# Patent

## Title
Graphene-based bolometer

## Abstract

A bolometer. In one embodiment a graphene sheet is configured to absorb electromagnetic waves. The graphene sheet has two contacts connected to an amplifier, and a power detector connected to the amplifier. Electromagnetic power in the evanescent electromagnetic waves is absorbed in the graphene sheet, heating the graphene sheet. The power of Johnson noise generated at the contacts is proportional to the temperature of the graphene sheet. The Johnson noise is amplified and the power in the Johnson noise is used as a measure of the temperature of the graphene sheet, and of the amount of electromagnetic wave power absorbed by the graphene sheet.

## Background
CROSS-REFERENCE TO RELATED APPLICATION(S)
The present application is a continuation in part of U.S. application Ser. No. 14/794,591, filed Jul. 8, 2015, published as Publication No. 2016/0370232-A1 on Dec. 22, 2016 and entitled “GRAPHENE-BASED INFRARED BOLOMETER”, the entire content of which is incorporated herein by reference, which claims priority to and the benefit of U.S. Provisional Application No. 62/181,177, filed Jun. 17, 2015, entitled “GRAPHENE-BASED INFRARED BOLOMETER”, the entire content of which is incorporated herein by reference.


BACKGROUND
1. Field
One or more aspects of embodiments according to the present invention relate to detection of infrared light or microwaves, and more particularly to a high-sensitivity, high-bandwidth bolometer for detecting infrared light or microwaves.
2. Description of Related Art
Bolometers have multiple applications, including applications in sensitive imaging systems and in communications systems. Constructing a bolometer with good sensitivity for wavelengths in the range spanning from 10 microns or more to 1 micron may be challenging, in part because the thermal inertia of sensing elements of related art bolometers may be sufficient to impair their bandwidth and to reduce their sensitivity. Both bandwidth and sensitivity may be important for communications applications; such applications may use a wavelength of 1550 nm. Sensitivity may also be important for imaging applications, and bandwidth may be important for high-speed imaging. Thus, there is a need for a high-sensitivity, high-bandwidth bolometer.
SUMMARY
Aspects of embodiments of the present disclosure are directed toward an infrared or microwave bolometer. In one embodiment a graphene sheet is configured to absorb electromagnetic waves. The graphene sheet has two contacts connected to an amplifier, and a power detector connected to the amplifier. Electromagnetic power in the evanescent electromagnetic waves is absorbed in the graphene sheet, heating the graphene sheet. The power of Johnson noise generated at the contacts is proportional to the temperature of the graphene sheet. The Johnson noise is amplified and the power in the Johnson noise is used as a measure of the temperature of the graphene sheet, and of the amount of electromagnetic wave power absorbed by the graphene sheet.
According to an embodiment of the present invention there is provided a bolometer including: a graphene sheet having a first pair of contacts and configured: to be coupled to received electromagnetic waves; to have a temperature, when electromagnetic power in the received electromagnetic waves is absorbed by the graphene sheet, corresponding to the amount of electromagnetic power absorbed by the graphene sheet; and to generate thermal noise at the first pair of contacts at a level corresponding to the temperature a Fabry-Perot resonator including two mirrors, the graphene sheet being between the two mirrors; and a circuit connected to the first pair of contacts, the circuit configured to measure the thermal noise level.
In one embodiment, the bolometer includes a refrigerator configured to cool the graphene sheet to a temperature below 4 K.
In one embodiment, the refrigerator is a pulse tube refrigerator.
In one embodiment, the refrigerator is a Gifford-McMahon cooler.
In one embodiment, the graphene sheet substantially has the shape of a rectangle, the rectangle having a length and a width, the length being greater than or equal to the width.
In one embodiment, the length of the rectangle is less than 20 microns.
In one embodiment, the product of the length of the rectangle and the width of the rectangle is less than 1000 square microns.
In one embodiment, the graphene sheet has an electron mobility of more than 100,000 cm2/V/s.
In one embodiment, the bolometer includes a first layer of hexagonal boron nitride immediately adjacent to a first surface of the graphene sheet, and a second layer of hexagonal boron nitride immediately adjacent to a second surface of the graphene sheet.
In one embodiment, each of the first layer of hexagonal boron nitride and the second layer of hexagonal boron nitride has a thickness greater than 4 nm and less than 40 nm.
In one embodiment, the circuit includes an amplifier connected to the first pair of contacts.
In one embodiment, the bolometer includes a matching circuit connected between the first pair of contacts and the amplifier.
In one embodiment, the bolometer includes a power detector connected to the amplifier.
In one embodiment, the graphene sheet consists of a single atomic layer of graphene.
In one embodiment, the graphene sheet includes two atomic layers of graphene.
According to an embodiment of the present invention there is provided an imaging system including an array of bolometers, each of the bolometers of the array having an electromagnetic wave input, the electromagnetic wave inputs forming an array of electromagnetic wave inputs; and an imaging system configured to project an image onto the array of electromagnetic wave inputs.
According to an embodiment of the present invention there is provided a bolometer including: a graphene sheet having a first pair of contacts and a second pair of contacts and being configured: to be coupled to received electromagnetic waves; to have a temperature, when electromagnetic power in the received electromagnetic waves is absorbed by the graphene sheet, corresponding to the amount of electromagnetic power absorbed by the graphene sheet; and to generate thermal noise at the first pair of contacts at a level corresponding to the temperature; and a circuit connected to the first pair of contacts, the circuit configured to measure the thermal noise level, wherein a first contact of the second pair of contacts, the graphene sheet, and a second contact of the second pair of contacts together form a part of a microstrip transmission line.
In one embodiment, the bolometer includes a second end of the microstrip transmission line, forms a quarter-wave open stub connected to the graphene sheet.
According to an embodiment of the present invention there is provided a bolometer including: a graphene sheet having a first pair of contacts and a second pair of contacts and being configured: to be coupled to received electromagnetic waves; to have a temperature, when electromagnetic power in the received electromagnetic waves is absorbed by the graphene sheet, corresponding to the amount of electromagnetic power absorbed by the graphene sheet; and to generate thermal noise at the first pair of contacts at a level corresponding to the temperature; and a circuit connected to the first pair of contacts, the circuit configured to measure the thermal noise level, wherein each contact of the second pair of contacts is connected to a respective conductor of a pair of conductors of a log periodic antenna.



BRIEF DESCRIPTION OF THE DRAWINGS
Features, aspects, and embodiments are described in conjunction with the attached drawings, in which:
FIG. 1 is conceptual diagram illustrating the operation of an infrared bolometer, according to an embodiment of the present invention;
FIG. 2 is a block diagram of an infrared bolometer according to an embodiment of the present invention;
FIG. 3A is a perspective view of a bolometer sensor assembly according to an embodiment of the present invention;
FIG. 3B is a schematic plan view of a bolometer sensor assembly according to an embodiment of the present invention;
FIG. 3C is a perspective view of a communications system including mobile transceivers according to an embodiment of the present invention;
FIG. 3D is a block diagram of an imaging system according to an embodiment of the present invention;
FIG. 3E is a schematic side view of a graphene sheet sandwiched between two layers of hexagonal boron nitride, according to an embodiment of the present invention;
FIG. 4 is a block diagram of a Johnson noise measuring circuit according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a front end circuit according to an embodiment of the present invention;
FIG. 6A is a block diagram of a thermal model of a graphene sheet according to an embodiment of the present invention; and
FIG. 6B is a graph of the thermal conductance of a graphene sheet as a function of temperature according to an embodiment of the present invention.
FIG. 7A is a hybrid schematic diagram and plan view of a portion of a bolometer, according to an embodiment of the present invention;
FIG. 7B is a hybrid schematic diagram and plan view of a portion of a bolometer, according to an embodiment of the present invention;
FIG. 8A is a plan view of a portion of a bolometer, according to an embodiment of the present invention;
FIG. 8B is a plan view of a portion of a bolometer, according to an embodiment of the present invention; and
FIG. 8C is a plan view of a portion of a bolometer, according to an embodiment of the present invention.



DETAILED DESCRIPTION
The detailed description set forth below in connection with the appended drawings is intended as a description of exemplary embodiments of a graphene-based infrared bolometer provided in accordance with the present invention and is not intended to represent the only forms in which the present invention may be constructed or utilized. The description sets forth the features of the present invention in connection with the illustrated embodiments. It is to be understood, however, that the same or equivalent functions and structures may be accomplished by different embodiments that are also intended to be encompassed within the spirit and scope of the invention. As denoted elsewhere herein, like element numbers are intended to indicate like elements or features.
Referring to FIG. 1, in one embodiment, an infrared bolometer includes a graphene sheet 120, configured to absorb infrared electromagnetic waves 105. Electrons in the graphene sheet are weakly coupled to phonons in the graphene sheet, and the mechanisms by which heat escapes the electrons of the graphene sheet may provide heat paths with a relatively low total thermal conductivity. As a result, even for relatively little absorbed infrared electromagnetic power, the temperature of the electrons in the graphene sheet may increase significantly, as shown conceptually by the illustration of thermometer 122.
Referring to FIG. 2, in one embodiment, the infrared bolometer includes an infrared waveguide 110 and a graphene sheet 120 forming a bolometer sensor assembly 124, and a thermal noise or “Johnson noise” measuring circuit 130 for monitoring the Johnson noise generated by the graphene sheet 120. When infrared electromagnetic waves propagate in the waveguide 110, evanescent waves outside the waveguide 110 overlap with, and couple to, the graphene sheet 120. This coupling allows power to be absorbed from the electromagnetic waves by the graphene sheet 120, raising the temperature of the graphene sheet 120 to a temperature corresponding to the amount of electromagnetic power absorbed by the graphene sheet 120. The temperature may be measured by measuring the Johnson noise (i.e., the thermal noise) produced by the graphene sheet 120.
When power is absorbed from infrared electromagnetic waves by the graphene sheet 120, the absorption occurs primarily through interaction of the electromagnetic waves with the electronic degrees of freedom of the graphene sheet 120, because the interactions between the electromagnetic waves and the nuclei of the graphene sheet 120 are significantly weaker than the interactions between the electromagnetic waves and the electrons of the graphene sheet 120. Electrons in the graphene sheet 120 are weakly coupled to phonons in the graphene sheet 120, and, in part because of this, the total thermal conductivity corresponding to mechanisms by which the electrons may lose heat (e.g., coupling through the contacts, coupling to the lattice, and coupling to the electromagnetic environment) is relatively small. As a result, the absorption of power from the electromagnetic waves results in a relatively high electron temperature, which in turn results in a relatively high Johnson noise level (i.e., a relatively high thermal noise level) in the potential between any pair of spatially separated points on the graphene sheet 120. The Johnson noise may be measured at two contacts 330, disposed, for example, at two ends of a rectangular graphene sheet 120 (FIG. 3A).
In some embodiments, the infrared waveguide 110 may be absent, and infrared radiation (e.g., infrared electromagnetic waves propagating in free space) may instead illuminate the graphene sheet 120 directly, or the graphene sheet 120 may be placed between parallel mirrors forming a Fabry-Perot resonator, and received infrared radiation (e.g., infrared electromagnetic waves propagating in free space) may be resonantly amplified, resulting in higher infrared irradiance at the graphene sheet than in the received infrared radiation. In other embodiments, illustrated for example in FIGS. 7A-8C and described in further detail below, a bolometer may detect electromagnetic waves having longer wavelengths than those of infrared radiation, e.g., microwaves. As used herein, the term “microwave” includes the portion of the electromagnetic spectrum suitable for receiving with an antenna and guiding with conductors, and includes frequencies in the range from 1 MHz to 1 THz. Photons in such microwave electromagnetic waves may be absorbed by the graphene sheet 120, producing a signal in a manner similar to that described above for infrared radiation.
Referring to FIG. 3A, the waveguide 110 and the graphene sheet 120 of the bolometer sensor assembly 124 may be fabricated as an integrated component on a substrate 310. The waveguide 110 may be fabricated by any of various methods known in the art for fabricating a waveguide 110 on the surface of a substrate 310. In one embodiment, a layer of silicon dioxide is formed on a silicon substrate 310, and patterned using photolithography to form the waveguide 110 as a raised structure. A layer 320 of silicon nitride may then be formed over the waveguide 110 and the surrounding area, so that the waveguide 110 core has silicon nitride on both sides of it and above it. This structure may then be polished, so that the upper surface of the structure is flat and smooth. In other embodiments, the waveguide 110 may be formed by depositing a layer of silicon dioxide on a silicon substrate 310, depositing a layer of silicon on the silicon dioxide, and patterning the silicon layer using photolithography to form the core of the waveguide 110 as a raised silicon structure. This structure may then be planarized, i.e., made flat and smooth, by depositing an additional layer of silicon dioxide and polishing it down to the top surface of the raised silicon structure. In other embodiments the waveguide 110 may be composed of another first material, surrounded by one or more other materials having a lower index of refraction than the first material. The resulting waveguide structure may have a thickness of between 50 nm and 2000 nm; in one embodiment it has a thickness of between 100 nm and 1000 nm. The transverse dimensions of the waveguide structure may be somewhat smaller or considerably smaller than the wavelength of the infrared light to be detected. The waveguide 110 may be single-mode or multi-mode when guiding light at the wavelength of the infrared light to be detected. The substrate may be substantially flat, e.g., within 1 micron of being flat over the area including the waveguide, and the waveguide may be formed, e.g., using one of the processes described above, in a layer having a thickness greater than 50 nanometers and less than 2 microns. The front end of the waveguide 110 may extend to the edge of the substrate 310 as shown, and off-chip coupling optics 340 may be used to launch infrared light into the waveguide 110. In other embodiments portions of the coupling optics may be fabricated on the substrate 310. In some embodiments the waveguide 110 is omitted and infrared light propagating in free space illuminates the graphene sheet 120 directly.
The waveguide 110 may be straight, and, to increase the amplitude of the evanescent waves overlapping the graphene sheet 120, it may be part of an optical resonator, constructed, for example, by forming a reflector (e.g., a Bragg reflector) at each end of a section of the waveguide 110. Bragg reflectors may be formed by creating periodic defects in or adjacent to the waveguide 110, e.g., by forming holes in or adjacent the waveguide structure with a focused ion beam. The reflector at the front end of the waveguide 110 (i.e., the end first encountered by the arriving infrared light) may be partially reflective, to allow the infrared light to enter the resonator, and the reflector at the other end (the “back” end) of the waveguide 110 may be highly reflective, to avoid allowing light to escape from the back end of the waveguide 110. In some embodiments only one reflector is used, at the back end of the waveguide 110.
In other embodiments the waveguide 110 may not be straight, but may have one or more curves, increasing the length of the section of waveguide 110 that is adjacent to the graphene sheet 120, and from which evanescent waves may interact with the graphene sheet 120. A curved section in the waveguide may have a radius of curvature less than the length of the graphene sheet, and in the curved section the direction of the waveguide may change by 45 degrees or more. The increased length of the section of waveguide 110 adjacent to the graphene sheet 120 may increase the fraction of the electromagnetic energy launched into the waveguide 110 that is absorbed by the graphene sheet 120. The waveguide 110 may have a double spiral shape as illustrated in FIG. 3A. In other embodiments the waveguide 110 may have the shape of a single spiral, with the back end of the waveguide in the center of the spiral. The back end of the waveguide 110 may be at an edge of the substrate 310 as illustrated in FIG. 3A, or it may be elsewhere on the substrate 310, e.g., near the middle in the case of a waveguide 110 in the shape of a single spiral.
Referring to FIG. 3B, in one embodiment the waveguide 110 may have a meandering shape, covering a region that roughly corresponds to the extent of the graphene sheet 120 as illustrated.
In yet other embodiments, the waveguide 110 may have one or more curves and also form part of a resonator, to further increase the fraction of the electromagnetic energy launched into the waveguide 110 that is absorbed by the graphene sheet 120.
Infrared light may be launched into the waveguide 110 by any of several systems known to those of skill in the art. For example, referring to FIG. 3C, transceivers using coupling to free-space propagating waves may be used for mobile communications e.g., between ships 380 and a tower 385. In such an application, the infrared light may be coupled into the waveguide 110 using one or more suitable powered optics, such as lenses or curved mirrors. In other communications applications, if the infrared light to be detected is initially propagating in an optical fiber, it may be launched into the waveguide 110 of the bolometer using any suitable one of a variety of fiber-to-chip couplers known to those of skill in the art.
Referring to FIG. 3D, in one embodiment an infrared imaging system may employ an array of bolometer sensor assemblies 124 constructed according to an embodiment of the present invention. Each of the bolometer sensor assemblies 124 has an optical input (e.g., the input of the waveguide 110, or the input of coupling optics 340, or the input of a fiber coupled to the waveguide 110). The optical inputs form an array that is illuminated through imaging optics that project an image onto the array of optical inputs. The array of bolometer sensor assemblies 124 is read out by a set of readout electronics, which may for example be an array of Johnson noise measuring circuits 130. In one embodiment the imaging optics include an array of coupling lenses to couple light into the waveguides 110 of the array of bolometer sensor assemblies 124, or to couple light into a corresponding array of fibers, each of which is coupled to a respective bolometer sensor assembly 124 in the array of bolometer sensor assemblies. In other embodiments an analogous imaging system (e.g., a microwave reflector) may be used to form microwave images on a bolometer array.
The graphene sheet 120 may be a single-layer sheet, i.e., it may be one atomic layer thick, or it may be a multi-layer graphene sheet 120, having, e.g., 2, 3, 4, or more layers. Referring to FIG. 3E, in one embodiment, the graphene sheet 120 is encapsulated in hexagonal boron nitride (hBN). As is known to those of skill in the art, a sandwich is formed, with the graphene sheet 120 sandwiched between two layers 290 of hexagonal boron nitride. Each layer 290 of hexagonal boron nitride may be between 4 nm and 40 nm thick; these layers 290 of hexagonal boron nitride may keep the surface of the graphene sheet 120 clean, i.e., they may prevent surface contamination from compromising the properties of the graphene sheet 120. The sandwich, composed of the two outer layers 290 of hexagonal boron nitride encapsulating the graphene sheet 120, may then be disposed on the portion of the substrate 310 that includes the waveguide 110.
Each hexagonal boron nitride layer 290 may be a single crystal, with an atomically flat surface facing the graphene sheet 120. Each hexagonal boron nitride layer 290 may be annealed, e.g., at 250° C. for 10-15 minutes, before the sandwich is assembled. The sandwich may be formed by first bringing a first layer 290 of hexagonal boron nitride into contact with the graphene sheet 120, resulting in adhesion of the graphene sheet 120 to the hexagonal boron nitride by van der Waals forces, and then bringing the graphene sheet 120, on the first layer 290 of hexagonal boron nitride, into contact with the second layer 290 of hexagonal boron nitride, resulting in adhesion, again by van der Waals forces, at the interface between the graphene sheet 120 and the second layer 290 of hexagonal boron nitride. The edges of the sandwich may then be etched, e.g. using plasma etching, so that the edges of the two layers 290 of hexagonal boron nitride and the edges of the graphene sheet 120 in the structure remaining after the etch process coincide (i.e., are aligned).
The graphene sheet 120 may be rectangular as illustrated in FIG. 3A, with a length and a width, the length being greater than or equal to the width. The total area of the graphene sheet 120 may be less than 1000 square microns. In one embodiment the graphene sheet 120 is about 10 microns by 10 microns. In one embodiment the graphene sheet 120 has a length in the range 1.0-100.0 microns and a width in the range 1.0-100.0 microns. An electrical contact 330 may be provided at each of two opposing sides or ends of the graphene sheet 120. In one embodiment, contact is made with the edge of the graphene sheet 120, using a layer of metal deposited onto the edge of the sandwich.
For good performance, the graphene sheet 120 may be made as small as possible, kept as clean as possible, and operated at as low a temperature as possible. In one embodiment, the graphene sheet 120 is cooled to 4 K, using, for example, a pulse tube refrigerator or a Gifford-McMahon (GM) cooler. In other embodiments direct cooling with liquid helium, or with liquid helium in a partial vacuum (e.g., using a 1 K pot, to reach temperatures below 4 K) may be used to cool the graphene sheet 120.
The Johnson noise power at the two contacts may be proportional to the electron temperature of the graphene sheet 120. As used herein, the temperature of the graphene sheet 120 refers to the temperature of the electrons in the graphene sheet 120; when electromagnetic power in the evanescent waves of the waveguide 110 is absorbed by the graphene sheet 120, the electron temperature may differ from the phonon temperature.
In one embodiment, referring to FIG. 4, a Johnson noise measuring circuit 130 includes a front end circuit 410 for amplifying the Johnson noise and a power detector 420 that converts the noise signal to a power signal or temperature signal having a value (e.g., a voltage) corresponding to (e.g., proportional to) the noise power. Referring to FIG. 5, the front end circuit 410 may include an amplifier 510 that may include a quantum noise limited amplifier followed by a high electron mobility transistor (HEMT) amplifier. The front end circuit 410 may also include a matching network, e.g., an inductor-capacitor (LC) matching network, for transforming the impedance of the graphene sheet 120, which may be about 1,000 ohms, to the input impedance of the amplifier 510 (which may be about 50 ohms). In one embodiment the amplifier 510 has a bandwidth of about 80 MHz around a frequency of about 1.1 GHz, and the matching network is tuned for a frequency of 1.1 GHz. In some embodiments the quantum noise limited amplifier may be a radio frequency superconducting quantum interference device (RF SQUID) amplifier, or it may be a travelling wave parametric amplifier, or a tuned system parametric amplifier (TPA), or any other kind of amplifier with a suitable frequency response that is quantum noise limited or nearly quantum noise limited. In some embodiments the amplifier 510 does not include quantum noise limited amplifier, and has a HEMT amplifier as the first stage instead.
The front end may also include components and connections that may be used for diagnostics, e.g., during manufacturing, operation, or service. A bias tee may be used, for example, to drive a low-frequency current through the graphene sheet 120, modulating its temperature, and the presence of a corresponding modulation at the output of the power detector may then be used to verify the functioning of the device. The differential thermal conductance of the graphene sheet 120 may also be measured in this manner. A directional coupler may be used to supply microwave power to the graphene sheet 120, while monitoring the output of the power detector; this microwave power is essentially entirely absorbed, and this technique may be used to measure the differential thermal conductance as well. A circulator may be used at the input of the amplifier 510 to prevent reflections, backwards-propagating amplifier noise, or signals travelling in reverse through the amplifier 510, from heating the graphene sheet 120.
The power detector of FIG. 4 may be a circuit for producing an output signal proportional to the total power at its input. It may include, for example, a Schottky diode biased (e.g., with a bias tee) so that, in addition to the bias current, it conducts a low-frequency current approximately proportional to the square of the microwave signal applied across its terminals. This low-frequency current may then be measured (e.g., as a change in the bias current). In other embodiments the power detector may be constructed according to another of various power detector circuits known to those of skill in the art. The output of the power detector need not be proportional to the input power, and may, for example, be a nonlinear function of the input power. The output of the Johnson noise measuring circuit 130 may be the (e.g., analog) output of the power detector 420, or a sampling circuit (e.g., an analog to digital (A/D) converter) may be connected between the output of the power detector 420 and the output of the Johnson noise measuring circuit 130, so that the output of the Johnson noise measuring circuit 130 is a digital data stream. In one embodiment the sampling rate of such an A/D converter is about 50 MHz.
The sensitivity of the bolometer may depend on the size of the graphene sheet 120, its cleanliness, and its temperature. Referring to FIG. 6A, a thermal model for the graphene sheet 120 in the bolometer sensor assembly 124 may include the thermal mass (i.e., the heat capacity) of the graphene sheet 120, the electromagnetic power 105 heating the graphene sheet 120, and a thermal conductance 605 to a thermal reservoir 610. The smaller the heat capacity, the greater the bandwidth of the bolometer sensor assembly 124, and the smaller the thermal conductance 605, the higher the steady-state temperature for a given amount of electromagnetic power 105 heating the graphene sheet 120. Referring to FIG. 6B, in the clean graphene limit, the thermal conductance Gep (between the electrons and the phonons of the graphene sheet 120) may be given by

Gep=4ΣoAT3 

where T is the temperature, A is the area of the graphene sheet 120, and Σc is the electron-phonon coupling constant in the clean graphene limit. This coupling constant Σc is independent of the temperature T and of the area A of the graphene sheet 120, but increases with increasing impurity density level, i.e., with decreasing electron mobility. For disordered graphene, the thermal conductance Gep (between the electrons and the phonons of the graphene sheet 120) may be given by

Gep=3ΣdAT2 

where Σd is the electron-phonon coupling constant for disordered graphene.
The graph of FIG. 6B shows the expected thermal conductance Gep for a graphene sheet 120 with an area of 100 square microns (e.g., a 10 micron by 10 micron square graphene sheet 120). The sensitivity of a bolometer using a graphene sheet with the characteristic of FIG. 6B may be estimated by multiplying the thermal conductance by the noise of the amplifier 510 (FIG. 5). For example, for amplifier noise of 1 mK/sqrt (Hz), and for Gep=10 pW/K (e.g., from FIG. 6B, for a graphene sheet 120 at 1 K), the expected sensitivity is 10 fW/sqrt (Hz).
In some embodiments, as mentioned above, a graphene sheet may be used to detect microwave electromagnetic radiation. Referring to FIG. 7A, in one embodiment the electromagnetic radiation may be coupled (e.g., by a suitable receiving antenna, such as a horn antenna or a patch antenna) to an input transmission line 805, and the resulting guided waves may propagate toward the graphene sheet 120 on the input transmission line 805 (e.g., a microstrip transmission line), through an impedance matching network 810, and through a detector transmission line 815 (that includes the graphene sheet 120), to ground 820. The detector transmission line 815 is illustrated, in FIG. 7A, in part schematically (as a line) and in part in a plan view, as a conductor having substantially constant width. When the received electromagnetic waves generate current in the graphene sheet 120, the electron temperature of the graphene sheet may increase, resulting in an increase in Johnson noise as described above. A Johnson noise measuring circuit 130 may be connected to the two contacts 330 to detect such a temperature increase. Chokes 825 may be used to isolate the detector transmission line 815 from the Johnson noise measuring circuit 130 over the range of frequencies of the electromagnetic radiation to be detected. Contacts between the detector transmission line 815 and the graphene sheet 120 may be formed at two respective edges of the graphene sheet 120, and contacts 330 through which the graphene sheet 120 is connected to the Johnson noise measuring circuit 130 may be at two other respective edges of the graphene sheet 120, as illustrated in FIG. 7A.
Referring to FIG. 7B, in an embodiment similar to that of FIG. 7A, the received electromagnetic waves propagating on the input transmission line 805 may be capacitively coupled to the detector transmission line 815 by a coupling capacitor 830 (which may be a gap, as shown, in a microstrip transmission line). A half-wave (or “lambda-over-two”) microwave resonator 835 with the graphene sheet 120 at the center (i.e., forming a quarter-wave open stub on one side—the left side in the illustration of FIG. 7B—of the graphene sheet 120) may result in the formation of standing waves having a current antinode 840 (and a voltage node) at or near the graphene sheet 120. The overlap of the current antinode 840 and the graphene sheet 120 can result in critical coupling of the received electromagnetic radiation to the bolometer for enhanced detection efficiency. If the graphene sheet is part of a sandwich (e.g., between layers of boron nitride), contact between the detector transmission line 815 and the graphene sheet 120 may be made at the edges of the sandwich, as described above with respect to the contacts 330 through which the graphene sheet 120 is connected to the Johnson noise measuring circuit 130.
In some embodiments a diplexer may be used to separate the received microwave electromagnetic waves and the Johnson noise signals sent to the Johnson noise measuring circuit 130. In such an embodiment, the graphene sheet 120 may be connected to a detector transmission line 815 (e.g., in the manner illustrated in FIG. 7B). In such an embodiment, the other two connections to the graphene sheet 120 (shown in FIG. 7B), through the contacts 330, as well as the contacts 330 themselves, may be absent. The diplexer may have a common port connected to the graphene sheet 120 via the detector transmission line 815, a high frequency (HF) port connected to the input transmission line 805, and a low frequency (LF) port connected to the Johnson noise measuring circuit 130. The diplexer may separate signals according to frequency, transmitting received electromagnetic waves from the input transmission line 805 (connected to the high frequency port of the diplexer) to the graphene sheet 120 (through the common port of the diplexer, via the detector transmission line 815), and transmitting Johnson noise received (at the common port of the diplexer, via the detector transmission line 815) from the graphene sheet 210 to the Johnson noise measuring circuit 130 (connected to the low frequency port of the diplexer).
Referring to FIG. 8A, in one embodiment a log periodic antenna includes two conductive patches 910, and may be used to couple microwave electromagnetic radiation propagating in free space into a graphene sheet 120, at the center of the log periodic antenna, which may be coupled to a Johnson noise measuring circuit 130. Referring to FIGS. 8B and 8C, the two conductive patches 910 may extend, at the center of the log periodic antenna, along two sides (e.g., the long sides) of a rectangular graphene sheet 120, which may have on its other two (short) sides contacts 330 (not shown in FIG. 8B) through which the graphene sheet 120 is connected to the Johnson noise measuring circuit 130. Referring to FIG. 8C, in another embodiment the two conductive patches 910 may extend, at the center of the log periodic antenna, along the short sides of a rectangular graphene sheet 120, which may have on its other two (long) sides contacts 330 through which the graphene sheet 120 is connected to the Johnson noise measuring circuit 130. As in the embodiments of FIGS. 7A and 7B, the embodiments of FIGS. 8A, 8B, and 8C may include additional circuitry (not shown in FIGS. 8A, 8B, and 8C) including chokes to isolate the received electromagnetic waves from the Johnson noise measuring circuit 130. The embodiments of FIGS. 8A, 8B, and 8C may be suitable for detecting electromagnetic radiation in a frequency range extending from about 100 GHz to about 1 THz.
Although limited embodiments of a graphene-based bolometer have been specifically described and illustrated herein, many modifications and variations will be apparent to those skilled in the art. Accordingly, it is to be understood that a graphene-based bolometer employed according to principles of this invention may be embodied other than as specifically described herein. The invention is also defined in the following claims, and equivalents thereof.

## Claims

1. A bolometer comprising:
a graphene sheet having a first pair of contacts and configured:
to be coupled to received electromagnetic waves;
to have a temperature, when electromagnetic power in the received electromagnetic waves is absorbed by the graphene sheet, corresponding to the amount of electromagnetic power absorbed by the graphene sheet; and
to generate thermal noise at the first pair of contacts at a level corresponding to the temperature

a Fabry-Perot resonator comprising two mirrors, the graphene sheet being between the two mirrors; and
a circuit connected to the first pair of contacts, the circuit configured to measure the thermal noise level.

2. The bolometer of claim 1, further comprising a refrigerator configured to cool the graphene sheet to a temperature below 4 K.

3. The bolometer of claim 2, wherein the refrigerator is a pulse tube refrigerator.

4. The bolometer of claim 2, wherein the refrigerator is a Gifford-McMahon cooler.

5. The bolometer of claim 1, wherein the graphene sheet substantially has the shape of a rectangle, the rectangle having a length and a width, the length being greater than or equal to the width.

6. The bolometer of claim 5, wherein the length of the rectangle is less than 20 microns.

7. The bolometer of claim 5, wherein the product of the length of the rectangle and the width of the rectangle is less than 1000 square microns.

8. The bolometer of claim 5, wherein the graphene sheet has an electron mobility of more than 100,000 cm2/V/s.

9. The bolometer of claim 1, comprising a first layer of hexagonal boron nitride immediately adjacent to a first surface of the graphene sheet, and a second layer of hexagonal boron nitride immediately adjacent to a second surface of the graphene sheet.

10. The bolometer of claim 9, wherein each of the first layer of hexagonal boron nitride and the second layer of hexagonal boron nitride has a thickness greater than 4 nm and less than 40 nm.

11. The bolometer of claim 1, wherein the circuit comprises an amplifier connected to the first pair of contacts.

12. The bolometer of claim 11, further comprising a matching circuit connected between the first pair of contacts and the amplifier.

13. The bolometer of claim 11, further comprising a power detector connected to the amplifier.

14. The bolometer of claim 1, wherein the graphene sheet consists of a single atomic layer of graphene.

15. The bolometer of claim 1, wherein the graphene sheet comprises two atomic layers of graphene.

16. An imaging system comprising:
an array of bolometers, each of the bolometers of the array being a bolometer according to claim 1 and having an electromagnetic wave input, the electromagnetic wave inputs forming an array of electromagnetic wave inputs; and
an imaging system configured to project an image onto the array of electromagnetic wave inputs.