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| Design of bromine-intercalated graphene inductors. a, Schematic of the two-turn inductor design: top: perspective view; bottom: cross-sectional view. b, The cross-sectional STEM image of the intercalated MLG showing the randomly distributed doping. c, EDX mapping image of the bromine-K signal from the same region as in b. d, Raman spectra before and after Br-intercalation. e-g, Optical images of octagonal (e), narrow square (f) and wide square (g) intercalated MLG on-chip inductors. G and S represent the ground line and signal line of the GSG CPWs, respectively. h,i, Photos of a fabricated chip with intercalated MLG inductor arrays placed on paper (h) and clamped by a tweezer (i). j, Optical microscope image of an inductor array.
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On-chip metal inductors that revolutionized radio frequency electronics in the 1990s suffer from an inherent limitation in their scalability in state-of-the-art radio frequency integrated circuits. This is because the inductance density values for conventional metal inductors, which result from magnetic inductance alone, are limited by the laws of...
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... and fabrication of intercalated MLG inductors. Our spiral inductor design based on intercalated MLG is shown in Fig. 2a. Intercalated graphene/MLG, or namely graphite intercalation compounds (GICs), have a long research history, and have shown surprising properties 19,20 . It is worth noting that MLG and graphite are the same material in principle, because of the same lattice structure and stacking order, although graphite usually has a greater number ...
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... down to 0.5 Pa, the samples were exposed to Br 2 gas at room temperature for 90 minutes using a two-zone vapour transport method (see Supplementary Section 6 for more details). The cross-sectional scanning transmission electron microscopy (STEM) and energydispersive X-ray spectroscopy (EDX) images of the intercalated samples are shown in Fig. 2b,c, respectively, where dark signals Magnetic field induced ...
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... stack of graphene layers, forming a heterogeneous mixture of highly doped MLG and lowly doped MLG. The average thickness increment measured by atomic force microscopy (AFM) is around 6.7% of the original thickness. The average concentration of bromine atoms is about 3%, as confirmed by X-ray spectroscopy (XPS) measurements. Raman spectroscopy ( Fig. 2d) confirmed the existence of intercalation (due to appearance of a new Br-peak and a GIC-peak, as well as a shift of the G-peak) and a GIC stage number (number of graphene layers over number of intercalation layers) of about 3 in the highly doped region. According to Hall measurements, intercalated MLG shows five times higher ...
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... without degrading carrier mobility, with respect to undoped MLG. More details about the various characterizations of bromine-intercalated MLG are provided in Supplementary Section 6. Subsequently, the intercalated MLG flakes were patterned into spiral inductor coils using photolithography followed by oxygen inductive coupled plasma etching (Fig. 2b). In this work, a set of two-turn layouts with an outer diameter of 200 μ m were designed as examples to demonstrate the intercalated MLG technique (Fig. 2e-g). Such a layout works mainly in the relatively high frequency range (10-50 GHz) (see Supplementary Section 7), which is of greater interest in this work for next-generation radio ...
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... in Supplementary Section 6. Subsequently, the intercalated MLG flakes were patterned into spiral inductor coils using photolithography followed by oxygen inductive coupled plasma etching (Fig. 2b). In this work, a set of two-turn layouts with an outer diameter of 200 μ m were designed as examples to demonstrate the intercalated MLG technique (Fig. 2e-g). Such a layout works mainly in the relatively high frequency range (10-50 GHz) (see Supplementary Section 7), which is of greater interest in this work for next-generation radio frequency electronics. It is the general trend that almost all wireless applications operate at increasingly higher frequencies as technology scales. This is ...
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... at increasingly higher frequencies as technology scales. This is due to the increase in transistor cut-off frequencies, as well as the need for greater bandwidths. Other than the square-shaped structures simulated in the theoretical works [13][14][15] , for comparative study, three slightly different layouts have been designed-octagonal shape (Fig. 2e), narrow square shape (Fig. 2f) and wide square shape (Fig. 2g). The inter-turn distances are 5 μ m, 10 μ m and 5 μ m for the three layouts, respectively. According to the simulations of metal inductors (see Supplementary Section 7), these parameters provide the optimal L M and C S , and hence optimal Q-factors for each ...
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... as technology scales. This is due to the increase in transistor cut-off frequencies, as well as the need for greater bandwidths. Other than the square-shaped structures simulated in the theoretical works [13][14][15] , for comparative study, three slightly different layouts have been designed-octagonal shape (Fig. 2e), narrow square shape (Fig. 2f) and wide square shape (Fig. 2g). The inter-turn distances are 5 μ m, 10 μ m and 5 μ m for the three layouts, respectively. According to the simulations of metal inductors (see Supplementary Section 7), these parameters provide the optimal L M and C S , and hence optimal Q-factors for each ...
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... is due to the increase in transistor cut-off frequencies, as well as the need for greater bandwidths. Other than the square-shaped structures simulated in the theoretical works [13][14][15] , for comparative study, three slightly different layouts have been designed-octagonal shape (Fig. 2e), narrow square shape (Fig. 2f) and wide square shape (Fig. 2g). The inter-turn distances are 5 μ m, 10 μ m and 5 μ m for the three layouts, respectively. According to the simulations of metal inductors (see Supplementary Section 7), these parameters provide the optimal L M and C S , and hence optimal Q-factors for each ...
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... inductor coils and the overlap metal pads. Subsequently, metal contacts and pads (Ni/Au: 10 nm / 2,000 nm) were deposited and patterned. The metal pads are designed as ground-signal-ground (GSG) coplanar waveguide (CPW) 22 structures with an intercalated MLG inductor in the signal path for twoport scattering parameter (S-parameter) measurements (Fig. 2e-g). The entire fabrication process is illustrated in Supplementary Section 8. To demonstrate the repeatability and to find the thickness dependence, tens of intercalated MLG inductors with different thicknesses (different series resistances) were fabricated on the same 1 cm × 1 cm die. Fig. 2h,i shows the entire chip and Fig. 2j shows a ...
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... scattering parameter (S-parameter) measurements (Fig. 2e-g). The entire fabrication process is illustrated in Supplementary Section 8. To demonstrate the repeatability and to find the thickness dependence, tens of intercalated MLG inductors with different thicknesses (different series resistances) were fabricated on the same 1 cm × 1 cm die. Fig. 2h,i shows the entire chip and Fig. 2j shows a micrograph of an intercalated MLG inductor array on the ...
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... measurements (Fig. 2e-g). The entire fabrication process is illustrated in Supplementary Section 8. To demonstrate the repeatability and to find the thickness dependence, tens of intercalated MLG inductors with different thicknesses (different series resistances) were fabricated on the same 1 cm × 1 cm die. Fig. 2h,i shows the entire chip and Fig. 2j shows a micrograph of an intercalated MLG inductor array on the ...
Citations
... In practical inks for electronic, thermal resistance, and anticorrosion purposes, graphene can be used. The conduction potentials connected with graphene encourage the ink as graphene is incorporated into ink construction, causing it to develop conductivity [65]. ...
... Theoretical limitations and fabrication constraints restrict performance and are closely related to quality factor, frequency bandwidth, and temporal response [31][32][33][34] . More recent innovative devices have demonstrated improved properties by utilizing approaches such as three-dimensional fabrication; [35][36][37][38] mechanically self-assembled coils [38][39][40][41] ; air-core or airsuspended coils 35,[42][43][44] ; and alternative materials such as graphene, carbon, ZnO and others [45][46][47][48][49] . However, complex designs are not easily integrated into standard fabrication processes. ...
Circuit-integrated electromagnets are fundamental building blocks for on-chip signal transduction, modulation, and tunability, with specific applications in environmental and biomedical micromagnetometry. A primary challenge for improving performance is pushing quality limitations while minimizing size and fabrication complexity and retaining spatial capabilities. Recent efforts have exploited highly involved three-dimensional synthesis, advanced insulation, and exotic material compositions. Here, we present a rapid nanofabrication process that employs electron beam dose control for high-turn-density diamond-embedded flat spiral coils; these coils achieve efficient on-chip electromagnetic-to-optical signal conversion. Our fabrication process relies on fast 12.3 s direct writing on standard poly(methyl methacrylate) as a basis for the metal lift-off process. Prototypes with 70 micrometer overall diameters and 49–470 nm interturn spacings with corresponding inductances of 12.3–12.8 nH are developed. We utilize optical micromagnetometry to demonstrate that magnetic field generation at the center of the structure effectively correlates with finite element modeling predictions. Further designs based on our process can be integrated with photolithography to broadly enable optical magnetic sensing and spin-based computation.
... Multi-layer graphene (MLG) is expected to be applied to metallization and high frequency devices as a conductor material with low resistance, high current density tolerance, and high kinetic inductance density due to the long mean free path of carriers and the strong bonding between carbon (C) atoms. [1][2][3][4][5] Chemical vapor deposition (CVD) of MLG on metal catalysts such as copper (Cu), nickel (Ni), and cobalt (Co) has been developed extensively due to the capability of high crystallinity and uniform MLG deposition. However, CVD requires transfer processes from the catalyst metal substrates onto a device substrate for device applications, which may degrade the quality of MLG films. ...
Solid-phase deposition (SPD) is a preferable method to fabricate multi-layer graphene (MLG) for device applications since MLG can be deposited directly on substrates without transfer. Previously, we reported that current application during SPD enhances the MLG growth. In this study, we investigated the effects of applied current and heating rate on the crystallinity and uniformity of MLG precipitated from carbon (C) / nickel (Ni) structures. It was found that higher current and slower heating rate lead to improve the MLG crystallinity. Moreover, the uniformity was improved by the optimization of Ni and C thickness which could control the nucleation and growth of MLG during SPD. As a result, a uniform MLG with a high G/D ratio of 5.5 was obtained at a low temperature of 365 °C.
... An established example is the so-called kinetic inductor, in which the energy is stored as the kinetic energy of mobile charge carriers. When considering the Drude model of conduction electrons, one can immediately find that the inductance defined using the imaginary part of the angular-frequency (ω)-dependent resistivity, ρ(ω), agrees with the inductance defined using the total kinetic energy of electrons [2]. ...
Metals hosting gradually varying spatial magnetic textures are attracting attention as a new class of inductor. Under the application of an alternating current, the spin-transfer-torque effect induces oscillating dynamics of the magnetic texture, which subsequently yields the spin-motive force as a back action, resulting in an inductive voltage response. In general, a second-order tensor representing a material's response can have an off-diagonal component. However, it is unclear what symmetries the emergent inductance tensor has and also which magnetic textures can exhibit a transverse inductance response. Here we reveal both analytically and numerically that the emergent inductance tensor should be a symmetric tensor in the so-called adiabatic limit. By considering this symmetric tensor in terms of symmetry operations that a magnetic texture has, we further characterize the magnetic textures in which the transverse inductance response can appear. This finding provides a basis for exploring the transverse response of emergent inductors, which has yet to be discovered.
... In this case, the LRC element corresponds to the intrinsic and contact resistance, dominated by the GNP aggregates, that behave as microcapacitors and resistive-inductive elements. 46 On the other hand, the RC element simulates the electrical properties associated with the tunneling effect, which are dominated by the barrier height properties of the insulating medium. In this regard, Figure 4 summarizes the EIS measurements and the fitted results for the complex impedance analysis by using the proposed equivalent circuit. ...
The temperature effect on electronic transport mechanisms in graphene nanoplatelet (GNP) doped polydimethylsiloxane (PDMS) for temperature sensing applications has been investigated under electrical impedance spectroscopy (EIS) analysis. AC measurements showed a very prevalent frequency-dependent behavior in low filled nanocomposites due to the lower charge density. In fact, 4 wt % GNP samples showed a nonideal capacitive behavior due to scattering effects. Therefore, the standard RC-LRC circuit varies with the substitution of capacitive elements by CPEs, where a CPE is a constant phase element which denotes energy dissipation. In this regard, the temperature promotes a prevalence of scattering effects, with an increase of resistance and inductance and a decrease of capacitance values in both RC (intrinsic and contact mechanisms) and LRC (tunneling mechanisms) elements and, even, a change from ideal to nonideal capacitive behavior as in the case of 6 wt % GNP samples. In this way, a deeper understanding of electronic mechanisms depending on GNP content and temperature is achieved in a very intuitive way. Finally, a proof-of-concept carried out as temperature sensors showed a huge sensitivity (from 0.05 to 11.7 °C-1) in comparison to most of the consulted studies (below 0.01 °C-1), proving, thus, excellent capabilities never seen before for this type of application.
... Examples of the proposed geometries comprise planar structures, like spiral and meander inductors sandwiched between two magnetic films, 1 and 3D structures, like solenoids and toroids with magnetic film cores. 2,3 More recent advances in the field 4 have shown the effectiveness of newly developed technologies, e.g., on-chip intercalated graphene inductors, 5 self-rolled-up membranes, 6 and 3D-printed polymer/metal microcoils, 7 and some of them also include magnetic cores. However, the integration of on-chip inductors and magnetic films comes with several issues such as: (i) process compatibility, 8 (ii) magnetic core saturation at high bias currents, 9 and (iii) losses due to eddy currents and hysteresis loops. ...
Integration of inductors on silicon chips is becoming more and more relevant for monolithic electronic applications. In this Letter, we investigate the impact of minor hysteresis loops in an integrated inductor with spiral geometry sandwiched between two soft magnetic layers made of MoNiFe/Cr multilayers. Despite high magnetic susceptibility and low coercivity of optimized multilayers, we find that the inductance is strongly dependent on the AC voltage applied to the device, showing a bell-shaped behavior. Comparing the measured inductance with magneto-optical Kerr effect and vibrating sample magnetometry measurements, we show that the low-signal behavior is limited by domain wall pinning/depinning, which determine the effective susceptibility associated with minor hysteresis loops driven by the applied AC voltage.
... These characteristics make it an attractive material for RF passive components such as inductors and capacitors. Through graphene's kinetic inductance and high conductivity, it claims an improvement of Qfactors and an increase of inductance density values, thus reducing the total area of integrated circuits [2,5,[8][9][10][11]. Furthermore, graphene capacitors can make use of their tunability to enable variable capacitors that are controlled through direct current (DC) biasing, making use of its quantum capacitance [2,[12][13][14]. ...
Graphene has unique properties that can be exploited for radiofrequency applications. Its characterization is key for the development of new graphene devices, circuits, and systems. Due to the two-dimensional nature of graphene, there are challenges in the methodology to extract relevant characteristics that are necessary for device design. In this work, the Thru-Reflect-Line (TRL) calibration was evaluated as a solution to extract graphene’s electrical characteristics from 1 GHz to 65 GHz, where the calibration structures’ requirements were analyzed. It was demonstrated that thick metallic contacts, a low-loss substrate, and a short and thin contact are necessary to characterize graphene. Furthermore, since graphene’s properties are dependent on the polarization voltage applied, a backgate has to be included so that graphene can be characterized for different chemical potentials. Such characterization is mandatory for the design of graphene RF electronics and can be used to extract characteristics such as graphene’s resistance, quantum capacitance, and kinetic inductance. Finally, the proposed structure was characterized, and graphene’s resistance and quantum capacitance were extracted.
... To facilitate the miniaturization of RF ICs, the scaling down of on-chip spiral inductors is inevitable [4]. However, there exists an inherent limitation in the scalability of conical spiral inductors, as the inductance value is limited by the laws of electromagnetic induction [5]. This is, the magnetic flux is proportional to the surface area, and the magnetic inductance cannot be scaled to retain desired inductance density. ...
... In comparison with CNT, graphene is more compatible with the traditional CMOS process [11], and there are ways to control graphene chirality and doping levels [12]. Graphene-based on-chip spiral inductors were explored in-depth recently [5,13]. It was experimentally demonstrated that the graphene kinetic inductance is beneficial for improving the inductor performance. ...
... As the magnetic flux is proportional to the inductor area, the decreased size degrades the inductance density, thereby limiting the scaling of RF ICs. Kinetic inductance, which originates in the kinetic energy required by mobile charge carriers in alternative electromotive force, is usually ignored in conventional metals due to their small relaxation time and large conducting channel number [5]. However, the momentum relaxation time of graphene is on the order of picoseconds, and therefore, graphene possesses large kinetic inductance, which makes it suitable for building on-chip spiral inductors in future scaled RF ICs. Figure 4a shows the structure of a multilayer GR interconnect with side contacts [12]. ...
This paper investigates the electrical performance of graphene-based on-chip spiral inductors by virtue of a physics-based equivalent circuit model. The skin and proximity effects, as well as the substrate loss effect, are considered and treated appropriately. The graphene resistance and inductance are combined into the circuit model. It is demonstrated that the electrical characteristics of the on-chip square spiral inductor can be improved by replacing copper with graphene. Moreover, graphene exhibits more effectiveness in improving the inductance in tapered inductors than uniform ones.
... In contrast, the kinetic energy of charge carriers that participate in the flow of current determines the LK. [12][13][14] Therefore, at terahertz frequencies, where small size of the devices limit LG, realizing giant enhancement of LK provides an attractive solution to realize compact superinductors. ...
... Intrinsically LK depends on the scattering time (), and DC conductivity (0) of the material and is expressed as, = = * 2 , where * , n and e are the effective mass, number density, and charge of the current-carrying carriers, respectively. 15 The material having heavier charge carriers with longer scattering time provides a sizeable LK. 13,14,16 In metallic systems, LK is negligible at terahertz frequencies (ω ~10 12 rad s -1 ) due to the short scattering time of charge carriers (τ < 10 -14 s), leading ...
Ginzburg-Landau (GL) parameters formed the basis for Abrikosov discovery of the quantum vortex of a supercurrent in type-II superconductor with a normal core of size $\xi$, the superconductor coherence length and circulating supercurrent induced magnetic field diverging as $log(1/r)$ from the core with a decay length of the London penetration depth, $\lambda_L.$ In 1964, J. Pearl predicted the slowly decaying $(1/r^2)$ field around a vortex spreading out to Pearl length, $P_L=2\lambda_L^2/t$, in a superconductor film of thickness $t < \lambda_L$. However, his quintessential theory failed to predict the existence of giant kinetic inductance (GKI) that arises from the enlarged screening currents of the vortex. Here, we discover giant kinetic inductance in a $high-T_c$ metasurface due to the 1400% expansion of the vortex screening supercurrent from $\lambda_L$ to 14$\lambda_L$ in ultrathin film meta-atom of $\lambda_L/7$ thickness, which leads to the emergence of terahertz superinductance possessing quantum impedance exceeding the resistance quantum limit of $R_Q=h/(2e)^2 =6.47 k\Omega$ by 33%. Our discovery presents a new class of $high-T_c$ superconductor electronic, photonic, and quantum devices enabled through metasurface designed at the Pearl length scales, providing novel applications in quantum circuitry, metrology, and single photon kinetic inductance detectors.
... Research on the conductor applications of MLG is advancing, not only for LSI interconnects but also for electrodes of LEDs, 39) solar cells, 53) power devices, 54) electro-magnetic shield layers 55) and high-frequency devices, such as inductors 56) and antennas. 57) Since graphene has unique characteristics of carrier transport based on its band structure and it leads to the high kinetic inductance, it is expected to have a unique response to high frequencies. ...
... High inductance density was demonstrated by fabricating I-MLG spiral inductors using exfoliated HOPG and Br 2 intercalation, and a 1.5 times increase in the inductance density and 30% reduction in the inductor area were obtained. 56) In order to obtain this large kinetic inductance, intercalation is inevitable, not only for increasing the carriers but also for separating graphene layers to obtain single-layer-like transport characteristics in MLG. ...
Multilayer graphene (MLG) has been expected as an alternative material for nanometer wide interconnects. However, it has not been put into practical use, since the process technology that leads to practical use has been immature. Recent advances in the MLG processes and applications such as MLG capped copper interconnects, direct deposition of MLG by solid-phase deposition at a low-temperature, stable intercalation doping to MLG, and selective CVD of high crystallinity MLG for inductor and antenna applications are reviewed. According to these advances, MLG is considered to be approaching to the practical applications for device metallization and high frequency devices. Based on the characteristics of MLG as a conductor and recent development trends, the prospects and issues for future practical use of MLG graphene are discussed.
