Development of simultaneous detection method of millimeter-wave ESR and EDMR signals of phosphorous-doped silicon

Development of simultaneous detection method of millimeter-wave ESR and EDMR signals of phosphorous-doped silicon | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Development of simultaneous detection method of millimeter-wave ESR and EDMR signals of phosphorous-doped silicon Hayato Ito, Yuta Shimizu, Akinori Ohashi, Tsunehiro Omija, Yutaka Kurachi, and 8 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8998506/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract We report the development of a measurement system enabling simultaneous detection of millimeter-wave electron spin resonance (ESR) and electrically detected magnetic resonance (EDMR) signals in lightly phosphorus-doped silicon (Si:P). Such simultaneous detection is motivated by the need to clarify spin-dependent transport and dynamic nuclear polarization mechanisms in high magnetic-field and low-temperature conditions relevant to Si:P-based quantum computing architectures. A Si:P sample was mounted on a Fabry-Pérot resonator and was equipped with comb-shaped electrodes optimized for millimeter-wave transmission, allowing ESR excitation while monitoring the resistance changes under optical illumination. Using a 130 GHz millimeter-wave source, we successfully observed ESR absorption signals and corresponding EDMR responses simultaneously at temperatures around 5 K. The EDMR signals exhibited sharper linewidths compared to ESR. These results demonstrate the feasibility of combined ESR–EDMR measurements and provide a foundation for future studies on coupled electron–nuclear spin dynamics, including the simultaneous observation of ESR and EDMR. Electron spin resonance (ESR) Electrically detected magnetic resonance (EDMR) Millimeter wave Phosphorus-doped silicon Spin-dependent transport Figures Figure 1 Figure 2 Figure 3 Figure 4 1 Introduction Phosphorus-doped silicon (Si:P) has long been regarded as a promising platform for solid-state quantum computing due to the long coherence times of donor electron and nuclear spins, from the viewpoint of DiVincenzo’s criteria [ 1 ]. In particular, Kane’s proposal for a silicon-based quantum computer highlights the importance of operating under conditions of very low temperature ( T ) and high magnetic field ( B ), where electron spins are nearly fully polarized [ 2 ]. Precise control and sensitive detection of donor spin states under such high B/T conditions are essential for realizing Kane’s model and closely related spin-based quantum computers. Conventional continuous-wave (cw) ESR detects spin resonance through microwave absorption and typically requires a large number of spins. In contrast, EDMR indirectly detects ESR via changes in electrical resistance caused by spin-dependent recombination processes, providing an order-of-magnitude higher sensitivity [ 3 , 4 ]. Previous EDMR studies on Si:P have revealed unconventional spin dynamics, including dynamic nuclear polarization with a sign opposite to that induced by conventional ESR [ 5 ]. To elucidate the origin of these differences, it is highly desirable to observe ESR and EDMR signals simultaneously under identical conditions. To perform simultaneous millimeter-wave (mm-wave) ESR and EDMR measurements, the electrode-equipped sample must be placed within the mm-wave field. As demonstrated by McCamey and co-workers [ 5 , 6 ], it is possible to position a thin linear electrode aligned with mm-wave polarization. We have been performing cryogenic mm-wave ESR and ESR/nuclear magnetic resonance (NMR) double magnetic resonance measurements using Fabry-Pérot resonators (FPR) [ 7 – 10 ]. The electromagnetic wave inside our FPR is linearly polarized owing to the polarization of the connected rectangular waveguide. Therefore, thin linear electrodes can be inserted into the FPR without disturbing the resonant mode. This paper reports the first example of simultaneous measurement of mm-wave ESR and EDMR signals from an electrode-equipped Si:P sample at a very low temperature. 2 Experimental 2.1 Sample preparation Figure 1 (a) shows a cross-sectional schematic of the FPR. The spot size of the resonant mode TEM 00 q ( q : integer) of the FPR is less than 4 mm in diameter, since the radius of curvature of the spherical concave mirror is 10 mm [ 11 ] 1 . Further, the resistance of the sample must be below the measurable upper limit (several M Ω) even at very low temperatures. Considering these conditions, we designed the comb-shaped electrode which consists of 50 parallel lines with a line width of 10 µm and a spacing of 10 µm as shown in Figs. 1 (b) and 1(c). The overlapping region between opposing electrodes spans 3 mm in length. In order to avoid disturbance of the electromagnetic modes in the FPR, the electrode pads should be placed outside the diameter approximately twice that of the mm-wave spot [ 8 ]. A 10 mm × 12 mm rectangular piece was cut from a commercially purchased Si:P wafer (0.09 Ω⋅cm at room temperature, thickness 0.2 mm). The dopant concentration is approximately 1×10 17 cm –3 , which is lower than critical concentration 3.75 × 10 18 cm –3 [ 12 ]. After the oxidized layer on the Si:P sample surface was removed using hydrofluoric acid, the electrode patterns were defined using maskless LED lithography. Aluminum electrodes with thickness approximately 0.1 µm were deposited using a vacuum evaporation system. The sample was annealed at 400°C for 20 min in a forming gas (H 2 5% + N 2 95%). At room temperature, the resistivity of Si:P sample is low enough to disturb the resonant mode of FPR when the sample is put in the FPR. In order to check the resonant mode of the FPR with the electrode-patterned sample at room temperature, a non-doped Si sample with the same electrode design was also fabricated. It was confirmed at room temperature by using a mm-wave vector network analyzer (MVNA8-350-2, AB Millimetre) that mm-wave transmitted through the non-doped electrode-patterned sample in the FPR when the electrode orientation was aligned with the polarization direction in the FPR. 2.2 Experimental setup An overview of the experimental setup is drawn in Fig. 2 . Cw-ESR measurements were performed using a conventional magnetic-field-modulation technique. The mm-wave radiation was generated using an active multiplier chain (Virginia Diodes, Inc., VDI AMC 425), which covers the frequency range from 129.5 to 134.5 GHz with a maximum output power of approximately 100 mW. The transmitted mm-wave was guided to the FPR through magic-T hybrid. The reflected mm-wave was detected using a liquid-helium-cooled InSb hot-electron detector system (QMC Instruments Ltd., Type QFI/XBI). Magnetic-field modulation was achieved using a 50-turn coil installed around the sample region. An AC current of 0.2 A was supplied by a bipolar power supply (Kikusui PBZ40-10) to the modulation coil during ESR measurements, producing a modulation field of approximately 1.5 G p-p . The output of the InSb detector was processed using a lock-in amplifier. The lock-in detection output was recorded on a PC, while the main magnetic field produced by the superconducting magnet (Oxford Instruments plc.) was swept. The resonance frequency of FPR can be adjusted by changing the distance between spherical and flat mirrors. In the current experiment, the vertical position of the flat mirror of FPR was adjusted by a piezo positioner (ANPz51, attocube systems) which was controlled by a piezo driver (ANC300 with a stepping module ANM150, attocube systems). For optical excitation for EDMR measurements, a white LED (CREE XLamp XB-D, 150 lm at 0.35 A) was employed. The emitted light was passed through an infrared-cut filter and coupled to an optical fiber (Mitsubishi Chemical, Eska CK60) using convex lenses. Note that the optical fiber and the LED were inexpensive (a few euros for each). The light was guided to the sample region inside the FPR, and the optical intensity was controlled by adjusting the driving current of the LED up to 1.0 A. For EDMR measurements, the electrical current across the Si:P sample was measured by applying a fixed AC voltage using a lock-in amplifier. All lock-in measurements in this study were performed using lock-in amplifiers (SR830 DSP, Stanford Research Systems). As shown in the next section, we first measured temperature dependence of the resistance of the sample. It is important for EDMR measurements to check whether the resistance is sufficiently reduced by the optical excitation. An AC resistance bridge (AVS-47, PICOWATT) was employed for resistance measurements. The experimental setup was essentially the same as that described above for the EDMR measurements, except that the resistance bridge was used instead of a lock-in amplifier. 3 Results and Discussion We performed a 2-terminal measurement between the comb-shaped electrodes. Figure 3 shows the temperature dependence of the resistance. The measured resistance includes the resistance of the short Al wires and bonding interfaces. At zero magnetic field, the resistance of Si:P sample increased to the MΩ range below approximately 18 K. Under optical illumination with the LED drive current of 0.3 A, the resistance was significantly reduced, allowing reliable resistance measurements even at the lowest temperatures investigated in this study. Furthermore, the resistance increased upon application of a magnetic field of 4.6 T; for LED currents of 0.3 A around 10 K, the resistance at 4.6 T reached approximately five times that at zero field while remaining within a measurable range. Although the temperature and magnetic field dependences of the resistance possibly involve interesting physics, further discussions are beyond the scope of this paper. Figure 4 (a) shows the representative cw-ESR spectra obtained at approximately 130 GHz with optical illumination. The LED drive current was 1.0 A, which generates approximately 300 lm emission, during the measurement. Two well-resolved resonance lines corresponding to the hyperfine-split transitions of isolated phosphorus donors [ 5 , 7 , 10 , 13 ] were observed. An additional line appeared between the two lines, which is most likely attributed to phosphorus clusters [ 14 ]. The ESR line shapes were absorption-like in spite of the magnetic field-modulation method, which is attributed to the passage effect under the present experimental conditions [ 15 ]. Simultaneously, EDMR signals (Fig. 4 (b)) appeared at magnetic fields corresponding to the ESR transitions of isolated donors. In contrast, no clear EDMR signals associated with the phosphorus clusters were detected. The typical EDMR signal amplitude was Δ \(I\) ≈ 60 pA, corresponding to a relative change of Δ \(I\) / \(I\) ≈ 0.13%. Because the Si:P surface area in the comb-shaped electrode overlapping area excluding the electrodes is approximately 3 mm 2 which is inside the spot size, we can estimate that 6 × 10 13 spins possibly contribute to the signal. This value is overestimated because the illuminated light can only penetrate to a depth of roughly fractions of a micrometer from the surface of silicon [ 16 ]. A direct comparison between ESR and EDMR responses reveals that the EDMR resonance lines are significantly sharper than the corresponding ESR lines. One may notice that the observed ESR linewidth of approximately 8 G is broader than 3–4 G linewidth which is due to randomly distributed 29 Si hyperfine shifts [ 10 , 17 ]. This broadening is also attributed to the passage effect under the present experimental conditions [ 15 ]. In contrast, EDMR selectively probes spin-dependent recombination processes including interface level close to oxidized surface involving a subset of donor spins [ 4 , 6 , 18 ], which is not directly related to the passage condition, whereas ESR reflects the ensemble-averaged response of all resonant spins. Further, considering that the EDMR process involves the interface level, the absence of the P-cluster central peak in the EDMR spectrum may indicate fewer clusters near the interface. The EDMR signal intensity exhibits a pronounced dependence on the magnetic-field modulation frequency, reaching a maximum at approximately 2 kHz. This behavior suggests the presence of characteristic timescales associated with carrier recombination and spin relaxation processes, which govern the EDMR mechanism. The detailed data with discussion will appear elsewhere. These results demonstrate that simultaneous ESR and EDMR measurements provide complementary information on donor spin systems. While ESR offers a direct spectroscopic probe of the spin energy levels, EDMR highlights the subset of spins actively participating in transport-related processes. The microscopic mechanism for the observed discrepancies between ESR and EDMR responses is open question at present. Nevertheless, we believe that our results underscore the importance of combined detection for elucidating the microscopic origin of spin-dependent phenomena in Si:P. In principle, it should be possible to add NMR to our simultaneous ESR and EDMR measurement system. We expect this system to provide a foundation for future research on the dynamics of the coupled electron-nuclear spin system. 4 Summary In summary, we have demonstrated simultaneous mm-wave ESR and EDMR measurements on lightly doped Si:P using FPR under optical excitation. While ESR spectra exhibit resonance lines from both isolated donors and phosphorus clusters, EDMR signals were observed only for isolated donor states with significantly sharper line shapes compared with ESR lines. The absence of cluster-related EDMR signals and the modulation-frequency dependence of the EDMR signal intensity remain open issues. These results demonstrate that EDMR selectively probes spin-dependent transport processes, and further investigations are required to clarify the microscopic mechanisms involved. We have shown the feasibility of combined ESR–EDMR measurements which provides a foundation for future studies of coupled electron–nuclear spin dynamics, including simultaneous observation of ESR and EDMR. Declarations Acknowledgements This work was supported by JSPS KAKENHI Grant Number JP21KK0047 and the Cooperative Research Program of Research Center for Development of Far-Infrared Region, University of Fukui (R05FIRDP002C, R06FIRDG006D). This work was also performed under the Cooperative Research Program of “Network Joint Research Center for Materials and Devices (MEXT).” Authors are grateful to Mr. Shoichi Sakakihara (The University of Osaka) for his support on making Si:P samples, to Prof. Seitaro Mitsudo (University of Fukui) for his advice on constructing the experimental setup. One of the authors (Y. F.) expresses sincere thanks to Mr. Ei-ichi Kobayashi and staff of Cryogenic Laboratory, University of Fukui, for their support to the experiments. Funding This work was supported by JSPS KAKENHI Grant Number JP21KK0047 and the Cooperative Research Program of Research Center for Development of Far-Infrared Region, University of Fukui (R05FIRDP002C, R06FIRDG006D). This work was also performed under the Cooperative Research Program of “Network Joint Research Center for Materials and Devices (MEXT).” Conflict of interests The authors declare no competing interests. Data availability Data sets generated during the current study are available from the corresponding author on reasonable request. Author contributions Members of University of Fukui (H. I., Y. S., A. Ohashi, T. O., Y. K., K. H., Y. I. and Y. F.) and A. F. developed measurement systems and performed all measurements for the present work. Members of The University of Osaka (X.-F. L., G.M. G., M. M. and A. Oiwa) with H. I., Y. S., A. Ohashi, T. O., Y. F. and A. F. contributed sample preparation. H. I., Y. S. and A. Ohashi prepared drafts of all figures. Y. F. wrote the main manuscript text and finalized all figures with A. F. All authors reviewed the manuscript. References D.P. DiVincenzo, Science. 270 , 255 (1995). https://doi.org/10.1126/science.270.5234.255 B.E. Kane, Nat. (London). 393 , 133 (1998). https://doi.org/10.1038/30156 D.R. McCamey, H. Huebl, M.S. Brandt, W.D. Hutchison, J.C. McCallum, R.G. Clark, A.R. Hamilton, Appl. Phys. Lett. 89 , 182115 (2006). https://doi.org/10.1063/1.2358928 H. Morishita, L.S. Vlasenko, H. Tanaka, K. Semba, K. Sawano, Y. Shiraki, M. Eto, K.M. Itoh, Phys. Rev. B 80 , 205206 (2009). https://doi.org/10.1103/PhysRevB.80.205206 D.R. McCamey, J. van Tol, G.W. Morley, C. Boehme, Phys. Rev. Lett. 102 , 027601 (2009). https://doi.org/10.1103/PhysRevLett.102.027601 D.R. McCamey, G.W. Morley, H.A. Seipel, L.C. Brunel, J. van Tol, C. Boehme, Phys. Rev. B 78 , 045303 (2008). https://doi.org/10.1103/PhysRevB.78.045303 Y. Fujii, Y. Ishikawa, K. Ohya, S. Miura, Y. Koizumi, A. Fukuda, T. Omija, S. Mitsudo, T. 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Phys. 2 , 835–838 (2006). https://doi.org/10.1038/nphys465 Footnotes [1] The spot size on the flat mirror of a flat-concave FPR is given by , where , and are the wavelength, the distance between the mirrors and the radius of curvature of the spherical concave mirror, respectively. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 08 Apr, 2026 Editor assigned by journal 05 Mar, 2026 Submission checks completed at journal 05 Mar, 2026 First submitted to journal 28 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8998506","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622327868,"identity":"a8540287-614e-4a2b-917e-0d63b93017d6","order_by":0,"name":"Hayato Ito","email":"","orcid":"","institution":"University of Fukui","correspondingAuthor":false,"prefix":"","firstName":"Hayato","middleName":"","lastName":"Ito","suffix":""},{"id":622327869,"identity":"d915ccde-4ccf-441f-9439-82dd4aa8eef1","order_by":1,"name":"Yuta Shimizu","email":"","orcid":"","institution":"University of 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Field-modulation coil placed around the flat mirror and most of aluminum wires are omitted for visual clarity. The spacer between the flat mirror and the sample is a ring-shaped circuit board. The electric field intensity of the TEM003 resonant mode is shown in shades of gray. (b) A photograph of top view of the Si:P sample with electrodes on the spacer and the flat mirror. The lands on the spacer and the electrodes on the sample are bonded with 25 μm aluminum wires. (c) Overview of the electrode design on the sample (left) and enlarged view (right). Two-terminal measurement electrodes were used for resistance and EDMR measurements. Four-terminal electrodes were prepared for checking resistance of the Si:P sample. (d) A microscope photograph of deposited electrodes on Si:P. The approximate location of the shooting area is indicated by the blue dotted line on panel (c). Dark areas are Si:P and light-colored stipes indicate deposited aluminum electrodes.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8998506/v1/c319b8da83b70b15e1749f91.png"},{"id":106996571,"identity":"3faa9570-b64a-4e9a-8ba6-23925d79486d","added_by":"auto","created_at":"2026-04-15 15:30:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":163036,"visible":true,"origin":"","legend":"\u003cp\u003eAn overview of the experimental setup for ESR and EDMR measurements. The mm-wave output from an active multiplier chain (AMC) is guided to the sample via a magic-T hybrid. An oversized waveguide is used to reduce the attenuation between room temperature and low-temperature regions. The reflected mm-wave is guided to the InSb hot-electron detector. ESR signals are measured by lock-in detection of the InSb detector output at the magnetic field modulation frequency. The field-modulation coil is fixed around the flat mirror. The current for the modulation field, \u003cem\u003eI\u003c/em\u003e\u003csub\u003emod\u003c/sub\u003e, is supplied by a bipolar source which is controlled by an external input from a low-frequency signal generator. For the EDMR measurement, a lock-in amplifier supplies the bias voltage, \u003cem\u003eV\u003c/em\u003e\u003csub\u003eout\u003c/sub\u003e, and detects the sample current, \u003cem\u003eI\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e, using the current input mode. Details of the coupling method from LED to the optical fiber are omitted for simplicity. A piezo positioner is utilized to adjust the resonance frequency of FPR. The main magnetic field \u003cem\u003eB\u003c/em\u003e is produced vertically using a superconducting magnet (SCM).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8998506/v1/1924527229e518e38a4cbd11.png"},{"id":106997790,"identity":"a7dc8718-9202-4805-8804-3df36aedf240","added_by":"auto","created_at":"2026-04-15 15:35:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":107632,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature dependence of resistance obtained by the 2-terminal measurements between the comb-shaped electrodes. Black, blue and red circles show data for zero magnetic field without LED illumination, zero magnetic field with LED drive current of 0.3 A, and under 4.6 T with LED drive current of 0.3 A, respectively.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8998506/v1/7f1d47b8fa373ccb9abc27f1.png"},{"id":106996572,"identity":"b9bc47f9-d3b6-4567-b41a-1ffdfeea5ec8","added_by":"auto","created_at":"2026-04-15 15:30:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":109735,"visible":true,"origin":"","legend":"\u003cp\u003eSimultaneously recorded (a) ESR spectrum and (b) EDMR signals obtained at 5.1 K and at 129.6672 GHz under optical illumination from LED driven with 1.0 A.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8998506/v1/51052c7495c3bcbf83a8f5af.png"},{"id":107001506,"identity":"b6a6d055-a2d0-41d8-b464-9c9331319b1b","added_by":"auto","created_at":"2026-04-15 15:45:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1180011,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8998506/v1/c2eb7038-5672-4ad6-9b47-24abf46a61a9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Development of simultaneous detection method of millimeter-wave ESR and EDMR signals of phosphorous-doped silicon","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePhosphorus-doped silicon (Si:P) has long been regarded as a promising platform for solid-state quantum computing due to the long coherence times of donor electron and nuclear spins, from the viewpoint of DiVincenzo\u0026rsquo;s criteria [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In particular, Kane\u0026rsquo;s proposal for a silicon-based quantum computer highlights the importance of operating under conditions of very low temperature (\u003cem\u003eT\u003c/em\u003e) and high magnetic field (\u003cem\u003eB\u003c/em\u003e), where electron spins are nearly fully polarized [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Precise control and sensitive detection of donor spin states under such high \u003cem\u003eB/T\u003c/em\u003e conditions are essential for realizing Kane\u0026rsquo;s model and closely related spin-based quantum computers.\u003c/p\u003e \u003cp\u003eConventional continuous-wave (cw) ESR detects spin resonance through microwave absorption and typically requires a large number of spins. In contrast, EDMR indirectly detects ESR via changes in electrical resistance caused by spin-dependent recombination processes, providing an order-of-magnitude higher sensitivity [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Previous EDMR studies on Si:P have revealed unconventional spin dynamics, including dynamic nuclear polarization with a sign opposite to that induced by conventional ESR [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. To elucidate the origin of these differences, it is highly desirable to observe ESR and EDMR signals simultaneously under identical conditions.\u003c/p\u003e \u003cp\u003eTo perform simultaneous millimeter-wave (mm-wave) ESR and EDMR measurements, the electrode-equipped sample must be placed within the mm-wave field. As demonstrated by McCamey and co-workers [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], it is possible to position a thin linear electrode aligned with mm-wave polarization. We have been performing cryogenic mm-wave ESR and ESR/nuclear magnetic resonance (NMR) double magnetic resonance measurements using Fabry-P\u0026eacute;rot resonators (FPR) [\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The electromagnetic wave inside our FPR is linearly polarized owing to the polarization of the connected rectangular waveguide. Therefore, thin linear electrodes can be inserted into the FPR without disturbing the resonant mode. This paper reports the first example of simultaneous measurement of mm-wave ESR and EDMR signals from an electrode-equipped Si:P sample at a very low temperature.\u003c/p\u003e"},{"header":"2 Experimental","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Sample preparation\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) shows a cross-sectional schematic of the FPR. The spot size of the resonant mode TEM\u003csub\u003e00\u003cem\u003eq\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eq\u003c/em\u003e: integer) of the FPR is less than 4 mm in diameter, since the radius of curvature of the spherical concave mirror is 10 mm [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003csup\u003e1\u003c/sup\u003e. Further, the resistance of the sample must be below the measurable upper limit (several M Ω) even at very low temperatures. Considering these conditions, we designed the comb-shaped electrode which consists of 50 parallel lines with a line width of 10 \u0026micro;m and a spacing of 10 \u0026micro;m as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b) and 1(c). The overlapping region between opposing electrodes spans 3 mm in length. In order to avoid disturbance of the electromagnetic modes in the FPR, the electrode pads should be placed outside the diameter approximately twice that of the mm-wave spot [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA 10 mm \u0026times; 12 mm rectangular piece was cut from a commercially purchased Si:P wafer (0.09 Ω\u0026sdot;cm at room temperature, thickness 0.2 mm). The dopant concentration is approximately 1\u0026times;10\u003csup\u003e17\u003c/sup\u003e cm\u003csup\u003e\u0026ndash;3\u003c/sup\u003e, which is lower than critical concentration 3.75 \u0026times; 10\u003csup\u003e18\u003c/sup\u003e cm\u003csup\u003e\u0026ndash;3\u003c/sup\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. After the oxidized layer on the Si:P sample surface was removed using hydrofluoric acid, the electrode patterns were defined using maskless LED lithography. Aluminum electrodes with thickness approximately 0.1 \u0026micro;m were deposited using a vacuum evaporation system. The sample was annealed at 400\u0026deg;C for 20 min in a forming gas (H\u003csub\u003e2\u003c/sub\u003e 5% + N\u003csub\u003e2\u003c/sub\u003e 95%).\u003c/p\u003e \u003cp\u003eAt room temperature, the resistivity of Si:P sample is low enough to disturb the resonant mode of FPR when the sample is put in the FPR. In order to check the resonant mode of the FPR with the electrode-patterned sample at room temperature, a non-doped Si sample with the same electrode design was also fabricated. It was confirmed at room temperature by using a mm-wave vector network analyzer (MVNA8-350-2, AB Millimetre) that mm-wave transmitted through the non-doped electrode-patterned sample in the FPR when the electrode orientation was aligned with the polarization direction in the FPR.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental setup\u003c/h2\u003e \u003cp\u003eAn overview of the experimental setup is drawn in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Cw-ESR measurements were performed using a conventional magnetic-field-modulation technique. The mm-wave radiation was generated using an active multiplier chain (Virginia Diodes, Inc., VDI AMC 425), which covers the frequency range from 129.5 to 134.5 GHz with a maximum output power of approximately 100 mW. The transmitted mm-wave was guided to the FPR through magic-T hybrid. The reflected mm-wave was detected using a liquid-helium-cooled InSb hot-electron detector system (QMC Instruments Ltd., Type QFI/XBI). Magnetic-field modulation was achieved using a 50-turn coil installed around the sample region. An AC current of 0.2 A was supplied by a bipolar power supply (Kikusui PBZ40-10) to the modulation coil during ESR measurements, producing a modulation field of approximately 1.5 G\u003csub\u003ep-p\u003c/sub\u003e. The output of the InSb detector was processed using a lock-in amplifier. The lock-in detection output was recorded on a PC, while the main magnetic field produced by the superconducting magnet (Oxford Instruments plc.) was swept.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe resonance frequency of FPR can be adjusted by changing the distance between spherical and flat mirrors. In the current experiment, the vertical position of the flat mirror of FPR was adjusted by a piezo positioner (ANPz51, attocube systems) which was controlled by a piezo driver (ANC300 with a stepping module ANM150, attocube systems).\u003c/p\u003e \u003cp\u003eFor optical excitation for EDMR measurements, a white LED (CREE XLamp XB-D, 150 lm at 0.35 A) was employed. The emitted light was passed through an infrared-cut filter and coupled to an optical fiber (Mitsubishi Chemical, Eska CK60) using convex lenses. Note that the optical fiber and the LED were inexpensive (a few euros for each). The light was guided to the sample region inside the FPR, and the optical intensity was controlled by adjusting the driving current of the LED up to 1.0 A. For EDMR measurements, the electrical current across the Si:P sample was measured by applying a fixed AC voltage using a lock-in amplifier. All lock-in measurements in this study were performed using lock-in amplifiers (SR830 DSP, Stanford Research Systems).\u003c/p\u003e \u003cp\u003eAs shown in the next section, we first measured temperature dependence of the resistance of the sample. It is important for EDMR measurements to check whether the resistance is sufficiently reduced by the optical excitation. An AC resistance bridge (AVS-47, PICOWATT) was employed for resistance measurements. The experimental setup was essentially the same as that described above for the EDMR measurements, except that the resistance bridge was used instead of a lock-in amplifier.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and Discussion","content":"\u003cp\u003eWe performed a 2-terminal measurement between the comb-shaped electrodes. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the temperature dependence of the resistance. The measured resistance includes the resistance of the short Al wires and bonding interfaces. At zero magnetic field, the resistance of Si:P sample increased to the MΩ range below approximately 18 K. Under optical illumination with the LED drive current of 0.3 A, the resistance was significantly reduced, allowing reliable resistance measurements even at the lowest temperatures investigated in this study. Furthermore, the resistance increased upon application of a magnetic field of 4.6 T; for LED currents of 0.3 A around 10 K, the resistance at 4.6 T reached approximately five times that at zero field while remaining within a measurable range. Although the temperature and magnetic field dependences of the resistance possibly involve interesting physics, further discussions are beyond the scope of this paper.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) shows the representative cw-ESR spectra obtained at approximately 130 GHz with optical illumination. The LED drive current was 1.0 A, which generates approximately 300 lm emission, during the measurement. Two well-resolved resonance lines corresponding to the hyperfine-split transitions of isolated phosphorus donors [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] were observed. An additional line appeared between the two lines, which is most likely attributed to phosphorus clusters [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The ESR line shapes were absorption-like in spite of the magnetic field-modulation method, which is attributed to the passage effect under the present experimental conditions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Simultaneously, EDMR signals (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b)) appeared at magnetic fields corresponding to the ESR transitions of isolated donors. In contrast, no clear EDMR signals associated with the phosphorus clusters were detected. The typical EDMR signal amplitude was Δ\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(I\\)\u003c/span\u003e\u003c/span\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;60 pA, corresponding to a relative change of Δ\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(I\\)\u003c/span\u003e\u003c/span\u003e/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(I\\)\u003c/span\u003e\u003c/span\u003e \u0026asymp; 0.13%. Because the Si:P surface area in the comb-shaped electrode overlapping area excluding the electrodes is approximately 3 mm\u003csup\u003e2\u003c/sup\u003e which is inside the spot size, we can estimate that 6 \u0026times; 10\u003csup\u003e13\u003c/sup\u003e spins possibly contribute to the signal. This value is overestimated because the illuminated light can only penetrate to a depth of roughly fractions of a micrometer from the surface of silicon [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA direct comparison between ESR and EDMR responses reveals that the EDMR resonance lines are significantly sharper than the corresponding ESR lines. One may notice that the observed ESR linewidth of approximately 8 G is broader than 3\u0026ndash;4 G linewidth which is due to randomly distributed \u003csup\u003e29\u003c/sup\u003eSi hyperfine shifts [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This broadening is also attributed to the passage effect under the present experimental conditions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. In contrast, EDMR selectively probes spin-dependent recombination processes including interface level close to oxidized surface involving a subset of donor spins [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], which is not directly related to the passage condition, whereas ESR reflects the ensemble-averaged response of all resonant spins. Further, considering that the EDMR process involves the interface level, the absence of the P-cluster central peak in the EDMR spectrum may indicate fewer clusters near the interface.\u003c/p\u003e \u003cp\u003eThe EDMR signal intensity exhibits a pronounced dependence on the magnetic-field modulation frequency, reaching a maximum at approximately 2 kHz. This behavior suggests the presence of characteristic timescales associated with carrier recombination and spin relaxation processes, which govern the EDMR mechanism. The detailed data with discussion will appear elsewhere.\u003c/p\u003e \u003cp\u003eThese results demonstrate that simultaneous ESR and EDMR measurements provide complementary information on donor spin systems. While ESR offers a direct spectroscopic probe of the spin energy levels, EDMR highlights the subset of spins actively participating in transport-related processes. The microscopic mechanism for the observed discrepancies between ESR and EDMR responses is open question at present. Nevertheless, we believe that our results underscore the importance of combined detection for elucidating the microscopic origin of spin-dependent phenomena in Si:P. In principle, it should be possible to add NMR to our simultaneous ESR and EDMR measurement system. We expect this system to provide a foundation for future research on the dynamics of the coupled electron-nuclear spin system.\u003c/p\u003e"},{"header":"4 Summary","content":"\u003cp\u003eIn summary, we have demonstrated simultaneous mm-wave ESR and EDMR measurements on lightly doped Si:P using FPR under optical excitation. While ESR spectra exhibit resonance lines from both isolated donors and phosphorus clusters, EDMR signals were observed only for isolated donor states with significantly sharper line shapes compared with ESR lines. The absence of cluster-related EDMR signals and the modulation-frequency dependence of the EDMR signal intensity remain open issues. These results demonstrate that EDMR selectively probes spin-dependent transport processes, and further investigations are required to clarify the microscopic mechanisms involved. We have shown the feasibility of combined ESR\u0026ndash;EDMR measurements which provides a foundation for future studies of coupled electron\u0026ndash;nuclear spin dynamics, including simultaneous observation of ESR and EDMR.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u0026nbsp;\u003c/strong\u003eThis work was supported by JSPS KAKENHI Grant Number JP21KK0047 and the Cooperative Research Program of Research Center for Development of Far-Infrared Region, University of Fukui (R05FIRDP002C, R06FIRDG006D). This work was also performed under the Cooperative Research Program of \u0026ldquo;Network Joint Research Center for Materials and Devices (MEXT).\u0026rdquo; Authors are grateful to Mr. Shoichi Sakakihara (The University of Osaka) for his support on making Si:P samples, to Prof. Seitaro Mitsudo (University of Fukui) for his advice on constructing the experimental setup. One of the authors (Y. F.) expresses sincere thanks to Mr. Ei-ichi Kobayashi and staff of Cryogenic Laboratory, University of Fukui, for their support to the experiments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u0026nbsp; This work was supported by JSPS KAKENHI Grant Number JP21KK0047 and the Cooperative Research Program of Research Center for Development of Far-Infrared Region, University of Fukui (R05FIRDP002C, R06FIRDG006D). This work was also performed under the Cooperative Research Program of \u0026ldquo;Network Joint Research Center for Materials and Devices (MEXT).\u0026rdquo;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interests\u0026nbsp;\u003c/strong\u003e The authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u0026nbsp; Data sets generated during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u0026nbsp; Members of University of Fukui (H. I., Y. S., A. Ohashi, T. O., Y. K., K. H., Y. I. and Y. F.) and A. F. developed measurement systems and performed all measurements for the present work. Members of The University of Osaka (X.-F. L., G.M. G., M. M. and A. Oiwa) with H. I., Y. S., A. Ohashi, T. O., Y. F. and A. F. contributed sample preparation. H. I., Y. S. and A. 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Phys. \u003cb\u003e2\u003c/b\u003e, 835\u0026ndash;838 (2006). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/nphys465\u003c/span\u003e\u003cspan address=\"10.1038/nphys465\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003cp\u003e[1]\u0026nbsp;The spot size\u0026nbsp;\u003cimg width=\"17\" height=\"20\" src=\"data:image/png;base64,R0lGODlhGgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAACwAYAA4AhAAAAAAAAAAAOgAAZgA6kABmtjoAADoAZjqQ22YAAGY6AGZmOmaQZmaQ22a222a2/5A6AJDb/7ZmALb/27b//9uQOtu2Ztv///+2Zv/bkP//tv//2wECAwECAwECAwECAwWFIBYECGBmRgmgAXGZMFwFBSzWpqjGMIoDEpptQOHFUK6VofUC7owATSIpKUiIq0NxpQgIGrANhJjRXinih0laspBM4sEEUqoIIpVfBStOAgULSRgCDFgAfU17WzN3OSNqcBB+dhEmMzsoT4iWjVBQmwCKnp5nJhJ+ozyZSpCpRhZLAg4mIQA7\" v:shapes=\"_x0000_i1025\" alt=\"image\"\u003e\u0026nbsp;on the flat mirror of a flat-concave FPR is given by\u0026nbsp;\u003cimg width=\"115\" height=\"29\" src=\"data:image/png;base64,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\" v:shapes=\"_x0000_i1025\" alt=\"image\"\u003e\u0026nbsp;, where\u0026nbsp;\u003cimg width=\"8\" height=\"20\" src=\"data:image/png;base64,R0lGODlhDAAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABQAMABAAhAAAAAAAAAAAOgAAZgA6ZgA6kABmtjoAADpmtjqQ22YAAGa2/5A6AJA6ZpBmAJDb25Db/7ZmALbb/7b//9uQOtu2Ztv///+2Zv/bkP//tv//2wECAwECAwECAwECAwECAwVKICAC1REU1jheiIUdiyprTCKrtH2Pkb5nCt8tEhCqLoHiT1FwGEURwYMRkyENtOoIOJhkZcTYd3VK5bYKAUREwzYkRIOKEiBIACEAOw==\" v:shapes=\"_x0000_i1025\" alt=\"image\"\u003e,\u0026nbsp;\u003cimg width=\"9\" height=\"20\" src=\"data:image/png;base64,R0lGODlhDQAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABQANABAAhAAAAAAAAAAAOgAAZgA6kABmtjoAADo6OjpmZjpmtjqQ22YAAGaQ22a222a2/5A6AJDb/7ZmALaQZrb//9uQOtu2Ztu2kNv///+2Zv/bkP//2wECAwECAwECAwECAwECAwVTICCOIhYExEWuZrGumaG8pOnQIzVMuBilJI3EEBAgFq6R5iFoAJaB2ygSnQogoxjQt8tVRcvt8pqVKR9d3/eJ5gEwB/I04KwwIldLQgVtvol7ACEAOw==\" v:shapes=\"_x0000_i1025\" alt=\"image\"\u003e\u0026nbsp;and\u0026nbsp;\u003cimg width=\"10\" height=\"20\" src=\"data:image/png;base64,R0lGODlhDwAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABgAOAA8AhAAAAAAAAAAAOgAAZgA6ZgA6kABmtjoAADo6ZjqQ22YAAGY6AGaQtma222a2/5A6AJBmAJC225Db/7ZmALbb/7b//9uQOtu2Ztvbttv///+2Zv/bkP/btv//tv//2wECAwVfICBOQWkikah6UJCI3BM46ihI6nYU2foMldyuJ9IZaprAUZV8iTyPW80yE2EWgkYNagoIGERVR8EDUJ1IpWgMrJmrAKi0NpkDSDSxoi1KLkUXAQM4RUN9JnNjAQQUACEAOw==\" v:shapes=\"_x0000_i1025\" alt=\"image\"\u003e\u0026nbsp;are the wavelength, the distance between the mirrors and the radius of curvature of the spherical concave mirror, respectively.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-low-temperature-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jltp","sideBox":"Learn more about [Journal of Low Temperature Physics](http://link.springer.com/journal/10909)","snPcode":"10909","submissionUrl":"https://submission.nature.com/new-submission/10909/3","title":"Journal of Low Temperature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Electron spin resonance (ESR), Electrically detected magnetic resonance (EDMR), Millimeter wave, Phosphorus-doped silicon, Spin-dependent transport","lastPublishedDoi":"10.21203/rs.3.rs-8998506/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8998506/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe report the development of a measurement system enabling simultaneous detection of millimeter-wave electron spin resonance (ESR) and electrically detected magnetic resonance (EDMR) signals in lightly phosphorus-doped silicon (Si:P). Such simultaneous detection is motivated by the need to clarify spin-dependent transport and dynamic nuclear polarization mechanisms in high magnetic-field and low-temperature conditions relevant to Si:P-based quantum computing architectures. A Si:P sample was mounted on a Fabry-P\u0026eacute;rot resonator and was equipped with comb-shaped electrodes optimized for millimeter-wave transmission, allowing ESR excitation while monitoring the resistance changes under optical illumination. Using a 130 GHz millimeter-wave source, we successfully observed ESR absorption signals and corresponding EDMR responses simultaneously at temperatures around 5 K. The EDMR signals exhibited sharper linewidths compared to ESR. These results demonstrate the feasibility of combined ESR\u0026ndash;EDMR measurements and provide a foundation for future studies on coupled electron\u0026ndash;nuclear spin dynamics, including the simultaneous observation of ESR and EDMR.\u003c/p\u003e","manuscriptTitle":"Development of simultaneous detection method of millimeter-wave ESR and EDMR signals of phosphorous-doped silicon","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-15 15:10:20","doi":"10.21203/rs.3.rs-8998506/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2026-04-08T06:37:52+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-05T13:51:27+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-05T13:48:28+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Low Temperature Physics","date":"2026-03-01T00:55:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-low-temperature-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jltp","sideBox":"Learn more about [Journal of Low Temperature Physics](http://link.springer.com/journal/10909)","snPcode":"10909","submissionUrl":"https://submission.nature.com/new-submission/10909/3","title":"Journal of Low Temperature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8e81eaf1-9bb2-446c-997a-199b342093b0","owner":[],"postedDate":"April 15th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-15T15:10:21+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-15 15:10:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8998506","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8998506","identity":"rs-8998506","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}