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Akitomi Shirachi, [Motoya Shinozaki](https://orcid.org/0000-0001-9460-9156), Yasuhide Tomioka, [Hisashi Inoue](https://orcid.org/0009-0008-6307-3772), Kenta Itoh, [Yusuke Kozuka](https://orcid.org/0000-0001-7674-600X), [Takanobu Watanabe](https://orcid.org/0000-0002-9421-8195), Shoichi Sato, Takeshi Kumasaka, [Tomohiro Otsuka](https://orcid.org/0000-0003-2532-643X)

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Akitomi Shirachi, Motoya Shinozaki, Yasuhide Tomioka, Hisashi Inoue, Kenta Itoh, Yusuke Kozuka, Takanobu Watanabe, Shoichi Sato, Takeshi Kumasaka, Tomohiro Otsuka; On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties. Appl. Phys. Lett. 13 October 2025; 127 (15): 153501 and may be found at https://doi.org/10.1063/5.0299758[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties](https://mdr.nims.go.jp/datasets/8c6e4262-0b24-4024-b14e-053adfa83eab)

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On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor propertiesOn-board calibrated radio-frequency measurement at cryogenic1temperatures for determination of SrTiO3-based capacitor properties2Akitomi Shirachi,1, 2 Motoya Shinozaki,3 Yasuhide Tomioka,4 Hisashi Inoue,4 Kenta Itoh,5, 6 Yusuke Kozuka,5, 63Takanobu Watanabe,5 Shoichi Sato,3 Takeshi Kumasaka,3 and Tomohiro Otsuka1, 2, 3, 7, 841)Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577,5Japan62)Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Aoba 6-6-05, Aramaki, Aoba-Ku,7Sendai 980-8579, Japan83)WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577,9Japan104)National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8565,11Japan125)Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555,13Japan146)Research Center for Materials Nanoarchitechtonics (MANA), National Institute for Material Science (NIMS), 1-2-1 Sengen,15Tsukuba 305-0047, Japan167)Center for Science and Innovation in Spintronics, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577,17Japan188)RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198,19Japan20(*Electronic mail: tomohiro.otsuka@tohoku.ac.jp)21(Dated: 29 August 2025)22Quantum computing has emerged as a promising technology for next-generation information processing, utilizing semi-conductor quantum dots as one of the candidates for quantum bits. Radio-frequency (rf) reflectometry plays an impor-tant role in the readout of quantum dots but requires a precise rf measurement technique at cryogenic temperatures.While cryogenic calibration techniques, essential for rf reflectometry, have been developed, on-board calibration nearthe device remains an important challenge. In this study, we develop an on-board calibrated rf measurement systemoperating at 4 K for characterizing SrTiO3-based varactors, which are promising components for tunable impedancematching circuits. Our system enables accurate measurements by eliminating errors associated with long rf circuitlines. We investigate the effects of annealing conditions, crystal orientation, and Ca doping of SrTiO3 crystals onthe varactor properties in the frequency range for rf reflectometry. Our results provide insights for optimizing thesecomponents for cryogenic rf applications in quantum information processing systems.Quantum computers have attracted attention as next-23generation information processing systems. Semiconductor24quantum dots are considered one of the promising candidates25for their essential building blocks, quantum bits (qubits)1,2.26Radio frequency (rf) technologies play an important role27in controlling3 and reading4–6 the states of semiconductor28qubits. Since semiconductor quantum dots operate at cryo-29genic temperatures, various components of the rf circuits must30be placed on the cryogenic stages of the refrigerator. These31components are required to exhibit their expected character-32istics in the driving frequency range under cryogenic condi-33tions7–10. While it is crucial to evaluate their characteristics34at cryogenic temperature, many commercial components are35supplied with their datasheets calibrated at room temperature36or over 100 K. Moreover, calibration techniques inside the37refrigerator are not yet well established, which means many38commercial components cannot promise their functionality at39cryogenic temperatures. The performance of rf components40at cryogenic temperatures can be verified through functional41circuits including quantum devices. This leads to a challenge42for designing measurement systems when components show43unexpected behavior under cryogenic conditions.44To address this issue, several calibration techniques have45been developed using a coaxial switch that operates over a46wide temperature range, from cryogenic to room tempera-47tures11–21. These techniques perform calibration at the end48of the circuit where the components will be placed for accu-49rate characterisation, using a coaxial switch to toggle between50calibration standards and the device under test. For exam-51ple, a calibrated rf measurement of up to 26.5 GHz has been52reported using this system20, enabling the evaluation of a cir-53culator’s characteristics at cryogenic temperatures. These ad-54vances highlight the growing demand for calibrated measure-55ment systems at cryogenic temperatures, as they are important56for the reliable characterization of components in their actual57operating environment.58For semiconductor quantum dots, rf reflectometry is a well-59established measurement technique commonly referred to as60broadband measurement4–6,22. This method employs an LC61resonator including quantum dots, where capacitance plays62an important role in determining the resonator characteris-63tics. This resonator transforms a device resistance into 50 Ω64to satisfy an impedance matching condition with the rf cir-65cuit line. While rf reflectometry has been applied to quan-66tum dots in some material systems such as GaAs, Si23, and67ZnO24 owing to various efforts of engineering, this technique68is still difficult to apply to high-resistance systems such as69silicon metal oxide semiconductor-based quantum dots25,2670mailto:tomohiro.otsuka@tohoku.ac.jpOn-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties 2VNA Port1 SwitchCalibration50 Ω300 K 4 K3 mSwitchOpenShortLoad50 Ω(a)(b)(c)1 MHz1 GHzOpen Short LoadOpen Short LoadPCBReference planeFIG. 1. (a) Experimental setup of the calibrated measurement system utilizing HEMT switches on a PCB to divide circuit lines betweencalibration and measurement ports. (b) Smith charts for open, short, and load conditions at the PCB calibration port while calibrated at thevicinity of the VNA. (c) Smith charts after calibration at the PCB port, showing ideal responses for all conditions.and two-dimensional materials like graphene27–30 due to their71high contact resistance31. Varactor capacitors, externally con-72trolled capacitors, are expected to optimize the resonator char-73acteristics even when we employ high-resistance systems, en-74abling high-sensitivity reading32,33.75Strontium titanate (SrTiO3) has emerged as a promising76candidate for cryogenic varactor materials. It is a quantum77paraelectric material that maintains a high dielectric constant78at cryogenic temperatures without transitioning to a ferroelec-79tric state34, making it ideal for tunable capacitive applica-80tions. While previous studies have demonstrated its potential81as a varactor33, including its robustness to magnetic fields35,82its dielectric properties at cryogenic temperature have only83been experimentally evaluated at frequencies much lower than84those typically used in rf reflectometry34 or specific frequency85of a resonator35. To evaluate rf-dependent characteristics of86the varactor, we should calibrate on a printed circuit board87(PCB). On-board calibration defines the reference plane close88to surface-mounted components on the PCB, enabling accu-89rate evaluation that would be difficult with conventional coax-90ial switch-based setups11–21. In this study, we develop an on-91board cryogenic calibration circuit to evaluate the properties92of SrTiO3-based varactors in the radio frequency regime.93Figure 1(a) shows an experimental setup of our calibrated94On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties 3(a) (b)FIG. 2. (a) Smith chart for a 15 pF capacitor with frequency sweepfrom 1 to 500 MHz. (b) Frequency dependence of the calculatedcapacitance from the Smith chart.measurement system. We use high electron mobility transis-95tor (HEMT) switches on the PCB to divide circuit lines to96calibration and measurement ports. The calibration circuit is97constructed by open, short, and load ports, which are also di-98vided by HEMT switches. A circuit length from the vector99network analyzer (VNA) to the PCB is approximately 3 m.100This coaxial cable length affects the measurement accuracy101due to frequency-dependent phase shifts. These circuit line102effects would introduce errors in the characterization of com-103ponents at cryogenic temperatures, especially at higher fre-104quencies where wavelengths become comparable to the cir-105cuit scales. Furthermore, a reference plane is set close to the106measurement port to enable a more accurate evaluation. Fig-107ure 1(b) shows Smith charts under open, short, and load con-108ditions at the PCB calibration port while they are calibrated109in the vicinity of the VNA. All conditions show unexpected110trajectories with sweeping the frequency ranging from 1 MHz111to 1 GHz. After calibration using the PCB calibration port,112we observe ideal results with all conditions as illustrated in113Fig. 1(c). This calibration is also useful at cryogenic temper-114atures. We confirm that multiple resistors of the same model115used for the load standard are approximately 49.2 to 49.5 Ω116at 4 K. This deviation from the nominal 50 Ω corresponds to117a reflection coefficient error of less than 0.8%. Therefore, we118believe that the accuracy of the calibration is preserved even119at cryogenic temperatures.120As a reference, we measure a capacitor with a known ca-121pacitance of 15 pF at 4 K. Figure 2(a) shows the Smith chart122with sweeping the frequency ranging from 1 to 500 MHz. The123trajectory of normalized impedance appears along the 50 Ω124circle in the lower region, indicating a capacitive component.125From the Smith chart, we obtain a frequency dependence of126the capacitance value as shown in Fig. 2(b). Owing to our cal-127(a) (b)d mmSrTiO3Ti/Au200 mm(c) (d)(e) (f)w/o annealing w/ annealingVg = -15 V30 VVg = -5 V30 Vw/o annealing w/ annealing1 mｍFIG. 3. (a) Schematic illustration of the varactor structure with aTi/Au circular electrode deposited on a SrTiO3 crystal. (b) Top viewoptical image of a typical device with dimensions of approximately1 mm. Frequency dependence of capacitance for (c) un-annealed and(d) annealed (110) SrTiO3 devices at 4 K under various gate volt-ages. Gate voltage dependence of capacitance at 200 MHz for (e)un-annealed and (f) annealed devices.ibration system, the capacitance is evaluated to be 15 pF and128maintains its value across the entire frequency range. This fre-129quency range covers that typically used in rf reflectometry for130resistive readout22.131Figure 3(a) illustrates the structure of the SrTiO3-based var-132actor. Here, SrTiO3 single crystals are grown by the Verneuil133process (Shinkosha Co.). A Ti/Au layer is deposited on a134SrTiO3 crystal and processed into a circular electrode with135a diameter of 200 µm by photolithography. A top view of a136typical device is shown in Fig. 3(b). We shape devices into137squares with dimensions of approximately 1 mm.138At first, we prepare two devices, where one is annealed for13930 h at 1250 ◦C in the air environment with thickness d of140330 µm and the other is not annealed with d of 260 µm. Both141On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties 4crystals have the (110) orientation and are not Ca-doped. Fig-142ures 3(c) and (d) show the frequency dependences of the ca-143pacitance from our calibrated measurement at 4 K. For the de-144vice without annealing, the capacitance remains almost con-145stant with frequency up to 250 MHz under all gate voltage146Vg conditions. The device with annealing shows larger ca-147pacitance than that of the un-annealed one, even though it148is thicker. Annealing is considered to fill the residual oxy-149gen vacancy and thus exhibit a higher dielectric constant36.150Note that the capacitance of the annealed device appears to151decrease with increasing frequency. One of the possible rea-152sons of this decay might result from the difference between153the actual value of series resistance to the capacitor and the154reference value of 50 Ω. The total impedance of the mea-155surement port can be described as R + 1/ jωC, where R is156the series resistance, j the imaginary unit, and C the capaci-157tance of the device. When this actual resistance deviates from158the 50 Ω reference used in the calculation, the calculated ca-159pacitance value is underestimated at higher frequencies where160the resistive component is dominant over the total impedance.161Therefore, such underestimation is more pronounced in the162higher capacitance region shown in Fig. 3(d), consistent with163our model. Even after considering this scenario, intrinsic fre-164quency dependence still appears to remain. Further investiga-165tions are necessary to understand this decay in detail.166We extract the capacitance values at 200 MHz, typically167used in rf reflectometry, and show the Vg dependence of both168devices in Figs. 3(e) and (f). Both cases show clear Vg modula-169tion without noticeable hysteresis during roundtrip sweeping,170which is attributed to the SrTiO3 remaining in the paraelectric171state at cryogenic temperature. The peak of the capacitance172shows an offset from zero bias due to the asymmetric top and173back electrodes as we employ Ag paste on the back of the de-174vice to be grounded. Therefore, the difference in work func-175tions between the Ti/Au top electrode and Ag back electrode176creates an effective internal electric field37, causing the offset.177In order to investigate the potential of SrTiO3 varactors in178the rf frequency region, we measure the crystal orientation179and Ca doping dependence. For a fair comparison account-180ing for device geometry, especially the substrate thickness, we181perform simulations using COMSOL Multiphysics® to con-182vert the measured capacitance C to relative permittivity εr, as183shown in Fig. 4(a). Using these calculated relationships, we184compare εr between devices with SrTiO3 (110), SrTiO3 (111),185and Ca-doped SrTiO3 (110). Here, the thickness d of the186non-doped devices is 310 µm while that of the doped one is187600 µm, and the doped Ca concentration is 0.0015. Note that188the Ca-doped device is grown by the floating zone method and189annealed for 30 h at 1350 ◦C in an Ar/H2 environment, while190non-doped devices at 1250 ◦C in air. Figure 4(b) summarizes191the Vg dependence of the εr of each device. The device with192the non-doped (110) crystal exhibits higher εr values com-193pared to the (111) crystal, consistent with previous reports on194the anisotropic dielectric properties of SrTiO338,39. Regarding195the effect of Ca doping, we observe that the Ca-doped device196shows reduced εr values compared to its non-doped counter-197part. This reduction might result from oxygen vacancies and198interfacial dielectric characteristics between the substrate and199(a) (b)d=310 μm600 μm(110)Ca-doped(111)FIG. 4. (a) The relationships between the capacitance and relativepermittivity for different substrate thicknesses, estimated by COM-SOL simulation. (b) Gate voltage dependence of the relative permit-tivity for devices with different crystal orientations (110), (111), andCa doping.Ag paste, whereas an enhancement in εr would be expected at200low frequencies40. We also observe slight hysteresis during Vg201sweeping, suggesting a ferroelectric transition at this doping202concentration and temperature.203In this study, we have developed the on-board calibrated204radio-frequency measurement system operating at cryogenic205temperatures for the determination of SrTiO3-based varac-206tor properties. Our calibration technique, utilizing HEMT207switches on a PCB, enables accurate impedance measure-208ments directly at the device location at 4 K, eliminating errors209associated with long transmission lines. Our setup provides210reliable capacitance values across the frequency range using211rf reflectometry. By using this system, we have investigated212dependencies on annealing conditions, crystal orientation, and213Ca doping effects of SrTiO3 varactors. These findings con-214tribute to the understanding of SrTiO3-based varactors in the215rf frequency range at cryogenic temperatures, providing es-216sential insights for their application in quantum device mea-217surements. The calibration technique developed in this study218can be further applied to characterize various cryogenic mi-219crowave components such as superconducting inductors, sup-220porting the advancement of quantum information processing221systems.222ACKNOWLEDGMENTS223The authors thank A. Kurita, RIEC Fundamental Tech-224nology Center, and the Laboratory for Nanoelectronics and225Spintronics for technical support. Part of this work was sup-226ported by MEXT Leading Initiative for Excellent Young Re-227searchers, Grants-in-Aid for Scientific Research (21K18592,228On-board calibrated radio-frequency measurement at cryogenic temperatures for determination of SrTiO3-based capacitor properties 522H04958, 23K26482, 23H04490), FRiD Tohoku University,229and by TIA “KAKEHASHI” program. AIMR and MANA230are supported by World Premier International Research Cen-231ter Initiative (WPI), MEXT, Japan.232AUTHOR DECLARATIONS233Conflict of Interest234The authors have no conflicts to disclose.235Author Contributions236Akitomi Shirachi: Data Curation (lead); Investigation237(lead); Methodology (equal); Visualization (equal); Writ-238ing/Review & Editing (equal). Motoya Shinozaki: Con-239ceptualization (equal); Data Curation (equal); Investigation240(equal); Methodology (equal); Visualization (lead);; Writ-241ing/Original Draft (lead); Writing/Review & Editing (equal);242Yasuhide Tomioka: Investigation (equal); Resources (lead);243Writing/Review & Editing (equal); Hisashi Inoue: In-244vestigation (equal); Resources (equal); Writing/Review &245Editing (equal); Kenta Itoh: Investigation (equal); Soft-246ware (lead); Writing/Review & Editing (equal); Yusuke247Kozuka: Conceptualization (equal); Investigation (equal);248Resources (equal); Software (equal); Writing/Review & Edit-249ing (equal); Takanobu Watanabe: Investigation (equal);250Software (equal); Writing/Review & Editing (equal); Shoichi251Sato: Methodology (equal); Resources (equal); Writ-252ing/Review & Editing (equal); Takeshi Kumasaka: Re-253sources (equal); Writing/Review & Editing (equal); To-254mohiro Otsuka: Conceptualization (lead); Methodology255(lead); Funding Acquisition (lead); Supervision (lead); Writ-256ing/Review & Editing (lead).257DATA AVAILABILITY STATEMENT258The data that support the findings of this study are available259from the corresponding authors upon reasonable request.260APPENDIX: DETAILS OF THE CALIBRATION SETUP261Figure 5 shows the details of our calibration setup on262the PCB. 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