Near-zero-field magnetoresistive magnetometer and magnetometry method

Abstract

A magnetometer includes a first substrate, a bare semiconductor die, a first conductive trace, a second conductive trace, a second substrate, and a planar magnetic-field coil. The first substrate is composed of a high-temperature electrically insulating material. The bare semiconductor die is affixed to the first substrate and includes a p-n junction that contains paramagnetic recombination centers. The first and second conductive traces are on the first substrate. The first conductive trace is electrically connected to an anode of the p-n junction. The second conductive trace is electrically connected to a cathode of the p-n junction. The second substrate is composed of a high-temperature electrically insulating material and is affixed to the first substrate. The planar magnetic-field coil is composed of a metal trace formed on the second substrate.

Description

PATENT Attorney Docket No. QCAD.P2001WO / 00646474 NEAR-ZERO-FIELD MAGNETORESISTIVE MAGNETOMETER AND MAGNETOMETRY METHOD RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 601,306, filed 30 September 2024, which is incorporated herein by reference in its entirety. GOVERNMENT RIGHTS

[0002] This invention was made with government support under grant number HR00112390114 awarded by the Defense Advanced Research Projects Agency and under grant number 80NSSC23CA145 awarded by the National Aeronautics and Space Administration. The government has certain rights in the invention. SUMMARY OF THE EMBODIMENTS

[0003] Silicon carbide (SiC) is renowned for its exceptional thermal stability, making it a crucial material for high-temperature power devices in extreme environments. While optically detected magnetic resonance (ODMR) in SiC has been widely studied for magnetometry, it requires complex setups involving optical and microwave sources. Similarly, electrically detected magnetic resonance (EDMR) in SiC, which relies on an electrical readout of spin resonance, has also been explored for magnetometry. However, both techniques require microwave excitation, which limits their scalability.

[0004] Spin-dependent-recombination (SDR) currents in SiC enable a purely electrical approach to magnetometry through the near-zero-field magnetoresistance (NZFMR) effect, where the device resistance changes in response to small magnetic fields. Despite its potential, NZFMR remains underexplored for high-temperature applications. Embodiments disclosed herein perform NZFMR in SiC diodes for high- temperature relative magnetometry and achieve sensitive detection of weak magnetic fields at temperatures up to 600°C. Embodiments provide a simple and cost-effective alternative to other magnetometry architectures, eliminating the need for a microwave source or complex setup. 1LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0005] In embodiments, the NZFMR signal is modulated by an external magnetic field, which alters the singlet-triplet pair ratio controlled by hyperfine interactions between nuclear and electron / hole spins, as well as dipole-dipole / exchange interactions between electron and hole spins, providing a novel mechanism for relative magnetometry sensing at elevated temperatures. A critical advantage of our approach is the sensor head's low power consumption, which is less than 0.5 W at 600°C for magnetic fields below 5 G. This approach provides a sensitive, reliable, and scalable solution with promising applications in space exploration, automotive systems, and industrial sectors, where high performance in extreme conditions is essential.

[0006] Embodiments disclosed herein are directed to an all-electrical electronically detected magnetoresistive magnetometer, which may be used for high- temperature applications using SiC electronics.

[0007] In a first aspect, a magnetometer is disclosed. The magnetometer includes a first substrate, a bare semiconductor die, a first conductive trace and a second conductive trace, a second substrate, and a planar magnetic-field coil. The first substrate is composed of a high-temperature electrically insulating material. The bare semiconductor die is affixed to the first substrate and includes a p-n junction that contains paramagnetic recombination centers. A first conductive trace and a second conductive trace are on the first substrate. The first conductive trace is electrically connected to an anode of the p-n junction. The second conductive trace is electrically connected to a cathode of the p-n junction. The second substrate is composed of a high- temperature electrically insulating material and is affixed to the first substrate. The planar magnetic-field coil is composed of a metal trace formed on the second substrate

[0008] In a second aspect, a high-temperature magnetometry method is disclosed. The method includes driving a bias current through the p-n junction of the bare semiconductor die of the magnetometer of the first aspect. The method also includes driving the magnetic-field coil of the magnetometer to generate, at the p-n junction, a compensating DC magnetic field; sensing a variation in the bias current. The method also includes determining, based on the variation in the bias current, the magnitude of an external magnetic field applied to the p-n junction. 2LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 BRIEF DESCRIPTION OF THE FIGURES

[0009] FIG.1 is a schematic of an embodiment of a magnetometer sensor head.

[0010] FIG.2 is a schematic of a magnetometer sensor head, which is an example of the magnetometer sensor head of FIG.1.

[0011] FIG.3 is a schematic of a magnetometer that includes the magnetometer sensor head of FIG.1, in an embodiment.

[0012] FIG.4 and FIG.5 show averaged NZFMR signals and forward bias measurements, respectively, for an embodiment of a magnetometer of FIG.3.

[0013] FIG.6 shows NZFMR signals generated by an embodiment of the magnetometer of FIG.3.

[0014] FIG.7 is a plot of sensitivity as a function of bandwidth for various temperatures for an embodiment of the magnetometer of FIG.3.

[0015] FIG.8 is a plot of magnetoresistance response as a function of magnetic field applied to a diode of an embodiment of the magnetometer of FIG.3.

[0016] FIG.9 is a flowchart illustrating an embodiment of a method for fabricating the magnetometer sensor head of FIG.1.

[0017] FIG.10 is a flowchart illustrating an embodiment of a method for calibrating the magnetometer sensor head of FIG.1.

[0018] FIG.11 is a flowchart illustrating a method for high-temperature magnetometry, which may be implemented with the magnetometer of FIG.4. DETAILED DESCRIPTION OF THE EMBODIMENTS 1. Silicon Carbide and the Near-Zero-Field Magnetoresistance (NZFMR) Effect

[0019] Due to its unique thermal, mechanical, and electronic properties, silicon carbide (SiC) has emerged as a crucial material in high-power electronics and devices designed for operation in harsh environments. Its wide bandgap (approximately 3.2 eV for 4H-SiC) allows SiC to sustain high electric fields, high voltages, efficient heat dissipation, and operation at temperatures far exceeding those of silicon-based devices. These attributes make this material indispensable in applications requiring durability and efficiency under extreme conditions, such as power electronics, automotive systems, smart grids, and aerospace, to cite a few. Additionally, SiC hosts defects that exhibit optically and electrically active spin states, making it a versatile material for quantum sensing and spintronics. Unlike nitrogen-vacancy centers in diamonds, SiC defects are 3LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 compatible with modern semiconductor fabrication techniques, offering a scalable platform for quantum technologies.

[0020] A concrete example of SiC’s pivotal role lies in small-size, weight, and power consumption (SWaP) magnetometry for high-temperature environments, crucial for applications ranging from engine monitoring and chip quality control to space exploration. Conventional magnetometers, such as fluxgates, face significant limitations in size, power consumption, and susceptibility to thermal noise. Fluxgate magnetometers also require frequent calibration and are prone to performance degradation due to noise interference. Optically detected magnetic resonance (ODMR) techniques have achieved high sensitivity for magnetic field detection at smaller scales. However, ODMR systems, such as optically pumped magnetometry (OPM), rely on microwave excitation and optical detection, complicating their integration into SWaP devices. Similarly, electronically detected magnetic resonance (EDMR), which monitors spin-dependent phenomena by detecting changes in electrical current, improves signal readout but still requires microwave fields, limiting its practicality in miniaturized devices. These techniques also struggle to function in high-temperature environments, with fluxgates degrading above 150–200°C, OPMs suffering from instability in atomic vapor cells, and EDMR experiencing reduced spin coherence and increased thermal noise.

[0021] Near-zero-field magnetoresistance (NZFMR) is emerging as a powerful defect metrology alternative, overcoming many of the limitations of traditional magnetometry. NZFMR does not require microwave sources or large magnetic fields, significantly reducing system complexity, power consumption, and cost. By avoiding RF fields, NZFMR enables spectroscopy below metallization layers to detect point defects in fully processed semiconductor devices, making it highly valuable for integrated circuit reliability. Moreover, NZFMR allows for self-calibrating magnetometry. Similar to the EDMR, NZFMR involves spin-dependent changes in current, but instead of relying on resonance at higher fields, the change is centered at near-zero magnetic fields. Low-field hyperfine mixing and electron-electron dipolar interactions alter the singlet-to-triplet pairing ratio in an NZFMR response, enabling the detection of changes in the recombination current with external magnetic field variations. Additionally, the magnetic isotopes of host and dopant atoms involved in hyperfine interactions act as natural, stable markers, allowing self-calibration over time and temperature. This 4LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 stability is rooted in the stable energy levels of SiC’s defects, which remain unaffected by temperature fluctuations, ensuring consistent performance across various conditions.

[0022] By utilizing NZFMR to probe the spin properties of active defects in standard SiC p-n junction devices, we have demonstrated an all-electrical SWaP relative magnetometry capable of operating at temperatures up to 600°C without isotopic purification or design enhancements. The proposed technology represents a significant advancement, overcoming the limitations of existing magnetometry techniques and opening new avenues for metrology and space exploration. It provides a reliable, scalable, cost-effective solution for extreme environments without sacrificing sensitivity, setting a new standard for high-performance magnetic field sensing across the most challenging conditions. 2. Methods

[0023] The present embodiments rely on near-zero-field spin-dependent recombination (SDR), which enables the electrical readout of a current that encodes the magnetic field in which the sensor is immersed. In an example of SDR, a conduction electron and a trapped electron couple to form an intermediate spin state. The singlet- triplet pairs mix due to a nuclear magnetic field and a small external magnetic field B. The local magnetic field sensed by each electron is then the vector sum of these two fields. The singlet pair contributes to the device current through SDR. Other embodiments may correspond to any other low-field-dependent contribution to the current in a semiconductor device, including trap-assisted tunneling and other mechanisms.

[0024] The intrinsic defects of the SiC device dictate the response of the SDR current in this embodiment. In embodiments, when a semiconductor junction device is biased to yield a pronounced recombination current, carriers couple with deep-level (spin-dependent) defect electrons. These spin states can be singlet or triplet states. Due to the Pauli exclusion principle, electron-hole recombination is allowed only in a singlet spin configuration, creating a bottleneck when the pair is in a triplet state. At near-zero magnetic fields, this bottleneck is alleviated by low hyperfine interactions, which flip the defect electron’s spin triplet into singlet states. This process remains active despite the thermal energy being orders of magnitude larger than the single-triplet mixing energy. Similar spin bottleneck dynamics are possible for higher spin combinations or other 5LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 spin manifolds for which spin-selective recombination processes, or other current- contributing processes, occur due to differences in transition rates or spin-dependent energy structure.

[0025] FIG.1 is a schematic of a magnetometer sensor head 100, hereinafter sensor head 100. FIG.1 and others herein depict orthogonal axes A1, A2, and A3. Unless otherwise specified, heights and depths of objects herein refer to the object’s extent along axis A3. Also, herein, a horizontal plane (or horizontal direction) is parallel to the A1–A2 plane, a width refers to an object’s extent along axis A1 or axis A2, and a vertical direction is along axis A3. Sensor head 100 may operate over a temperature range of ^^^^to ^^^^. ^^^^may be 20°C. ^^^^may be 532°C or 600°C. In such embodiments, each component of sensor head 100 maintains its functionality and a same material phase within this temperature range.

[0026] Sensor head 100 includes at least one of a substrate 110, a substrate 120, a substrate 130, a semiconductor die 150, a conductive trace 111, a conductive trace 112, a planar magnetic field coil 160, and a magnetic field coil 170. Substrate 110 may be between substrates 120 and 130. Coil 160 and coil 170 may function as a modulation coil and a nulling coil, respectively. Even though the nulling coils can cancel out unwanted background magnetic fields in real-world applications, they are utilized to generate quasi-DC magnetic field measured herein.

[0027] Each of coil 160 and coil 170 may include multiple coils. Hence, statements herein about coil 160 or coil 170 pertain, respectively, to one or more coils 160 and to one or more coils 170. The coils may include multiple stacked coils having reversed spiral directions, which results in enhanced magnetic fields. For example, coil 160 and / or coil 170 may include a first coil and a second coil having, respectively, a clockwise spiral direction and counterclockwise spiral direction from the coil edge to the coil center. The first coil and the second coil may be on opposite sides of the same substrate, e.g., substrate 120 or substrate 130.

[0028] Semiconductor die 150 and substrate 120 are affixed to substrate 110. Semiconductor die 150 includes a p-n junction 155, herein also diode 155, which may be a p-i-n junction. Semiconductor die 150 may be a bare semiconductor die and may be affixed to substrate 110 via wire bonding. In embodiments, semiconductor die 150 is attached to substrate 110 using gold-nanoparticle sintered pastes, with gold pads and routing lines directly formed onto substrate 110. 6LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0029] One or more of substrates 110, 120, and 130 may be composed of a high- temperature electrically insulating material, examples of which include alumina, zirconia, fused silica, crystalline sapphire, aluminum nitride, silicon nitride, a glass, a glass ceramic, or any combination thereof. In embodiments, semiconductor die 150 and p-n junction 155 are formed from a wide band-gap semiconductor, such as diamond, silicon carbide, gallium nitride, zinc oxide, boron nitride, an alloy thereof, or a combination thereof. The wide band-gap semiconductor may be a single polymorph of a crystalline material (e.g., the 3C-SiC, 4H-SiC, 6H-SiC, or 15R-SiC polymorph of silicon carbide) or a combination of polymorphs of one or more crystalline materials. Semiconductor die 150 and / or p-n junction 155 may include paramagnetic recombination centers.

[0030] Diode 155 may be a SiC diode, and may be a traditional SiC diode, e.g., one not specifically designed for magnetometry and / or including isotopically purified materials, thereby offering a cost-effective solution. Alternatively, e.g., for higher- precision applications, diode 155 may include purified SiC material, or another purified semiconductor, which reduces hyperfine interactions, leading to a narrower line width σ and an enhanced signal. In embodiments, diode 155 is encapsulated by vapor-deposited SiO₂ and Si₃N₄ films.

[0031] Diode 155 may be a lateral p⁺ / i / n⁺ diode intended for high-temperature operation, featuring an ion-implanted p-well within a low-doped n-epitaxial region on a mid-cut 4H-SiC conductive N⁺ substrate. Diode 155 may be fabricated on a wafer, which may contain aluminum-doped (i.e., p-type) epitaxial layers, which in turn were grown on conductive highly doped n+(nitrogen-doped) 4H-SiC substrates. Such a substrate may have a 4° miscut to the c-axis.

[0032] In embodiments, diode 155 is formed within an ion-implanted p-well region (with27Al at a concentration ~ 918 cm-3at around 0.7-μm depth). The p+and n+contact regions may be formed with ion implantation of27Al and14N, respectively, at concentrations ~920 cm-3. Ohmic contact metallization may be achieved through sputtered and high-temperature annealed nickel. Final pad metal may be gold deposited over ohmic metal and other interconnect refractory metals. In embodiments, diode 155 is encapsulated with vapor-deposited dielectric films of silicon oxide and silicon nitride. The backside of the metal may be metalized with nickel (subsequently silicided by annealing at high temperature) and thick gold. 7LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0033] Embodiments of sensor head 100 include one or more standoffs 103, each of which has a first end affixed to substrate 110 and a second end affixed to substrate 120. Embodiments of sensor head 100 include one or more standoffs 104, each of which has a first end affixed to substrate 110 and a second end affixed to substrate 130. Each of standoffs 103 and 104 may be a metal standoff.

[0034] Magnetic field coil 160 is on substrate 120 and may include, or be formed of, a metal trace 161 on substrate 120. In embodiments, coil 160 is configured to generate a magnetic field, at p-n junction 155, of at least 35 G / A. Sensor head 100 may include either or both of a diffusion barrier 123 and a dielectric layer 127, which functions as an oxidation-protective layer. Diffusion barrier 123 is between coil 160 and second substrate 120. Dielectric layer 127 is on coil 160 such that coil 160 is between diffusion barrier 123 and dielectric layer 127.

[0035] Inset 102 of FIG.1 depicts a plan view of coil 160. Coil 160 may form a planar spiral with a plurality of loops, as shown in inset 102. Inset 102 denotes a width 162, which may be a width of metal trace 161. Width 162 may be between 10 µm and 1 mm, e.g., between 10 µm and 300 µm. The number of loops may be five or more, and have an interloop spacing 164. Spacing 164 may be between 10 µm and 1 mm, e.g., between 10 µm and 300 µm.

[0036] Diode 155 has an anode 155a and a cathode 155c. Conductive traces 111 and 112 are on substrate 110 and are electrically connected to anode 155a and cathode 155c, respectively. Sensor head 100 may include wires 114(1) and 114(2) electrically connected to conductive traces 111 and 112, respectively. Each of wires 114 may be a high-temperature wire, e.g., one that maintains its conductivity and does not melt, within a temperature range of 20°C to 600°C. Wires 114 may be ceramic-coated to withstand high temperatures.

[0037] Magnetic field coil 170 is on substrate 130 and may include, or be formed of, a metal trace 171 on substrate 130. A material composition of coils 160 and 170 (e.g., of metal trace 161 and 171) may include platinum, tungsten, molybdenum, gold, silver, aluminum, copper, or any combination thereof.

[0038] Embodiments of sensor head 100 may have a compact form factor (e.g., 1.1 to ten times the coil diameter) and / or low power consumption of under 0.5 W at 600°C for magnetic fields below 5 G, which makes this solution especially attractive. 8LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 Such a robust and low-SWaP design positions sensor head 100 as a promising option for all-electrical relative magnetometry in harsh environments.

[0039] FIG.2 is an isometric view of a sensor head 200, which is an example of sensor head 100. Sensor head 200 includes substrates 210, 220, and 230, and a coil 260, which are respective examples of substrates 110, 120, and 130, and coil 160 of sensor head 100.

[0040] Embodiments of sensor head 100 may achieve a sensitivity ofif the ratio between the current used and the signal is increased to 1% with a 0.2-mT linewidth (see Figure 6 and the related discussion of sensitivity in C. J. Cochrane et al., “Vectorized magnetometer for space applications using electrical readout of atomic scale defects in silicon carbide,” Scientific Reports 6, 37077 (2016)). The sensitivity in terms of magnetic field per root hertz is critical in assessing the performance and potential applications of NZFMR devices in various settings and thus we describe such sensitivity in FIG.7 (with magnetic field in tesla on the y axis and bandwidth in hertz on the x axis), allowing the sensitivity to be read off FIG.7.

[0041] In the realm of device fabrication for sensor head 100, the utilization of isotopically pure SiC represents a significant advancement. By using SiC crystals that are depleted of isotopes^^Si or^^C , we can effectively sharpen the linewidth of the device. This refinement in the linewidth directly contributes to pushing the sensitivity of embodiments of sensor head 100 toward its theoretical limits, thereby enhancing its performance in precise magnetic field detection.

[0042] In embodiments, sensor head 100 detects DC magnetic fields via the response of diode 155 using lock-in amplification. For example, sensor head 100 may be part of a magnetometer 300, shown in FIG.3. FIG.3 is a schematic of a magnetometer 300. Magnetometer 300 includes at least one of the following components: sensor head 100, a computer 311, a power source 313, a nulling-coil amplifier 315, a signal generator 317, a microcontroller 321, a modulation-coil amplifier 333, an oven 336, an analog-to- digital converter 331 (ADC 331), a lock-in amplifier 343, and a preamplifier 347.

[0043] In an example use scenario, signal generator 317 ramps a signal 317s (e.g., a voltage) applied to nulling-coil amplifier 315 from a negative to a positive value over a sweep period, e.g., sixty seconds. Signal 317s may be an AC signal. This controlled voltage sweep alters the background magnetic field experienced by diode 155 of sensor head 100, which is in oven 336. Repeating this sweep multiple times, multiple datasets 9LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 can be acquired under the same conditions and then averaged to enhance signal quality and reduce noise.

[0044] In embodiments, nulling-coil amplifier 315 is assembled entirely from commercially available components, such as an OPA541-based, high-voltage, high- current audio amplifier board, providing a budget-friendly alternative to specialized lab instrumentation. Similarly, modulation-coil amplifier 333 may include a TPA3116D2- based XH-M543 dual-channel stereo audio amplifier board. Both amplifiers 315 and 333 may be powered by power source 313, which may be a programmable DC power source (e.g., Rigol DP932E).

[0045] Coil 160 may generate alternating magnetic fields driven by signal 317s, which interact with a p-n junction 155 to modulate its magnetization. The modulation frequency of signal 317s may be chosen to enhance signal sensitivity significantly when suppressing low-frequency noise. Besides their different functionalities, coil 160 may have a 28-AWG cross-sectional area and a field efficiency of 40 G / A. Coil 160 may be wire-bonded with ceramic-coated wire, secured with through-hole connectors, and further enhanced with conductive paste to reduce resistance to create the stack shown in FIG.2.

[0046] To handle the weak signals produced by diode 155, magnetometer 300 may integrate preamplifier 347, lock-in amplifier 343 (e.g., SR850 from Stanford Research Instruments), and different control components. Preamplifier 347 strengthens the weak SDR signals while lock-in amplifier 343 isolates and enhances the signal of interest by locking onto the modulation frequency. This lock-in technique improves the signal-to-noise ratio, thus facilitating extraction of meaningful data from the noisy environment. Lock-in amplifier 343 may be tuned to the modulation frequency, allowing selective detection of the resonant responses induced by the alternating magnetic field. ADC 331 digitizes amplified analog signals received from lock-in amplifier 343. Microcontroller 321 receives the digital signals from ADC 331 and sends them to computer 311. ADC 331 may be part of microcontroller 321.

[0047] Embodiments of magnetometer 300 are not limited to DC detection. By adequately changing the electronics and the features of lock-in amplifier 343 to detect a signal characterized by frequencies of the order of kilohertz, magnetometer 300 may be configured to detect AC magnetic fields. 10LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 3. Magnetometer Measurements

[0048] FIG.4 and FIG.5 show averaged NZFMR signals and forward bias measurements, respectively, of diode 155 in embodiments of sensor head 100 of FIG.1 at different operating temperatures. As the temperature increases, the NZFMR signals shift and the relative current exhibits a gradual change across the magnetic field range (FIG.4). This shift stems from the local change in the magnetic field background sensed by diode 155 at higher temperatures. The data of FIG.4 are averaged over twenty measurements at each temperature. Without this averaging, the temperature-induced drift would mask the NZFMR signal, making it challenging to detect magnetic field- related changes. Although the NZFMR signal weakens at higher temperatures, the correlation between the magnetic field and current remains evident, confirming that embodiments of sensor head 100 can detect NZFMR under extreme thermal conditions. At high temperatures, diode 155 becomes more conductive. In embodiments, a bias voltage applied to diode 155 is reduced at higher temperatures to maintain a constant current (e.g., of 200 nA) flowing through diode 155, which helps minimize thermal effects.

[0049] FIG.6 and FIG.7 demonstrate how an applied offset magnetic field affects NZFMR measurements and device sensitivity, respectively. FIG.6 shows NZFMR signals for three offset fields: +1.5 G (trace 601), 0 G (trace 602), and −1.5 G (trace 603). Each of traces 601–603 exhibits a systematic vertical shift in relative current as the offset field varies. Traces 601 and 603 intersect a horizontal reference line 628, originating from the zero-offset trace 602, at approximately −1.25 G and +1.5 G, respectively. These values match the applied offset fields within a precision of ±0.25 G. This shift indicates a clear correlation between changes in the magnetic environment and the relative current response, demonstrating NZFMR magnetometry at high temperatures.

[0050] FIG.7 is a plot of sensitivity as a function of bandwidth for various temperatures, for an embodiment of sensor head 100 of FIG.1. The sensitivity isestimated using the relation ^^⁄ ^Δ^ = 2^^^^^^ ! ⁄ Δ ", where ^ is the electroniccharge,!is the DC current responsible for the flicker noise, Δ^ is the measurement bandwidth, Δ is the current change, and ^ is the signal line width. As the bandwidth increases, the magnetometer’s sensitivity decreases because more noise is introduced over a broader range of frequencies, which lowers the signal-to-noise ratio, thereby making it harder to detect small changes in the magnetic field. 11LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0051] Simultaneously, FIG.7 also shows a temperature dependence, with lower temperatures yielding better sensitivity. This behavior is due to increased thermal noise, raising the temperature. This reduction in sensitivity at elevated temperatures is primarily driven by two factors: the broadening of the NZFMR signal (i.e., ^) and a decrease in the current response (i.e., Δ ) to magnetic fields.

[0052] Higher temperatures reduce the current response to applied magnetic fields due to increased carrier recombination and thermal excitations that compete with the magnetoresistive effect. Despite these factors, the sensitivity reduction is modest (almost two orders of magnitude), demonstrating that sensor head 100 remains robust for high-temperature magnetic field detection, even though not specifically designed for magnetometry applications.

[0053] Embodiments of sensor head 100 may have a line width of approximately 2 G, as shown in FIG.8. FIG.8 shows EDMR data taken at a −2.65-V bias on the p-n junction 155, under a 430-MHz RF field, averaging 27 scans together. The current measured was approximately 0.16 µA, which translates to a proportion of 102 pA / 0.16 µA, equating to 0.07%. The observed peaks occurred at −310.21 G, 3.95 G, and 317.94 G, compared to the analytically expected peak around 316.1 G. This linewidth corresponds to σ = 0.2 mT, which when combined with the 0.07% signal-to-driving- current ratio, means we expect a sensitivity of about 1.1 µT / Hz1 / 2, which may be increased with optimization. 4. Calibration and Fabrication Methods

[0054] FIG.9 is a flowchart illustrating a method 900 for fabricating embodiments of sensor head 100. Herein, the description of methods, such as method 900, include parenthetical numbers following terms recited by the method. The parenthetical number indicates that the element associated with the number in parentheses is an example of the term. For example, the description of step 910 below recites “a PN junction (155),” which means that p-n junction 155 of sensor head 100 of FIG.1 is an example of the modulation coil introduced in step 910.

[0055] Method 900 includes at least one of steps 910, 920, 930, 940, and 950. Step 910 includes forming a PN junction (155) in a silicon carbide wafer. Step 920 includes introducing paramagnetic recombination centers into the junction region by electron irradiation at an energy and fluence sufficient to create vacancies at a target 12LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 depth, followed by annealing at elevated temperature to stabilize the defect population. Step 930 includes dicing the wafer into dies (150). Step 940 includes bonding, e.g., wire bonding, each die onto a ceramic substrate (110) bearing the integrated modulation coils (160) and nulling coils (170) using high-temperature solder. Step 950 includes providing contacts (111) to enable DC biasing and readout.

[0056] FIG.10 is a flowchart illustrating a method 1000 for calibrating embodiments of sensor head 100. Method 1000 includes at least one of steps 1010, 1020, 1030, 1040, and 1050. Step 1010 includes applying a low-frequency magnetic field modulation around zero field via a modulation coil (160) while applying a compensating field with a nulling coil (170). Step 1020 includes acquiring the NZFMR response and computing its derivative with respect to the applied field to identify a point of maximal slope near zero field.

[0057] Step 1030 includes adjusting the nulling coil current in a closed-loop feedback manner to maintain the sensor at that maximal-slope point as a zero-field offset. Step 1040 includes intermittently superimposing a known test magnetic field and measuring the corresponding change in the NZFMR response to determine a field-to- drive scaling factor. Step 1050 includes updating in real time the mapping from coil drive to magnetic field using the determined offset and scale factor to provide corrected absolute field readings over time.

[0058] FIG.11 is a flowchart illustrating a high-temperature magnetometry method 1100. Method may be implemented with embodiments of magnetometer 300 of FIG.3. Method 1100 includes at least one of steps 1110, 1120, 1130, and 1140, at least two of which may occur simultaneously.

[0059] Step 1110 includes driving a bias current through the p-n junction (155) of the bare semiconductor die (150) of a magnetometer (300). Step 1120 includes driving the magnetic-field coil (160) of the magnetometer to generate, at the p-n junction, a compensating DC magnetic field. Step 1130 includes sensing a variation in the bias current. In embodiments, steps 1110 and 1120 occur simultaneously.

[0060] Step 1140 includes determining, based on the variation in the bias current, the magnitude of an external magnetic field applied to the p-n junction. In step 1140, said determining may be based on a zero-field offset and a scale factor. In such embodiments, method 1100 may further include calibrating the magnetometer, e.g., via method 1000, to determine the zero-field offset and the scale factor. 13LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0061] At least one of steps 1110–1140 may occur when the magnetometer is at a temperature between 400°C and 600°C, for example, between 500°C and 600°C. At least one of steps 1110–1140 may occur without any microwave or optical excitation of the silicon-carbide p-n junction. Combinations of Features

[0062] Features described above, as well as those claimed below, may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations.

[0063] Embodiment 1. A magnetometer includes a first substrate, a bare semiconductor die, a first conductive trace and a second conductive trace, a second substrate, and a planar magnetic-field coil. The first substrate is composed of a high- temperature electrically insulating material. The bare semiconductor die is affixed to the first substrate and includes a p-n junction that contains paramagnetic recombination centers. A first conductive trace and a second conductive trace are on the first substrate. The first conductive trace is electrically connected to an anode of the p-n junction. The second conductive trace is electrically connected to a cathode of the p-n junction. The second substrate is composed of a high-temperature electrically insulating material and is affixed to the first substrate. The planar magnetic-field coil is composed of a metal trace formed on the second substrate.

[0064] Embodiment 2. The magnetometer of embodiment 1, the first substrate and the second substrate being a same common substrate having a first side and a second side opposite the first side, wherein: the bare semiconductor die, the first conductive trace, and the second conductive trace are on the first side; and the planar magnetic-field coil is on the second side.

[0065] Embodiment 3. The magnetometer of either one of embodiments 1 or 2, configured to operate over a temperature range of 20°C to 600°C.

[0066] Embodiment 4. The magnetometer of any one of embodiments 1–3, each of the first and second high-temperature substrates being composed of alumina, zirconia, fused silica, crystalline sapphire, a glass, a glass ceramic, or any combination thereof.

[0067] Embodiment 5. The magnetometer of any one of embodiments 1–4, the p- n junction being composed of silicon carbide. 14LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474

[0068] Embodiment 6. The magnetometer of any one of embodiments 1–5, the p- n junction including a p-i-n junction.

[0069] Embodiment 7. The magnetometer of any one of embodiments 1–6 further includes: a third substrate composed of a high-temperature electrically insulating material; and a second magnetic-field coil composed of a metallic trace formed on the second substrate; wherein the first substrate is between the second substrate and the third substrate.

[0070] Embodiment 8. The magnetometer of any one of embodiments 1–7, further including one or more metallic standoffs, each of the one or more metallic standoffs having a first end and a second end, the first end being affixed to the first high- temperature substrate, the second end being affixed to the second high-temperature substrate.

[0071] Embodiment 9. The magnetometer of any one of embodiments 1–8, the magnetic-field coil being configured to generate a magnetic field, at the p-n junction, of at least 35 G / A.

[0072] Embodiment 10. The magnetometer of any one of embodiments 1–9, the metal trace being composed of platinum, tungsten, molybdenum, gold, silver, aluminum, copper, or any combination thereof.

[0073] Embodiment 11. The magnetometer of any one of embodiments 1–10, further including one or both of: a diffusion barrier between the metal trace and the second substrate; and an oxidation-protective dielectric layer on the metal trace, the metal trace being between the diffusion barrier and the oxidation-protective dielectric layer.

[0074] Embodiment 12. The magnetometer of any one of embodiments 1–11, the metal trace forming a planar spiral with at least five loops.

[0075] Embodiment 13. The magnetometer of any one of embodiments 1–12, wherein: the metal trace has a trace width between 10 and 200 microns; and the planar magnetic-field coil forms a plurality of loops with an inter-loop spacing between 10 and 200 microns.

[0076] Embodiment 14. A method for high-temperature magnetometry includes: driving a bias current through the p-n junction of the bare semiconductor die of the magnetometer of embodiment 1; driving the magnetic-field coil of the magnetometer to generate, at the p-n junction, a compensating DC magnetic field; sensing a variation in 15LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 the bias current; and determining, based on the variation in the bias current, the magnitude of an external magnetic field applied to the p-n junction.

[0077] Embodiment 15. The method of embodiment 14, wherein said driving the bias current and said driving the magnetic-field coil comprise simultaneously driving the bias current and the magnetic field coil.

[0078] Embodiment 16. The method of either one of embodiments 14 or 15, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur while the magnetometer is at a temperature between 400°C and 600°C.

[0079] Embodiment 17. The method of embodiment 16, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur while the magnetometer is at a temperature between 500°C and 600°C.

[0080] Embodiment 18. The method of any one of embodiments 14–17, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur without any microwave or optical excitation of the p-n junction.

[0081] Embodiment 19. The method of any one of embodiments 14–18, wherein said determining the magnitude of the external magnetic field is based on a zero-field offset and a scale factor.

[0082] Embodiment 20. The method of embodiment 19, further including calibrating the magnetometer to determine the zero-field offset and the scale factor.

[0083] Changes may be made in the above methods and systems without departing from the scope of the present embodiments. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments.

[0084] As used in this specification, any appendices thereto, and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. It should also be noted that the term “or” is generally employed in its sense including “and / or” unless the content clearly dictates otherwise. Regarding instances of the terms “and / or” and “at least one of,” for example, in the cases of “A and / or B,” “at least one of A and B,” and “at least one of A or B,” such phrasing 16LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 encompasses the selection of (i) A only, or (ii) B only, or (iii) both A and B. In the cases of “A, B, and / or C, ” “at least one of A, B, and C,” and “at least one of A, B, or C,” such phrasing encompasses the selection of (i) A only, or (ii) B only, or (iii) C only, or (iv) A and B only, or (v) A and C only, or (vi) B and C only, or (vii) each of A and B and C. This may be extended for as many items as are listed.

[0085] The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween. 17LEGAL\79413339\18

Claims

Attorney Docket No. QCAD.P2001WO / 00646474 CLAIMS What is claimed is:

1. A magnetometer comprising: a first substrate composed of a high-temperature electrically insulating material; a bare semiconductor die affixed to the first substrate, the bare semiconductor die including a p-n junction that contains paramagnetic recombination centers; a first conductive trace and a second conductive trace on the first substrate, the first conductive trace being electrically connected to an anode of the p-n junction, the second conductive trace being electrically connected to a cathode of the p-n junction; a second substrate composed of a high-temperature electrically insulating material, the second substrate being affixed to the first substrate; and a planar magnetic-field coil composed of a metal trace formed on the second substrate.

2. The magnetometer of claim 1, the first substrate and the second substrate being a same common substrate having a first side and a second side opposite the first side, wherein: the bare semiconductor die, the first conductive trace, and the second conductive trace are on the first side; and the planar magnetic-field coil is on the second side.

3. The magnetometer of claim 1, configured to operate over a temperature range of 20°C to 600°C.

4. The magnetometer of claim 1, each of the first and second high-temperature substrates being composed of alumina, zirconia, fused silica, crystalline sapphire, a glass, a glass ceramic, or any combination thereof.

5. The magnetometer of claim 1, the p-n junction being composed of silicon carbide.

6. The magnetometer of claim 1, the p-n junction being composed of diamond. 18LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 7. The magnetometer of claim 1, the p-n junction comprising a p-i-n junction.

8. The magnetometer of claim 1, further comprising: a third substrate composed of a high-temperature electrically insulating material; and a second magnetic-field coil composed of a metallic trace formed on the second substrate; wherein the first substrate is between the second substrate and the third substrate.

9. The magnetometer of claim 1, further comprising one or more metallic standoffs, each of the one or more metallic standoffs having a first end and a second end, the first end being affixed to the first high-temperature substrate, the second end being affixed to the second high-temperature substrate.

10. The magnetometer of claim 1, the magnetic-field coil being configured to generate a magnetic field, at the p-n junction, of at least 35 G / A.

11. The magnetometer of claim 1, the metal trace being composed of platinum, tungsten, molybdenum, gold, silver, aluminum, copper, or any combination thereof.

12. The magnetometer of claim 1, further comprising one or both of: a diffusion barrier between the metal trace and the second substrate; and an oxidation-protective dielectric layer on the metal trace, the metal trace being between the diffusion barrier and the oxidation-protective dielectric layer.

13. The magnetometer of claim 1, wherein: the metal trace has a trace width between 10 and 200 microns; and the planar magnetic-field coil forms a plurality of loops with an inter-loop spacing between 10 and 200 microns.

14. A method for high-temperature magnetometry, comprising: driving a bias current through the p-n junction of the bare semiconductor die of the magnetometer of claim 1; 19LEGAL\79413339\18Attorney Docket No. QCAD.P2001WO / 00646474 driving the magnetic-field coil of the magnetometer to generate, at the p-n junction, a compensating DC magnetic field; sensing a variation in the bias current; and determining, based on the variation in the bias current, the magnitude of an external magnetic field applied to the p-n junction.

15. The method of claim 14, wherein said driving the bias current and said driving the magnetic-field coil comprises simultaneously driving the bias current and the magnetic field coil 16. The method of claim 14, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur while the magnetometer is at a temperature between 400°C and 600°C.

17. The method of claim 16, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur while the magnetometer is at a temperature between 500°C and 600°C.

18. The method of claim 14, wherein said driving the bias current, said driving the magnetic-field coil, said sensing, and said determining occur without any microwave or optical excitation of the p-n junction.

19. The method of claim 14, wherein said determining the magnitude of the external magnetic field is based on a zero-field offset and a scale factor.

20. The method of claim 19, further comprising calibrating the magnetometer to determine the zero-field offset and the scale factor. 20LEGAL\79413339\18

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