates through the first force-sensing component  214   b  and the backlight assembly  205  such that the gap  218   c  is closed. Once the gap  218   c  is closed, the deflection propagates through the display layer  204   b  and the cover sheet  208   b . In response to the transmitted deflection, the cover sheet  208   b  moves or deflects at a location  226   b  that substantially corresponds to the location of the haptic actuator  224   b  on the support structure  220   b . The cover sheet  208   b  around the deflected location  226   b  is substantially unaffected by the haptic output produced by the haptic actuator  224   b . A user can detect the local deflection of the cover sheet  208   b  and perceive the deflection as localized haptic feedback. 
     The array  240  of haptic actuators  224   b , the circuit layer  222   b , and the support structure  220   b  collectively form a deflection module  201   b . In embodiments that omit the circuit layer  222   b , the deflection module  201   b  includes the array  240  of haptic actuators  224   b  and the support structure  220   b.    
     Additionally, in some embodiments, the support structure  220   b  and/or the support plate  223  can be attached to, or suspended from, the cover sheet  208   b , the enclosure  202   b  (e.g.,  102  in  FIG. 1 ), and/or another support component such that haptic output is produced on a different region or surface in the electronic device  200   b . In one non-limiting embodiment, the support structure  220   b  can attach to the enclosure  202   b  such that haptic output is applied to the bottom surface of the enclosure  202   b . In another non-limiting embodiment, the support plate  223  can be included in an I/O device (e.g., a button, a trackpad, or I/O device  106  in  FIG. 1 ) such that haptic output is applied to a surface of the I/O device. 
       FIGS. 3A-3D  illustrate cross-sections of example haptic actuators, including various configurations of layers comprising a haptic actuator.  FIG. 3A  depicts a first example haptic actuator  324   a , in the form of a piezoelectric transducer. The haptic actuator  324   a  includes a piezoelectric material  332   a  coupled to a pair of conductive pads  328   a ,  336   a . The piezoelectric material  332   a  may be formed from a suitable material, such as a ceramic piezoelectric material. Example materials include potassium-based ceramics (e.g., potassium-sodium niobate. potassium niobate), lead-based ceramics (e.g., PZT, lead titanate), quartz, bismuth ferrite, and other suitable piezoelectric materials. 
     In some embodiments, the piezoelectric material  332   a  takes a different shape than that depicted. For example, the piezoelectric material  332   a  may have a cross-shape such as depicted in  FIGS. 30B and 30C . In such implementations, the haptic actuator  324   b  may also have the same or a similar shape. The piezoelectric material  332   b  may be 3 cm in width and may be approximately 100 μm thick although other dimensions may be used. 
     When a voltage is applied across the piezoelectric material  332   a , the voltage may induce the piezoelectric material  332   a  to expand or contract in a direction or plane orthogonal to the applied voltage (e.g., the x-y plane). If the piezoelectric material  332   a  is constrained from moving in the direction orthogonal to the applied voltage (e.g., the x-y plane), it may instead deflect in a direction parallel to the applied voltage (e.g., the z-direction). 
     For example, returning to  FIG. 2B , the haptic actuator  224   a  may be affixed to the support structure  220   a , constraining the movement of the piezoelectric material  332   a  in the x-y plane. Accordingly, when a voltage is applied, the piezoelectric material  332   a  of the haptic actuator  224   a  moves in the z-direction. This is depicted in further detail with respect to  FIGS. 5A-11H  below. 
     To apply a voltage across the piezoelectric material  332   a , it may be coupled to a first conductive pad  328   a  (e.g., a top electrode) and a second conductive pad  336   a  (e.g., a bottom electrode). The conductive pads  328   a ,  336   a  may be formed from a suitable conductive material, such as metals (e.g., copper, aluminum, gold, silver), polyethyleneioxythiophene (PEDOT), indium tin oxide (ITO), graphene, piezoresistive semiconductor materials, piezoresistive metal materials, and the like. The first conductive pad  328   a  may be formed from the same material as the second conductive pad  336   a , while in other embodiments the conductive pads  328   a ,  336   a  may be formed from different materials. 
     The conductive pads  328   a ,  336   a  may be coupled to the piezoelectric material  332   a  through a first adhesive layer  330  and a second adhesive layer  334 . The adhesive layers  330 ,  334  may be any adhesive or bonding agent suitable for promoting adhesion between the conductive pads  328   a ,  336   a  and the piezoelectric material  332   a . In some embodiments, the adhesive layers  330 ,  334  may be formed from a pressure-sensitive adhesive. The first adhesive layer  330  may be made from the same adhesive as the second adhesive layer  334 , while in other embodiments the two layers  330 ,  334  may be made from different adhesives. 
     The first conductive pad  328   a  may provide an active voltage, while the second conductive pad  336   a  may serve as a reference or ground. The first conductive pad  328   a  may be activated through an electrical signal from the connected circuit layer  322   a . The second conductive pad  336   a  may be connected to the ground layer  338   a  as a reference. In other embodiments, the roles of the first conductive pad  328   a  and second conductive pad  336   a  may be reversed. 
     In some embodiments, the conductive pads  328   a ,  336   a  may be formed or deposited directly on the piezoelectric material  332   a . The conductive pads  328   a ,  336   a  may be formed using a suitable disposition technique such as, but not limited to: vapor deposition, sputtering, plating, printing, roll-to-roll processing, gravure, pick and place, adhesive, mask-and-etch, and so on. In further embodiments, the conductive pads  328   a ,  336   a  may be electrically coupled to the circuit layer  322   a  by an adhesive layer, such as an isotropic or anisotropic conductive film. 
       FIG. 3B  depicts a second example haptic actuator  324   b , which may be a piezoelectric transducer. The haptic actuator  324   b  includes a sheet of piezoelectric material  332   b . Two electrodes are provided on opposite faces of the piezoelectric material  332   b . For example, a first conductive pad  328   b  (e.g., a top electrode) can be formed on a top face of the piezoelectric material  332   b  and a second conductive pad  336   b  (e.g., a bottom electrode) can be formed on a bottom face of the piezoelectric material  332   b.    
     The first conductive pad  328   b  and the second conductive pad  336   b  can be formed in any number of suitable ways. In one embodiment, the first conductive pad  328   b  and the second conductive pad  336   b  are thin-film layers formed by sputtering, physical vapor deposition, printing, or any other suitable technique. The first conductive pad  328   b  and the second conductive pad  336   b  are typically formed from metal or a metal alloy such as silver, silver ink, copper, copper-nickel alloy, and so on. In other embodiments, other conductive materials can be used. 
     The haptic actuator  324   b  may also include a first bonding material  331   b  provided on the first conductive pad  328   b  and a second bonding material  335   b  provided on the second conductive pad  336   b . The bonding material may be used to couple two flexible circuits to the haptic actuator  324   b . For example, the haptic actuator  324   b  may include a circuit layer  322   b  and a ground layer  338   b.    
     In particular, the first conductive pad  328   b  forms a first electrical connection, via the first bonding material  331   b , with a top electrical contact  321   b  that extends from a circuit layer  322   b . In some embodiments, the top electrical contact  321   b  is a drive trace for the haptic actuator  324   b . Similarly, the second conductive pad  336   b  forms a second electrical connection, via a second bonding material  335   b , with a bottom electrical contact  337   b  that extends from a ground layer  338   b . In some embodiments, the bottom electrical contact  337   b  is a ground trace for the haptic actuator  324   b . In other embodiments, the ground layer  338   b  may be above the piezoelectric material  332   b  and the circuit layer  322   b  may be below the piezoelectric material  332   b.    
     The first bonding material  331   b  and second bonding material  335   b  can be formed from any suitable electrically conductive material or combination of materials such as, but not limited to: electrically conductive adhesive, electrically conductive tape or film (isotropic or anisotropic), solder, and so on. In other cases, one or both of the first bonding material  331   b  and the second bonding material  335   b  may be nonconductive. In these examples, the piezoelectric material  332   b  can be driven capacitively. 
     The circuit layer  322   b  and the ground layer  338   b  can be made from any number of suitable materials, such as described above with respect to  FIG. 2 . In this particular embodiment the circuit layer  322   b  and the ground layer  338   b  are formed from a nonconductive material such as, for example, polyimide. The electrical contacts  321   b ,  337   b  are made of copper although other materials may be used. 
     In this particular embodiment, the top electrical contact  321   b  and the bottom electrical contact  337   b  are formed from copper. Although copper is specifically mentioned, the top electrical contact  321   b  and the bottom electrical contact  337   b  may be formed from silver or any other metal or electrically conductive materials. 
     The haptic actuator  324   b  also includes shield  339   b  positioned adjacent the ground layer  338   b . The shield  339   b  acts to reduce or eliminate electromagnetic interference between the components of the haptic actuator  324   b . In the illustrated embodiment, the shield  339   b  is made from copper, although other materials may be used. 
     In some embodiments, the haptic actuator  324   b  may also include a stiffener, such as a support structure  320   b . The support structure  320   b  may be used to enhance the haptic output as the haptic actuator  324   b  deflects. The support structure  320   b  is coupled to the circuit layer  322   b  using an adhesive layer  319   b . In some cases, the adhesive layer  319   b  is a nonconductive bonding material such as an adhesive, a tape, a film and so on. 
     In the embodiment illustrated in  FIG. 3B , copper and polyimide are used with the flexible circuits due to the high reliability of these materials. However, the cost of these materials may be prohibitive. Accordingly,  FIG. 3C  illustrates a cross-section of a third example haptic actuator  324   c . The haptic actuator  324   c  includes similar components to the haptic actuator  324   b  described above. For example, the haptic actuator  324   c  includes a piezoelectric material  332   c , a first conductive pad  328   c  (e.g., a top electrode) on a top face of the piezoelectric material  332   c  and a second conductive pad  336   c  (e.g., a bottom electrode) on a bottom face of the piezoelectric material  332   c.    
     The haptic actuator  324   c  also includes a circuit layer  322   c  and a ground layer  338   c . The first conductive pad  328   c  forms a first electrical connection, via the first bonding material  331   c , with a top electrical contact  321   c  that extends from the circuit layer  322   c . Similarly, the second conductive pad  336   c  forms a second electrical connection, via a second bonding material  335   c , with a bottom electrical contact  337   c  that extends from a ground layer  338   c.    
     In this particular implementation, the circuit layer  322   c  and the ground layer  338   c  may be made from any nonconductive material, such as, for example, polyethylene terephthalate (PET). The electrical contacts  321   c ,  337   c  are made of silver although other materials may be used. 
     The haptic actuator  324   c  also includes a shield  339   c  coupled or otherwise adjacent the ground layer  338   c . In this embodiment, the shield  339   c  may be made from silver although other materials may be used. The haptic actuator  324   c  also includes a support structure  320   c  coupled to the circuit layer  322   c  via an adhesive layer  319   c . Each of these components may function in a similar manner described above. 
     The haptic actuator  324   c  may be cheaper to produce than the haptic actuator  324   b  described above with respect to  FIG. 3B  due to the difference in the cost of materials. However, the flexible circuits made from silver and PET may be less reliable than the flexible circuits made from copper and polyimide. For example, the flexible circuits made from silver and PET may exhibit electrochemical migration or other undesirable effects when used in a high voltage application. 
       FIG. 3D  depicts a cross-section view of a fourth example haptic actuator  324   d . The haptic actuator  324   d  is a hybrid haptic structure that incorporates components from the haptic actuator  324   b  of  FIG. 3B  and the haptic actuator  324   c  of  FIG. 3C  to balance cost and reliability. 
     The haptic actuator  324   d  includes a piezoelectric material  332   d , a first conductive pad  328   d  on a top face of the piezoelectric material  332   d , and a second conductive pad  336   d  on a bottom face of the piezoelectric material  332   d.    
     The haptic actuator  324   d  also includes a circuit layer  322   d  and a ground layer  338   d . The first conductive pad  328   d  forms a first electrical connection, via the first bonding material  331   d , with a top electrical contact  321   d  that extends from the ground layer  338   d . Similarly, the second conductive pad  336   d  forms a second electrical connection, via a second bonding material  335   d , with a bottom electrical contact  337   d  that extends from a circuit layer  322   d.    
     In this embodiment, the ground layer  338   d  is PET or other such nonconductive material and the top electrical contact  321   d  is a silver drive trace. The circuit layer  322   d  is polyimide or other such nonconductive material and the bottom electrical contact  337   d  is a copper ground trace. 
     A shield  339   d  may be positioned adjacent the circuit layer  322   d . In some embodiments, the shield may be made of copper, silver or any other material that reduces or eliminates interference. As with the other embodiments described herein, the haptic actuator  324   d  may also include a support structure  320   d  coupled to the circuit layer  322   d  using an adhesive layer  319   d.    
     As shown in  FIG. 3D , the circuit layer  322   d , bottom electrical contact  337   d , and shield  339   d  may have a width that is less than a width of the remainder of the haptic actuator  324   d . The decrease in width reduces the cost of producing the haptic actuator  324   d  while maintaining reliability. In addition, the reduction in width may improve actuation performance as there is less material constraining the deflection of the piezoelectric material  332   d.    
     Further, since silver is used as the top electrical contact  321   d  and functions as the ground trace and only a positive voltage is applied to the bottom electrical contact  337   d , electrochemical migration of the top electrical contact  321   d  is less likely due to the outgoing electric field direction. 
     Although the decrease in width of the drive flexible circuit is shown with respect to  FIG. 3C , the drive flex of any of the other embodiments may also be reduced in a similar manner. However, in order to prevent the haptic actuator  324   d  and, more specifically, the piezoelectric material  332   d  from breaking or cracking, the surface area of the piezoelectric material  332   d  may be supported by the ground layer  338   d.    
     The haptic actuators  324   a - 324   d  depicted in  FIGS. 3A-3D  may be one of an array of haptic actuators, as depicted below with respect to  FIG. 4 . The circuit layer  322   a - 322   d  may be common to more than one haptic actuator  324   a - 324   d , and in some embodiments the circuit layer  322   a - 322   d  may be common to all haptic actuators  324   a - 324   d . Each individual haptic actuator  324   a - 324   d  can receive an electrical signal via the circuit layer  322   a - 322   d  independent of the other haptic actuators  324   a - 324   d . This may provide localized haptic feedback as depicted in  FIGS. 2B and 2D . 
     In some embodiments, the ground layer  338   a - 338   d  may additionally or alternatively be common to multiple or all haptic actuators  324   a - 324   d . The ground layer  338   a - 338   d  may provide a common reference voltage to all haptic actuators  324   a - 324   d  within the array. For clarity, the ground layer  338   a - 338   d  is omitted from  FIGS. 2C, 2D, 4-13C, and 17-21 . 
       FIG. 4  depicts a plan view of one example of the deflection module shown in  FIGS. 2A-2D , as viewed from below. Although the array  440  of haptic actuators  424  is shown as having twelve haptic actuators, other embodiments are not limited to this configuration. The array  440  of haptic actuators  424  can include one or more haptic actuators  424  in still other embodiments. Each haptic actuator  424  is depicted in a square shape. In some embodiments the haptic actuators  424  may have any given shape, such as a round, rectangular, triangular, or other geometric shape (including non-regular geometric shapes). 
     The haptic actuators  424  are attached and electrically connected to the circuit layer  422 . The circuit layer  422  may correspond to the circuit layer  322   a - 322   d  of  FIGS. 3A-3D , and may be configured to provide electrical signals to each individual haptic actuator  424  to selectively actuate one or more haptic actuators  424  concurrently, with some overlap in time, or sequentially. Any suitable attachment method can be used to affix the haptic actuators  424  to the circuit layer  422 . For example, in one embodiment an adhesive is used to attach the haptic actuators  424  to the circuit layer  422 . 
     Similarly, the circuit layer  422  is attached to the support structure  420  using any suitable attachment method. In one non-limiting embodiment, an adhesive is used to attach the circuit layer  422  to the support structure  420 , which may be a pressure-sensitive adhesive. 
     The circuit layer  422  may be operatively (e.g., electrically) connected to a signal generator  444  through one or more circuit layer extensions  442 . The one or more circuit layer extensions  442  transmit electrical signals from the signal generator  444  to respective conductors or traces in the circuit layer  422 . The signal lines or electrical traces in the circuit layer  422  transmit one or more electrical signals to at least one haptic actuator  424 . A ground layer (not shown), which may correspond to the ground layer  338   a - 338   d  of  FIGS. 3A-3D , may also be attached to each haptic actuator  424 . The transmitted signal may apply a voltage to the haptic actuator  424  and actuate the haptic actuator  424 . In other embodiments, the signal generator  444  is operatively connected to the circuit layer  422  through contact pads or wires instead of through the one or more circuit layer extensions  442 . 
     A processing unit  446  is operatively (e.g., electrically) connected to the signal generator  444 . The processing unit  446  is configured to control the generation of the electrical signals for the array  440  of haptic actuators  424 . The processing unit  446  can be implemented as any electronic device capable of processing, receiving, or transmitting data or instructions. For example, the processing unit  446  can be a microprocessor, a central processing unit (CPU), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), or combinations of multiple such devices. As described herein, the term “processing unit” is meant to encompass a single processor or processing unit, multiple processors, multiple processing units, or other suitably configured computing element or elements. 
     In some embodiments, a memory  448  can be operatively (e.g., electrically) connected to the processing unit  446  and/or to the signal generator  444 . The memory  448  can be configured as any type of memory. By way of example only, memory  448  can be implemented as random access memory, read-only memory, Flash memory, removable memory, or other types of storage elements, in any combination. 
     The memory  448  can store electronic data that can be used by the signal generator  444 . For example, the memory  448  can store electrical data or content, such as timing signals, algorithms, and one or more different electrical signal characteristics that the signal generator  444  can use to produce one or more electrical signals. The electrical signal characteristics include, but are not limited to, an amplitude, a phase, a frequency, and/or a timing of an electrical signal. The processing unit  446  can cause the one or more electrical signal characteristics to be transmitted to the signal generator  444 . In response to the receipt of the electrical signal characteristic(s), the signal generator  444  can produce an electrical signal that corresponds to the received electrical signal characteristic(s). 
     In some embodiments, each haptic actuator  424  can produce different types of haptic output based on the signal characteristic(s) of the electrical signal (e.g., the stimulus) that is used to actuate the haptic actuator  424 . For example, a haptic actuator  424  can generate haptic output that varies in magnitude and/or frequency based on the particular signal characteristics of the electrical signal used to activate the haptic actuator  424 . 
     The support structure  420  may be formed from a rigid material which can impact the actuation performance (e.g., the energy creation) of a haptic actuator  424  and the effectiveness of the transmission of that energy from the back of one or more intermediate layers to the surface of the cover sheet. For example, in some situations, the magnitude of the haptic output (e.g., the amount of energy) produced by a haptic actuator  424  may be limited or reduced by the size of the support structure  420 . When one or more haptic actuators  424  are activated, the material in the support structure  420  around the activated haptic actuator(s)  424  (in all directions of the x-y plane) is pulled in to deflect the support structure  420 . With a larger-sized support structure  420 , the amount of material around the haptic actuator(s)  424  can be considerable, which limits the amount of material the one or more haptic actuators  424  can pull in during actuation. Consequently, the magnitude of the haptic output produced by the haptic actuator(s)  424  may be reduced, which decreases the magnitude of the haptic feedback to the user. 
     To overcome any reduction in the haptic output produced by a haptic actuator  424 , the support structure may be shaped to instead amplify the output of the haptic actuator  424 . Section I,  FIGS. 5A-11H  depict embodiments of the support structure which are shaped or designed to amplify the output of the haptic actuator  424 . 
     In some embodiments, the signal generator  444  may be configured to provide pre-stress signals to pre-stress one or more haptic actuators  424 . The processing unit  446  may be configured to control the generation of the pre-stress and actuation signals by the signal generator  444 . Section II,  FIGS. 12-23  depict embodiments in which the haptic actuators  424  may be pre-stressed to increase actuator performance. 
     In some embodiments, the haptic actuators  424  may be attached to the support structure in a manner to relieve strain. Strain relief may increase the deflection of the support structure  420  and consequently increase the deflection at a cover sheet of the electronic device. Section III,  FIGS. 24-28  depict embodiments in which the support structure  420  may include strain relief to increase deflection. 
     In some embodiments, the piezoelectric material of the haptic actuators  424  may be shaped to reduce cost and increase haptic performance. Section IV,  FIGS. 29-32  depict embodiments in which the piezoelectric material has a different shape, such as a cross shape. 
     A system diagram of additional components which may be included in an electronic device according to the present invention are depicted in Section V,  FIG. 33 . 
     I. Support Structures for Haptic Output Amplification 
       FIGS. 5A and 5B  depict an example of a first deflection module  501  having a support structure  520  shaped to amplify the output of a haptic actuator  524 .  FIG. 5A  depicts the deflection module  501  when the haptic actuators  524  are not actuated, while  FIG. 5B  portrays the deflection module  501  when a haptic actuator  524  is actuated. The deflection module  501  includes a haptic actuator  524  coupled to a circuit layer  522 . The haptic actuator  524  may be similar to the haptic actuator  324  depicted in  FIG. 3 , and the circuit layer  522  may be similar to the circuit layer  322   a - 322   d  depicted in  FIGS. 3A-3D . Other components of the haptic actuator  324  depicted in  FIGS. 3A-3D , such as the ground layer  338   a - 338   d , have been omitted from  FIGS. 5A and 5B  for clarity. The circuit layer  522  may be coupled to a geometrically tuned support structure  520 . 
     The support structure  520  is geometrically tuned to amplify the output of a haptic actuator  524 . The support structure  520  may include one or more cavities  550  in a surface of the support structure  520  adjacent each haptic actuator  524 . In one embodiment, a cavity  550  may be substantially centrally positioned over each haptic actuator  524 . The cavity  550  may amplify the output of a haptic actuator  524  by reducing the thickness of the support structure  520  directly above the haptic actuator  524 , which in turn increases the flexibility of the support structure  520  such that it is more responsive to deflection at a location  526  directly above the haptic actuator  524 . In the illustrated embodiment, a cavity  550  is formed in the bottom surface of the support structure  520  above each haptic actuator  524 . In other embodiments, one or more cavities  550  may be formed in the bottom and/or top surface of the support structure  520 . 
     Each cavity  550  may span a portion of a dimension (e.g., width and/or length) of the corresponding haptic actuator  524 . As depicted, the cavity  550  may be substantially hemispherically shaped. However, in other embodiments the cavity  550  may be shaped as a semi-cylinder, a pyramid, a rectangular cavity, or another suitable geometric shape, including a non-regular shape. The cavity  550  may be formed within the support structure  520  by a suitable technique, such as molding, cutting, etching, etc. 
     Each haptic actuator  524  may be affixed to a portion of the support structure  520  (e.g., via the circuit layer  522 ) toward one or more edges of the haptic actuator  524 . This may impose a boundary condition on the haptic actuator  524 . When the haptic actuator  524  is actuated, as depicted in  FIG. 5B , the haptic actuator  524  may compress in all directions of the x-y plane. As the haptic actuator  524  is affixed to the support structure  520  surrounding the cavity  550 , the compression of the haptic actuator  524  may cause a similar compression in the support structure  520 . This may cause the support structure  520  in turn to deflect in the z-direction at the location  526  directly above the haptic actuator  524 . 
     The cavity  550  may cause an amplified deflection at the location  526  by making the support structure  520  thinner (and consequently more flexible) and/or by allowing greater compression of the support structure  520  across the cavity  550 . The amplified deflection at the location  526  directly above the haptic actuator  524  may in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., the cover sheet  108  in  FIG. 1 ) of the electronic device. 
     The support structure  520  may in some embodiments further include a relief  551  in the top surface of the support structure  520  (e.g., the side opposite the cavity  550 ). The relief  551  may be positioned between a pair of cavities  550 , and in some embodiments a relief  551  may be positioned between adjacent cavities  550  in an array of cavities  550  corresponding to an array of haptic actuators  524 . The relief  551  may be shaped as a rounded channel or slot (e.g. semi-cylinder) formed in the surface of the support structure  520 . The relief  551  may run substantially along a dimension (e.g., width) of the cavity  550 . In other embodiments the relief  551  may be shaped as a hemisphere, a pyramid, a rectangular trench, or another suitable geometric shape, including a non-regular shape. In still other embodiments, one or more reliefs  551  may be formed in the top and/or bottom surface of the support structure  520 . The relief  551  may be formed within the support structure  520  by a suitable technique, such as molding, cutting, etching, etc. 
     The relief  551  may isolate the portion of the support structure  520  above one haptic actuator  524  from the haptic response of another haptic actuator  524 . The relief  551  may additionally or alternatively assist to amplify the haptic response of a haptic actuator  524  by adding flexibility to the support structure  520  and/or relieving tension in the bulk portion of the support structure  520  caused by the compression at the cavity  550 . 
       FIGS. 6A and 6B  depict an example of a second deflection module  601  having a support structure  620  shaped to amplify the output of a haptic actuator  624 .  FIG. 6A  depicts the deflection module  601  when the haptic actuators  624  are not actuated, while  FIG. 6B  portrays the deflection module  601  when a haptic actuator  624  is actuated. Similar to the example in  FIGS. 5A and 5B , the deflection module  601  includes a haptic actuator  624  coupled to a circuit layer  622 . The circuit layer  622  may be coupled to a materially tuned support structure  620 . 
     The support structure  620  is materially tuned to amplify the output of a haptic actuator  624 . Portions of the support structure  620  may be formed from distinct materials bonded together. For example, a force concentration region  652  may be formed from a material having a lower Young&#39;s Modulus of Elasticity (E) compared to surrounding materials. A force concentration region  652  may be positioned above each haptic actuator  624  and may amplify the output of the haptic actuator  624  by increasing the flexibility of the support structure  620  at a location  626  directly above the haptic actuator  624 . 
     As described above, the force concentration region  652  is formed from a material with a lower E than the surrounding material of the support structure  620 . For example, the surrounding material may be formed from a stiff metal (e.g., steel), while the force concentration region  652  is formed from a more elastic metal (e.g., aluminum). In other embodiments, different materials and combinations of materials may be used, including metals, plastics, ceramics, glass, etc. The material of the force concentration region  652  may be bonded to the surrounding support structure  620  material by a suitable technique. For example, the force concentration region  652  may be fused, welded, molded, or otherwise adhered to the surrounding material. 
     Each force concentration region  652  may span a portion of a dimension (e.g., width, length) of the corresponding haptic actuator  624 . As depicted, the force concentration region  652  may comprise the entire height of the support structure  620 . In other embodiments, the force concentration region  652  may only comprise a portion of the height (e.g., filling a cavity formed within the support structure  620 ), or the force concentration region  652  may be comprised of multiple layers of lower and higher E materials. In still other embodiments, more than one force concentration region  652  may be positioned above each haptic actuator  624 . 
     Each haptic actuator  624  may be affixed to the support structure  620  (e.g., via the circuit layer  622 ) along substantially the entire width and/or length of the haptic actuator  624 . This may impose a boundary condition on the haptic actuator  624 . When the haptic actuator  624  is actuated, as depicted in  FIG. 6B , the haptic actuator  624  may compress in all directions of the x-y plane. As the haptic actuator  624  is affixed to the support structure  620 , the haptic actuator  624  may compress primarily along the bottom of the haptic actuator  624 , causing the haptic actuator  624  to deflect in the z-direction. This may cause an amplified deflection in the support structure  620  at the location  626  directly above the haptic actuator  624 . 
     The force concentration region  652  may cause an amplified deflection by making the support structure  620  more flexible at the location  626  directly above each haptic actuator  624  and/or by allowing greater compression of the support structure  620  across the force concentration region  652  to result in a higher z-deflection. The amplified deflection at the location  626  directly above the haptic actuator  624  may in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
     The support structure  620  may in some embodiments further include a relief region  653  between a pair of force concentration regions  652 , and in some embodiments a relief region  653  may be positioned between adjacent force concentration regions  652  in an array of force concentration regions  652  corresponding to an array of haptic actuators  624 . The relief region  653  is formed from a material with a lower Young&#39;s Modulus E than the surrounding material of the support structure  620  (e.g., the same or a different material than the force concentration region  652 ). For example, the surrounding material may be formed from a stiff metal (e.g., steel), while the relief region  653  is formed from a more elastic metal (e.g., aluminum). In other embodiments, different materials and combinations of materials may be used, including metals, plastics, ceramics, glass, etc. The material of the relief region  653  may be bonded to the surrounding support structure  620  material by a suitable technique (e.g., the same or a different technique than the force concentration region  652 ). For example, the relief region  653  may be fused, welded, molded, or otherwise adhered to the surrounding material. 
     As depicted, the relief region  653  may comprise the entire height of the support structure  620 . In other embodiments, the relief region  653  may only comprise a portion of the height (e.g., filling a relief formed within the support structure  620  on an opposite side from the haptic actuator  624 ), or the relief region  653  may be comprised of multiple layers of lower and higher E materials. In still other embodiments, more than one relief region  653  may be positioned above each haptic actuator  624 . 
     The relief region  653  may isolate a portion of the support structure  620  above one haptic actuator  624  from the haptic response of another haptic actuator  624 . The relief region  653  may additionally or alternatively assist to amplify the haptic response of a haptic actuator  624  by adding flexibility to the support structure  620  and/or relieving tension in the portion of the support structure  620  surrounding the force concentration region  652 . 
       FIGS. 7A and 7B  depict an example of a third deflection module  701  having a support structure  720  shaped to amplify the output of a haptic actuator  724 .  FIG. 7A  depicts the deflection module  701  when the haptic actuators  724  are not actuated, while  FIG. 7B  portrays the deflection module  701  when a haptic actuator  724  is actuated. The deflection module  701  may combine features of the examples in  FIGS. 5A-6B , and may similarly include haptic actuators  724  coupled to a circuit layer  722 . The circuit layer  722  may be coupled to a multi-feature support structure  720 , as described below. 
     The support structure  720  combines the features of the previous figures ( FIGS. 5A-6B ) to further amplify the output of a haptic actuator  724 . The support structure  720  may include one or more cavities  750  in a surface of the support structure  720  adjacent each haptic actuator  724 . Each cavity  750  may be substantially similar to those described above with respect to  FIGS. 5A and 5B . 
     Additionally, a portion of the support structure  720  above each cavity  750  may be formed from a material having a lower Young&#39;s Modulus E than the surrounding material of the support structure  720 , forming a force concentration region  752 . The force concentration region  752  may be substantially similar to those described above with respect to  FIGS. 6A and 6B . 
     Each haptic actuator  724  may be affixed to a portion of the support structure  720  (e.g., via the circuit layer  722 ) toward one or more edges of the haptic actuator  724 . This may impose a boundary condition on the haptic actuator  724 . When the haptic actuator  724  is actuated, as depicted in  FIG. 7B , the haptic actuator  724  may compress in all directions of the x-y plane. As the haptic actuator  724  is affixed to the support structure  720  surrounding the cavity  750 , the compression of the haptic actuator  724  may cause a similar compression in the support structure  720 . This may cause the support structure  720 , in turn, to deflect in the z-direction at the location  726  directly above the haptic actuator  724 . 
     The combined cavity  750  and force concentration region  752  may cause an amplified deflection by making the support structure  720  thinner and more flexible at the location  726  directly above the haptic actuator  724  and/or by allowing greater compression of the support structure  720  across the cavity  750  and force concentration region  752 . The amplified deflection at the location  726  directly above the haptic actuator  724  may in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
     The support structure  720  may in some embodiments further include a relief region  751  between a pair of haptic actuators  724 . In some embodiments the relief region  751  may be positioned between adjacent haptic actuators  724  in an array of force concentration regions  752 . The relief region  751  includes a relief formed in a surface of the support structure  720 , as described above with respect to  FIGS. 5A and 5B , and the relief region  751  is formed from a material having a lower Young&#39;s Modulus E than the surrounding material of the support structure  720 , as described above with respect to  FIGS. 6A and 6B . 
     The relief region  751  may further isolate a portion of the support structure  720  above one haptic actuator  724  from the haptic response of another haptic actuator  724 . The relief region  751  may additionally or alternatively assist to amplify the haptic response of a haptic actuator  724  by adding flexibility to the support structure  720  and/or relieving tension in the support structure  720  between haptic actuators  724 . 
       FIGS. 8A and 8B  depict an example of a fourth deflection module  801  having a support structure  820  shaped or configured to amplify the output of a haptic actuator  824 .  FIG. 8A  depicts the deflection module  801  when the haptic actuator  824  is not actuated, while  FIG. 8B  portrays the deflection module  801  when the haptic actuator  824  is actuated. Similar to the examples in  FIGS. 5A-7B , the deflection module  801  includes a haptic actuator  824  coupled to a circuit layer  822 . The circuit layer  822  may be coupled to a pre-curved support structure  820 . 
     In the illustrated embodiment, the support structure  820  is pre-curved in order to provide a “pop” response to amplify the output of a haptic actuator  824 . The support structure  820  may curve away from an intermediate layer  855  (illustrated here as a dashed line, which may correspond to an intermediate layer such as the force sensor layer depicted above with respect to  FIGS. 2A and 2B ). The support structure  820  may be formed with a curved channel, and a radial width of the channel may substantially match a dimension (e.g., width) of the haptic actuator  824 . In other embodiments the support structure  820  may be formed with a hemispherical shape or another suitable geometric shape. In still other embodiments, the support structure  820  may be placed under mechanical strain to create a similar curve away from the intermediate layer  855 . For example, rigid supports  854  may hold the support structure  820  under mechanical strain. 
     The support structure  820  may be bonded on each side to rigid supports  854 . The rigid supports  854  may impose a boundary condition on the support structure  820  such that it may primarily deflect along the z-direction, rather than along the x-y plane. The support structure  820  may be bonded to the rigid supports  854  through a suitable technique, such as fusing, welding, molding, or otherwise adhering the support structure  820  to the rigid supports  854 . In some embodiments, the rigid supports  854  may simply be positioned adjacent to the support structure  820  without bonding. In other embodiments the rigid supports  854  and support structure  820  may be formed as a single piece. The rigid supports  854  may be formed from a rigid material, such as a metal or plastic (e.g., the same or a different material from the support structure  820 ). 
     The curved shape of the support structure  820  may act as a spring when the haptic actuator  824  is actuated. The haptic actuator  824  may be affixed to the support structure  820  (e.g., via the circuit layer  822 ) along substantially the entire width and/or length of the haptic actuator  824 . This may impose a boundary condition on the haptic actuator  824 . When the haptic actuator  824  is actuated, as depicted in  FIG. 8B , the haptic actuator  824  may compress in all directions of the x-y plane. As the haptic actuator  824  is affixed to the support structure  820 , the haptic actuator  824  may compress primarily along the bottom of the haptic actuator  824 , causing the haptic actuator  824  to deflect in the z-direction. 
     Because the rigid supports  854  impose a boundary condition on the support structure  820 , as the haptic actuator  824  begins to deflect in the z-direction, it may cause the support structure  820  to deflect in the z-direction at the location  826  directly above the haptic actuator  824 . As the support structure  820  deflects, it may become mechanically unstable as the support structure  820  is compressed. The support structure  820  may also store potential energy as its curved shape becomes flattened, which potential energy may be released with a “pop” as the support structure  820  continues deflecting upward through a midpoint, suddenly deflecting and contacting the intermediate layer  855 . The deflection may be transmitted through the intermediate layer  855  and in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
     The support structure  820  may return to its original, unactuated state in response to a reverse signal being applied to the haptic actuator  824  (e.g., by applying a voltage with a reversed polarity across the haptic actuator  824 ). In other embodiments, compression forces in layers above the support structure  820  may cause it to return once the haptic actuator  824  is de-energized. 
       FIGS. 9A and 9B  depict an example of a fifth deflection module  901   a  having a support structure  920   a  shaped to amplify the output of a haptic actuator  924   a .  FIG. 9A  depicts the deflection module  901   a  when the haptic actuator  924   a  is not actuated, while  FIG. 9B  portrays the deflection module  901   a  when the haptic actuator  924   a  is actuated. Similar to the examples in  FIGS. 5A-8B , the deflection module  901   a  includes a haptic actuator  924   a  coupled to a circuit layer  922 . The circuit layer  922  may be coupled to a scissor support structure  920   a.    
     The support structure  920   a  depicted in  FIGS. 9A and 9B  may include a first scissor arm  956  and a second scissor arm  958  positioned a distance below an intermediate layer  955 . The second scissor arm  958  may be rotatably coupled to the first scissor arm  956  at a hinge  957   a . The hinge  957   a  may be positioned at an end of the second scissor arm  958  and a corresponding point (e.g., middle region) of the first scissor arm  956 . The hinge  957   a  may be any appropriate hinge mechanism, such as a pin or similar linkage. 
     The haptic actuator  924   a  may be affixed to the support structure  920   a  (e.g., via the circuit layer  922 ) at an interface with the first scissor arm  956  and an interface with the second scissor arm  958 . This may impose a boundary condition on the haptic actuator  924   a . When the haptic actuator  924   a  is actuated, as depicted in  FIG. 9B , the haptic actuator  924   a  may compress in all directions of the x-y plane. As the haptic actuator  924   a  is affixed to the first scissor arm  956  and the second scissor arm  958 , the compression of the haptic actuator  924   a  may move the scissor arms  956 ,  958  together. Because the end of the second scissor arm  958  is coupled to the first scissor arm  956  at a hinge  957   a , when the scissor arms  956 ,  958  move together the end of the first scissor arm  956  may be displaced and contact the intermediate layer  955 . The displacement may cause a deflection to be transmitted through the intermediate layer  955 , which in turn causes an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
       FIGS. 9C and 9D  depict another embodiment of the fifth deflection module  901   b  depicted in  FIGS. 9A and 9B .  FIG. 9C  depicts the deflection module  901   b  when the haptic actuator  924   c  is not actuated, while  FIG. 9D  portrays the deflection module  901   b  when the haptic actuator  924   c  is actuated. The deflection module  901   b  includes a haptic actuator  924   c  coupled to a circuit layer  922 . The circuit layer  922  may be coupled to a scissor support structure  920   c.    
     The support structure  920   c  depicted in  FIGS. 9C and 9D  may be substantially similar to the support structure  920   a  depicted in  FIGS. 9A and 9B , with the hinge  957   c  positioned at substantially a midpoint of the support structure  920   c . When the haptic actuator  924   c  is actuated, as depicted in  FIG. 9D , the end of the first scissor arm  956  and the end of the second scissor arm  958  may be displaced and contact the intermediate layer  955 , transmitting a deflection in the intermediate layer  955  upward. While this may result in a haptic effect which may not be as strong as the previous example at a corresponding location of the surface of the electronic device, the area of the haptic effect may be larger than the support structure  920   a  depicted in  FIGS. 9A and 9B . 
       FIGS. 10A and 10B  depict an example of a sixth deflection module  1001  having a support structure  1020  shaped to amplify the output of a haptic actuator  1024 .  FIG. 10A  depicts the deflection module  1001  when the haptic actuator  1024  is not actuated, while  FIG. 10B  portrays the deflection module  1001  when the haptic actuator  1024  is actuated. Similar to the examples in  FIGS. 5A-9D , the deflection module  1001  includes a haptic actuator  1024  coupled to a circuit layer  1022 . The circuit layer  1022  may be coupled to a support structure  1020  having a central flexure  1063 . 
     The support structure  1020  may include a flexure  1063  at substantially a center of the support structure  1020 . The flexure  1063  may be formed by reliefs  1060 ,  1061  formed in the top and bottom surfaces of the support structure  1020  respectively. The reliefs  1060 ,  1061  may be shaped as a rounded slot (e.g. semi-cylinder) formed in the surface of the support structure  1020 . In other embodiments the reliefs  1060 ,  1061  may be shaped as a hemisphere, a pyramid, a rectangle, or another suitable geometric shape, including a non-regular shape. The reliefs  1060 ,  1061  may be formed within the support structure  1020  by a suitable technique, such as molding, cutting, etching, etc. 
     The reliefs  1060 ,  1061  may form a flexure  1063 , a point at which the support structure  1020  bends in a hinge-like manner. The flexure  1063  may also divide the support structure  1020  into two arms. The haptic actuator  1024  may be affixed to the support structure  1020  (e.g., via the circuit layer  1022 ) at one or more edges of the haptic actuator  1024 . This may impose a boundary condition on the haptic actuator  1024 . When the haptic actuator  1024  is actuated, as depicted in  FIG. 10B , it may compress in all directions of the x-y plane. As the edges of the haptic actuator  1024  are affixed to the support structure  1020 , the support structure  1020  may bend upward (e.g., along the z-direction) at the flexure  1063 , and may deflect upward and contact the intermediate layer  1055 . When the support structure  1020  deflects, the top relief  1060  may widen, while the bottom relief  1061  narrows, allowing for greater flexibility at the flexure  1063 . In other words, the flexure  1063  flexibly connects the two arms of the support structure  1020 , allowing a second end of each arm to deflect upward and contact the intermediate layer  1055 . The deflection may be transmitted through the intermediate layer  1055  and in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
       FIGS. 11A and 11B  depict an example of a seventh deflection module  1101  having a support structure  1120   a ,  1120   b  shaped to amplify the output of a haptic actuator  1124 .  FIG. 11A  depicts the deflection module  1101  when the haptic actuator  1124  is not actuated, while  FIG. 11B  portrays the deflection module  1101  when the haptic actuator  1124  is actuated. The deflection module  1101  includes a haptic actuator  1124  coupled to a circuit layer  1122 . The circuit layer  1122  may be coupled between an upper support structure  1120   a  and a lower support structure  1120   b.    
     The upper support structure  1120   a  and the lower support structure  1120   b  may amplify the output of the haptic actuator  1124 . The upper support structure  1120   a  and the lower support structure  1120   b  may both be pre-curved, and the lower support structure  1120   b  may rest on a lower layer  1162 . Each may curve away from the circuit layer  1122 . Both support structures  1120   a ,  1120   b  may be formed with a curved channel  1121   a ,  1121   b  having a dimension (e.g., width, length) greater than a corresponding dimension of the haptic actuator  1124 . In other embodiments, the support structures  1120   a ,  1120   b  may be formed with a hemispherical shape or another suitable geometric shape. In some embodiments, the upper support structure  1120   a  may have a different shape from the lower support structure  1120   b . In still other embodiments, the support structures  1120   a ,  1120   b  may be placed under mechanical strain to create a similar curve away from the circuit layer  1122 . 
     The curved shape of the upper support structure  1120   a  may substantially match the curved shape of the lower support structure  1120   b . The support structures  1120   a ,  1120   b  may be affixed to the circuit layer  1122 , and may enclose the haptic actuator  1124  and a portion of the circuit layer  1122  within a round or ovular cavity. Because the support structures  1120   a ,  1120   b  are affixed to the circuit layer  1122 , a deflection of the circuit layer  1122  along the x-y plane may cause a deflection in the support structures  1120   a ,  1120   b.    
     When the haptic actuator  1124  is actuated, as depicted in  FIG. 11B , the haptic actuator  1124  may compress in all directions of the x-y plane. As the haptic actuator  1124  is affixed to the circuit layer  1122 , the actuation may in turn cause the circuit layer  1122  to compress along the x-y plane. This in turn may compress the support structures  1120   a ,  1120   b.    
     When the upper support structure  1120   a  is compressed along the x-y plane, its curved shape may cause it to deflect along the z-direction. The lower support structure  1120   b  may similarly deflect along the z-direction. As the lower support structure  1120   b  rests on a lower layer  1162 , which may be a rigid layer, the deflection of the lower support structure  1120   b  may be transferred upward to amplify the deflection of the upper support structure  1120   a  (e.g., by lifting the upper support structure  1120   a ). Thus the upper support structure  1120   a  is deflected and contacts the intermediate layer  1155 . The deflection may be transmitted through the intermediate layer  1155  and in turn cause an amplified haptic effect at a corresponding location of the surface (e.g., cover sheet  108  in  FIG. 1 ) of the electronic device. 
     Because in the example deflection module  1101  depicted in  FIGS. 11A and 11B  the deflection module  1101  moves vertically, the deflection module  1101  may typically include a linking mechanism to allow movement while directing the haptic response into the intermediate layer  1155 , and consequently to the surface of the electronic device. Example linking mechanisms are further illustrated below with respect to  FIGS. 11C-11H . 
       FIGS. 11C and 11D  depict an embodiment of the seventh deflection module  1101  depicted in  FIGS. 11A and 11B , illustrating a first example linking mechanism.  FIG. 11C  depicts the deflection module  1101  when the haptic actuator  1124  is not actuated, while  FIG. 11D  portrays the deflection module  1101  when the haptic actuator  1124  is actuated. The deflection module  1101  includes a haptic actuator  1124  coupled to a circuit layer  1122 . The circuit layer  1122  may be coupled between an upper support structure  1120   a  and a lower support structure  1120   b.    
     The first example linking mechanism is a binding material  1164  linking adjacent support structures  1120   a ,  1120   b . The binding material  1164  may be compliant and/or formed from a material with a lower Young&#39;s Modulus E than the support structures  1120   a ,  1120   b . For example, the support structures  1120   a ,  1120   b  may be formed from a stiff metal (e.g., steel), while the binding material  1164  is formed from a more elastic metal (e.g., aluminum). In other embodiments, different materials and combinations of materials may be used, including metals, plastics, ceramics, glass, etc. A binding material  1164  may be bonded to the upper support structure  1120   a  and the lower support structure  1120   b  by a suitable technique. For example, the binding material  1164  may be fused, welded, molded, or otherwise adhered to the support structures  1120   a ,  1120   b.    
     The binding material  1164  may bind adjacent support structures  1120   a ,  1120   b  together while allowing the deflection module  1101  to move vertically. When the haptic actuator  1124  is in an unactuated state, the deflection module  1101  may rest in parallel with an adjacent deflection module  1101 . When the haptic actuator  1124  is actuated, as depicted in  FIG. 11D , it may cause deflection and vertical movement as described above with respect to  FIG. 11B . The binding material  1164  may allow for this vertical movement while isolating adjacent deflection module  1101 s from the movement. 
       FIGS. 11E and 11F  depict another embodiment of the seventh deflection module  1101  depicted in  FIGS. 11A and 11B , illustrating a second example linking mechanism.  FIG. 11E  depicts the deflection module  1101  when the haptic actuator  1124  is not actuated, while  FIG. 11F  portrays the deflection module  1101  when the haptic actuator  1124  is actuated. The deflection module  1101  includes a haptic actuator  1124  coupled to a circuit layer  1122 . The circuit layer  1122  may be coupled between an upper support structure  1120   a  and a lower support structure  1120   b.    
     The second example linking mechanism includes brackets  1166   a ,  1166   b  on either side of the support structures  1120   a ,  1120   b , which allow for vertical movement while restricting horizontal movement. The brackets  1166   a ,  1166   b  may be fixed in place, and may be attached to other components of the electronic device. An upper portion of a bracket  1166   a  may provide an upper boundary on vertical motion, while a lower portion of a bracket  1166   b  may provide a lower boundary on vertical motion. 
     When the haptic actuator  1124  is in an unactuated state, the lower support structure  1120   b  may rest against a flange of the lower portion of the brackets  1166   b . When the haptic actuator  1124  is actuated, as depicted in  FIG. 11F , it may cause deflection and vertical movement as described above with respect to  FIG. 11B . The brackets  1166   a ,  1166   b  may allow for this vertical movement, and the upper support structure  1120   a  may rest against a flange of the upper portion of the brackets  1166   a  in the actuated state. In some examples, the brackets  1166   a ,  1166   b  may be formed differently. For example, the brackets  1166   a ,  1166   b  may omit one or both flanges. 
       FIGS. 11G and 11H  depict another embodiment of the seventh deflection module  1101  depicted in  FIGS. 11A and 11B , illustrating a third example linking mechanism.  FIG. 11G  depicts the deflection module  1101  when the haptic actuator  1124  is not actuated, while  FIG. 11H  portrays the deflection module  1101  when the haptic actuator  1124  is actuated. The deflection module  1101  includes a haptic actuator  1124  coupled to a circuit layer  1122 . The circuit layer  1122  may be coupled between an upper support structure  1120   a  and a lower support structure  1120   b.    
     The third example linking mechanism is a pin  1168  through the lower support structure  1120   b . The lower support structure  1120   b  may be fixed in place by a pin  1168  or similar mechanism which retains the lower support structure  1120   b  in place while allowing the upper support structure  1120   a  to deflect upward when the haptic actuator  1124  is actuated, as depicted in  FIG. 11H . The pin  1168  may be placed through a point substantially at the center of the lower support structure  1120   b  and into the lower layer  1162 . 
     The example linking mechanisms depicted in  FIGS. 11C-11H  are described for illustrative purposes, and it should be understood that other linking mechanisms would be within the scope of the present disclosure. 
     II. Pre-Stressed Haptic Actuators 
     Turning to  FIGS. 12-23 , in some embodiments, the processing unit (such as processing unit  446  depicted in  FIG. 4 ) is configured to cause one or more haptic actuators  1224   a ,  1224   b  to be placed in a pre-stressed state based on an application program running on the electronic device. For example, a user interface can include one or more icons or input regions that a user will interact with during the operation of the application program. Based on the known locations of the icon(s) or input regions, the processing unit may cause the haptic actuator(s)  1224   a ,  1224   b  located below and/or adjacent the icon(s) or input regions to be placed in a pre-stressed state. Thus, in some embodiments, only a portion of the haptic actuators  1224   a ,  1224   b  may be placed in the pre-stressed state. Additionally or alternatively, the processing unit can cause the array  1240  of haptic actuators  1224   a ,  1224   b  to be placed in the pre-stressed state. 
     As depicted in  FIG. 12 , in some situations, the support structure  1220  of the electronic device  1200  and/or the support plate  1223  can slump or sag over time due at least in part to gravity and/or damage caused by an impact (e.g., a drop event). The sagging support structure  1220  and/or support plate  1223  causes the size of the gap  1218  to vary across the width and/or length of the deflection module. As shown in  FIG. 12 , at least one distance (e.g., distance D 2 ) between a haptic actuator  1224   a  and the first force-sensing component  1214  may differ from the distances between the haptic actuators  1224   b  and the first force-sensing component  1214  (e.g., distances D 1  and D 3 ). The differing distances can result in a non-uniform deflection of the cover sheet  1208 . For example, when the haptic actuators  1224   a ,  1224   b  are activated simultaneously, the top surface of the cover sheet  1208  at the location corresponding to the haptic actuators  1224   b  can deflect ahead of the location corresponding to the haptic actuator  1224   a  because the portion of the support structure  1220  (or the portion of the second force-sensing component  1216 ) associated with the haptic actuator  1224   a  (e.g., the portion over and possibly surrounding the haptic actuator  1224   a ) has to travel a greater distance to close the gap  1218  and contact the first force-sensing layer  1214 . Due to the differing distances, the actuation performances of the haptic actuators  1224   a ,  1224   b  can be non-linear across the array  1240 . In other words, if all of the haptic actuators  1224   a ,  1224   b  are activated simultaneously, the timing and magnitude of the deflections in the cover sheet  1208  can differ depending on the location(s) of the haptic actuators  1224   a ,  1224   b  in the array  1240 . 
     Accordingly, in some embodiments, one or more haptic actuators  1224   a ,  1224   b  are electrically pre-stressed to position the haptic actuator(s)  1224   a ,  1224   b  closer to the cover sheet  1208 . In some situations, the haptic actuator(s)  1224   a ,  1224   b  are electrically pre-stressed to close the gap  1218  such that the second-force sensing component  1216  contacts the first force-sensing component  1214  without deflecting (or substantially deflecting) the top surface of the cover sheet  1208 . In other situations, the one or more haptic actuators  1224   a ,  1224   b  are electrically pre-stressed such that the second force-sensing component  1216  and the support structure  1220  move into the gap  1218  but do not close the gap  1218 . Additionally, the gap  218   c  ( FIG. 2 ) may be closed when the haptic actuator(s)  1224   a ,  1224   b  are electrically pre-stressed. 
     Pre-stressing the haptic actuators  1224   a ,  1224   b  can reduce, minimize, or cancel the non-uniform and/or non-linear actuation performances of the haptic actuators  1224   a ,  1224   b . Additionally, one or more of the pre-stressed haptic actuators  1224   a ,  1224   b  may deflect the cover sheet  1208  to provide haptic feedback faster than when not pre-stressed. In other words, the time lag between the time when a pre-stressed haptic actuator  1224   a ,  1224   b  is activated and the time when a deflection is produced in the cover sheet  1208  may be reduced. 
     In other embodiments, one or more haptic actuators  1224   a ,  1224   b  are electrically pre-stressed to position the haptic actuator(s)  1224   a ,  1224   b  farther from the cover sheet  1208 . An example embodiment is shown in  FIG. 14 . 
     The haptic actuators  1324  are electrically pre-stressed by applying a pre-stress signal (e.g., a direct current signal) to each haptic actuator  1324 .  FIGS. 13A-13C  depict the operations of pre-stressing an array  1340  of haptic actuators  1324  and providing a haptic output with one of the pre-stressed haptic actuators  1324 .  FIG. 13A  depicts a cross-sectional view of another example electronic device with the haptic actuators  1324  in a non-actuated state. 
     An electronic device  1300  includes a cover sheet  1308  and a support structure  1320 . In the illustrated embodiment, the support structure  1320  is a U-shaped support structure that includes a support plate  1323  and sides  1325  that extend from the support plate  1323  and attach to the cover sheet  1308 . The support structure  1320  is configured to attach to, and suspend from, the cover sheet  1308  such that a gap  1318  is defined between the cover sheet  1308  and the support plate  1323 . 
     An array  1340  of haptic actuators  1324  is attached to the bottom surface of the support plate  1323 . In the illustrated embodiment, the array  1340  includes three haptic actuators  1324 . In other embodiments, the array  1340  can include one or more haptic actuators  1324 . As shown in  FIGS. 13A-13C , the haptic actuators  1324  are attached directly to a bottom surface of a support plate  1323 . In other embodiments, the haptic actuators  1324  can be coupled to the support plate  1323  through a circuit layer. 
     The support structure  1320  and the array  1340  of haptic actuators  1324  collectively form a deflection module  1301 . In  FIG. 13A , the deflection module  1301  is shown in a rest configuration.  FIG. 13B  depicts the deflection module  1301  in a pre-stressed configuration. The pre-stressed configuration is produced by applying a pre-stress signal to each haptic actuator  1324  in the array  1340  to place the haptic actuators  1324  in a pre-stressed state. 
     In the illustrated embodiment, when the haptic actuators  1324  are in the pre-stressed state, the support structure  1320  deflects such that the support plate  1323  and the haptic actuators  1324  move upward into the gap  1318 . When the deflection module  1301  is in the pre-stressed configuration, the array  1340  of haptic actuators  1324  are positioned closer to the cover sheet  1308 . In the illustrated embodiment, the top surface of the support plate  1323  contacts the bottom surface of the cover sheet  1308 , although this is not required. In some embodiments, the support plate  1323  and the haptic actuators  1324  can move into the gap  1318  to position the haptic actuators  1324  closer to the cover sheet  1308  without having the top surface of the support plate  1323  contact the bottom surface of the cover sheet  1308 . Thus, the deflection module  1301  can be placed in multiple pre-stress configurations with each pre-stress configuration placing the haptic actuators  1324  closer to (or farther from) the cover sheet  1308 . 
       FIG. 13C  depicts the electronic device shown in  FIG. 13B  with one haptic actuator in a haptic output state. In the illustrated embodiment, an actuation signal (e.g., an alternating current signal) is applied to the haptic actuator  1324  to place the haptic actuator  1324  in a haptic output state. The haptic output state increases the deflection of the support plate  1323  locally (e.g., above and around the haptic actuator  1324 ), which in turn produces a localized deflection in the cover sheet  1308 . In other words, a deflection is produced in the cover sheet  1308  at a location  1326  that substantially corresponds to the location of the haptic actuator  1324  on the support structure  1320 . The cover sheet  1308  further or distal from the deflection is substantially unaffected by the haptic output produced by the haptic actuator  1324 . The area of the cover sheet  1308  that is deflected depends at least in part on the type of haptic actuators  1324 , the signal level of the actuation signal, and the density of the haptic actuators  1324  in the array  1340 . 
     In some embodiments, an intermediate layer (e.g., one or more layers) can be positioned between the top surface of the support plate  1323  and the bottom surface of the cover sheet  1308 . In such embodiments, the top surface of the support plate  1323  can contact, or be positioned closer to, the bottom surface of the intermediate layer when the deflection module  1301  is in the pre-stressed configuration. For example, in one embodiment, the electronic device  1300  is constructed similar to the electronic device  100  shown in  FIG. 2C . When the deflection module  201   b  is in the pre-stressed configuration, the second force-sensing component  216   b  contacts, or is positioned closer to, the first force-sensing component  214   b.    
       FIG. 14  depicts an example graph representing the deflection of a cover sheet in response to the application of a signal to a haptic actuator. In the plot  1400 , the signal (e.g., a voltage signal) is represented on the horizontal axis while the amount of displacement or deflection in the cover sheet is represented on the vertical axis. A pre-stress signal  1402  places the haptic actuator in a pre-stressed state and an actuation signal  1404  produces a displacement or deflection in the cover sheet. The pre-stress signal  1402  extends along the horizontal axis between zero and a first signal (voltage) level  1406 . The haptic actuator is placed in the pre-stressed state when a signal level of the pre-stress signal  1402  is greater than zero and less than or equal to the first signal level  1406 . Thus, the pre-stressed state of a haptic actuator includes a range of pre-stressed levels or sub-states. 
     For example, in the embodiment shown in  FIG. 2D , the signal level  1406  represents the signal level that causes the support structure  220   b  to deflect such that the second force-sensing component  216   b  contacts the first force-sensing component  214   b  but does not produce a deflection in the cover sheet  208   b . In another example, the first signal level  1406  represents the signal level that causes the support structure  1320  in  FIG. 13B  to deflect such that the support plate  1323  contacts the cover sheet  1308 . 
     The actuation signal  1404  produces a displacement or deflection in the cover sheet. Thus, the haptic actuator is placed in a haptic output state (a state that produces a deflection in the cover sheet) when a signal level of the actuation signal  1404  is greater than the first signal level  1406  and less than or equal to a second signal level  1408 . In the illustrated embodiment, the signal level  1408  represents a signal level that produces a maximum displacement in the cover sheet. Accordingly, the haptic output state of the haptic actuator includes a range of displacement magnitudes up to the maximum displacement. 
     Some embodiments can use one or more haptic actuators or another type of sensor to detect the amount of deflection of the support structure. For example, in  FIG. 13C , the haptic actuator  1324  may be configured to detect when the top surface of the support plate  1323  contacts the bottom surface of the cover sheet  1308  (e.g., detect when the gap  1318  is closed). One type of haptic actuator that can be used to deflect the support structure  1320  and to detect the closure of the gap  1318  is a haptic actuator that includes a piezoelectric material. When an actuation signal is applied to the piezoelectric material, the piezoelectric material converts the actuation signal into physical movement. This physical movement can be used to deflect the support structure  1320  and, ultimately, the cover sheet  1308 . Additionally, a piezoelectric material accumulates charge in response to an applied stress or pressure. This accumulated charge can be sensed from the piezoelectric material as an output signal (e.g., a current signal). This output signal may be used to detect when the gap  1318  is closed. 
       FIGS. 15A and 15B  depict first technique for pre-stressing a haptic actuator and sensing the closure of a gap.  FIGS. 15A and 15B  are described in conjunction with the haptic actuators  1324  shown in  FIGS. 13A-13C .  FIG. 15A  illustrates an example plot of an input signal that can be applied to the haptic actuator  1324 . The input signal  1500  includes a pre-stress signal  1502  and an actuation signal  1504 . The pre-stress signal  1502  can be applied to the array  1340  of haptic actuators  1324  to place the haptic actuators  1324  in a pre-stressed state ( FIG. 13B ). The increasing pre-stress signal  1502  can be applied to the haptic actuators  1324  over a period of time (e.g., from zero to a time  1506 ). 
     In embodiments where the haptic actuators  1324  include a piezoelectric material, the mechanical deflection (e.g., the movement and/or vibrations) of each haptic actuator  1324  produces an output signal (e.g., an alternating current signal) in each haptic actuator.  FIG. 15B  depicts an example output signal that is produced by the haptic actuator  1324  based on the input signal shown in  FIG. 15A . The output signal  1508  includes a first output signal  1510  that is associated with the pre-stressed state of the haptic actuator  1324  ( FIG. 13B ) and a second output signal  1512  that is associated with the actuation state of the haptic actuator ( FIG. 13C ). Application of the pre-stress signal  1502  to the haptic actuator  1324  over time produces the increasing first output signal  1510 . 
     Time  1506  represents the time when the gap  1318  is closed and the support plate  1323  contacts the cover sheet  1308 . A signal displacement  1514  occurs in the output signal  1508  when the support plate  1323  contacts the cover sheet  1308 . The signal displacement  1514  occurs because the deflection of the haptic actuator  1324  changes when the support plate  1323  contacts the cover sheet  1308 . 
     The haptic actuator is maintained in the pre-stressed state during the time period between time  1506  and time  1516 . At time  1516 , the actuation signal  1504  is applied to the haptic actuator  1324  to place the haptic actuator  1324  in the haptic output state and produce a deflection in the cover sheet  1308 . Accordingly, at time  1516 , the second output signal  1512  increases based on the increased actuation of the haptic actuator  1324 . As the actuation signal  1504  increases, a deflection is produced in the cover sheet  1308  at a location  1326  that substantially corresponds to the location of the haptic actuator  1324  on the support structure  1320  (see  FIG. 13C ). The second output signal  1512  increases after time  1516  because the pressure applied to the haptic actuator  1324  by the deflection of the cover sheet  1308  increases after time  1516 . 
     In some embodiments, the closure of the gap  1318  is detected by sensing or identifying the signal displacement  1514  in the output signal  1508 . A processing unit can receive an output signal from one or more haptic actuators  1324  in the array  1340  and analyze the output signal(s) to detect the signal displacement  1514 . When the processing unit detects a signal displacement in an output signal received from a respective haptic actuator  1324 , the processing unit can cause the signal level of the corresponding pre-stress signal  1502  for that haptic actuator  1324  to be maintained at that signal level. This allows the haptic actuator  1324  to remain in the pre-stressed state until the haptic actuator  1324  receives an actuation signal  1504 , or until the haptic actuator  1324  stops receiving the pre-stress signal  1502 . 
       FIG. 16A  depicts a top view of an example haptic actuator that can be used to sense the closure of a gap. The haptic actuator  1624  includes a sense electrode  1670  positioned between a first drive electrode  1672  and a second drive electrode  1674 . In some embodiments, an insulating (e.g., ground) electrode  1676 ,  1678  is positioned between each drive electrode  1672 ,  1674  and the sense electrode  1670  to electrically isolate the sense electrode  1670  from the first and the second drive electrodes  1672 ,  1674 . In other embodiments, the electrodes  1676 ,  1678  can be omitted and air gaps may be used to electrically isolate the sense electrode  1670  from the first and the second drive electrodes  1672 ,  1674 . 
     The sense electrode  1670  is used to sense or receive an output signal from the haptic actuator  1624 . As described earlier, a processing unit can receive the output signal from the haptic actuator  1624  and analyze the output signal to detect a signal displacement (e.g., signal displacement  1514  in  FIG. 15B ). The signal displacement indicates the gap between a cover sheet or intermediate layer and the support structure is closed. 
     The first and the second drive electrodes  1672 ,  1674  are used to apply an input signal to the haptic actuator  1624 . As discussed earlier, the input signal includes a pre-stress signal that places the haptic actuator  1624  in a pre-stressed state and an actuation signal that places the haptic actuator  1624  in a haptic output state. In some embodiments, the pre-stressed state causes a support structure to deflect to position the haptic actuator  1624  closer to a spaced-apart overlying layer (e.g., the first force-sensing component  214   b  in  FIG. 2D  or the cover sheet  1308  in  FIG. 13B ). The actuation signal causes the deflection of the support structure to increase locally to produce a deflection in the cover sheet (e.g., the cover sheet  1308  in  FIG. 13C ). 
       FIG. 16B  depicts a side view of the haptic actuator  1624  shown in  FIG. 16A . A piezoelectric material  1632  is positioned below the sense electrode  1670  and the first and the second drive electrodes  1672 ,  1674 . A conductive pad (e.g., third electrode)  1636  (e.g., a ground electrode) is disposed below the piezoelectric material  1632 . As described earlier, any suitable piezoelectric material can be used. For example, the piezoelectric material  1632  can include a piezoelectric polymer material such as a polyvinylidene fluoride, a piezoelectric ceramic material such as lead zirconate titanate, a semiconductor material, or a lead-free piezoelectric material such as potassium-sodium niobate. 
       FIG. 17  depicts a second technique for pre-stressing a haptic actuator  1724  and sensing the closure of a gap. An electronic device  1700  includes a cover sheet  1708  and a support structure  1720 . In the illustrated embodiment, the support structure  1720  is a U-shaped support structure that includes a support plate  1723  and sides  1725  that extend from the support plate  1723  and attach to the cover sheet  1708 . The support structure  1720  is configured to attach to, and suspend from, the cover sheet  1708  such that a gap  1718  is defined between the cover sheet  1708  and the support plate  1723 . As described earlier, other embodiments can configure the support structure  1720  and/or the support plate  1723  differently. 
     A haptic actuator  1724  is attached to the bottom surface of the support plate  1723 . Although only one haptic actuator  1724  is shown in  FIG. 10 , other embodiments can include two or more haptic actuators. In the illustrated embodiment, the haptic actuator  1724  is attached directly to a bottom surface of a support plate  1723 . In other embodiments, the haptic actuator  1724  can be coupled to the support plate  1723  through a circuit layer. 
     A strain sensor (e.g., a force sensor)  1711  is attached to the top surface of the support plate  1723 . Although only one strain sensor  1711  is shown in  FIG. 17 , other embodiments can include two or more strain sensors. Additionally, in some embodiments, the one or more strain sensors can be attached to the cover sheet  1708 , or to both the cover sheet  1708  and the support structure  1720 . For example, strain sensors may be affixed to the cover sheet  1708 , the support plate  1723 , and/or to at least one side  1725  of the support structure. 
     Any suitable strain sensor  1711  can be used. In a non-limiting embodiment, the strain sensor  1711  is a strain gauge. The strain gauge can be made of any suitable transparent, translucent, or opaque strain-responsive material. Example strain-responsive materials include, but are not limited to, polyethyleneioxythiophene (PEDOT), indium tin oxide (ITO), carbon nanotubes, graphene, piezoresistive semiconductor materials, piezoresistive metal materials, metallic nanowires, strain-responsive elastomers, metals or metal alloys, and the like. 
     Closure of the gap  1718  can be detected based on an output or strain signal produced by the strain sensor  1711 . When a pre-stress signal is applied to the haptic actuator  1724 , the support structure  1720  deflects such that the support plate  1723  moves upward toward the cover sheet  1708 . When the support plate  1723  moves into the gap  1718  such that the strain sensor  1711  contacts the bottom surface of the cover sheet  1708 , a stress is applied to the strain sensor  1711 . The stress produces strain in the strain-responsive material of the strain sensor  1711 , which causes an electrical property of the strain-responsive material (e.g., a resistance) to change. This change in electrical property can be detected by applying an input or drive signal (e.g., current signal) to the strain-responsive material in the strain sensor  1711  and receiving an output or strain signal (e.g., current) from the strain-responsive material in the strain sensor  1711 . 
     For example, in some embodiments, drive circuitry can be coupled to the strain sensor  1711  and configured to apply the drive signal to the strain-responsive material. Sense circuitry may also be coupled to the strain-responsive material and configured to receive the strain signal from the strain-responsive material in the strain sensor  1711 . Drive circuitry and sense circuitry may form part of a signal generator (e.g., signal generator  44  in  FIG. 4 ) or other circuitry coupled to a processing unit. A processing unit can be configured to receive the strain signal and correlate the strain signal to an applied stress (or to an absence of applied stress). In some embodiments, a strain signal is received continuously from the strain sensor  1711  during the time period between a pre-stress signal being transmitted to the haptic actuator  1724  and an actuation signal being transmitted to the haptic actuator  1724  (or until the pre-stress signal is no longer transmitted to the haptic actuator  1724 ). 
     In embodiments where the strain sensor  1711  is affixed to the bottom surface of the cover sheet  1708 , the top surface of the support plate  1723  can contact the strain sensor  1711  when a pre-stress signal is applied to the haptic actuator  1724 . In such embodiments, a stress is applied to the strain sensor  1711 , which produces strain in the strain-responsive material in the strain sensor  1711 . This strain can be detected by applying a drive signal to the strain-responsive material in the strain sensor  1711  and receiving a strain signal from the strain-responsive material in the strain sensor  1711 . 
       FIGS. 18A and 18B  depict a third technique for pre-stressing a haptic actuator  1824  and sensing the closure of a gap. The electronic device  1800  includes a cover sheet  1808  and a support structure  1820 . In the illustrated embodiment, the support structure  1820  is a U-shaped support structure that includes a support plate  1823  and sides  1825  that extend from the support plate  1823  and attach to the cover sheet  1808 . The support structure  1820  is configured to attach to, and suspend from, the cover sheet  1808  such that a gap  1818  is defined between the cover sheet  1808  and the support plate  1823 . As described earlier, other embodiments can configure the support structure  1820  and/or the support plate  1823  differently. 
     A haptic actuator  1824  is attached to the bottom surface of the support plate  1823 . Although only one haptic actuator  1824  is shown in  FIGS. 18A and 18B , other embodiments can include two or more haptic actuators. In the illustrated embodiment, the haptic actuator  1824  is attached directly to a bottom surface of a support plate  1823 . In other embodiments, the haptic actuator  1824  can be coupled to the support plate  1823  through a circuit layer. 
     A first force-sensing component  1814  is disposed within the cover sheet  1808 . In other embodiments, the first force-sensing component  1814  can be positioned at different locations within the electronic device  1800 . For example, the first force-sensing component  1814  may be attached to a bottom surface of the cover sheet  1808 . 
     A second force-sensing component  1816  is positioned below the support structure  1820 . In other embodiments, the second force-sensing component  1816  can be positioned at different locations within the electronic device  1800 . For example, the second force-sensing component  1816  may be attached to a top surface or a bottom surface of the support plate  1823 . 
     The first force-sensing component  1814  represents a first array of electrodes and the second force-sensing component  1816  a second array of electrodes. The first and the second arrays of electrodes can each include one or more electrodes. Each electrode in the first array of electrodes is aligned in at least one direction (e.g., vertically) with a respective electrode in the second array of electrodes to form an array of capacitive sensors. The capacitive sensors are used to detect a displacement in the cover sheet  1808  through measured capacitances or changes in capacitances. 
     For example, when a pre-stress signal is applied to the haptic actuator  1824 , the support structure  1820  deflects such that the support plate  1823  moves into the gap  1818 . When the cover sheet  1808  begins to deflect based on the pre-stress signal, as illustrated by the deflection at location  1836  in  FIG. 18B , a distance D 1  between the electrodes in at least one capacitive sensor changes to D 2 , which varies the capacitance of that capacitive sensor. Drive and sense circuitry can be coupled to each capacitive sensor and configured to sense or measure the capacitance of each capacitive sensor. A processing unit may be coupled to the drive and sense circuitry and configured to receive signals representing the measured capacitance of each capacitive sensor. The processing unit can be configured to correlate the measured capacitances into a displacement in the cover sheet  1808 . The processing unit can be configured to cause the pre-stress signal to be reduced until the measured capacitances indicate the displacement is gone. 
     In another embodiment, the support structure  1820  can deflect to increase or expand the gap  1818  (see also  FIG. 14 ). In such embodiments, the displacement of the support structure  1820  (e.g., the support plate  1823 ) can be detected based on capacitance changes between the support plate  1823  and one of the force sensing components (e.g., second force-sensing component  1816 ). In such embodiments, the support plate  1823  may be made of any suitable conductive material. When the support structure  1820  deflects, the support plate  1823  moves closer to the second force-sensing component  1816  (e.g., expanding the gap  1818 ) and the distance between the support plate  1823  and the second force-sensing component  1816  changes (e.g., becomes shorter). This distance change varies the capacitance of at least one capacitive sensor. Drive and sense circuitry can be coupled to each capacitive sensor and configured to sense or measure the capacitance of each capacitive sensor. A processing unit may be coupled to the drive and sense circuitry and configured to receive signals representing the measured capacitance of each capacitive sensor. The processing unit can be configured to correlate the measured capacitances into a displacement of the support plate  1823 . 
       FIG. 19  depicts a fourth technique for pre-stressing a haptic actuator  1924   a  and sensing the closure of a gap. The electronic device  1900  includes a cover sheet  1908  and a support structure  1920 . In the illustrated embodiment, the support structure  1920  is a U-shaped support structure that includes a support plate  1923  and sides  1925  that extend from the support plate  1923  and attach to the cover sheet  1908 . The support structure  1920  is configured to attach to, and suspend from, the cover sheet  1908  such that a gap  1918  is defined between the cover sheet  1908  and the support plate  1923 . As described earlier, other embodiments can configure the support structure  1920  and/or the support plate  1923  differently. 
     A first haptic actuator  1924   a  is attached to the bottom surface of the support plate  1923 . Although only one first haptic actuator  1924   a  is shown in  FIG. 19 , other embodiments can include two or more first haptic actuators. In the illustrated embodiment, the first haptic actuator  1924   a  is attached directly to a bottom surface of a support plate  1923 . In other embodiments, the first haptic actuator  1924   a  can be coupled to the support plate  1923  through a circuit layer. 
     A second haptic actuator  1924   b  is attached to a top surface of the support plate  1923 . Although only one second haptic actuator  1924   b  is shown in  FIG. 19 , other embodiments can include two or more second haptic actuators. The second haptic actuator  1924   b  includes a piezoelectric material (e.g., piezoelectric material  1632  in  FIG. 16B ). When a pre-stress signal is applied to the first haptic actuator  1924   a , the support structure  1920  deflects such that the support plate  1923  moves into the gap  1918 . When the support plate  1923  moves into the gap  1918  such that the second haptic actuator  1924   b  contacts the bottom surface of the cover sheet  1908 , a stress is applied to the second haptic actuator  1924   b . The stress produces an electrical signal in the piezoelectric material in the second haptic actuator  1924   b . This electrical or output signal can be detected and used to determine the gap  1918  is closed. 
     For example, in some embodiments, drive circuitry can be coupled to the first haptic actuator  1924   a  and configured to apply the pre-stress signal to the first haptic actuator  1924   a . Sense circuitry may be coupled to the second haptic actuator  1924   b  and configured to receive the output signal from the second haptic actuator  1924   b . Drive circuitry and sense circuitry may form part of a signal generator (e.g., signal generator  44  in  FIG. 4 ) or other circuitry coupled to a processing unit. A processing unit can be configured to receive the output signal and determine the gap  1918  is closed. 
     In other embodiments, one or more second haptic actuators  1924   b  can be attached to a bottom surface of the cover sheet  1908 . When the support plate  1923  moves into the gap  1918  such that the top surface of the support plate  1923  contacts at least one second haptic actuator  1924   b , a stress is applied to the at least one second haptic actuator  1924   b . The stress produces an electrical signal in the piezoelectric material in the at least one second haptic actuator  1924   b . This electrical or output signal can be detected and used to determine the gap  1918  is closed. 
     Additionally or alternatively, in some embodiments, the first haptic actuator  1924   a  can be used to decrease or close the gap  1918  and the second haptic actuator  1924   b  may be used to deflect the cover sheet  1908  and produce the haptic output. In such embodiments, the first haptic actuator  1924   a  receives a DC signal (e.g., a DC current) to place the first haptic actuator  1924   a  in a pre-stressed state, which causes the support structure  1920  to deflect and position the support plate  1923  closer to (or farther from) the cover sheet  1908 . The second haptic actuator  1924   b  receives an AC signal (e.g., an AC current) to place the second haptic actuator  1924   b  in a haptic output state to produce a deflection in the cover sheet  1908 . In some embodiments, the second haptic actuator  1924   b  may also be used to detect the closure of the gap  1918 . The AC signal may be applied to the second haptic actuator  1924   b  after the electrical signal indicating closure of the gap  1918  is received from the second haptic actuator  1924   b.    
       FIG. 20  depicts a cross-sectional view of another example of the electronic device taken along line A-A in  FIG. 1 . The electronic device  2000  is similar to the electronic device  200   b  shown in  FIGS. 2C and 2D , except for the omission of the gaps  218   b ,  218   c  and the first and the second force-sensing components  214   b ,  216   b . In the illustrated embodiment, the array  2040  of haptic actuators  2024  can be placed in a pre-stressed state to cause the support structure  2020  to deflect. In such embodiments, the support plate  2023  can move toward the cover sheet  2008  and produce a deflection in the backlight assembly  2005  and in the display layer  2002  without producing a noticeable or significant deflection in the cover sheet  2008 . Thus, the pre-stressed state moves the haptic actuators  2024  closer to the cover sheet  2008  without producing a noticeable deflection in the cover sheet  2008 . 
       FIG. 21  depicts a cross-sectional view of another example of the electronic device  2100  taken along line A-A in  FIG. 1 , where the haptic actuators are in a pre-stressed state. In the illustrated embodiment, the display layer  2102  is positioned below the cover sheet  2108  and the first force-sensing component  2116  is positioned between the display layer  2102  and the backlight assembly  2105 . 
     An array  2140  of haptic actuators  2124  is affixed to a surface of the support structure  2120  (e.g., to the support plate  2123 ). As shown in  FIG. 21 , the array  2140  of haptic actuators  2124  is coupled to a bottom surface of the support plate  2123 , although this is not required. Additionally, the array  2140  of haptic actuators  2124  can include one or more haptic actuators  2124 . 
     The array  2140  of haptic actuators  2124  is attached and electrically connected to the circuit layer  2122 . In the illustrated embodiment, the circuit layer  2122  is positioned on the sides of the haptic actuators  2124  that are opposite the support plate  2123 . In other embodiments, the circuit layer  2122  may be positioned between the array  2140  of haptic actuators  2124  and the support structure  2120 . Alternatively, the circuit layer  2122  can be omitted and the array  2140  of haptic actuators  2124  attached to the support structure  2120 . Signal lines or electrical traces may be included in the support structure  2120  (or on the surface of the support structure) and electrically connected to the haptic actuators  2124 . 
     As described earlier, the circuit layer  2122  includes signal lines that are electrically connected to the haptic actuators  2124 . The signal lines can be used to transmit pre-stress signals to each haptic actuator  2124  to place the haptic actuators  2124  in a pre-stressed state. However, in the illustrated embodiment, the pre-stressed state expands the gap  2118  and positions the support plate  2123  and the haptic actuators  2124  farther from the cover sheet  2108 . When an actuation signal is transmitted to at least one haptic actuator  2124  to place the haptic actuator(s) in the haptic output state, the activated haptic actuator(s) moves (e.g., contracts) and deflects the support structure  2120  such that the support plate  2123  traverses the gap  2118  and produces a localized deflection in the cover sheet  2108 . When the support plate  2123  deflects, the momentum of that movement transfers to the backlight assembly  2105 , the first force-sensing component  2114 , and the display layer  2102  (e.g., the intermediate layers) to deflect the intermediate layers and produce the localized haptic output in the cover sheet  2108 . 
       FIG. 22  depicts a flowchart of a method of calibrating the pre-stress signals for an array of haptic actuators. As described earlier, an array of haptic actuators can include one or more haptic actuators. Initially, as shown in block  2200 , the signal levels of the initial pre-stress signals that vary the size of the gap are determined. For example, the signal levels of the initial pre-stress signals that cause a support structure to deflect such that the support plate contacts a spaced-apart overlying layer (e.g., first force-sensing component  214   b  in  FIGS. 2C and 2D  or the cover sheet  1308  in  FIG. 13B ) may be determined. Additionally or alternatively, the signal levels of another set of initial pre-stress signals that cause a support structure to deflect such that the support plate moves into the gap a given distance can be determined. In some implementations, the signal levels of another set of initial pre-stress signals that cause the support plate to deflect and increase the size of the gap may be determined. Thus, in some embodiments, multiple sets of pre-stress signals can be determined. Which set of pre-stress signals are used to place the array of haptic actuators in a pre-stressed state can be based on a pre-stress magnitude for the array of haptic actuators. For example, the array of haptic actuators can be placed in different pre-stressed states based on the applications the user is interacting with and/or the amount of actuation latency. The actuation latency refers to the time between transmitting an actuation signal to a haptic actuator and the time a deflection is produced in a surface. 
     Next, as shown in block  2202 , the initial pre-stress signals (or the pre-stress signal characteristics such as amplitude) are stored in a memory (e.g., memory  448  in  FIG. 4 ). Thereafter, as the user interacts with the electronic device, the closure or the expansion of the gap is monitored to determine an effectiveness of the initial pre-stress signals (block  2204 ). 
     A determination may be made at block  2206  as to whether the initial pre-stress signals need to be adjusted. The process waits at block  2204  when the initial pre-stress signals do not need to be adjusted. If the initial pre-stress signals need to be adjusted, the method passes to block  2208  where an adjusted signal level for one or more pre-stress signals is determined. The adjusted pre-stress signal(s) are then stored in the memory (block  2210 ) and the process returns to block  2204 . 
       FIG. 23  depicts a flowchart of a method of operating an electronic device. Initially, as shown in block  2300 , a user interacts with the electronic device. A determination may be made at block  2302  as to whether or not an array of haptic actuators is to be pre-stressed. The determination to pre-stress the array of haptic actuators can be based on one of several conditions. For example, in one embodiment, the array of haptic actuators may be pre-stressed when a body part (e.g., a finger) is approaching or in contact with a surface of the electronic device. In such embodiments, an output signal from one or more sensors (e.g., touch sensor layer  210  in  FIG. 2 ) may be used to detect a body part (e.g., a finger) is approaching or is in contact with the surface of the electronic device. 
     Additionally or alternatively, the array of haptic actuators may be placed in a pre-stressed state based on the state of an application. For example, the array of haptic actuators may be placed in a pre-stressed state when the user is interacting with a gaming application that will produce haptic feedback to the user. In another example, the array of haptic actuators can be placed in a pre-stressed state when the user is interacting with a graphical user interface. And in yet another example, the array of haptic actuators may be placed in a pre-stressed state when the user is interacting with an application that requires various inputs, such as entering data into a dialog box or selecting various input elements (e.g., icons, buttons, and the like). 
     The process returns to block  2300  if the array of haptic actuators will not be placed in a pre-stressed state. The method passes to block  2304  if the array of haptic actuators will be placed in a pre-stressed state. At block  2304 , pre-stress signals are transmitted to the haptic actuators to place the array of haptic actuators in the pre-stressed state. 
     Next, as shown in block  2306 , the displacement of the support structure can be detected to either ascertain the closure of the gap or the expansion of the gap. A determination may then be made at block  2308  as to whether one or more haptic actuators are to be actuated (e.g., placed in a haptic output state). The process continues at block  2310  when the one or more haptic actuators is to be placed in a haptic output state. At block  2310 , an actuation signal is transmitted to one or more haptic actuators to place the haptic actuator(s) in the haptic output state. The one or more haptic actuators produce one or more deflections in a surface of the electronic device when the haptic actuators are in the haptic output state. 
     After the one or more deflections are produced in the surface of the electronic device, a determination is made at block  2312  as to whether the array of haptic actuators is to be placed in the pre-stressed state. For example, the haptic actuators can transition from the pre-stressed state to the haptic output state multiple times while a user interacts with the electronic device. 
     The method returns to block  2304  when the array of haptic actuators is to be placed in the pre-stressed state. Otherwise, the process returns to block  2300  when the array of haptic actuators will not be placed in the pre-stressed state. 
     Returning to block  2308 , the method continues at block  2314  if one or more haptic actuators will not be placed in the haptic output state. At block  2314 , a determination is made as to whether the array of haptic actuators is to remain in the pre-stressed state. If so, the process passes to block  2308 . If the array of haptic actuators will not remain in the pre-stressed state, the method continues at block  2316  where the array of haptic actuators is placed in the rest state. The pre-stress signals are not transmitted to the haptic actuators to place the haptic actuators in the rest state. Thereafter, the process returns to block  2300 . 
     Although the embodiments have been described herein as electrically pre-stressing the haptic actuators to close a gap, other embodiments are not limited to this implementation. In some embodiments, the support structure or support plate may be pre-stressed through mechanical components or constraints. For example, a shim or a foam structure can be positioned below a support plate to situate the support plate closer to a surface to be deflected (e.g., partially or completely close a gap). Alternatively, in some embodiments, the support plate can be formed in a pre-stressed shape that positions the support plate closer to a surface to be deflected. In another embodiment, the support plate may be pre-stressed (e.g., shaped or bent) and then mechanically held in the pre-stressed state. For example, once in the pre-stressed state, the ends of the support plate can be attached to a structure that maintains the support structure in the pre-stressed state. 
     III. Relaxing Strain in Support Structures 
       FIGS. 24-28  illustrate increasing deflection at a cover sheet of an electronic device by relaxing strain.  FIG. 24  depicts one example of a first deflection module that is configured to produce increased deflection. For simplicity, the deflection module  2401  is illustrated with only one haptic actuator  2424 . Those skilled in the art will recognize that more than one haptic actuator can be used. For example, two haptic actuators can be included in the deflection module  2401 . 
     The haptic actuator  2424  is attached and electrically connected to a circuit layer  2422 . The circuit layer  2422  is attached to a support structure. In the illustrated embodiment, the support structure is configured as a support structure stripe  2420 , with two longer sides (e.g., top and bottom sides) and two shorter sides  2419 ,  2421 . In other words, the support structure stripe  2420  has four sides, with two lateral sides  2419 ,  2421  having a length that is less than the length of the other two sides. In the illustrated embodiment, the length of the opposing sides  2419 ,  2421  in the support structure stripe  2420  are not much longer than the length of the sides  2481 ,  2483  of the haptic actuator  2424 . 
     All of the sides of the haptic actuator  2424  are rigidly affixed (bonded) to the circuit layer  2422  (indicated by the thicker lines). However, only the shorter sides  2419 ,  2421  (the sides having the smaller length) of the support structure stripe  2420  are rigidly attached (indicated by the thicker lines) to a component in an electronic device (e.g., an enclosure, a frame, an input surface, or a cover sheet). Because only the two lateral sides  2419 ,  2421  of the support structure stripe  2420  are rigidly attached to a component, strain is relaxed in the support structure stripe  2420 . The support structure stripe  2420  can experience a greater amount of deflection. The support structure stripe  2420  can buckle in response to the actuation of the haptic actuator  2424 . 
     In some embodiments, an electronic device may use a support structure that is larger than a support structure stripe. In such embodiments, multiple haptic actuators may be used to deflect the larger-sized support structure.  FIG. 25  depicts one example of a second deflection module that is configured to produce increased deflection. A haptic actuator  2524  is attached and electrically connected to a circuit layer  2522 . The circuit layer  2522  is attached to a support structure  2520 . All of the sides of the support structure  2520  are rigidly affixed to a component (indicated by the thicker lines) in an electronic device (e.g., a frame or input surface). However, only two sides  2580 ,  2582  of the haptic actuator  2524  are rigidly attached to the circuit layer  2522  (indicated by the thicker lines). Because only two sides (e.g., opposing lateral sides) of the haptic actuator  2524  are rigidly attached to the circuit layer  2522 , the support structure  2520  may be able to experience a greater amount of deflection. The support structure  2520  can buckle in response to the actuation of the haptic actuator  2524  because the un-bonded sides of the haptic actuator  2524  relax the strain in the support structure  2520 . 
     Although the deflection module  2501  is shown with only one haptic actuator  2524 , those skilled in the art will recognize that more than one haptic actuator can be used. In some embodiments, two or more haptic actuators may be disposed on the support structure  2520 . 
       FIG. 26  depicts one example of a third deflection module that is configured to produce increased deflection. The deflection module  2601  includes an array  2640  of haptic actuators  2624 . As discussed earlier, in some embodiments, each haptic actuator  2624  may be attached and electrically connected to a circuit layer. The circuit layer is omitted from  FIG. 26  for clarity and ease of understanding. 
     The circuit layer is affixed to a support structure  2620 . All of the sides of the support structure  2620  are rigidly attached (indicated by the thicker lines) to a component in an electronic device. Two sides  2680 ,  2682  of each haptic actuator  2624  are rigidly affixed (indicated by the thicker lines) to the circuit layer. In the illustrated embodiment, the sides  2680 ,  2682  are opposing sides of each haptic actuator  2624 . 
     Openings or slits  2684 ,  2686  are formed through the support structure  2620  adjacent the sides of each haptic actuator  2624  that are not rigidly affixed to the circuit layer. The openings  2684 ,  2686  induce strain relaxation and locally transform the larger-sized sheet of the support structure  2620  into support structure stripes. As described in conjunction with  FIG. 24 , a support structure stripe can buckle in response to the actuation of one or more haptic actuators, which can produce a greater amount of deflection in the support structure  2620 . 
     The openings  2684 ,  2686  are shown as having a rectangular shape, but this is not required. The openings  2684 ,  2686  can have any given shape and/or dimensions. Additionally, in some embodiments, one or more openings may be formed through the support structure  2620 . The number of openings, as well as the location(s) of the openings, can be based on the amount of deflection a support structure  2620  is to experience. 
       FIG. 27  depicts one example of a fourth deflection module that is configured to produce increased deflection. The deflection module  2701  includes an array  2740  of haptic actuators  2724 . Each haptic actuator  2724  is attached and electrically connected to a circuit layer  2722 . The circuit layer  2722  is affixed to a support structure  2720 . All of the sides of the support structure  2720  are rigidly attached (indicated by the thicker lines) to a component in an electronic device. Similarly, all of the sides of each haptic actuator  2724  are rigidly affixed (indicated by the thicker lines) to the circuit layer  2722 . 
     The circuit layer  2722  is selectively bonded to the support structure  2720 . In particular, only one or more first sections  2785  of the circuit layer  2722  are rigidly affixed (indicated by the dashed lines) to the support structure  2720 . One or more second sections  2787  of the circuit layer  2722  are not attached to the support structure  2720 . In the illustrated embodiment, each first section  2785  is formed as a rectangular-shaped stripe that is positioned adjacent one or more haptic actuators (e.g., adjacent a line of haptic actuators) or between adjacent haptic actuators (e.g., between two lines of haptic actuators). Other embodiments can affix the one or more first sections  2785  of the circuit layer  2722  at different locations. Additionally or alternatively, each first section  2785  of the circuit layer  2722  can have any given shape and/or dimensions. The number of first sections  2785 , the location of each first section  2785 , the shape of each first section  2785 , and the dimensions of each first section  2785  can be based on the amount of deflection a support structure is to experience. Additionally, at least one first section  2785  can have a location, shape, and/or dimensions that differ from one or more other first sections  2785 . 
     Selectively bonding the circuit layer  2722  to the support structure  2720  relaxes the strain in the support structure  2720  in the directions around the sides of the haptic actuator  2724  that are not adjacent to a first section of the circuit layer  2722 . This allows the support structure  2720  to buckle in response to the actuation of one or more haptic actuators  2724 , which can produce a greater amount of deflection in the support structure  2720 . 
       FIG. 28  depicts a flowchart of a method of producing a deflection module that provides localized deflection in a surface of an electronic device that is positioned over the deflection module. Initially, as shown in block  2800 , a support structure is provided. A determination is then made at block  2802  as to whether one or more openings are to be formed through the support structure. If so, the process passes to block  2804  where the opening(s) are formed through the support structure. As described earlier, the number of openings, the dimensions of the openings, and/or the location(s) of the openings can be based on the amount of deflection a support structure is to experience. 
     Next, as shown in block  2806 , a determination may be made as to whether only one or more sections of a circuit layer are to be rigidly attached to at least one surface of the support structure. Although the embodiments shown in  FIGS. 26 and 27  were described separately, the embodiments can be combined in a haptic or deflection module. In some embodiments, one or more sections of the circuit layer can be selectively attached to the support structure, where the support structure includes opening(s) formed through the support structure. In such embodiments, corresponding opening(s) may be formed in the circuit layer, although this is not required. 
     If one or more sections of the circuit layer are to be rigidly attached to at least one surface of the support structure, the method continues at block  2808  where the section(s) of the circuit layer are rigidly attached to the surface(s) of the support structure. As described earlier, the number of sections, the location of each section, the dimensions of each section, and/or the shape of each section can be based on the amount of deflection a support structure is to experience. 
     After the section(s) of the circuit layer are selectively affixed to the surface(s) of the support structure, the process passes to block  2810  where one or more haptic actuators are attached to the circuit layer. The deflection module may then be attached to a component in the electronic device. As discussed earlier, the component can be an enclosure, a frame, an input surface, or a cover sheet in the electronic device. 
     When the circuit layer will not be selectively affixed to the surface(s) of the support structure at block  2806 , the method continues at block  2814  where the circuit layer is attached to the support structure. Blocks  2810  and  2812  may then be performed. 
     Although the haptic actuators shown in  FIGS. 4, 26, and 27  are arranged in an array (e.g., columns and rows), other embodiments are not limited to this configuration. The haptic actuators may be arranged in any pattern or placement. And as described earlier, one or more haptic actuators may be coupled to a top surface, a bottom surface, and/or a side of a support structure. 
     Additionally, the haptic actuators, the circuit layer, and the support structure are each shown in  FIGS. 4, 26, and 27  as having a square or rectangular shape, but other embodiments are not limited to this configuration. Each haptic actuator may have any given shape and/or dimensions. Additionally, the circuit layer and/or the support structure can each have any given shape and/or dimensions. 
     IV. Reduced Cost Piezoelectric Wafer 
       FIGS. 29-32  illustrate embodiments in which the piezoelectric material has a different shape, such as a cross shape.  FIG. 29  depicts an arrangement of haptic actuators  2924  that may be used to provide localized haptic output for an electronic device. The haptic actuators  2924  may be any one of the haptic actuators described herein. In some embodiments, each of the haptic actuators  2924  may be arranged in a master-slave configuration. In other cases, each haptic actuator  2924  may operate independently. 
     As shown in  FIG. 29 , each haptic actuator  2924  may include a piezoelectric material  2932 , a ground layer  2938 , and a circuit layer  2922 . The ground layer  2938  may include a ground trace made of silver and a PET flex such as described above with respect to  FIG. 3D . Likewise, the circuit layer  2922  may include a drive trace made of copper and a polyimide flex such as described with respect to  FIG. 3D . In order to further reduce costs, the piezoelectric material  2932  may have a cross-shape. Each haptic actuator  2924  may be coupled to a stiffener, such as a support structure  2920 . 
     As shown, at least one dimension (e.g., a width) of the circuit layer  2922  is smaller than a dimension (e.g., a width) of the ground layer  2938 . The reduction in the size of the circuit layer  2922  may reduce the overall cost of the haptic structure  2924  and also improve actuation performance of the haptic actuators  2924 . 
       FIG. 30A  depicts an example shape of a piezoelectric wafer  3033   a  that may be incorporated in the haptic structures described herein. For example, the piezoelectric wafer  3033   a  may be similar to the piezoelectric material described above with respect to  FIGS. 3A-3D, 16B, and 29 . 
     In this example, the piezoelectric wafer  3033   a  may have a square shape. However, when a signal is applied to the piezoelectric wafer  3033   a , the area shown by the dotted line  3029  contributes the majority of the actuation performance. Accordingly, in order to reduce costs while still maintaining desirable performance characteristics, the piezoelectric wafer  3033   a  may be cut in a cross-shape such as shown in  FIG. 30B . In the embodiment shown in  FIG. 30B , the piezoelectric wafer  3033   b  substantially maintains the performance of the piezoelectric wafer  3033   a  while saving  4 / 9  of the material. 
     In the embodiment shown in  FIG. 30C , the piezoelectric wafer  3033   c  may have rounded edges. Specifically, outward and inward right angles of the cross-shaped piezoelectric wafer  3033   c  may be susceptible to damage. Rounding the corners such as shown can reduce the risk of damage. In some embodiments, the rounded corners may be formed during the cutting/dicing of a piezoelectric sheet. In other implementations, one or more piezoelectric wafers  3033   b  may be stacked together and a router, a laser or other such tool may be used to round the corners. 
       FIG. 31  depicts an example piezoelectric sheet  3127  in which a number of cross-shaped piezoelectric elements have been formed. In some embodiments, the piezoelectric elements are arranged in a tessellated pattern such as shown. For example, a portion of one piezoelectric element is adjacent a portion of another piezoelectric element. 
     In some embodiments, the piezoelectric sheet  3127  undergoes a dicing process to produce the piezoelectric elements. The dicing process may be any cutting process such as, but not limited to, laser cutting, plasma cutting, sawing and so on. In some embodiments, the dicing of the piezoelectric sheet produces the cross-shaped piezoelectric wafer  3033   b  shown above with respect to  FIG. 30B . 
       FIG. 32  depicts another example piezoelectric sheet  3227  in which a number of rounded cross-shaped piezoelectric elements are formed. The piezoelectric sheet  3227  may be diced in order to produce the cross-shaped piezoelectric wafer  3033   c  shown above with respect to  FIG. 30C . As shown, the various piezoelectric elements in the sheet are arranged in a tessellated pattern once produced. Once cut, the piezoelectric elements shown in  FIGS. 31-32  may be used in the various haptic structures described herein. 
     IV. System Diagram 
       FIG. 33  depicts example components of an electronic device in accordance with the embodiments described herein. The schematic representation depicted in  FIG. 33  may correspond to components of the devices depicted in  FIGS. 1-11H , described above. However,  FIG. 33  may also more generally represent other types of electronic devices with a haptic actuator  3324  coupled to a support structure configured to amplify the haptic response. 
     As shown in  FIG. 33 , a device  3300  includes a processing unit  3346  operatively connected to computer memory  3348 . The processing unit  3346  may be operatively connected to the memory  3348  component via an electronic bus or bridge. The processing unit  3346  may include one or more computer processors or microcontrollers that are configured to perform operations in response to computer-readable instructions. The processing unit  3346  may be the central processing unit (CPU) of the device  3300 . Additionally or alternatively, the processing unit  3346  may include other processors within the device  3300  including application specific integrated chips (ASIC) and other microcontroller devices. The processing unit  3346  may be configured to perform functionality described in the examples above. 
     The memory  3348  may include a variety of types of non-transitory computer-readable storage media, including, for example, read access memory (RAM), read-only memory (ROM), erasable programmable memory (e.g., EPROM and EEPROM), or flash memory. The memory  3348  is configured to store computer-readable instructions, sensor values, and other persistent software elements. 
     In this example, the processing unit  3346  is operable to read computer-readable instructions stored on the memory  3348 . The computer-readable instructions may adapt the processing unit  3346  to perform the operations or functions described above with respect to  FIGS. 1-11H . The computer-readable instructions may be provided as a computer-program product, software application, or the like. 
     The device  3300  may also include a battery  3303  that is configured to provide electrical power to the components of the device  3300 . The battery  3303  may include one or more power storage cells that are linked together to provide an internal supply of electrical power. The battery  3303  may be operatively coupled to power management circuitry that is configured to provide appropriate voltage and power levels for individual components or groups of components within the device  3300 . The battery  3303 , via power management circuitry, may be configured to receive power from an external source, such as an alternating current power outlet. The battery  3303  may store received power so that the device  3300  may operate without connection to an external power source for an extended period of time, which may range from several hours to several days. 
     In some embodiments, the device  3300  includes one or more input devices  3390 . The input device  3390  is a device that is configured to receive user input. The input device  3390  may include, for example, a push button, a touch-activated button, or the like. In some embodiments, the input devices  3390  may provide a dedicated or primary function, including, for example, a power button, volume buttons, home buttons, scroll wheels, and camera buttons. Generally, a touch sensor and a force sensor may also be classified as input components. However, for purposes of this illustrative example, the touch sensor  3310  and force sensor  3312  are depicted as distinct components within the device  3300 . 
     The device  3300  may also include a touch sensor  3310  that is configured to determine a location of a finger or touch over the adaptable input surface of the device  3300 . The touch sensor  3310  may be implemented in a touch sensor layer, and may include a capacitive array of electrodes or nodes that operate in accordance with a mutual-capacitance or self-capacitance scheme. 
     The device  3300  may also include a force sensor  3312  in accordance with the embodiments described herein. As previously described, the force sensor  3312  may be configured to receive force touch input over the adaptable input surface of the device  3300 . The force sensor  3312  may also be implemented in a touch-sensing layer, and may include one or more force-sensitive structures that are responsive to a force or pressure applied to an external surface of the device. In accordance with the embodiments described herein, the force sensor  3312  may be configured to operate using a dynamic or adjustable force threshold. The dynamic or adjustable force threshold may be implemented using the processing unit  3346  and/or circuitry associated with or dedicated to the operation of the force sensor  3312 . 
     The device  3300  may also include a haptic actuator  3324 . The haptic actuator  3324  may be implemented as described above, and may be a ceramic piezoelectric transducer. The haptic actuator  3324  may be controlled by the processing unit  3346 , and may be configured to provide haptic feedback to a user interacting with the device  3300 . 
     The device  3300  may also include a communication port  3388  that is configured to transmit and/or receive signals or electrical communication from an external or separate device. The communication port  3388  may be configured to couple to an external device via a cable, adaptor, or other type of electrical connector. In some embodiments, the communication port  3388  may be used to couple the device  3300  to a host computer. 
     The device  3300  may also include a signal generator  3344 . The signal generator  3344  may be operatively connected to the haptic actuator  3324 , and may transmit electrical signals to the haptic actuator  3324 . The signal generator is also operatively connected to the processing unit  3346 . The processing unit  3346  is configured to control the generation of the electrical signals for the haptic actuator  3324 . 
     The memory  3348  can store electronic data that can be used by the signal generator  3344 . For example, the memory  3348  can store electrical data or content, such as timing signals, algorithms, and one or more different electrical signal characteristics that the signal generator  3344  can use to produce one or more electrical signals. The electrical signal characteristics include, but are not limited to, an amplitude, a phase, a frequency, and/or a timing of an electrical signal. The processing unit  3346  can cause the one or more electrical signal characteristics to be transmitted to the signal generator  3344 . In response to the receipt of the electrical signal characteristic(s), the signal generator  3344  can produce an electrical signal that corresponds to the received electrical signal characteristic(s). 
     The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the described embodiments. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the described embodiments. Thus, the foregoing descriptions of the specific embodiments described herein are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. It will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings.