Detection element, sensor and sensor array

Abstract

A microwire sensor comprises a conductive sensing element disposed above a substrate. The sensing element may be anchored to the substrate at one or more ends and may be formed by patterning a conductive layer formed on a flexible or other substrate. Conductive connection pads and bias resistors may be formed with the sensing element in a common conductive layer.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 63 / 219,317, filed July 7, 2021, which is incorporated herein by reference. The present disclosure relates to thermal microphones. [Background technology]

[0002] So-called "hot-wire" microphones use a heated wire that can be placed at the output of a Helmholtz resonator, where sound-generated airflow cools the heated wire. The cooling results in a change in the resistance of the hot wire that can be detected and amplified. Such microphones are described in Tucker, et al., "A selective hot-wire microphone," Phil. Trans. Royal Society A, January 1921, pp. 389-430, which is incorporated herein by reference. This microphone is useful at a single low frequency because the resonant frequency of the Helmholtz resonator is usually low. Also, because the heated wire is large and has a long cooling time constant, hot-wire microphones are not useful for high frequency applications. Such heated wires can also be used in anemometers and other applications, but are limited to low frequency applications. There is a need for an approach that provides high frequency response and allows multiple devices to be fabricated on rigid or flexible substrates. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Tucker, et al., "A selective hot-wire microphone," Phil. Trans. Royal Society A, January 1921, pp. 389-430. Summary of the Invention [Problem to be solved by the invention]

[0004] The present disclosure relates to sensors that include a sensing element, such as a portion of a conductive layer spaced apart from a substrate. The sensing element is typically heated or set to a predetermined temperature different from the ambient temperature, such that vibration of the sensing element cools or heats the sensing element, changing the electrical conductivity of the sensor element. Such sensors are capable of detecting and quantifying acoustic waves or disturbances. [Means for solving the problem]

[0005] The sensing element can be part of a conductive layer formed on a rigid or flexible substrate, including substrates provided as a roll. The substrate / sensing element gap can be selected to provide an appropriate response, and the gap can be in the range of 100 nm to 10 μm, or other ranges. Typically, the sensing element has portions that have a larger vibration amplitude in response to a vibration input, such as an acoustic signal, and the sensing element resistance is generally selected to be relatively large in these portions. Methods for making such sensors are also disclosed.

[0006] In some examples, the sensor comprises a substrate and a sensing element, at least one end of which is fixed to the substrate such that the sensing element is spaced apart from the substrate. A sensor circuit is coupled to the sensing element and operable to heat the sensing element and generate an output signal associated with the vibration of the sensing element. Typically, the output signal associated with the vibration of the sensing element corresponds to a change in temperature of the sensing element. In some examples, the sensing element is fixed to the substrate at a first end and a second end such that the sensing element extends from the first end to the second end and is suspended from the substrate. In a representative example, a spacer is disposed at at least one end of the sensing element to define a gap between the sensing element and the substrate. In some cases, the substrate is a flexible substrate such as polyethylene terephthalate. Typically, the sensing element is a metal. In a further example, a resistive conductor is coupled to the sensing element, and the sensor circuit is operable to heat the sensing element with a current conducted by the resistive conductor to the sensing element. At least one conductive pad can be defined on the substrate, the conductive pad and the sensing element being defined in a common conductive layer. In some cases, the at least one conductive pad includes a first, second, and intermediate conductive pad, and a resistor is defined in the common conductive layer, and the sensing element is coupled to the first conductive pad by the resistor and secured to the substrate at the second conductive pad. A spacer can be disposed between the first conductive pad, the second conductive pad, the intermediate conductive pad, and the resistor, and the sensing element is spaced from the substrate by the spacer, typically with a portion of the spacer periphery in contact with the spacer. According to one example, the resistor comprises a serpentine strip defined in the common conductive layer. In some examples, an enclosure is disposed around at least the sensing element, and the enclosure is filled with an inert gas.

[0007] A representative method includes forming a conductive layer coupled to a substrate and patterning the conductive layer to define a conductive sensing element spaced apart from the substrate, where a first fixed end and a second fixed end of the conductive sensing element are fixed to the substrate. The conductive layer can be formed on a spacer layer, and the conductive sensing element is spaced apart from the substrate by removing a portion of the spacer layer. The spacer layer can be formed on the substrate at a location associated with the conductive sensing element, and the conductive layer is formed on the exposed portion of the substrate and the spacer layer, and then removing the spacer layer such that the conductive sensing element is spaced apart from the substrate. A resistor can be defined in the conductive layer, and the resistor is operable to heat the conductive sensing element. In some cases, the resistor is defined as a serpentine conductive strip. The conductive sensing element can include a plurality of segments that are symmetrical about an axis.

[0008] In another example, the sensor array comprises a substrate and a plurality of sensors defined on the substrate. Each of the plurality of sensors can include a sensing element and at least one spacer coupled to the sensing element and the substrate to define a gap between the sensing element and the substrate. The sensing element and the at least one spacer of each of the sensing elements can be subsequently defined in a common conductive layer and a common spacer, respectively. Each sensor can further include first, second, and intermediate conductive pads defined in the common conductive layer and coupled to the sensing element, and a resistor defined in the common conductive layer and coupled to a selected one of the sensing element and the first, second, and intermediate conductive pads. In some examples, the substrate is a flexible substrate. At least some of the resistors and at least some of the sensing elements can have different shapes.

[0009] The above and other features and advantages of the disclosed technology will become more apparent from the following detailed description, which proceeds with reference to the accompanying drawings. [Brief description of the drawings]

[0010] [Figure 1A]FIG. 1 illustrates a sensor having a linear resistor defined on a flexible substrate. [Figure 1B] FIG. 1 illustrates a sensor having a linear resistor defined on a flexible substrate. [Figure 1B1] FIG. 4 is a diagram showing vibration modes of a sensing element included in the sensor of FIGS. 1A-B, illustrating the 1.7 kHz symmetric mode. [Figure 1B2] FIG. 4 is a diagram showing vibration modes of a sensing element included in the sensor of FIGS. 1A-B, illustrating the 1.8 kHz asymmetric mode. [Figure 1C] FIG. 4 shows an additional sensor that uses the sensing element of FIGS. 1A-2B but has a different resistive conductor. [Figure 1D] FIG. 4 shows an additional sensor that uses the sensing element of FIGS. 1A-2B but has a different resistive conductor. [Figure 1E] FIG. 1 illustrates an exemplary system including a suspended sensing element. [Figure 2A] FIG. 1 shows a representative cantilevered sensing element. [Figure 2B] FIG. 1 shows a representative cantilevered sensing element. [Figure 2C] FIG. 1 shows a representative cantilevered sensing element. [Figure 2D] 2D shows representative vibration modes of the sensing element of FIG. 2C. [Figure 2E] 2D shows representative vibration modes of the sensing element of FIG. 2C. [Figure 2F] 2D shows representative vibration modes of the sensing element of FIG. 2C. [Figure 2G] FIG. 13 illustrates another suspended sensing element. [Diagram 3] FIG. 1 shows a sensor configuration having a cantilevered sensor element. [Figure 4] FIG. 13 illustrates another representative sensor configuration. [Figure 4A] FIG. 5 is a cross-sectional view of the sensor configuration of FIG. [Figure 4B] FIG. 5 is a cross-sectional view of the sensor configuration of FIG. [Diagram 5] FIG. 1 shows different sensor arrangements. [Figure 6A] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 6B] FIG. 1 illustrates sensor fabrication according to one approach. [Figure 6C] FIG. 1 illustrates sensor fabrication according to one approach. [Figure 6D] FIG. 1 illustrates sensor fabrication according to one approach. [Figure 6E] FIG. 1 illustrates sensor fabrication according to one approach. [Figure 7A] FIG. 1 shows an arrangement of different sensors on a single substrate. [Figure 7B] FIG. 1 illustrates a sensor system including a sensor array. [Figure 8A] FIG. 1 shows a sensor having a serpentine resistor. [Figure 8B] FIG. 1 illustrates a sensor having sensing elements and contact pads of different materials. [Figure 9A] FIG. 1 illustrates a representative sensor system. [Figure 9B] FIG. 13 shows sensor sensitivity as a function of bias voltage (sensing element temperature). [Figure 9C] 9C corresponds to FIG. 9B but normalized based on bias voltage. [Figure 9D] FIG. 13 illustrates sensor frequency response versus range of sensing element versus substrate gap. [Figure 10A] FIG. 1 illustrates a representative sensing element. [Figure 10B] FIG. 1 illustrates a representative sensing element. [Figure 10C] FIG. 1 illustrates a representative sensing element. [Figure 10D] FIG. 1 illustrates a representative sensing element. [Fig. 10DD] FIG. 1E illustrates vibration modes of the sensor of FIG. 10D. [Figure 10E] FIG. 13 illustrates an additional representative sensing element. [Figure 10F] FIG. 13 illustrates an additional representative sensing element. [Figure 11A] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 11B] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 11C] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 12A] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 12B] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 12C] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 13A] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 13B] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 13C] 1A to 1C are diagrams illustrating a method for manufacturing a sensor. [Figure 14A] FIG. 2 shows a cantilever sensor element. [Figure 14B] FIG. 2 shows a cantilever sensor element. [Figure 15A] FIG. 1 shows sensors formed in a sheet of sensors, each sensor being positioned within an enclosed container. [Figure 15B] FIG. 1 shows sensors formed in a sheet of sensors, each sensor being positioned within an enclosed container. [Figure 16] FIG. 1 illustrates a geometric arrangement for estimating the minimum radius of curvature of a sensor. [Figure 17A] FIG. 1 shows a representative sensing element geometry for such a sensing element. [Figure 17B] FIG. 1 illustrates the nonlinear response of such a sensing element. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Introduction and Terminology Disclosed herein are microwire sensors and related methods and systems based on sensing elements that can have multiple resonant modes and resonant frequencies as well as low thermal mass. The disclosed approach also allows for fabrication with flexible or rigid substrates so that large arrays of devices can be formed, and sheets of such sensors can be provided for applications requiring sensing at multiple locations or over a large area. The resonant modes exhibit low Q so that broadband resonances can overlap, allowing acoustic measurements at frequencies and frequency ranges where traditional approaches are not suitable. As used herein, "Q" refers to the ratio of device resonant frequency to device bandwidth (full width at half maximum). Examples of the disclosed sensors are generally based on relatively narrow and thin strips of sensor material, generally conductors such as gold, copper, aluminum, indium tin oxide, or other conducting or semiconducting materials, suspended over a rigid or flexible substrate and fixed relative to the substrate at one or more locations. As used herein, the suspended conductors (or other sensor materials), such as conductive strips, are referred to as sensing elements or sensing conductors. Such sensing elements may be in the form of elongated strips, strips following a serpentine or spiral path, or may be U-shaped or plate shaped with or without grooves or slots in the plate, or may follow a linear or non-linear path. The sensing elements may be formed from a common conductive layer used to form conductive pads for electrical connections, and conductive strips used to define resistors connecting to the sensing elements, although other configurations may be used. The sensing elements may be suspended or cantilevered at one or more fixed points. In one approach, suspension is achieved by removing an underlying sacrificial layer. In some disclosed examples, the combination of very small thermal mass due to the thin metal layer and high thermal conduction due to the small conductive gap between the sensing element and the substrate allows for fast response times.

[0012] As used in this application and the claims, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. Furthermore, the term "includes" means "comprises." Furthermore, the term "combined" does not exclude the presence of intermediate elements between the combined items.

[0013] The systems, devices, and methods described herein should not be construed as limiting in any way. Instead, the present disclosure is directed to all novel and non-obvious features and aspects of the various disclosed embodiments, alone and in various combinations and subcombinations with one another. The disclosed systems, methods, and devices are not limited to any particular aspect or feature or combination thereof, and the disclosed systems, methods, and devices do not require that any one or more particular advantages exist or problems be solved. Although theories of operation are intended for ease of explanation, the disclosed systems, methods, and devices are not limited to such theories of operation.

[0014] Although some operations of the disclosed methods are described in a particular sequential order for convenient presentation, it should be understood that the method of description encompasses reordering, unless a particular order is required by specific language described below. For example, operations described sequentially may in some cases be reordered or performed simultaneously. Moreover, for simplicity, the accompanying figures may not show the various ways in which the disclosed systems, methods, and apparatus can be used in combination with other systems, methods, and apparatus. Furthermore, the description may use terms such as "generate" and "provide" to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms will vary depending on the particular implementation and are readily discernible by those of ordinary skill in the art.

[0015] In some instances, values, procedures, or devices are referred to as "lowest," "best," "minimum," etc. Such descriptions are intended to indicate that selections can be made from among many functional alternatives used, with the understanding that such selections are not necessarily better, lesser, or otherwise preferred than other selections.

[0016] The examples are described with reference to directions indicated as "upper", "lower", "top", "bottom", etc. These terms are used for ease of description and do not imply a particular spatial orientation.

[0017] Example 1 1A-1B, the sensor 100 includes conductive pads 102, 104, 106 disposed on a substrate 112. In FIG. 1A, the pads are referred to as a supply voltage pad, a measurement voltage pad, and a ground pad, respectively, for ease of describing a representative circuit configuration for use with the sensor 100, although other electrical connections may be used. A resistive element 110 extends from the pad 102 to electrically connect to the pad 104 at a conductive connection 111. A sensing element 116 includes a first end 118 electrically coupled to the conductive connection 111 and a second end 120 electrically coupled to a bonding region 114 of the third pad 106. The sensing element 116 is spaced from the substrate 112 at a region 108 (which may be established using a sacrificial layer during fabrication), and the first end 118 and the second end 120 are fixed to the substrate 112. Vibration or other movement of the sensing element 116 relative to the substrate 112 that changes the gap between the sensing element 116 and the substrate 112 also changes the thermal conductivity between the sensing element 116 and the substrate 112. When the sensing element 116 is heated (or cooled), such change in thermal conductivity changes the cooling (or heating) rate of the sensing element and the sensing element temperature. The associated variation in electrical resistance is associated with the vibration or movement of the sensing element, as will be described in more detail below (see FIGS. 17A-B).

[0018] In this example, the sensing element 116 includes first and second interdigitated sets of segments 116A, 116B that are symmetrical about an axis 122 extending along a first end 118 and a second end 120. The resistive element 110 (i.e., resistor) is selected so that the temperature of the sensing element 116 can be established as needed. In some cases, the sensing element 116 is defined by forming a conductive layer on a sacrificial layer (such as photoresist) in the region 108 and then removing the sacrificial layer. In Figures 1A-1B, the sacrificial layer is only shown in the region 108, but it can be provided under the pads 102, 104, 106, the resistive element 110, and the conductive connections 111. This portion is typically removed to suspend the sensing element and is shown for illustrative purposes only. The sensing element 116 is spaced above the substrate 112 and is responsive to acoustic signals over a wide frequency range. The sensing element 116 can be heated by a current provided through the resistive element 110. Because heat transfer from the sensing element 116 depends on the spacing from the substrate 112 established by the sacrificial layer, vibration or other movement of the sensing element 116 (or either of the segments 116A, 116B) tends to modulate the heat transfer from and the temperature of the sensing element 116. These temperature changes result in changes in the electrical resistivity of the sensing element 116 that can be detected.

[0019] In a typical example, the gap between the sensing element 116 and the substrate 112 is 0.2-20 μm, 0.2 μm-10 μm, 0.5-10 μm, 1-5 μm, 1-3.5 μm, or other range, and the thermal resistance between the sensing element 116 and the substrate 112 allows for cooling. The sensing element 116 has a low mass, the conductive layers used to form the sensing element 116 can be thin (e.g., 0.1 μm-25 μm), and the total area of ​​the sensing element 116 can be small (e.g., 1 mm 2 ~10mm 2), the thermal mass of the sensing element can also be made small. In some cases, the gap between the sensing element 116 and the substrate 112 is determined by the sag of the sensing element. The gap is large enough to prevent the sensing element from contacting the substrate, but is otherwise made small. For an estimated sag S, the gap can be set as 1.1S, 1.2S, 1.3S, 1.4S, 1.5S, 1.75S, 2S, 2.5S, 3S, or any other value larger than S, with smaller gaps being associated with better sensor response. In the example of FIGS. 1A-1B, the gap is 1 μm, the design supply voltage is 1 V, and the target operating temperature is 100° C.

[0020] Typically, the sensing element is designed to keep sag small. In most applications, sensing orientation relative to gravity remains constant and sag-related effects are constant. Sag (including the constant sag expected at a fixed orientation) can be used with a selected sensing element gap, but in many practical applications, such considerations are not necessary. Generally, a small (or minimum) gap is selected to improve electro-thermal response, but the gap can also be selected with considerations of manufacturing capabilities, minimum radius of the rolled substrate during shipping and storage, and thin film damping and its effect on mechanical response.

[0021] Approximate dimensions of a representative example are shown in FIG. 1B. The length of the suspended area is about 253 μm. The lowest order modal frequency of the symmetric mode (or asymmetric mode) is about 1.7-1.8 kHz. FIGS. 1B1-1B2 show representative symmetric and asymmetric modes, respectively. A satisfactory response should extend to at least 5 kHz, with a typical frequency range being 1.5 kHz-5 kHz. In some applications, a supply voltage is applied to the pad 102 to generate a current capable of heating the resistive element 110 and / or the sensing element 116. The change in electrical resistance associated with the movement generates a corresponding voltage change at the pad 104, which can be coupled to an amplifier or other analog or digital circuit to generate a corresponding output signal. For example, referring to the electrical schematic of FIG. 1E, an amplifier 150 detects the resistance R of the sensing element 116 and detects the resistance R of the sensing element 116.S (t) is coupled to receive a signal generated by the variation of R S (t) is a function of time due to the resistance variation caused by the movement of the sensor element and the associated heating and cooling. The supply voltage Vs is S (t) and the resistance R of the resistive element 110 B and a series resistor which is the sum of

number

[0022] Vs can be any convenient voltage, such as any voltage between 0 and 20 V, and voltages of 1, 2, 3, and 4 V can be used. B is the intended R B / R S Depending on the ratio and the intended supply voltage, the range can be very large. For a resistance ratio of 99:1 and a supply voltage of 2V to 15V, the R B The values ​​are shown in the table below. [Table 1]

[0023] At the other extreme, for a 1:1 resistor ratio and a supply voltage less than 1 V, R B Typical values ​​are shown in the table below. [Table 2]

[0024] Nominal sensor resistance R s is determined by the target nominal temperature in the absence of sound or mechanical excitation, which in this example is: [Table 3]

[0025] The substrate 112 can be a flexible roll material such as a plastic roll material (e.g., polyethylene terephthalate (PET)), or a rigid material such as glass. The conductors can be made of copper, aluminum, indium tin oxide, or other conductors, semiconductors, or insulators with suitable temperature-dependent electrical resistance. It is convenient to have the conductors, pads, resistors, and sensor elements in a common layer, but different materials can be used for each. For example, the sensor elements are preferably heat resistant, durable, and have a resistance that changes with temperature. The conductive pads 102, 104, 06 preferably have low resistivity. Thus, the materials of the sensor elements and the conductive pads 102, 104, 106 can be different.

[0026] Although a single spacer layer can be used, multiple spacers and / or spacer layers can be used to space the sensing element from the substrate. In some examples described below, the suspended sensing element is bridged. The conductor portion coupled to the sensing element can be spaced from the substrate but wide or otherwise rigid enough that the sensing element does not exhibit excessive sag toward the substrate. The design / shape of the sensing element can be selected to provide a primary mode of resonance at the lowest frequency in the desired detection range or at a primary frequency desired for detection at a single ultrasonic or other sonic frequency based on the intended application.

[0027] 1C-1D show sensors 129, 139 having different resistive elements 130, 140 used with the sensing element 116. For example, different resistive elements can be used to establish different temperatures at the sensing element 116. In the example of FIG. 1C, the gap is 1 μm, the design supply voltage is 3 V, and the target operating temperature is 400° C. In the example of FIG. 1D, the gap is 1 μm, the design supply voltage is 5 V, and the target operating temperature is 200° C.

[0028] Example 2 2A-2C show a representative sensing element. The sensors of FIG. 2A-2C have various shapes and sizes. The shape and size of the sensor are determined based on the target frequency to be detected. With reference to FIG. 2A, a conductive sensing element 200 includes a metal sheet 202 fixed at fixed ends 204, 206 to conductive pads (not shown) and suspended relative to a substrate (not shown). A slot 208 is formed on a tab 210 extending from an area 212 in which slots 214-216 are formed. The slots 214-216 extend perpendicular to the slot 208, such that the sensing element 200 is symmetrical about the slot 208. In a typical application, the fixed ends 204, 206 are coupled to an amplifier or other circuit that provides an output signal associated with vibration of the sensing element 200 or a portion thereof, and a power source that provides an appropriate bias for heating the sensing element 200. In one example, such a sensing element exhibits a suspension sag of about 0.5 nm or less, thereby allowing sensing element / substrate gaps of 10 nm, 50 nm, 100 nm, 200 nm, 500 nm, 1 μm or more to be used without the sensor contacting the substrate. Any gap larger than the sensing element sag can be used. In the example of FIG. 2A, the resonant frequency of the lowest mode is 26.4 kHz. In this example, the target gap is 1 μm and the sensing element size is 116 μm×116 μm. The useful frequency range extends from 26 kHz (first mode) to 227 kHz (fifth mode of the type associated with cooling). This example is typically intended for use in situations where the transducer attached to the object to be detected emits sound at one of four of the first five mode frequencies: 26 kHz, 80 kHz, 163 kHz, or 227 kHz. The third of the first five modal frequencies is less suitable for sensing as it is not associated with sufficient out-of-plane motion (i.e., relative to the substrate) for cooling, and other modes are preferred.

[0029] FIG. 2B shows a representative conductive sensing element 220 including interleaved square spiral conductors 222, 224 with fixed ends 223, 225, respectively. The square spiral conductors 222, 224 terminate in a central conductive area 226. The fixed ends 223, 225 are typically fixed to conductive pads and suspended relative to a substrate. Other spirals can be used, including any curved or polygon-based spiral shape. In one example, such a sensing element exhibits a suspension sag of about 4.2 nm or less and a resonant frequency of the lowest mode is 8.9 kHz. In this example, the target gap is 1 μm and the sensing element is 114 μm by 114 μm. The useful frequency range extends from 8 kHz (first mode) to 55 kHz (fifth mode of the type associated with cooling).

[0030] FIG. 2C shows a U-shaped conductive sensing element 240 including sides 244, 246 with fixed ends 245, 247, respectively, and a bottom 248. The sensing element 240 is typically suspended with spacers or bridged to define a gap between the sensing element 240 and a substrate. In one example, such a sensing element exhibits a suspension sag of about 0.006 nm or less. In the example of FIG. 2C, the resonant frequencies include 241 kHz, 497 kHz, and 1.2 MHz. In this example, the target gap is 1 μm and the sensing element is about 150 μm by 150 μm. This sensor is intended for use in situations where a transducer attached to an object to be detected emits sound at one of the first three modal frequencies: 241 kHz, 497 kHz, or 1.2 MHz.

[0031] Sensing elements such as those described above may be suitable for high frequency applications, such as frequencies above 10 kHz, 250 kHz, 500 kHz, or 1 MHz. Figures 2D-2F show representative low order vibration modes of the sensing element of Figure 2C at frequencies of 241 kHz, 1.2 MHz, and 497 kHz. Such sensing elements can be used to detect objects such as robots, e.g., robotic vacuum cleaners, that have acoustic emissions at these high frequencies. Many of these sensors can be placed under the floor and used to detect and guide the robotic vacuum cleaner. In other examples, multiple such sensors are distributed throughout a surface or volume and used to detect and / or guide the robot. High frequency designs generally have a higher stiffness-to-inertia ratio and therefore less gravity sag. Designs can be selected based on a compromise between gravity sag and low frequency operation.

[0032] FIG. 2G shows another sensing element 250 supported at ends 252, 254 and having a serpentine shape. In the example of FIG. 2G, the resonant frequency of the lowest mode may be about 19.8 kHz. In this example, the target gap is 1 μm and the sensing element is about 124 μm by 157 μm. One application of this example is a situation where a transducer attached to an object to be detected is emitting sound somewhere in the range of 19.8 kHz or 25 kHz. Because of its finger-like structure, this sensing element has multiple modes close to each other at frequencies within that range.

[0033] Example 3 FIG. 3 illustrates a sensor 300 that includes connectors such as conductive pads 304, 313, 316 defined on a substrate 302. The conductive pad 304 is coupled to a resistor 306, which may be defined in a conductive layer, such as the layer used to define some or all of the conductive pads 304, 313, 316, or a separate resistor may be used. Conductive strips 308, 318 (or other conductors such as wires) couple the conductive pads 304, 313, 316 to a sensing element 310 as described above. The resistor 306 can be used to control heating of the sensing element 310 as well as to establish a resistive divider network with the sensor such that a voltage or current change based on vibration of the sensor 310 is coupled to the conductive pad 316 for output to an amplifier, analog-to-digital converter (ADC), or other processing circuitry. Because a DC level is associated with a fixed sensor and not an acoustic signal to be detected, the vibration-induced current or voltage can be capacitively coupled for output. Portions 304 A, 306 A, 308 A, 313 A, 316 A, 318 A remain between their respective conductor portions and substrate 302 while sensing element 310 is suspended from substrate 302 .

[0034] Example 4 FIG. 4 illustrates a sensor 400 that includes connectors, such as conductive pads 402-404 defined on a substrate 401. A sensing element 420 is coupled to the conductive pad 404 and a conductive strip 405, which may function as a resistor. The conductive pad 402 is coupled to the conductive strip 405 in close proximity to the sensing element 420. The conductive strip 405 and the sensing element 420 form a voltage divider that may generate a sensor output signal at the conductive pad 402 in response to vibration of the sensing element 420. Additional conductive pads 402 may also be provided.

[0035] 4A-4B are cross-sectional views of FIG. 4. In FIG. 4A, the conductive strip 405 is disposed on a spacer 415, which may be defined in a spacer layer of photoresist or other material. The conductive pad 404 is disposed on a spacer 414, which may be defined in a spacer layer of photoresist or other material. The spacers 414, 415 separate the conductive pad 404 and the conductive strip 405 from the substrate 401, and it may be convenient to define the spacers 414, 415 in a common layer, such as a common layer of photoresist. As shown in FIG. 4B, the first end 406 and the second end 407 of the sensing element 420 are disposed above the substrate 401. The spacers 414, 415 do not extend to be below the sensing element 420, but the spacers 414, 415 are shown in outline to indicate that they serve to space the sensing element 420 above the substrate 401.

[0036] Example 5 With reference to FIG. 5, sensors 500, 520, 540, 560, 580 are defined on a common substrate 501, such as a rigid or flexible substrate. The sensors can be fabricated using common layers and common processing steps, and can be patterned the same or differently. As shown, sensor 500 includes conductive pads 502, 504, 506, a serpentine conductive strip 508 that can function as a resistor, and a sensing element 510. Sensor 520 includes conductive pads 522, 524, 526, a linear conductive strip 528 that can function as a resistor, and a sensing element 530. Sensor 540 includes conductive pads 542, 544, 546, a serpentine conductive strip 548 that can function as a resistor, and a sensing element 550. Sensor 560 includes conductive pads 562, 564, 566, a serpentine conductive strip 568 that can function as a resistor, and a sensing element 570. The sensor 580 includes conductive pads 582, 584, 586, a serpentine conductive strip 588 that can function as a resistor, and a sensing element 590. In the example of FIG. 5, the conductive strips provided to function as resistors all have different shapes and / or sizes. In some applications, the sensor operating temperature is established based on the resistance of the conductive strips, and the selection of the particular shape and size of the conductive strips allows for the selection of the resistance. It can be convenient to provide heating using a readily available voltage or current source, and the selection of the conductive strips can be used to accommodate any convenient power source, allowing multiple different sensors to be thermally biased with the same current or voltage. In other examples, some or all of these conductive strips can have the same configuration. The associated resistances can be the same or different. Some or all of the sensing elements can be the same or different. As described above, the sensing element includes a fixed portion and a portion spaced apart from the substrate 501.

[0037] Example 6 6A-6E, an exemplary method 600 includes, at 602, forming a spacer layer 622 on a substrate 620. The substrate 620 can be rigid or flexible and can be provided as a sheet, wafer, plate, roll, or otherwise. Exemplary substrate materials include glass and plastic, including plastic encased in a roll. The spacer layer 622 can be an insulator, conductor, or semiconductor, and is typically selected to allow selective removal, as described below. In some cases, the spacer layer 622 is a photoresist or other insulating layer that is applied to the substrate by spin coating, spraying, slot-die coating, lamination, or other techniques. At 604, a conductor layer 624 is formed on the spacer layer 622, for example, by lamination, sputtering, plating, e-beam evaporation, or other process. In some examples, photoselective plating is used to form the conductor layer 624 only at selected sensor locations, such as conductive pads, conductive strips that function as resistors, or sensing elements suspended around the substrate. Photoselective plating of the conductor layer tends to eliminate or reduce the need for additional patterning of the conductor layer.

[0038] If a patterning process is not used to form the conductor layer 624 (or additional patterning is intended), as determined at 605, the conductor layer 624 is patterned at 606 to form the sensing element 632 and / or conductive pads and resistors, e.g., conductive pads 625, 626, 628 and resistor 630. In one example, the patterning includes forming a layer of photoresist, patterning and developing the photoresist such that the photoresist protects the portions of the conductor layer 624 associated with the sensing element and / or conductive pads and resistors. A wet or dry etching process, such as a plasma etch or an acid etch, is then used to remove the unprotected areas of the conductor layer. After etching, the portions of the conductor layer associated with the sensing element and / or conductive pads and resistors remain covered by the photoresist. Other portions of the conductor layer are removed. In some cases, the protective photoresist is removed before removing a spacer layer that separates the sensing element from the substrate, such that the sensing element is suspended above the substrate.

[0039] At 608, at least a portion of the spacer layer located between the sensing element and the substrate is removed to suspend the sensing element 632 above the substrate 620 to produce the sensor 640. Typically, a non-directional etch, such as a wet etch, is used to remove the spacer layer portion under the sensing element 632, and the spacer layer 622 is removed from other areas of the substrate 620 except where protected by the remaining portions of the conductor layer 624. The wet etch generally removes some of the spacer layer under and at the edges of the remaining conductor layer 624. The sensing element 632 is generally narrow enough (or includes multiple narrow features) such that this undercut suspends the sensing element while the spacer layer 622 remains under other features (such as pads).

[0040] During operation, the sensing element is typically heated using resistive heating provided by a conductive strip with suitable resistance. Although higher temperatures may be associated with better sensor performance, these higher temperatures may also cause degradation of the sensing element as well as pads or other features defined in the conductor layer. At 610, at least the sensing element is placed in an enclosure, which is then filled and sealed at 612 with a non-reactive gas, such as a noble gas, nitrogen, or other gas that tends to reduce oxidation or other degradation of the sensing element. The enclosure may be formed as a cavity defined around the sensor in an additional layer, such as a flexible layer, which forms cavity walls 650 and is then covered with a cap layer.

[0041] Example 7 Referring to FIG. 7A, a representative array 700 of sensors, such as sensor 702, is defined on a section 701 of a substrate roll. Each sensor in the array can have a different resistive conductor and sensing element. Alignment marks 708 are provided for use in the patterning operation. The sensors can be separated for individual use, or some or all of the sensors in the array 700 can be used together to provide the same or different sensitivity and / or the same or different bandwidth. Two or more sensors can be provided in a common configuration for redundancy.

[0042] 7B illustrates a sensor system 750 including a sensor array 751 having sensors 752-757. The sensor array 751 is illustrated as a rectangular array including multiple sensors on the same substrate or multiple sensors that may be distributed throughout an area of ​​interest. As illustrated, each of the sensors 752-757 receives the same bias voltage V from a bias source 760. BIAS, but different bias voltages may be provided to some or all of the sensors 752-757. The sensor outputs are coupled to a multiplexer (mux) 762 that can selectively deliver the output from a selected sensor to an amplifier 764 or other electronics such as a filter, an analog-to-digital converter (ADC), additional amplifiers, or other digital or analog circuitry. A control circuit such as a microprocessor or other programmable logic device may be coupled to the mux 762 to enable sensor selection. In other examples, each sensor (or several sensors) is coupled to a dedicated amplifier or other electronics. In some alternatives, each of the sensors 752-757 is configured to operate at different frequencies, and the output signals from each of the sensors 752-757 may be combined into a single output and differentiated based on the signal frequency. Additionally, each of the sensors 752-757 may be associated with a particular location such that the signal identifies the location where the acoustic signal is present.

[0043] Example 8 Referring to FIG. 8A, the sensor 800 includes conductive pads 802, 804, 806 disposed on a substrate 801. In FIG. 8A, the pads are referred to as a supply voltage pad, a measurement voltage pad, and a ground pad, respectively, to facilitate the description of a representative circuit configuration for use with the sensor 800. A resistive element 810 extends from the pad 802 to electrically connect to the pad 804 at a conductive connection 811. A sensing element 808 includes a first end electrically coupled to the conductive connection 811 and a second end electrically coupled to the pad 806. The sensing element 808 is spaced apart from the substrate 801 at a region 820, and the first and second ends of the sensing element 808 are fixed to the substrate 801. In this example, the resistive element 810 is formed as a serpentine strip defined in a conductive layer.

[0044] As shown in FIG. 8B, the sensor 850 can have a sensing element 856 suspended between contact pads 852, 854 above a substrate 851. The contact pads 852, 854 and the sensing element 856 can be made of different materials, and if an integrated resistor is provided, the same or different materials can be used. For example, the sensing element 856 can be made of a material that has a large resistivity change with temperature or does not degrade when heated, while the materials of the pads and resistor can be selected for ease of fabrication, bonding, patterning, or to provide a selected resistance.

[0045] Example 9 9A, a representative sensor system 900 includes a sensing element 902 suspended above a substrate 904. A power source is a voltage V applied to the sensing element 902 through a resistor 906, which may be a separate component or may be defined in one or more layers located on the substrate 904. S An amplifier 908 is coupled to the sensing element 902 and provides a voltage V d Based on this voltage, the amplifier produces an output voltage V out Resistor 906 can also establish a current in sensing element 902 that heats the sensing element 902, although heating can be provided in other ways.

[0046] FIG. 9B shows the sensor voltage V associated with a nominal sensing element vibration of about 100 nm at a 1 μm gap. d 9. Curve 921 is associated with the lowest applied voltage V (and lowest heating of sensing element 902), and curve 929 is associated with the highest applied voltage V (and highest heating of sensing element 902). The curves located between curves 921 and 929 are S The curves in FIG. 9B show the sensor response as a function of time. At 0 ms, the voltage V Sis applied and at approximately 2 ms, the sensing element 902 begins to oscillate. The initial voltage rise before 2 ms is associated with the stabilization of the sensing element 902 at the selected applied voltage. The sensing element voltage oscillation in curve 929 begins to S 9C is greater than that in curve 921 due to the resulting higher temperature of the sensing element 902. Although a higher temperature would produce a larger output signal, the temperature of the sensing element is limited because melting must be avoided and prolonged use of higher temperatures may result in oxidation of the sensing element. For this reason, in some examples, the sensing element is placed in a vessel filled with an inert gas, e.g., a vessel filled with argon. FIG. 9C shows the normalized sensor response V for various sensing element temperatures, corresponding to FIG. 9B. d A larger normalized amplitude of vibration is associated with a higher temperature, indicating an advantage of higher temperature.

[0047] FIG. 9D shows the sensor response to a nominal 100 nm vibration for gaps ranging from about 500 nm to about 5 μm. Larger amplitudes of vibration are associated with smaller gaps. The applied voltage Vs is varied in this example, but the value of resistor 906 is similarly varied to show a linear relationship between temperature and the sensor response V d can bring about changes in

[0048] Example 10 10A-10E show additional sensing elements. In some of these examples, the sensing elements are shown as deforming in response to an acoustic signal. In these examples, the sensing elements are symmetric about one or more axes, while in other examples, the sensing elements lack such symmetry. Sensing element 1000 as shown in FIG. 10A includes fixed ends 1002, 1004 that are used to suspend and electrically connect the sensing element. Sensing element 1000 includes conductor sections 1001, 1003 that are symmetric about an axis 1006 that extends between fixed ends 1002, 1004. This example is associated with relatively high attenuation and low Q, and the detectable frequency range can be at least 2.2 kHz to 10 kHz starting slightly below the lowest order mode frequency.

[0049] FIG. 10B shows a sensing element 1020 including fixed ends 1022, 1024 used for suspending and electrically connecting the sensing element. The sensing element 1020 includes conductor quadrants 1021, 1023, and conductor quadrants 1025, 1027 shaped as a rectangular spiral that is symmetrical about an axis 1026 extending between the fixed ends 1022, 1024 and a vertical axis 1028 located between conductor quadrants 1021, 1023 and conductor quadrants 1025, 1027. In this example, high attenuation and low Q are expected, and the detectable frequency range may be at least 60-70 kHz. This example is intended for an application in which the transducer emits sound at a first mode frequency of 67 kHz, above the human hearing range.

[0050] FIG. 10C shows a sensing element 1060 including fixed ends 1062, 1064 of a central strip 1070, which are used to suspend and electrically connect the sensing element. The sensing element 1060 includes conductor quadrants 1061, 1063, 1065, 1067 shaped as rectangular plates connected to surrounding conductor strips such as strips 1069, 1071. The conductor quadrants 1061, 1063, 1065, 1067 are symmetrical about an axis 1066 extending between the fixed ends 1062, 1064 and a vertical axis (not shown in FIG. 10C) located between the conductor quadrants 1061, 1063 and the conductor quadrants 1065, 1067. The strips 1069, 1071 provide increased resistance, and this arrangement places the increased resistance in regions of the sensing element associated with large vibration amplitudes. For example, the lowest modal frequency is 12.4 kHz. Given that this example exhibits high attenuation and low Q, the useful frequency range may be at least 12 kHz to 30 kHz or more. Numerous modes are available, although some modes may be less suitable for cooling due to the direction of motion associated with the mode. The sensor element dimensions are relatively large at 500 μm x 500 μm.

[0051] FIG. 10D shows a sensing element 1080 similar to FIGS. 1A-1B including fixed ends 1082, 1084 used to suspend and electrically connect the sensing element. The sensor 1080 includes conductor sections 1081, 1083 shaped as a generally rectangular spiral connected to end conductor strips such as strips 1089, 1091. The conductor sections 1081, 1083 are symmetrical about an axis 1086 extending between the fixed ends 1082, 1084. FIG. 10DD shows, in one example, positions 0-5 associated with path resistances at 400° C., 200° C., and 25° C. of 0.48 Ω, 0.35 Ω, 6.95 Ω, 0.21 Ω, and 0.48 Ω on paths 0-1, 1-2, 2-3, 3-4, and 4-5, respectively, in the table below. The highest resistance (2-3) is generally associated with a larger vibration amplitude, improving the response of the sensing element. [Table 4]

[0052] FIG. 10E shows a sensing element 1040 (similar to that of FIG. 10C) including fixed ends 1042, 1044 used for suspending and electrically connecting the sensing element. The sensing element 1040 includes rectangular shaped conductor sections 1041, 1043 connected to end conductor strips such as strips 1045, 1046. The conductor sections 1041, 1043 are symmetrical about an axis extending between the fixed ends 1042, 1044. FIG. 10F shows a representative vibration mode of the sensing element 1040. The strips 1045, 1046 increase the resistance, and this arrangement places the increased resistance in the sensing element region associated with large vibration amplitudes. In the above FIGs. 10A-10E, the resonant frequencies are different, and therefore the detectable range of acoustic waves is different.

[0053] Example 11 11A-11C show another exemplary method of fabricating the disclosed sensor. As shown in FIG. 11A, a spacer 1106 made of photoresist is applied onto a protective layer, such as an oxide layer 1104, formed on a substrate 1102. The photoresist spacer 1106 can be generated by patterning a photoresist layer that is typically applied onto a surface 1103 of the protective layer 1104. As shown in FIG. 11B, a conductor layer 1108 is formed on the photoresist spacer 1106 and a portion of the surface 1103. As shown in FIG. 11C, the photoresist spacer 1106 is removed, and a sensing element is formed by a bridge portion 1112 of the conductor layer 1108 and a gap 1110 created by removing the photoresist. The photoresist spacer 1106 can be removed with a solvent in liquid or vapor form, such as acetone as a liquid or vapor.

[0054] Example 12 12A-12C show another exemplary method of fabricating the disclosed sensor. As shown in FIG. 12A, an oxide spacer 1206 is formed on a surface 1203 of a substrate 1202, and a conductor layer 1204 is formed on the oxide spacer 1206 and on the surface 1203. The oxide spacer 1206 can be produced by patterning the oxide layer using a patterned photoresist layer and an appropriate etching process. As shown in FIG. 12B, a portion of the conductor layer 1204 remote from the oxide spacer 1206 is removed. As shown in FIG. 12C, the oxide spacer 1206 is removed, forming a sensing element with a bridge portion 1212 of the conductor layer 1204 and a gap 1210 created by the removal of the oxide spacer 1206. In the case of a silicon substrate and silicon dioxide spacers, the oxide spacer 1206 can be removed using HF vapor or a buffered oxide etch (BOE) of HF and a buffer. These etches tend to remove silicon dioxide but do not etch silicon. Other etching techniques can be used and spacers other than silicon dioxide may require different etchants.

[0055] Example 13 13A-13C show another exemplary method of fabricating the disclosed sensor. As shown in FIG. 13A, a conductor layer 1308 is formed on photoresist spacers 1306, 1309 on a surface 1303 of an oxide layer 1304 on a substrate 1302. A photoresist layer 1310 is formed on the conductor layer 1308 and patterned to remove a portion of the conductor layer 1308 in a gap 1320. FIG. 13B shows the removal of the photoresist layer 1310 and partial removal of the photoresist spacers 1306, 1309 by wet solvent etching. The remaining portions of the photoresist spacers 1306, 1309 are protected by the conductor layer 1308 and a solvent vapor etch is used to produce the structure shown in FIG. 13C. Electrically separate sensing elements 1321, 1322 are suspended above the substrate 1302. Sensing element 1322 is anchored at two ends and sensing element 1321 is anchored at only one end.

[0056] Example 14 14A-14B show an exemplary sensor 1400 including a substrate 1402 and conductors 1404, 1406 secured to the substrate 1402. A sensing element 1407 includes first and second conductive extensions 1410, 1412 and a connecting conductor 1408, all of which are suspended above the substrate 1402. A spacer layer 1414 separates the conductors 1404, 1406 from the substrate 1402, but the spacer layer 1414 does not underlie the extensions 1410, 1412, or the connector 1408. The spacer layer 1414 is typically undercut by removing spacer material beneath the extensions 1410, 1412 and the connector 1408.

[0057] Example 15 15A-15B, a representative sensor 1500 includes a sensor conductor 1501 including a portion 1503 fixed to a substrate 1502 and a conductive sensing element 1504 suspended from the substrate 1502. The conductive sensing element 1504 is located within an enclosure volume 1510 of an enclosure defined by the substrate 1502, a cap layer 1508, and an enclosure wall 1506 extending from the substrate 1502. Multiple sensors can be formed using a single substrate and a single cap layer, with each sensor located within a respective enclosure. Such multiple sensors can have the same or different configurations of sensing elements, bias resistors, enclosure volumes, or other specifications.

[0058] Example 16 The disclosed sensors can be mounted on a rolled or bendable substrate, but there is a limit to the radius of curvature. Referring to FIG. 16, the minimum possible radius of curvature R for a sensor of length L with a gap G is:

number

[0059] Example 17 The disclosed sensors typically sample vibrations at about 10 Hz to 100 Hz, but respond to input signals up to 1 MHz or higher depending on the sensing element configuration. The resonant mode of the sensing element acts as a frequency filter such that a range of frequencies close to the resonant frequency of the sensing element can be sampled. For example, with a 1 μm air gap and vibration damping due to a thin sensing element, the sensing element acts as a filter with low Q and wide bandwidth sensing. The sensing element typically averages out the effects of motion near the resonant frequency by cooling the sensing element. The detection signal generated by the sensing element does not correspond precisely to either the frequency or the Fourier domain response due to the nonlinear relationship between cooling and vibration amplitude. Nevertheless, such a response is suitable for many applications.

[0060] 17A, the average thermal conductivity of a sensing element 1704 having a gap G with the substrate 1702 defined by a spacer 1706 is proportional to 1 / G. As an example, assume the gap G=1 μm. If the sensing element 1704 is subjected to a square wave acoustic signal such that the gap G alternates between 0.5 μm and 1.5 μm, the average conductivity is (0.5 μm) -1 and (1.5 μm) -1 17B, ​​where curve 1752 corresponds to a stationary sensing element and curve 1754 corresponds to a vibrating sensor element. It is clear that the average conductivity in response to the periodic signal is greater than that of a stationary sensing element. The average conductivity in response to a sinusoidal input is

number

[0061] Illustrative Examples Example 1 is a sensor comprising a substrate, a sensing element having at least one end fixed to the substrate such that the sensing element is spaced from the substrate, and a sensor circuit coupled to the sensing element and operable to heat the sensing element and generate an output signal associated with vibration of the sensing element. Example 2 includes the subject matter of example 1, further specifying that the output signal associated with the vibration of the sensing element corresponds to a change in temperature of the sensing element. Example 3 includes the subject matter of any of Examples 1-2, further specifying that the sensing element is secured to the substrate at a first end and a second end, such that the sensing element extends from the first end to the second end and is suspended from the substrate. Example 4 includes the subject matter of any of Examples 1-3, further including a spacer disposed on at least one end of the sensing element to define a gap between the sensing element and the substrate. Example 5 includes the subject matter of any of Examples 1-4, further specifying that the substrate is a flexible substrate. Example 6 includes the subject matter of any of Examples 1-5, further specifying that the substrate is polyethylene terephthalate. Example 7 includes the subject matter of any of Examples 1-6, further specifying that the sensing element is metallic. Example 8 includes the subject matter of any of examples 1-7, further including a resistive conductor coupled to the sensing element, wherein the sensor circuit is operable to heat the sensing element with a current conducted to the sensing element by the resistive conductor. Example 9 includes the subject matter of any of examples 1-8, further including at least one conductive pad defined on the substrate, wherein the conductive pad and the sensing element are defined in a common conductive layer. Example 10 includes the subject matter of any of examples 1-9, further including at least one conductive pad defined on the substrate, wherein the at least one conductive pad and the sensing element are defined by different materials. Example 11 includes the subject matter of any of Examples 1-10, further specifying that the at least one conductive pad comprises first, second, and middle conductive pads, and a resistor is defined in the common conductive layer, and the sensing element is coupled to the first conductive pad by the resistor and secured to the substrate at the second conductive pad. Example 12 includes the subject matter of any of Examples 1-11, further including a spacer disposed between the first, second, and intermediate conductive pads, and the resistor, wherein the sensing element is spaced from the substrate by a gap associated with a spacer thickness. Example 13 includes the subject matter of any of Examples 1-12, further specifying that the resistor comprises a serpentine strip defined within the same conductive layer. Example 14 includes the subject matter of any of Examples 1-13, further specifying that the at least one end includes a first end and a second end, and the sensing element is secured to the substrate at the first end and the second end and spaced apart from the substrate. Example 15 includes the subject matter of any of examples 1-14, further including an enclosure disposed around at least the sensing element. Example 16 includes the subject matter of any of examples 1-15, further specifying that the enclosure is filled with an inert gas. Example 17 includes the subject matter of any of Examples 1-16, further specifying that the enclosure includes an enclosure wall extending from the substrate and a cap layer sealed to the enclosure wall defining an enclosure volume. Example 18 is a method that includes forming a conductive layer coupled to a substrate and patterning the conductive layer to define a conductive sensing element spaced apart from the substrate, where a first fixed end and a second fixed end of the conductive sensing element are fixed to the substrate. Example 19 includes the subject matter of example 18, further specifying that the conductive layer is formed on a spacer layer, and the conductive sensing element is spaced from the substrate by removing a portion of the spacer layer. Example 20 includes the subject matter of any of Examples 18-19, further including forming a spacer layer on the substrate at a location associated with the conductive sensing element, where a conductive layer is formed on the exposed portion of the substrate and the spacer layer, and removing the spacer layer such that the conductive sensing element is spaced from the substrate. Example 21 includes the subject matter of any of examples 18-20, further including defining a resistor in the conductive layer, the resistor operable to heat the conductive sensing element. Example 22 includes the subject matter of any of Examples 18-21, further specifying that the resistor is defined as a serpentine conductive strip. Example 23 includes the subject matter of any of Examples 18-22, further specifying that the conductive sensing element includes a plurality of segments that are symmetric about an axis. Example 24 is a sensor array including a substrate, a plurality of sensors defined on the substrate, each of the plurality of sensors including a sensing element, and at least one spacer coupled to the sensing element of each of the plurality of sensors and to the substrate to define a gap between the sensing element and the substrate. Example 25 includes the subject matter of example 24, further specifying that the sensing element and the at least one spacer of each of the sensing elements are defined within the same conductive layer and the same spacer, respectively. Example 26 includes the subject matter of any of Examples 24-25, further specifying that each sensor of the plurality of sensors further includes first, second, and intermediate conductive pads defined in the same conductive layer and coupled to the sensing element, and a resistor defined in the same conductive layer and coupled to the sensing element and a selected one of the first, second, and intermediate conductive pads. Example 27 includes the subject matter of any of Examples 24-27, further specifying that the substrate is a flexible substrate. Example 28 includes the subject matter of any of Examples 24-26, further specifying that at least some of the resistors in the sensors have different shapes and at least some of the sensing elements in the sensors have different shapes. In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are only preferred and should not be construed as limiting the scope of the present disclosure. All that comes within the scope and spirit of the following claims is claimed as the invention.

Claims

1. A first segment and a second segment that are symmetrically arranged with respect to a first axis and each formed as a substantially rectangular spiral, A first strip electrically coupled to one end of the first segment and one end of the second segment, A second strip electrically coupled to the other end of the first segment and the other end of the second segment, A first end electrically coupled to the first strip and provided on the first axis, A second end electrically coupled to the second strip and provided on the first axis, and including: The first end and the second end are fixed to a substrate, The first segment, the second segment, the first strip, and the second strip are provided spaced apart from the substrate, A sensing element in which the shape of the first segment and the shape of the second segment are symmetric with respect to the first axis.

2. The sensing element according to claim 1, wherein each of the line widths of the first segment and the second segment is narrower than each of the line widths of the first strip and the second strip.

3. The sensing element according to claim 1, wherein a first resistance from the first end to the first strip and a second resistance from the second end to the second strip are substantially equal.

4. The sensing element according to claim 1, wherein a third resistance from the first strip to the one end of the first segment and a fourth resistance from the second strip to the other end of the first segment are different.

5. The sensing element according to claim 1, wherein a fifth resistance from the one end to the other end of the first segment is greater than any of the first to fourth resistances.

6. The sensing element according to claim 1, wherein the substrate is a flexible substrate.

7. The sensing element according to claim 1, wherein the substrate is polyethylene terephthalate.

8. Further comprising a resistance element electrically coupled to the sensing element according to any one of claims 1 to 7, A sensor operable to heat the sensing element with a current supplied to the sensing element via the resistance element.

9. A sensor array having a plurality of the sensors according to claim 8.

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