Nanomechanical thermometry sensor

Abstract

A sensor includes a detection assembly including a first substrate with a first opening defined therein. A detection membrane extends across the first opening. A sample assembly includes a second substrate with a second opening defined therein. A sample membrane extends across the second opening. The detection assembly and the sample assembly are arranged in a stacked configuration to form a chamber between the sample assembly and the detection assembly. The sample membrane is configured for thermal contact with a sample for measurement.

Description

NANOMECHANICAL THERMOMETRY SENSOR CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US Provisional Patent Application No. 63 / 579,388, filed on August 29, 2023, and which is incorporated by reference herein in its entirety. BACKGROUND

[0002] Investigation of thermal transport phenomena at the micro or nano scale requires sensors with the resolution to measure such phenomena. Various types of high-resolution temperature sensors have been previously developed for investigation the micro or nano scale thermal transport including quantum dots, thermopiles, thermistors, resistance temperature detectors (RTD), micro-cantilevers, and optical sensors.

[0003] Prior optomechanical devices are used an interferometric system in a high vacuum environment and require an external laser to pump the cavity. The detection limit from these devices is quantified by the Allan deviation, intrinsic dissipation in SiN membranes, radiation pressure due to illumination of the membrane with a laser, and the dependency of resonant frequency on the coordinates for the focused lase spot on the membrane. Such devices are disclosed in Ferreiro-Vila, E. et al. “Micro-Kelvin resolution at room temperature using nanomechanical thermometry,” ACS Omega 6, 23052-23058 (2021); Serra, E. et al. “Silicon-nitride nanosensors toward room temperature quantum optomechanics,” J. Appl. Phys. 130 (2021); Sansa, M. et al. “Frequency fluctuations in silicon nanoresonators,” Nat. Nanotechnology 11, 552-558 (20216); Ekinci, K., et al. “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Applied Physics 95, 2682-2689 (2004); Singh, R. & Purdy, T.P. “Detecting acoustic blackbody radiation with an optomechanical antenna,” Phys. Rev. Lett. 125, 120603 (2020); and Naserbakht, S. & Danta, A. “Squeeze film pressure sensors based on SiN membrane sandwiches,” Sensors Actuators A: Phys. 298, 111588 (2019), each of which are incorporated by reference in their entireties.

[0004] US Patent No. 2,557,096, to M. J.E. Golay and entitled “Radiation Detecting Device” is also incorporated herein by reference. The ‘096 patent discloses a radiation absorbing membrane and a flexible mirror which deflects in response to changes in pressure. An opticalsystem measures the deflection of the flexible mirror in relation to the radiation absorbed by the membrane. BRIEF DISCLOSURE

[0005] Measuring local temperature at the micro or nano scale requires high-resolution thermometry due to the ultra-low thermal transport. A thermometry sensor with sub micro-Kelvin (~10-8K) to nano-Kelvin (~10-9K) resolution is disclosed herein. A silicon nitride (SiN) membrane is measured for deflection. The resulting heat output resolution of the disclosed device is sub nano- Watt and therefore suitable for measuring thermal transport at the micro and nano scales.

[0006] An example of a sensor includes a detection assembly including a first substrate with a first opening defined therein. A detection membrane extends across the first opening. A sample assembly includes a second substrate with a second opening defined therein. A sample membrane extends across the second opening. The detection assembly and the sample assembly are arranged in a stacked configuration to form a chamber between the sample assembly and the detection assembly. The sample membrane is configured for thermal contact with a sample for measurement.

[0007] In examples of the sensor, a seal is between the detection assembly and the sample assembly. At least one of the detection membrane and the sample membrane is silicon nitride (SiN). The first substrate includes a third opening opposite the first opening and the third opening is larger than the first opening. The second substrate includes a fourth opening opposite the second opening and the fourth opening is larger than the second opening. The detection membrane is deposited on the first substrate and the first and third openings are etched through the first substrate defining first angled sidewalls between the first opening and the third opening. The sample membrane is deposited on the second substrate and the second and fourth openings are etched through the second substrate defining second angled sidewalls between the second opening and the fourth opening. A sample well is defined within the second substrate by the sample membrane and the second angled sidewalls. The second opening has a smaller area than the third opening. The first opening has a smaller area than the second opening.

[0008] In additional examples of the sensor, the detection membrane has a thickness of 20- 25 nm and the sample membrane has a thickness between 10-30 times the thickness of the detection membrane. A resistive heater is provided on the sample membrane. A current source is configuredto provide an AC and a DC bias current to the resistive heater, whereby the bias current through the resistive heater provides a thermal bias and an off-resonance frequency bias to the chamber. A channel extends into the chamber. The channel is coupled to a valve. The valve is operable to open the chamber to an environment exterior of the chamber. A microfluidic channel positioned on the sample membrane. The microfluidic channel is configured to receive a sample and place the sample in contact with the sample membrane. The microfluidic channel is constructed of polydimethylsiloxane (PDMS). A target is positioned on the sample membrane and the target includes graphene and polymethyl methacrylate (PMMA).

[0009] Further examples of the sensor include a detector arranged relative to the detection membrane. The sample membrane is configured to for thermal transport of heat from the sample into the chamber causing a change in pressure within the chamber and displacement of the detection membrane. The detector is configured to provide an indication of the displacement of the detection membrane. A controller is configured to receive the indication of the displacement from the detector and to calculate a thermal change in the chamber from the measured displacement. A metal layer is over the detection membrane. An electrode is spaced apart from the metal layer. The electrode and the metal layer form a capacitor. A capacitance to digital converter measures a change in capacitance between the metal layer and the electrode. The change in capacitance is indicative of the displacement of the detection membrane. An optical sensor is positioned relative to the detection membrane. The optical sensor is configured to measure a displacement of the detection membrane.

[0010] An example of a sensor system includes a detection assembly and a sample assembly. The detection assembly includes a first substrate with a first opening defined therein and a detection membrane extending across the first opening. The detection membrane includes silicon nitride (SiN). The sample assembly includes a second substrate with a second opening defined therein; and a sample membrane extending across the second opening. The sample membrane includes silicon nitride (SiN). The sample membrane is configured for thermal contact with a sample for measurement and is 10-30 times a thickness of the detection membrane. A chamber is defined between detection membrane and the sample membrane by the detection assembly and the sample assembly arranged in a stacked configuration. A seal is between the detection assembly and the sample assembly. A resistive heater is on the sample membrane. A current source is configured to provide an AC and a DC bias current to the resistive heater. Thebias current through the resistive heater provides a thermal bias and an off-resonance frequency bias to the chamber. A detector is arranged relative to the detection membrane. The sample membrane is configured for thermal transport of heat from the sample into the chamber, causing a change in pressure within the chamber and displacement of the detection membrane. The detector is configured to indicate the displacement of the detection membrane. A controller is connected to the detector. The controller receives a signal from the detector and is configured to calculate a thermal change in the chamber from the displacement of the detection membrane.

[0011] A further example of the sensor system includes a vacuum flask at least partially surrounding the detection assembly and the sample assembly. The vacuum flask is configured to environmentally isolate the chamber. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a sectional view of an example of a thermometry sensor.

[0013] Figures 2A and 2B depict the thermo-mechanical operation of the sensor.

[0014] Figure 3 is a schematic diagram of example features of the sensor.

[0015] Figure 4 is a schematic diagram of a sensing system incorporating the sensor.

[0016] Figures 5A-C are schematic examples of configurations of the sensor.

[0017] Figures 6A and 6B are system diagrams of the thermometry sensor.

[0018] Figure 7 is a graph of the thermal noise of a sensor membrane.

[0019] Figure 8 is a graph of membrane displacement as a function of surface temperature difference. DETAILED DISCLOSURE

[0020] Measuring local temperature at the micro or nano scale requires high-resolution thermometry due to the ultra-low thermal transport. A thermometry sensor with sub micro-Kelvin (~10-8K) to nano-Kelvin (~10-9K) resolution at room temperature and 1 atm is disclosed herein. High-resolution thermometry seeks to resolve the smallest heat flow output by both minimizing thermal conductance, Gth, and achieving temperature resolution of the sensor, ΔTth, via Q̇res = Gth × ΔTth. The sensors provided herein exhibit high-resolution thermometry suitable for measuring less than nano-watt heat currents for investigation of nanoscale heat transport. Furthermore, thesensors provide a comparatively large temperature sensing area for ease of target placement and sample acquisition.

[0021] Figure 1 is a sectional view of an example of the thermometry sensor 10 as disclosed herein. The sensor 10 is exemplarily constructed of two components, a detection assembly 40 and sample assembly 50. The detection assembly 40 includes a thin detection membrane 12 supported on a silicon wafer 16. The detection membrane 12 is exemplarily constructed of silicon nitride (SiN). SiN membranes may be constructed by low-pressure chemical vapor deposition (LPCVD) to provide a uniform membrane of nanoscale thickness. An LPCVD SiN film can be constructed to meet tensile / compressive residual stresses with an overall flat / wrinkle-free membrane. SiN membranes are further chemically inert and bio-compatible which facilitates the use of the disclosed sensor with cells, and chemicals to be positioned directly on or in contact with the sensor. In an example, the membrane 12 has a thickness of 20nm, while in other examples the thickness of the membrane is 20-25nm or <25nm. The detection membrane 12 is supported on the silicon wafer 16. Due to the chemical etch process described herein, the silicon wafer 16 exhibits the characteristic {111} crystal planes forming angled silicon side walls 18. The detection membrane 12 is suspended across a detection opening 20 in the silicon wafer 16. The side walls 18 angle away from the detection opening 20 to an opposite opening 24, which is necessarily larger than the detection opening 20.

[0022] The sample assembly 50 includes a sample membrane 22. The sample membrane 22 is similarly constructed of SiN as the detection membrane 12, but is substantially thicker e.g. at least 10x than the detection membrane 12. In examples, the sample membrane 22 is 500nm, or exemplarily 25x the thickness of the detection membrane 12. In other examples, the sample membrane 22 is 10-30x the detection membrane thickness, 10-25x, 15-25x, 10-20x, or 20-25x, or other ranges as will be recognized based upon the present disclosure.

[0023] The sample membrane 22 is supported on a silicon wafer 25 and is constructed in a similar manner as described with a chemical etch process. The sample membrane 22 is suspended across a sample opening 21. Side walls 27 of the silicon wafer 25 exhibit the characteristic angle away from the sample opening 21 to an opening 23.

[0024] The detection assembly 40 and the sample assembly 50 are secured together to form the sensor 10. The detection assembly 40 and the sample assembly 50 are exemplarily secured with a seal 31, exemplarily formed of epoxy. The epoxy creates a seal 31 between the detectionassembly 40 and the sample assembly 50. The combination of the detection assembly 40 and the sample assembly 50 define a chamber 14 between the respective detection membrane and the sample membrane 22. Apart from the further details disclosed herein, the seal 31 isolates the chamber 14 to prevent inflow of gas. suspended over a chamber 14. While the chamber 14 may be described herein as an air chamber, it will be recognized that in examples, chamber 14 may be filled with another gaseous composition besides air. As will be described in further detail herein, the sample / target is placed in contact with the sample membrane 22. Heat associated with the sample / target increases the pressure within the chamber 14, causing the detection membrane 12 to bulge away from the chamber 14. This deflection is measured and the heat from the sample / target calculated therefrom.

[0025] The sensor 10 of Figure 1 is exemplarily constructed using standard micromachining techniques. In examples, the sensor 10 is constructed using cleanroom nanofabrication techniques including optical lithography, reactive ion etching (RIE), and anisotropic wet silicon etching. A 20nm SiN membrane is conformally deposited by LPCVD on a 725 µm silicon wafer 16 with an exemplary resistivity of 10 Ω-cm, for example as available from Rogue Valley Microdevices. It will be recognized that the wafer 16 may have other compositions including but not limited to germanium. The silicon wafer is etched from the side opposite the SiN membrane in a potassium hydroxide solution (KOH, 30% w / w) at 60 C for 28 hours. The silicon etch is bounded by the characteristic crystal planes forming the angled silicon side walls 18 of the chamber 14. With the underlying silicon etched away, the detection membrane 12 is suspended flat across the detection opening 20 due to the low tensile residual stress of the SiN film. In an example, an 11 MPa tensile stress was measured across the membrane.

[0026] The sample membrane 22 is constructed in a similar manner as the detection membrane 12, exemplarily on a same silicon wafer as described above. A 500nm SiN membrane is conformally deposited by LPCVD on a 725 µm silicon wafer 25 with an exemplary resistivity of 10 Ω-cm, for example as available from Rogue Valley Microdevices. The sample membrane 22 is secured across the sample opening 21. At an exemplary thickness of 500nm, the sample membrane 22 is exemplarily 25x thicker than the detection membrane 12. In other examples, the sample membrane 22 is 10-30x the detection membrane thickness, 10-25x, 15-25x, 10-20x, or 20- 25x, or other ranges as will be recognized based upon the present disclosure. Due to the comparatively large thickness disparity between the detection membrane 12 and the samplemembrane 22, the detection membrane 12 is similarly e.g. 10x, 20x, 25x, or more times more sensitive to deflect in response to changes in temperature as described herein compared to the sample membrane 22. This difference in deflection sensitivity concentrates the thermo-mechanical effects with the detection membrane 12, as described further herein.

[0027] Figures 2A and 2B provide a general example of the operation of the sensor 10. As discussed, above, the sensor 10 includes a detection membrane 12 and a sample membrane 22, defining a chamber 14 therebetween. The sample membrane 22 is configured to be placed in thermal contact with the target / sample to be evaluated with the sensor 10. In examples, the sample may be biological, chemical, mechanical, electromechanical, or others. In examples, the sample membrane 22 may be constructed comparatively large in comparison to the sample to be detected. In an example, the sample membrane may be 1mm x 1mm square (1000 µm x 1000 µm), while a single cell for evaluation is about 10 µm x 10 µm. In this case, the cell has an area of 100 µm2while the sample membrane has an area of 1,000,000 µm2. The sample membrane 22 may thus be configured to have a surface area about 10,000x that of the target sample. It will be recognized that the sample membrane 22 may also be used with larger samples, and may be less than 10,000x the surface area, or may be 1x-10,000x the surface area. In still further examples, the surface area of the sample membrane may be less than 1000x of the sample. The sample membrane 22 may thus be on the order of 1x, 10x, 100x, 1000x, or 10,000x the surface area of the intended sample / target. The sample membrane 22 thus may provide a large target for the placement of the target sample. In still further examples as will be explained herein the sample may be within a liquid or solution which is in contact with the entire surface area of the sample membrane, while in other examples, the sample may be confined to contact with only a portion of the sample membrane, for example with the use of microfluidic channels and / or an energy absorbing target.

[0028] As will be explained in further detail herein, there is variation in the arrangement and construction of the components of the sensor 10. Generally, but not limiting, the detection membrane 12 is smaller in surface area than the sample membrane 22. This relationship maximizes the surface area between the sample in thermal contact with the sample membrane 22 and the chamber 14, while minimizing the surface area of the detection membrane 12 causing increased deflection response to the pressure changes described herein. Thermal transport through the sample membrane 22 from the sample heats the isolated gas within the chamber 14 (e.g. air). For this reason, a sample membrane 22 with thermally conductive properties, including, but not limited tomembrane thickness (e.g. decrease in membrane thickness increases thermal transport therethrough) is suitable in the presently disclosed arrangement. As noted above, the comparatively large surface of the sensing membrane compared to a potential sample size can accommodate a sample at any location on the membrane and provide the proper thermal contact between the sensing element and the nano / microscale samples.

[0029] As represented by Figs. 2A and 2B, when heat, ΔQ, from the sample is applied to the chamber 14, for example through the 500nm thick membrane, the temperature of the air in the chamber 14 is increased by the following equation wherein n is the number of moles of air in the air chamber and Cv is the molar heat capacity at constant volume of the air. ΔT =^^ ^^^(Eq. 1)

[0030] From the ideal gas law for a 14bounded detection membrane 12, sample membrane 22, and sealed by with the seal 31, the an increased temperature ΔT results in an increased pressure, Δp, within the chamber 14 and can be written in the following Eq. 2 where p is pressure, V is volume, R is the ideal gas constant, ^ is the density of the gas, and Rsis the mass specific gas constant. ^^ =^^^^ ^= ^^^ΔT (Eq. 2)From plate theory, two differentthe measured deflection in the detection membrane 12. The total strain energy in a rectangular membrane is the summation of the strain energy from plate bending and the elastic strain energy from internal tensile stresses. When the deflection is smaller than the membrane’s thickness, the majority of the strain energy contribution is from the plate bending term, and a plate approach should be applied to calculate the ΔT. When the deflection is larger than the membrane’s thickness, the membrane approach should be used, as is provided in further detail. The plate theory equation for ∆T is provided by the following Eq.3, where ξ is 16 / 0.00126, a is half of the square membrane’s length, D is the flexural rigidity, ρ is the density of the gas, and Rs is the mass-specific gas constant. ∆T = ξ (D δ / ρRsa4) (Eq. 3)

[0031] The equation for the membrane theory calculation is provided in further detail herein. The deflection of the tensile stressed detection membrane 12 under the applied pressure is represented by the following Eq. 4. In this equation Δp is the increase in pressure in the chamber 14, δ is the center deflection of the membrane, a is one half of the membrane’s edge length, t isthe membrane thickness, E is Young’s modulus, σ is the stress in the membrane, and v is the in- plane Poisson’s ratio. Eq.3 may be approximated as Eq.5 since the second term of Eq.4 is orders of magnitude smaller than the first term under standard configuration and operation conditions of the sensor 10. For example, E ~ 290 GPa, σ ~ 10MPa – 300MPa, a ~ 0.5 mm, and δ < 100 µm.

[0032] From Eq. 5 theΔF is the total force experienced by the membrane. ^^ ^^,^= ^= 4^^^σ (Eq. 6)

[0033] Combiningcan be written according to Eq. 7. Thus according to Eq. 7, the temperature change in the air chamber ΔT can be estimated by measuring the deflection δ of the detection membrane 12. In examples, the dynamic range of the sensor 10 is about 10°K from a baseline equilibrium, ranges may include but are not limited to 0-15°K, more exemplarily 0-10°K or less than 10°K. Since the dynamic temperature range of the device is within this range, any change in parameters such as the density of the gas (^) or the density of the gas or the mass specific gas constant the mass specific gas constant (^_^) will be negligible for any variation in the composition of the gas in the chamber 14. ΔT = ^! & ^ "^ ^$δ = ',(δ (Eq. 7)

[0034] The springmembrane is needed to determine the resolution of the temperature measurement based upon the measured deflection δ according to Eq. 7. Therefore, once the deflection is measured, an equation is selected for the calculation of ΔT based upon the size of the deflection versus the thickness of the detection membrane 12. If the measured deflection is less than the thickness of the detection membrane, then the plate theory as represented by Eq.3 is used. If the measured deflection is greater than the thickness of the detection membrane, then the membrane theory as represented by Eq. 7 is used. It will thus be understood that at the smallest ΔT resolutions, the plate theory (Eq. 3) may be used.A summary of the stiffness of the 20 nm thick membranes using three different methods is presented in the table below for various example sizes of the detection membrane 12 in thesensor 10.

[0035] The value ka,dwas calculated from Eq. 6 with a distributed load. The value kωwas calculated from Eq. 8 below with meff / mo = 0.62 using resonant frequencies measured with the Polytec MSA-100-3D. The value kA,ωwas calculated from ANSYS modal analysis using Eq. 8 with meff / mo= 0.62. The stiffness of the membrane is used to calculate the minimum temperature resolution of the device as provided in Eq. 7. The natural frequency of the membrane resonator can be expressed in terms of its stiffness, kω, and an effective mass (meff) as: *+ = 2-.^,^ ^ & / 0 (Eq. 8)

[0036] The sampleit advantageous for micro / nanoscale thermal transport studies. The heat flow resolution of the sensor 10 depends on the thermal conductance Gth through the sample membrane 22 to the chamber 14. The temperature resolution of the device can be obtained by measuring the thermal conductance. As discussed above, either the plate or the membrane approach depending on the δ should be used. The measured Gthof the device from the step power response was 2810−3 W / K and the smallest heat power that the membrane device can resolve was 0.21 nW and δ is 0.74 nm. Since the measured δ was smaller than the thickness of the membrane (20 nm), the plate approach was applied to calculate ∆Tres. Using δ = 0.74 nm, the corresponding ∆T is 5.6010−9K. The Gthis 37.5 10−3W / K, which agrees with the measured Gth of the device (28 10−3W / K). The thermal conductance depends on the geometry and configuration of the device, for example, in the manners as described above. Thermal and measurement noise present challenges to the measurable displacement of the detection membrane 12 and resulting temperature measurement. The detection membrane as disclosed herein may achieve a temperature resolution of ~10-8K to ~10-9K if theenvironmental noise is limited to less than 1pm. It is believed that an optimized configuration may reach a potential resolution of ~10-12K.

[0037] Figures 3-6 all provide additional features of the sensor 10. For the sake of clarity and discussion, these are presented in separate figures, but it is recognized that the features as shown in each of these figures may be used alone or in combinations of the features described herein are contemplated for implementation of the disclosed sensor. Like reference numerals are used within these figures to identify like components, showing that these are considered to be optionally combined features of the disclosed sensor. As shown herein, such combinations may be adapted for particular use cases, although all are recognized to be within the scope of the presently disclosed sensor. Some or all of these features as disclosed herein may be used in combination with other features as disclosed herein to arrive at examples of the disclosed sensor.

[0038] Figure 3 depicts an example of the sensor 10, for example as described above, and further with two optional sensor components which when used alone or in combination with other features of the sensor 10, may improve performance and resolution thereof. The sensor 10 exemplarily includes a microchannel 42 that connects the chamber 14 exterior of the sensor 10. When the sensor is fabricated at room temperature and 1atm, the membrane can be either concave or convex due to the pressure (temperature) of the gas in the chamber 14 during fabrication being different from the environment when the measurement is performed. The microchannel 42 through or adjacent to the silicon wafer 16 connects the chamber 14 to the environment outside the sensor 10. The microchannel 42 may be fabricated in the same manners as described above with respect to the detection assembly 40. The microchannel 42 is connected to a valve 44 which is operable to open or close the microchannel 42 to the environment. The valve 44 is communicatively connected to a controller 36 which is operable to provide a control signal to the valve 44 upon which the valve 44 opens or closes. Operation of the valve 44 and the microchannel 42 to the open configuration enables the chamber 14 to reach an equilibrium with the environment outside the sensor 10. This equilibrium should remove any convex or concavity to the detection membrane 12 prior to measurement.

[0039] The sensor 10 may further include a microfabricated resistance heating element 46. As will be described in further detail herein, a manufacturing solution places the microfabricated resistance heating element 46 on the sample membrane 22. The heating element 46 is exemplarily a serpentine shape along a 100 µm by 100 µm area with a 5 µm wide and 80 nm thick nickel filmon the sample membrane 22. The controller 36 is exemplarily operable to deliver, e.g. along a lead 48, which may be a microfabricated wire, AC and DC current to heating element 46. The controller 36 exemplarily operates to deliver the DC bias current to provide a steady-state heating while the AC bias current serves to apply a minute oscillating power to the chamber 14. The frequency of the AC bias is exemplarily 3Hz. These bias heat and frequency operate to create a baseline from which the deflection measurements can be made and improve the overall signal to noise ratio of the sensor 10. In an example, a Keithley 6221 DC & AC current source may be operated by the controller 36 to provide the above-described bias current.

[0040] As described above, a heat and / or vibration bias may improve overall signal to noise ratio of the sensor 10. When the device and the temperature are both modulated, the sensor 10 provides the highest noise equivalent temperature (NET) resolution. An off-resonance vibration of 3Hz provides a ΔPvibration << ΔPtemperature and the modulation improved the temperature resolution achieved over DC modulation.

[0041] Figure 4 depicts an example of a sensor 10 with additional environmental isolation. Since the sensor 10 is configured for measuring small changes in temperature (and pressure), additional environmental isolation can protect the sensor 10 from any ambient temperature or pressure changes. The sensor 10 is exemplarily located within a vacuum flask, exemplarily, but not limitingly, a double-walled dewar 52. The dewar 52 defines a vacuum chamber 54 between two side walls 56A, 56B. A lid 58, exemplarily constructed from polycarbonate, is connected over the top of the dewar 52 with a seal 60, exemplarily of silicone. The sensor 10 is connected to the underside of the lid 58, and exemplarily set off from the underside of the lid 58 by stanchions 62. This leaves a space for the detection membrane 12 to outwardly deflect for detection. A bore 64 extends through the polycarbonate and is centered on the detection membrane 12. A glass cover 66 is across the bore 64 on the outside of the lid 58. The bore 64 provides an unobstructed area for a measurement laser 68 as described in further detail herein, to pass for measurement of the detection membrane 12. However, in other examples, other manners of membrane deflection detection may be used and the bore 64 and glass cover 66 may not be needed. This arrangement provides additional environmental isolation to reduce environmental temperature and pressure noise during measurement using the sensor 10.

[0042] Figures 5A-5C depict the sensor 10 in various configurations. As will be recognized, manufacturing places constraints on the manners in which the components of thesensor 10 may be made and arranged. Because both the detection assembly 40 and the sample assembly 50 are constructed from etching the silicon wafer from the SiN membrane secured thereon, additional components are generally deposited on the SiN membrane rather than between the SiN membrane and the silicon wafer. Therefore, additional components, including but not limited to the heating element 46 and leads 48 are deposited on the sample membrane 22 on a side opposite from the silicon wafer 25. It will be recognized that any of the examples of sensor 10 of Figs. 5A-5C are within the scope of the present disclosure and can be combined with any of the features as described with respect to Figs. 3-6.

[0043] Figure 5A discloses an arrangement of the sensor 10 for detection of radiation, for example IR radiation. A target 70, exemplarily comprising graphene is deposited on the sample membrane 22. The target 70 is exemplarily constructed of a combination of graphene and polymethyl methacrylate (PMMA). The radiation (e.g. IR radiation ) passes through the sample membrane 22, striking the target 70 which absorbs the radiation and converts the radiation into heat, raising the temperature (and pressure) within the chamber 14, causing the detection membrane 12 to bulge away from the sample membrane 22. In a still further example, the target 70 may be provided with the 3Hz signal to provide the vibratory component for NET improvement. Fig. 5A further depicts that the detection assembly 40 is stacked on the sample assembly 50, with the silicon wafer 16 on the sample membrane 22. The detection membrane 12 is exposed for detection in the direction of arrow 72. Fig.5A also exemplarily depicts that the construction of the detection assembly 40 and the sample assembly 50 may be such that the detection membrane 12 and the sample membrane 22 are generally the same size and shape. It will be recognized that since the sample opening 21 of the sample assembly 50 is smaller than the opposite opening 24 of the detection assembly 40, that the sample opening 21 exemplarily defines the effective size of the sample membrane 22. Any of the sensors 10 or combinations thereof may be constructed in this relationship between the sample assembly 50 and the detection assembly 40.

[0044] Figure 5B depicts an example of a sensor 10 wherein the sample assembly 50 is configured to provide a sample well 74. The structural arrangement of the sensor 10 in Fig. 5A and 5B are the same physical arrangement with the detection assembly 40 stacked on the sample assembly 50, with the silicon wafer 16 on the sample membrane 22. The sensor 10 of Fig. 5B is flipped over, so that the angled side walls 27 of the sample assembly 50 define a sample well 74 through the opening 23 onto the sample membrane 22 on a side opposite the chamber 14. A sample,for example a chemical or biological sample is in thermal contact with the sample membrane 22 for transport of the heat from the sample to the chamber 14. The detection membrane 12 is exposed for detection in the direction of arrow 72. Fig.5B further depicts an example wherein the effective area of the sample membrane 22 is larger than the effective area of the detection membrane 12. Any of the sensors 10 or combinations thereof may be constructed in this relationship between the sample assembly 50 and the detection assembly 40. As an example, this arrangement may provide benefits of maximized area through the sample membrane 22 for thermal transport into the chamber 14, with a smaller area of the detection membrane, resulting in increased deflection in response to volume change within the chamber 14. It will also be recognized that the sensor 10 may further be used as shown in Fig. 5A / 5B by placing the sensor in the orientation as shown in Fig. 5A and placing the sample in the sample well 74 in the form of a chamber defined by the sample membrane 22 and the angled side walls 27, while remaining within the scope of the present disclosure.

[0045] Figure 5C depicts an example of a sensor 10 wherein the sample assembly 50 is further configured with a microfluidic channel 76 for example within polydimethylsiloxane (PDMS). The microfluidic channel 76 is open to the sample membrane 22, and is thus operable to place a sample in thermal contact with the sample membrane 22. In an example, the microfluidic channel 76 may be dimensioned with a diameter suitable to pass a single biological cell therethrough at a time, this provides an arrangement by which single-cell thermal transport properties may be investigated and measured using the sensor 10. The microfluidic channel 76 may be used to pass individual cells therethrough sequentially. Fig. 5C further depict an example where the chamber 14 is defined between the sample membrane 22 and the detection membrane 12. Because the microfluidic channel 76 is on the sample membrane 22, the detection membrane is arranged to the opposite side of the sample membrane 22 from the microfluidic channel 76. In this arrangement, the sample assembly 50 is stacked on the detection assembly 40 with the silicon wafer 25 on the detection membrane 12. The detection membrane 12 is exposed for detection in the direction of arrow 72. Fig. 5C further depicts an example wherein the effective area of the sample membrane 22 is smaller than the effective area of the detection membrane 12. In an example, this arrangement may be suitable as the microfluidic channel 76 already confines the placement and contact of the sample with the sample membrane 22. Any of the sensors 10 orcombinations thereof may be constructed in this relationship between the sample assembly 50 and the detection assembly 40.

[0046] The sensor 10 as described herein produces a membrane displacement that is correlated to a temperature change induced from a target sample. Figures 6A and 6B depict non- limiting examples of systems arranged to measure the displacement of the detection membrane and to calculate the corresponding temperature change. It will be recognized that the detectors as shown and described in Figs. 6A and 6B may be used with any of the configurations of sensor 10 as described above with respect to Figs.5A-5C. The detectors as shown and described in Figs.6A and 6B are also to be recognized as being used in conjunction with the optional features as shown in Fig. 3 and / or in the arrangement as shown in Fig. 4 as such features are recognized as reducing noise and / or improving sensor resolution.

[0047] Figure 6A depicts an example of an arrangement for a capacitance-based measurement of the detection membrane displacement. A metal layer 30 is positioned on the detection membrane 12. The metal layer 30 may, for example, be evaporated or sputtered onto the detection membrane 12. An electrode 32 is positioned over the metal layer 30 with a suitable spacing to form a capacitor between the metal layer 30 and the electrode. In an example, the initial spacing between the metal layer 30 and the electrode 32 may be 100 µm. A suitable ADC 34 is positioned between the capacitor and a controller 36. In an example, an AD774624-bit, 2 channel capacitance to digital converter available from Analog Devices may be used to measure the capacitance as it varies due to the distance between the metal layer 30 and the electrode 32. Such ADC provides a capacitance resolution of 4aF which corresponds to a ~4nm displacement resolution. This capacitance measurement is provided to the controller 36 which converts the capacitance to a displacement and subsequently calculate the temperature change, for example, using Eq. 6 described above.

[0048] Fig. 6B depicts an example of optical measurement of the displacement of the detection membrane 12. An optical detector 38 is positioned relative to the detection membrane 12. Examples of optical detectors include, but are not limited to the Polytec MSA-100-3D and the Keyence CL-3000. While both of these optical systems can exhibit greater displacement measurement resolution, e.g. 1pm or better resolution. These systems add additional cost and complexity over the capacitive solution described with respect to Fig. 6A, while the noted environmental noise may limit the effectiveness of such increased resolution in certain use settings.In an example, the optical detector 38 as shown in Fig. 6B may be used in conjunction with the heat and / or frequency bias as shown and described with respect to Fig.3. In such an arrangement, a Keithley 2400 or other voltage sensor (not depicted) may further be used to measure the voltage drop across the microheater / target / resonator and provide this measured voltage drop to the optical detector as a reference voltage signal.

[0049] The sensor and system as described herein may be used in a variety of applications. These applications include, but are not limited to metabolic temperature measurements, calorimeter for chemical reactions on a nL scale, iodine clock cycle reaction measurements, temperature changes in delayed reactions, single cell temperature sensor, infra-red (IR) energy detector (e.g. bolometer) using an IR sensitive coating on the backing membrane, or a pressure sensor with µPa resolution. One such example may include investigating the exothermic processes during yeast life cycles including, but not limited to metabolic activity. Another microscale temperature sensor application is to measure temperature changes such as that due to a single-cell metabolic activity of micro / nanoscale samples and nanoscale material chemical interactions. In current solutions, placing a sample on the sensor to ensure the proper thermal contact between the sensor and sample can be a challenge. A precision micro-manipulator with bulky optics is typically employed to place a sample on the sensor sensing element. In the presently disclosed sensor, the sample can be placed in the sample chamber 26 and the entire area detection membrane at the chamber 14 is the sensing element.

[0050] Micro / nanoscale sample(s) can be placed in the sample chamber 26 or on the sample membrane 22 without any special or bulky aids. When the sensing element (membrane) faces upward, gravity assists to ensure the thermal contact between the sample(s) and the sensing element. The sensor as disclosed herein may further be used as an ultra-high resolution temperature sensor for chemical sensors, calorimeters, and biosensors, it can be also used as a bolometer to detect near infrared (NIR), mid infrared (MIR) and far infrared (FIR). Specific IR absorption materials can be coated on the sample membrane 22. The specific absorption film absorbs IR and converts it to heat causing the 20 nm thick membrane to deflect. The absorption film can increase the sensitivity and selectivity.

[0051] The response time of the sensor depends on the thermal time constant of the air chamber, which is proportional to the volume of the air chamber. Reducing the space between the thick membrane and thin membrane can reduce the thermal time constant of the device andincrease the bandwidth of the device. To achieve a desired bandwidth, the two membrane sides can face each other with a space of desired thickness. The space between the membrane should be chosen to accommodate the large deflection of the thin membrane, which can be as large as a few tens of micrometer.

[0052] When the device is fabricated at room temperature and 1 atm, the membrane can be either concave or convex due to the pressure (temperature) of the sealed air chamber formed during fabrication being different from the environment when the measurement is performed. Therefore, the air chamber needs to be in equilibrium with the environment, limiting the dynamic range of temperature measurement. A microchannel and valve can be integrated to create an equilibrium between the air chamber and the environment, which adds complexity to the sensor system.

[0053] A mechanical temperature sensor with a temperature resolution of sub 1 μK is presented. The ultimate detection limit of the 20 nm thick membrane sensor is suitable for nano / microscale heat transport studies. The theoretical temperature resolution depends on stiffness of the membrane. The analysis and measurements provided in the experimental results herein delineate the contributions of both the stiffness variations of ultra-thin membranes and the thermal noise resulting from the environment to the temperature regulation of the device. Our work shows that it is possible to resolve temperature changes well below 1 μK with the deflection of ultra-thin membrane-based thermometry. By carefully minimizing the thermal conductance of the device and achieving a temperature resolution of ∼10−7K, a heat-current resolution of ∼10−11W can be achieved. The heat flow resolution achieved by the 20 nm thick SiN membrane device is suitable for probing nano / microscale thermal transport.

[0054] The ultimate heat flow resolution of the sensor 10 depends on the thermal conductance (GTh) between the thermally isolated region and the thermal reservoir and the resolution (TRes) of the thermometer. The thermal conductance depends on the geometry and configuration of the device, including the detection membrane 12. The lumped thermal conductance of the device is measured by a step power response, which is exemplarily ~28 x 10-3W / K at 300K (e.g. room temperature). Once the thermal conductance is determined, the resolution of heat flow is determined by the temperature resolution of the device. The noise equivalent temperature (NET) represents the temperature resolution of the membrane and is based upon Eq 6 above.NET ^ ΔT^78 ^ ^ !^"^#^$ δ^9:87 (Eq. 9)

[0055] The δnoisebe obtained from the powerof the 0.5 mm x 0.5 mm membrane. PSD in m2 / Hz with a line of fit (y = αxβ+ γ) overlaid. The inset shows the PSD in dB with respect to 1 m2 / Hz. Fig. 8 is a graph the membranedisplacement as a function of the surface temperature difference of an applied Peltier device. The inset depicts the displacement of the membrane, measured by a Polytec MSA-100-3D, as a function of thermal actuation frequency. A 25 mHz electrical current is applied to the Peltier device causing the Peltier surface temperature oscillation.

[0056] The exemplary coefficients in the line of fit in Fig. 7 are α = 1.431 x10-19, β = - 2.989, and γ = 3.37. Using this fit, the δnoiseis 1.43x10-9m at 300K in a typical wide open lab environment. It is recognized that a lower δnoisecan be achieved with a thermally and mechanically isolated environment. Using this value of δnoise the NET is calculated to be 6.5x10-6K, which is suitable for studying nanoscale thermal transport and having a NET an order of magnitude higher resolution than the highest temperature resolution of a micro-RTD achieve by modeling both temperature and the sensing current (30 ± 8x10-6K).

[0057] An example of the sensor includes a detection assembly includes a first substrate with a first opening defined therein, a detection membrane extending across the first opening; and a sample assembly includes a second substrate with a second opening defined therein, a sample membrane extending across the second opening; wherein the detection assembly and the sample assembly are arranged in a stacked configuration to form a chamber between the sample assembly and the detection assembly, wherein the sample membrane is configured for thermal contact with a sample for measurement.

[0058] A sensor according to the preceding example includes a seal between the detection assembly and the sample assembly.

[0059] A sensor according to any preceding example, wherein at least one of the detection membrane and the sample membrane is silicon nitride (SiN).

[0060] A sensor according to any preceding example, wherein the first substrate comprises a third opening opposite the first opening and the third opening is larger than the first opening; and the second substrate comprises a fourth opening opposite the second opening and the fourth opening is larger than the second opening.

[0061] A sensor according to any preceding example, wherein the detection membrane is deposited on the first substrate and the first and third openings are etched through the first substrate defining first angled sidewalls between the first opening and the third opening; and wherein the sample membrane is deposited on the second substrate and the second and fourth openings are etched through the second substrate defining second angled sidewalls between the second opening and the fourth opening.

[0062] A sensor according to any preceding example includes a sample well defined within the second substrate by the sample membrane and the second angled sidewalls.

[0063] A sensor according to any preceding example, wherein the second opening is smaller in area than the third opening.

[0064] A sensor according to any preceding example, wherein the first opening is smaller in area than the second opening.

[0065] A sensor according to any preceding example, wherein the detection membrane has a thickness of 20-25 nm and the sample membrane has a thickness between 10-30 times the thickness of the detection membrane.

[0066] A sensor according to any preceding example includes a resistive heater on the sample membrane.

[0067] A sensor according to any preceding example includes a current source configured to provide an AC and a DC bias current to the resistive heater, whereby the bias current through the resistive heater provides a thermal bias and an off-resonance frequency bias to the chamber.

[0068] A sensor according to any preceding example includes a channel extending into the chamber, the channel coupled to a valve, wherein the valve is operable to open the chamber to an environment exterior of the chamber.

[0069] A sensor according to any preceding example includes a microfluidic channel positioned on the sample membrane, wherein the microfluidic channel is configured to receive a sample and place the sample in contact with the sample membrane.

[0070] A sensor according to any preceding example, wherein the microfluidic channel is constructed of polydimethylsiloxane (PDMS).

[0071] A sensor according to any preceding example includes a target positioned on the sample membrane, and the target comprises graphene and polymethyl methacrylate (PMMA).

[0072] A sensor according to any preceding example, includes a detector arranged relative to the detection membrane wherein sample membrane is configured to for thermal transport of heat from the sample into the chamber causing a change in pressure within the chamber and displacement of the detection membrane, the detector configured to provide an indication of the displacement of the detection membrane; and a controller configured to receive the indication of the displacement from the detector and to calculate a thermal change in the chamber from the measured displacement.

[0073] A sensor according to any preceding example, wherein the detector comprises a metal layer over the detection membrane; an electrode spaced apart from the metal layer, the electrode and the metal layer forming a capacitor; and a capacitance to digital converter that measures a change in capacitance between the metal layer and the electrode, the change in capacitance being indicative of the displacement of the detection membrane.

[0074] A sensor according to any preceding example, wherein the detector comprises an optical sensor positioned relative to the detection membrane wherein the optical sensor is configured to measure a displacement of the detection membrane.

[0075] An example of a sensor system includes a detection assembly includes a first substrate with a first opening defined therein; and a detection membrane extending across the first opening, the detection membrane including silicon nitride (SiN); a sample assembly includes: a second substrate with a second opening defined therein; and a sample membrane extending across the second opening, wherein the sample membrane comprises silicon nitride (SiN), is configured for thermal contact with a sample for measurement, and is 10-30 times a thickness of the detection membrane; a chamber defined between the detection membrane and the sample membrane by the detection assembly and the sample assembly arranged in a stacked configuration; a seal between the detection assembly and the sample assembly; a resistive heater on the sample membrane; a current source configured to provide an AC and a DC bias current to the resistive heater, whereby the bias current through the resistive heater provides a thermal bias and an off-resonance frequency bias to the chamber; a detector arranged relative to the detection membrane wherein the sample membrane is configured for thermal transport of heat from the sample into the chamber causing a change in pressure within the chamber and displacement of the detection membrane, the detector configured to indicate the displacement of the detection membrane; and a controller connected tothe detector, wherein the controller receives a signal from the detector and is configured to calculate a thermal change in the chamber from the displacement of the detection membrane.

[0076] A sensor according to any preceding example includes a vacuum flask at least partially surrounding the detection assembly and the sample assembly, wherein the vacuum flask is configured to environmentally isolate the chamber.

[0077] Citations to a number of references are made herein. The cited references are incorporated by reference herein in their entireties. In the event that there is an inconsistency between a definition of a term in the specification as compared to a definition of the term in a cited reference, the term should be interpreted based on the definition in the specification.

[0078] In the above description, certain terms have been used for brevity, clarity, and understanding. No unnecessary limitations are to be inferred therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes and are intended to be broadly construed. The different systems and method steps described herein may be used alone or in combination with other systems and methods. It is to be expected that various equivalents, alternatives, and modifications are possible within the scope of the appended claims.

[0079] This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to make and use the invention. The patentable scope of the invention is defined by the claims and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.

Claims

CLAIMS I claim:

1. A sensor comprising: a detection assembly comprising a first substrate with a first opening defined therein, a detection membrane extending across the first opening; and a sample assembly comprising a second substrate with a second opening defined therein, a sample membrane extending across the second opening; wherein the detection assembly and the sample assembly are arranged in a stacked configuration to form a chamber between the sample assembly and the detection assembly, wherein the sample membrane is configured for thermal contact with a sample for measurement.

2. The sensor of claim 1, further comprising a seal between the detection assembly and the sample assembly.

3. The sensor of claim 1, wherein at least one of the detection membrane and the sample membrane is silicon nitride (SiN).

4. The sensor of claim 1, wherein the first substrate comprises a third opening opposite the first opening and the third opening is larger than the first opening; and the second substrate comprises a fourth opening opposite the second opening and the fourth opening is larger than the second opening.

5. The sensor of claim 4, wherein the detection membrane is deposited on the first substrate and the first and third openings are etched through the first substrate defining first angled sidewalls between the first opening and the third opening; and wherein the sample membrane is deposited on the second substrate and the second and fourth openings are etched through the second substrate defining second angled sidewalls between the second opening and the fourth opening.

6. The sensor of claim 4, further comprising a sample well defined within the second substrate by the sample membrane and the second angled sidewalls.

7. The sensor of claim 4, wherein the second opening is smaller in area than the third opening.

8. The sensor of claim 1, wherein the first opening is smaller in area than the second opening.

9. The sensor of claim 1, wherein the detection membrane has a thickness of 20-25 nm and the sample membrane has a thickness between 10-30 times the thickness of the detection membrane.

10. The sensor of claim 1, further comprising a resistive heater on the sample membrane.

11. The sensor of claim 10, further comprising a current source configured to provide an AC and a DC bias current to the resistive heater, whereby the bias current through the resistive heater provides a thermal bias and an off-resonance frequency bias to the chamber.

12. The sensor of claim 1, further comprising a channel extending into the chamber, the channel coupled to a valve, wherein the valve is operable to open the chamber to an environment exterior of the chamber.

13. The sensor of claim 1, further comprising a microfluidic channel positioned on the sample membrane, wherein the microfluidic channel is configured to receive a sample and place the sample in contact with the sample membrane.

14. The sensor of claim 13, wherein the microfluidic channel is constructed of polydimethylsiloxane (PDMS).

15. The sensor of claim 1, further comprising a target positioned on the sample membrane, and the target comprises graphene and polymethyl methacrylate (PMMA).

16. The sensor of claim 1, further comprising: a detector arranged relative to the detection membrane wherein sample membrane is configured to for thermal transport of heat from the sample into the chamber causing a change in pressure within the chamber and displacement of the detection membrane, the detector configured to provide an indication of the displacement of the detection membrane; and a controller configured to receive the indication of the displacement from the detector and to calculate a thermal change in the chamber from the measured displacement.

17. The sensor of claim 16, wherein the detector comprises: a metal layer over the detection membrane; an electrode spaced apart from the metal layer, the electrode and the metal layer forming a capacitor; and a capacitance to digital converter that measures a change in capacitance between the metal layer and the electrode, the change in capacitance being indicative of the displacement of the detection membrane.

18. The sensor of claim 16, wherein the detector comprises: an optical sensor positioned relative to the detection membrane wherein the optical sensor is configured to measure a displacement of the detection membrane.

19. A sensor system comprising: a detection assembly comprising: a first substrate with a first opening defined therein; and a detection membrane extending across the first opening, the detection membrane comprising silicon nitride (SiN); a sample assembly comprising: a second substrate with a second opening defined therein; and a sample membrane extending across the second opening, wherein the sample membrane comprises silicon nitride (SiN), is configured for thermal contact with a sample for measurement, and is 10-30 times a thickness of the detection membrane;a chamber defined between the detection membrane and the sample membrane by the detection assembly and the sample assembly arranged in a stacked configuration; a seal between the detection assembly and the sample assembly; a resistive heater on the sample membrane; a current source configured to provide an AC and a DC bias current to the resistive heater, whereby the bias current through the resistive heater provides a thermal bias and an off- resonance frequency bias to the chamber; a detector arranged relative to the detection membrane wherein the sample membrane is configured for thermal transport of heat from the sample into the chamber causing a change in pressure within the chamber and displacement of the detection membrane, the detector configured to indicate the displacement of the detection membrane; and a controller connected to the detector, wherein the controller receives a signal from the detector and is configured to calculate a thermal change in the chamber from the displacement of the detection membrane.

20. The sensor system of claim 19, further comprising a vacuum flask at least partially surrounding the detection assembly and the sample assembly, wherein the vacuum flask is configured to environmentally isolate the chamber.

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