This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright © American Chemical Society after peer review. To access the final edited and published work see: https://dx.doi.org/10.1021/acs.nanolett.0c00467. Switchless Multiplexing of Graphene Active Sensor Arrays for Brain Mapping Ramon Garcia-Cortadella†,∇, Nathan Schäfer†,∇, Jose Cisneros‡, Lucia Ré‡,§, Xavi Illa‡,§, Gerrit Schwesig∥, Ana Moya‡, Sara Santiago⊥, Gonzalo Guirado⊥, Rosa Villa‡,§, Anton Sirota∥, Francesc Serra-Graells‡, Jose A. Garrido†,#* and Anton Guimerà-Brunet‡,§*, † Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain ‡ Instituto de Microelectrónica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra, Spain § Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid, Spain ∥ Bernstein Center for Computational Neuroscience Munich, Munich Cluster of Systems Neurology (SyNergy), Faculty of Medicine, Ludwig-Maximilians Universität München, Planegg- Martinsried, Germany ⊥ Departament de Química, Universitat Autònoma de Barcelona, 08193-Bellaterra, Barcelona, Spain # ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain 1 ABSTRACT: Sensor arrays used to detect electrophysiological signals from the brain are of major importance in neuroscience and biomedical engineering. However, the number of sensors that can be interfaced with macroscopic data acquisition systems currently limits the bandwidth of these devices. This bottleneck originates in the fact that, typically, sensors are addressed individually, requiring a connection for each of them. Herein, we present the concept of frequency-division multiplexing (FDM) of neural signals by graphene active sensors. We demonstrate the high performance of graphene transistors as mixers to perform amplitude modulation (AM) of neural signals in-situ, which is used to transmit multiple signals through a shared metal line. This technology eliminates the need for switches, remarkably simplifying the technical complexity of state-of-the-art multiplexed neural probes. Besides, the scalability of FDM graphene neural probes has been thoroughly evaluated and their sensitivity demonstrated in-vivo. Using this technology, we envision the implementation of a new generation of conformal neural probes with over a thousand channels for high bandwidth brain machine interfaces. GRAPHICAL TOC: KEYWORDS: Multiplexing, graphene, active sensors, bioelectronics, neural sensing 2 TEXT: Over the last decades, progress in neurotechnology has enabled a deeper understanding of brain functions such as motor control1,2 or speech processing and synthesis3,4. In turn, these insights have prompted the realization of technological breakthroughs in the field of brain- computer interfaces (BCIs) such as partial restoration of movement5 or decoding of speech from neural activity6. Cortical functions involved in such tasks often emerge from the integration of information in distinct brain regions, yet local activity from small groups of neurons carries essential information for neural coding7. Therefore, combining the coverage of large brain areas with high sensor density (i.e. high sensor count) is paramount for both neuroscientific and biomedical applications8–10. In this sense, one of the main limitations in current neurotechnologies originates in the need of individually connecting each sensing element to a signal amplifier. This constrain implies having as many conductive lines as sensors in the neural probes, which imposes a trade-off between sensor density and coverage area. One way to overcome this constrain is to perform multiplexing among sensors, which allows the transmission of multiple signals over a shared wire. State-of-the-art sensing technologies for neuroscientific research are mostly based on intra- cortical electrode arrays11–14. Intra-cortical electrode arrays can be fabricated on rigid substrates15, therefore enabling to incorporate integrated-circuits on the probes12 to amplify and multiplex the measured signals. However, intra-cortical probes cause serious tissue damage, limiting the mapping over large areas of the cortex, especially for biomedical applications. Alternatively, electrocorticography (ECoG) offers a minimally invasive way to acquire similar information 16,17, by recording local field potentials18 (LFP) from the surface of the brain. Nevertheless, planar µ- ECoGs must be fabricated on a flexible substrate to provide conformability to the surface 3 morphology of the brain8,19. This constrain strongly limits the use of nanofabrication methodologies and available materials to fabricate integrated circuits on the neural probe, thus restricting the implementation of in-situ signal amplification for time-division multiplexing (TDM) of neural signals20. Flexible materials have been proposed to perform switching among active sensors in an addressable array configuration, including organic semiconductors21 or ultra- thin silicon layers22. However, organic semiconductors present an insufficient mobility for high- speed operation, which is critical to achieve high sampling speed for large number of sensors, and the high complexity of ultra-thin silicon technology on flexible substrates limits its widespread application. Herein, we present a novel approach that uses frequency-division multiplexing (FDM) of graphene solution-gated field-effect-transistors (g-SGFETs) in order to eliminate the need for on- site switches and to reduce the fabrication complexity of high-count neural probes. In this approach, neural signals detected by different graphene active sensors on the array are amplitude modulated (AM) by different carrier signals, allowing to transmit multiple signals through a shared communication channel. We present the fabrication of g-SGFET arrays on an addressable column/row matrix configuration to demonstrate their high performance for FDM operation in- vivo, sensing wide-band neural activity from the surface of the rat brain. Besides, we carefully assess the scalability of this technique, demonstrating its potential for simultaneously recording from over a thousand channels. The simplification of the technological complexity, achieved by the elimination of switches and the use of graphene electronics, opens the door to the implementation of high-count flexible neural probes as a readily available technology for neuroscientific studies as well as clinical applications. 4 Figure 1: Frequency-domain multiplexing of g-SGFET arrays: a. Equivalent circuit of the g- SGFET together with an illustration of the device. b. Schematic of the neural probe layout. On the left, the whole probe is displayed. A zoom into the probe tip is shown on the top-right image. The orange/yellow colour represent the 1st/2nd metal layers, separated by a 2𝜇𝑚 thick polyimide layer. A zoom into a single pixel is shown within the red dashed-line square. The bottom schematic depicts a side view of the g-SGFET, showing the connection between the 1st and 2nd metal layer through a VIA hole in the PI. c. Typical 𝐺𝑑𝑠 − 𝑉𝑔𝑠 curve of g-SGFETs. The filled area represents the standard deviation (n = 8). The definition of normalized transconductance (𝑔𝑚 ) as the slope of 5 the 𝐺𝑑𝑠 − 𝑉𝑔𝑠 curve, is indicated in the graph. The g-SGFETs acts as a multiplier of the drain-to- source voltage and the signal at the gate. The resulting 𝐼𝑑𝑠 in the DC and AM modes is illustrated. d. The signal folded by the carrier is shown in the frequency domain (left). Demodulation scheme (middle): the multiplication of the modulated signal by an oscillator at the carrier frequency of interest and the 𝜋/2 radians phase shifted oscillator allows to recover the module of the signal in the baseband (right). e. Basic schematic of the addressable g-SGFET array, which allows modulating the signals at the gate of different g-SGFETs with different carrier frequencies. The mixed signals, containing multiple carrier frequencies, are demodulated after current-to-voltage conversion and digitalization. FREQUENCY-DIVISION MULTIPLEXING OF G-SGFET ARRAYS G-SGFETs have been proposed as signal transducers in the field of biosensing and bioelectronics19,23–25, presenting unique properties for the detection of full-band neural signals, from infra-slow to high-frequency components, with a high spatial resolution26. Besides, as active sensors, G-SGFETs provide an intrinsic pre-amplification of the signal and can be arranged in a column/row addressable matrix due to their two terminal (i.e. drain and source) configuration (see Fig. 1a and 1b). These properties, combined with their remarkable frequency response27, make g- SGFETs an ideal technology for the implementation of frequency-division sensor arrays. In g-SGFETs, the graphene channel is placed in contact with an electrolyte gate, i.e. the brain tissue in the case of neural sensing applications. Electrical potential fluctuations in the environment influence the conductivity of the transistor channel through the gate capacitance. The constant of proportionality between drain-source conductance (𝐺𝑑𝑠 ) and the electrical potential at 6 the interface (𝑉𝑔𝑠 ) is referred to as the transconductance28 (𝑔𝑚 ). g-SGFETs can be modelled by the equivalent circuit shown in Fig. 1a. Its stationary response to a constant bias (𝑉𝑔𝑠−𝐷𝐶 ) is described by the voltage dependent term 𝐺𝑑𝑠−𝐷𝐶 , while its dynamic response to a small-amplitude, time- dependent signal (𝑉𝑠𝑖𝑔 ) is characterised by the term 𝑉𝑠𝑖𝑔 𝑔𝑚 . In the typical operation mode (DC mode), the drain-source bias 𝑉𝑑𝑠 is constant; thus, the only time variations in the drain-source current (𝐼𝑑𝑠 ) are caused by variations in 𝐺𝑑𝑠 (Fig. 1c). On the other hand, in FDM (or amplitude modulation- AM mode), the drain-source bias is typically a pure tone signal (𝑉𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑡)). Therefore, 𝐼𝑑𝑠 results from the product of 𝑉𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑡)(𝑔𝑚 𝑉𝑠𝑖𝑔 (𝑡) + 𝐺𝑑𝑠−𝐷𝐶 ) (see Fig. 1c). The multiplication of 𝑉𝑐𝑎𝑟𝑟𝑖𝑒𝑟 and 𝑉𝑠𝑖𝑔 produces the folding of their frequencies. In the frequency-domain representation of 𝑉𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑡) ∗ 𝑉𝑠𝑖𝑔 (𝑡) (Fig. 1d-left), a peak at the carrier frequency (𝑓𝑐 ) can be observed, which is proportional to 𝐺𝑑𝑠−𝐷𝐶 . In addition, two side bands (at 𝑓𝑐 − 𝑓𝑠𝑖𝑔 and 𝑓𝑐 + 𝑓𝑠𝑖𝑔 ) appear, the amplitude of which is proportional 𝑔𝑚 𝑉𝑠𝑖𝑔 . This mixed signal can then be demodulated by a lock-in amplifier (see Fig. 1d-middle) producing the folding of the side bands back to the baseband frequency (see Fig. 1d-right), with the DC-offset corresponding to the stationary component of 𝐼𝑑𝑠 . This demodulation can be repeated for different carrier frequencies to recover the neural signals detected in each of the graphene sensors. The schematic in Fig. 1e represents the FDM of a 2x2 sensor array. Carrier signals with different frequencies (𝑓𝑐 ) are applied at each column of the array and independent data-acquisition channels are connected to each of the drains to reliably recover the information from the multiplexed sensors. Here, we present frequency-division multiplexed arrays of up to 4x8 graphene sensors fabricated on a flexible polyimide (PI) substrate (see Fig. 1b and supporting information for more details of the fabrication method). For the characterization of the FDM sensor arrays and their operation in-vivo, 7 we have developed a recording system based on a PXIe for high sampling speed and a custom built front-end amplifier for current-voltage conversion (see supporting information). IN-VITRO CHARACTERIZATION OF FDM GRAPHENE NEURAL PROBES In order to validate the suitability of g-SGFETs for frequency-division multiplexing, their sensitivity in the AM mode must be characterized and compared with the sensitivity in the DC mode. The characterization of 𝑔𝑚 can be performed following two approaches: from the derivative of the stationary 𝐺𝑑𝑠 − 𝑉𝑔𝑠 curve or from the dynamic response of g-SGFETs to signals with various frequency components applied at the gate (see Fig. 1c). Fig. 2a shows the 𝑔𝑚 − 𝑉𝑔𝑠 curves extracted following the first approach for a 3x3 g-SGFET array, demonstrating the equivalence of the stationary response in the DC and AM operation modes. Fig. 2b presents the frequency dependence of 𝑔𝑚 measured following the second approach. The magnitude of 𝑔𝑚 presents similar values in both modes for frequencies < 1𝑘𝐻𝑧, above which the effect of capacitive currents contributes significantly in the DC mode (see supporting information). In addition to the transconductance, the intrinsic electrical noise of the graphene transistors shall be considered in order to fully characterise the sensitivity of the graphene sensors. In Fig. 2c, the equivalent noise at the gate (𝑉𝑔𝑠−𝑟𝑚𝑠 ), defined as the RMS current noise (𝐼𝑑𝑠−𝑟𝑚𝑠 ) normalized by the transconductance, is represented under different 𝑉𝑔𝑠 bias conditions for a transistor area of 50𝜇𝑚 𝑥 50𝜇𝑚. Fig. 2c demonstrates that the sensitivity of g-SGFETs, defined by their noise performance, does not differ dramatically in both modes, showing only slight changes in its 𝑉𝑔𝑠 dependence. 8 Figure 2| In-vitro evaluation of g-SGFET performance in the amplitude modulation (AM) mode. a. 𝑔𝑚 − 𝑉𝑔𝑠 relationship in the AM and DC modes, measured in a 3x3 g-SGFET array. b. The magnitude of 𝑔𝑚 over frequency of the signal applied at the gate is shown for the two modes. The response was measured in a 2x2 g-SGFET array. c. 𝑉𝑔𝑠−𝑟𝑚𝑠 for an integration bandwidth of 1-10Hz measured in the AM and DC modes; measurements performed with r a 3x3 g-SGFET array. d. Schematic representation of a g-SGFET and the Fermi energy in the graphene for the DC and AM mode (top). The band structure at the CNP point is shown along the graphene channel for the DC (middle) and AM (bottom) modes. e. Dependence of 𝐼𝑑𝑠 on 𝑉𝑔𝑠 and 𝑉𝑑𝑠 , revealing the shift in the CNP, as well as the non-linearities in the 𝐼𝑑𝑠 − 𝑉𝑑𝑠 produced by the effective gating. f. 3- 9 dimensional representation of the 𝐼𝑑𝑠 dependence on 𝑉𝑔𝑠 and 𝑉𝑑𝑠 . The relation between shifts of 𝐼𝑑𝑠 − 𝑉𝑔𝑠 along the 𝑉𝑔𝑠 axis and non-linearities introduced in the 𝐼𝑑𝑠 − 𝑉𝑑𝑠 curves can be observed. g. Two carrier signals and their 2nd and 3rd order harmonics are represented in the frequency domain. The frequency which defines the bandwidth of operation (𝐹𝑚𝑎𝑥 ) and the position of the Nyquist frequency (𝐹𝑠 /2) with respect to 𝐹𝑚𝑎𝑥 are indicated by the vertical lines. h. The 𝐼𝑑𝑠 normalized by its value at 10kHz is shown for different channel lengths. The filled area represents the standard deviation (n=3). These slight discrepancies presumably arise from the differences in the drain-source bias in both modes. The gradient in the workfuntion of graphene along the channel induced by this bias causes a non-homogeneous effective gating of the transistor (see Fig. 2d and supporting information). In the DC mode this gradient is constant over time, producing a constant offset in the channel doping for a certain 𝑉𝑑𝑠 bias. Changing 𝑉𝑑𝑠 produces a shift of the transfer curves of the g-SGFETs along the 𝑉𝑔𝑠 axis (see Fig. 2e). This effective gating is also responsible for the dependence of 𝐺𝑑𝑠 on 𝑉𝑑𝑠 , which introduces non-linearities in the output characteristics shown in Fig. 2e. Fig. 2f shows a 3-dimensional representation of the 𝐼𝑑𝑠 − 𝑉𝑔𝑠 and 𝐼𝑑𝑠 − 𝑉𝑑𝑠 characteristic curves of the g-SGFETs. In the DC mode, the g-SGFETs are operated at a stationary point in the 𝑉𝑔𝑠 − 𝑉𝑑𝑠 plane, but in the AM mode the drain-source bias oscillates along the 𝑉𝑑𝑠 axis. In this way, non-linearities in the 𝐼𝑑𝑠 − 𝑉𝑑𝑠 curves will lead to distortion of the carrier signal, introducing harmonics at frequencies multiple of 𝑓𝑐 (see Fig. 2g and supporting information). Harmonic distortion constrains the selection of carrier frequencies that can be used for AM: high order harmonics must not lie within the frequency band of operation dedicated to the carrier signals. 10 Thereby, the frequency of all carriers must be below the 2nd order harmonic of the carrier of lowest frequency (see Fig. 2g). In addition, the Nyquist frequency (𝑓𝑠 /2) must be above the 2nd order harmonic of the highest carrier frequency in order to prevent folding of 3rd order harmonics into the band of operation by aliasing. Another important aspect affecting the selection of carrier frequencies is the frequency response of g-SGFETs. The graphene-electrolyte interface exhibits a capacitive response, which at high frequencies allows a displacement current to flow from drain to source through the electrolyte27, degrading the device performance. The characteristic cut-off frequency of this phenomenon appears at relatively high frequencies due to the high ratio between mobility and interface capacitance in graphene. Other active sensors, such as organic electrochemical transistors, which present a lower mobility and a larger interface capacitance29, are expected to present a worse frequency response27. Fig. 4e shows the frequency response of g-SGFETs for multiple channel lengths, demonstrating an approximately constant response for channels shorter than 100𝜇𝑚 and frequencies below 500𝑘𝐻𝑧 at least. SCALABILITY OF FDM GRAPHENE NEURAL PROBES Considering the ultimate goal of enabling high-density, large-area sensor arrays, the scalability of the FDM graphene neural probes has to be thoroughly explored. Important aspects limiting the scalability of FDM are the crosstalk in the g-SGFET array, the constrains in the selection of carrier frequencies, and the requirements for the electronics used to operate the arrays. In FDM, no switching among sensing sites is required. Although this feature bears a clear advantage for ease of fabrication of the neural probes, it prevents from doing on-site switching of 11 the sensors, and can therefore lead to an increased susceptibility to crosstalk. Crosstalk can appear between g-SGFETs in the same row (i.e. sharing a readout channel) as well as in the same column (i.e. biased by the same carrier) due to common-mode voltage (𝑉𝑐𝑜𝑚 ) oscillations in the resistance of metal tracks in series with the drain (𝑅𝑟𝑜𝑤 ) and source (𝑅𝑐𝑜𝑙 ). Analysing the equivalent circuit in Fig. 3a, an analytical expression can be derived, which indicates that crosstalk among rows and among columns is proportional to 𝑅𝑟𝑜𝑤 and 𝑅𝑐𝑜𝑙 respectively (see Fig. 3a and supporting information). Additionally, crosstalk signals couple with g-SGFETs that are out of the same column and row, causing a second order crosstalk (see supporting information S4). In order to experimentally determine the crosstalk level, we have patterned multiple polyelectrolyte gates on the graphene sensor arrays by inkjet printing (see Fig. 3a and supporting information S5). Fig. 3b shows the signal measured by an individually gated g-SGFET (black) and the crosstalk it induced on sensors in the same column (orange), the same row (blue) and on the rest of g-SGFETs (red), together with the fitting of the experimental data using the analytical expression presented in the supporting information. A crosstalk of ~36dB/~73dB is observed for g-SGFETs within/outside the same column or row, which corresponds to a 𝑅𝑟𝑜𝑤 ≈ 𝑅𝑐𝑜𝑙 = 50𝛺. In order to reduce the crosstalk to the level achieved using on-site switches (~65dB)30, the resistance of the tracks should be reduced to the range of few ohms. This target could be met by increasing the width of the metal lines, which can be implemented easily when translating this technology from rodents research into human clinical applications. . 12 Figure 4| Scalability of g-SGFET arrays multiplexed in the frequency-domain: a. Equivalent circuit of a 3x3 g-SGFET array. The metal track resistance of the columns and rows is modelled by 𝑅𝑐𝑜𝑙 and 𝑅𝑟𝑜𝑤 respectively. Each column is biased with a different carrier (𝑉𝑐𝑎𝑟1, 𝑉𝑐𝑎𝑟2 and 𝑉𝑐𝑎𝑟3). Common voltage oscillations (𝑉𝑐𝑜𝑚,𝑐𝑜𝑙 and 𝑉𝑐𝑜𝑚,𝑟𝑜𝑤 ) produce changes in 𝑉𝑑𝑠,𝑒𝑓𝑓 . The light blue area indicates the position of 4 polyelectrolyte gates printed on a 3x3 array. b. Response to a 10Hz signal measured in the g-SGFETs highlighted by a thicker colored line in part a. The solid lines indicate the fitting by the analytical model. The noise (dashed black line) was measured at 7Hz. c. The right axis indicates the normalized transconductance for g-SGFETs of (50𝜇𝑚 𝑥 50𝜇𝑚, n=4). The carrier frequencies selected for the in-vivo proof of concept (4x8 array) are shown in green and those proposed for a 32x32 sensor array are indicated in black. High order harmonics are indicated together with the required sampling frequency. d. Histograms of 𝑉𝑔𝑠−𝑟𝑚𝑠 from 3 neural probes of 32 g-SGFETs integrated in the 1-10Hz frequency. The log-normal 13 distribution indicates the mean and standard deviation of 𝑉𝑔𝑠−𝑟𝑚𝑠 . The values from the specific neural probe which was implanted in shown in the inset figure. e. Histogram of 32 superposed carriers with phase optimization to minimize the peak-to-peak amplitude (black), and with all carriers in phase (red). The inset shows a fragment of the resulting signals. f. Histogram of the 4 superposed carriers used for the in-vivo proof of concept compared to the amplitude of a 32-carrier signal with phase optimization. Another important aspect related to the scalability of FDM graphene neural probes is the selection of the carrier frequencies, which is constrained by the frequency response of g-SGFETs and the harmonic distortion of the carrier signals. The 𝑔𝑚 (𝑓𝑐 ) was characterized by sweeping 𝑓𝑐 and measuring the dynamic response of the graphene sensors to pure tone signals applied at the gate. Fig. 3c shows that 𝑔𝑚 remains approximately constant for carrier frequencies up to at least 600𝑘𝐻𝑧 and a channel length of 50𝜇𝑚. Sampling at four times this frequency limit (i.e. 𝐹𝑠 /2 ≥ 2𝐹𝑚𝑎𝑥 = 1.2 𝑀𝐻𝑧 ) allows to use carriers of up to ~600𝑘𝐻𝑧. Fig. 3c shows a combination of carrier frequencies which meets all the requirements to allow the operation of 32x32 graphene sensor arrays. In this configuration, operation in quadrature AM31 can be used to maximize the frequency bandwidth of each sensor to 10𝑘𝐻𝑧 (see Fig. 3c). Above this bandwidth, the signal will be filtered in the digital domain to eliminate any components corresponding to other carriers. The discrete electronics system designed for the validation of the technology in-vivo is limited to operate arrays of up to 4x8 g-SGFETs. This limitation comes from the constrained scalability of discrete electronics, in opposition to application specific integrated circuits (ASIC). Fig. 3c shows the combination of carrier frequencies used for the in-vivo proof of concept. The 𝑉𝑔𝑠−𝑟𝑚𝑠 from 3 probes of 4x8 g-SGFET arrays operated with this carriers configuration is shown in Fig. 3d, demonstrating a mean sensitivity of 6.29µV with a standard deviation of 1.37 µV and 14 a yield of 100%. This high sensitivity can eventually degrade due to the superposition of a large number of carrier signals, the large amplitude of which might challenge the resolution of the data acquisition (DAQ) system. The quantization error of the analog-to-digital converter (ADC), given by its less-significant bit (LSB), must be low enough to ensure signal integrity. When increasing the number of carriers, their amplitude (𝐴𝑐 ) must be reduced in order to prevent saturation of the ADC (see supporting information). This decrease in 𝐴𝑐 implies an attenuation of the transconductance (i.e. 𝐴𝑐 𝑔𝑚 ) of the g-SGFETs, while the LSB of the ADC remains unchanged. To minimize the amplitude of the carriers superposition for a certain 𝐴𝑐 , the phase of the carriers can be adjusted. Fig. 3e shows the improvement obtained by phase optimization for the combination of 32 carrier signals defined in Fig. 3c, revealing a threefold attenuation in the amplitude of the carrier superposition. The comparison with the superposition of the 4 carriers used for this proof of concept shows that upscaling to 32 carriers causes an increase in the amplitude by a factor of 2.8, which could be compensated by increasing the resolution of the ADC by 1-2 bits32. These results, together with the measure of crosstalk and the high frequency response of g-SGFETs, demonstrate the potential of this technology to reach over a thousand channels flexible neural probes. IN-VIVO EVALUATION OF FDM GRAPHENE NEURAL PROBES Previous works have shown that g-SGFETs operated in the DC mode present a high sensitivity for the recording of neural activity19,23. Moreover, g-SGFETs have demonstrated a unique capability for the recording of infra-slow neural activity with a high spatial resolution26. The FDM operation of g-SGFETs is not only expected to preserve their sensitivity for infra-slow signals, but to enhance their performance by eliminating flicker noise from the amplifiers due to the lock-in amplification in the AM mode. To validate the in-vivo functionality of FDM graphene 15 probes, we have recorded electrical activity from the cortex of a Long Evans rat in an acute setting using a 4x8 FDM graphene neural probe (see Fig. 4a-b and supporting information). The optimum 𝑉𝑔𝑠 which maximizes 𝑔𝑚 and the highest carriers amplitude (𝐴𝑐 ), which fills the dynamic range of the amplifiers were determined in-vivo (see Fig. 4c). The sensitivity of the sensors to high-frequency LFP activity was evaluated by measuring visually evoked potentials33 triggered by a blue LED emitting light-pulses of 100 ms every 5s. The sensors directly placed on the primary visual cortex V1 (lower left) exhibit a sharp response with 50 ms delay and 250 µV peak amplitude lasting until 100 ms after the initial trigger (Fig. 4d). Sensors placed further away from the V1 show a distance-dependent suppressed response of smaller amplitude and extended delay (Fig. 4e). This result is in full agreement with previously reported values33, demonstrating the preserved sensitivity of g-SGFETs in this frequency band in the FDM operation mode. Similarly, the distortion-free recording of infra-slow activity using g-SGFET has been previously shown in the DC mode by the recording of cortical spreading depression (CSD) events26. CSDs are a slowly propagating wave of depolarizing neurons and astrocytes, which has been clinically related to stroke, brain injury and migraine34,35. CSDs can be easily triggered by injecting KCl into the brain cortex and present a propagation speed of approximately 5 mm per minute across the cortex. Fig. 4f shows the spontaneous activity under anaesthesia where highly coherent transitions from up to down-states can be observed. Fig. 4g shows the signal from channel in position (1,5) filtered in the 1-50Hz frequency band (blue) together with the signal filtered in the 0.001-50Hz band. This spontaneous activity is strongly suppressed during the depolarization wave, which results in a large infra-slow signal drift with a duration over 70s. Fig. 3h shows the propagating front of the CSD wave across the array, demonstrating the capabilities 16 of FDM graphene neural probes to study topography of wide-band oscillatory dynamics in the brain. Figure 3| In vivo validation of FDM graphene neural probes for brain recordings: a. Acute experiment setting. The g-SGFET array interfaces the brain with the custom-built front-end amplifier. b. Illustration of a rat skull indicates the position of the craniotomy, the g-SGFET array, the LED and the place of KCl injection. c. Average and standard deviation of the 𝐼𝑑𝑠 − 𝑉𝑔𝑠 and 𝐼𝑑𝑠 − 𝐴𝑐 curves obtained in-vivo for the 32 channels. d. The visually evoked potential averaged 17 over 10 consecutive events is shown for the g-SGFET placed on the lower-left corner of the array. e. Visually evoked potential averaged over 10 consecutive events for all g-SGFETs on the 4x8 array. The colour map represents the delay between stimulus and the peak of the response. f. Map of spontaneous activity under anaesthesia. g. Spontaneous activity filtered in two different bands indicates the presence of low frequency components (< 1𝐻𝑧) for channel in position (1,5). h. CSD event recorded in a single g-SGFET. The top graph shows the activity in the 1-50Hz band (blue, left axis) and the wide-band activity (0.001 − 50𝐻𝑧) (black, right axis). The corresponding spectrogram in the 1-50Hz band is shown below. i. The colour maps indicate the signal amplitude in each of the g-SGFETs on the array at different times during the CSD propagation. Discussion In summary, we have presented the concept of frequency-division multiplexing of graphene active sensor arrays to reduce the number of wires required for high sensor-count neural probes. This novel approach presents two main advantages over time-division multiplexing resulting from its switchless operation. Firstly, the elimination of switches implies an enormous simplification of the technological complexity, eliminating the need for high-mobility and wide band-gap flexible materials, such as ultra-thin SiO2. Secondly, FDM operates in a continuous mode, fully circumventing the problems derived from limited switching speed and artefacts in TDM, which ultimately limit the scalability of the arrays. Moreover, the signals from all sensors are continuously sampled at high speed, in the MHz range. Although the frequency separation between carriers determines the bandwidth of the sensors, the high sampling speed allows to acquire the neural signals with an arbitrarily high oversampling. Finally, the modulation and subsequent demodulation of the signals in the FDM mode is based on a lock-in amplification 18 scheme, which eliminates flicker noise from the amplifiers and improves the sensitivity of the system in the infra-slow frequency band. Our results demonstrate the high performance of g-SGFETs as mixers to perform on-site amplitude modulation of neural signals. We have shown their high sensitivity for wide-band neural signals both in the beaker as well as in-vivo. Besides, we have also demonstrated the outstanding drain-source frequency response of solution-gated graphene sensors, validating their performance for high carrier frequencies, required for the operation of large-scale arrays. In addition, we have evaluated the crosstalk among sensing sites, which could reach the same level as for TDM with on-site switches when translating this technology to human scale neural probes. In order to maintain the sensitivity of the system for large arrays, with up to 32 superposed carriers, we have described the use of carrier phase optimization as well as the requirements for the DAQ system, which could be met by an ASIC32. The viability of large arrays controlled by an ASIC allows to envision the realization of a new generation of high-density and large-area sensor arrays with thousands of sensing sites. The simplicity and robustness of the switchless, FDM methodology compared to state of the art alternatives30,36, together with the high sensitivity, flexibility and biocompatibility of graphene active sensors make the implementation of these technologies very promising for both neuroscientific research as well as clinical applications. 19 ASSOCIATED CONTENT Supporting Information. Fabrication process of the graphene sensor arrays. Electrical setup hardware and software for device characterization and in-vivo proof of concept. Animal handling and device implantation. High frequency response in DC-mode. Non-homogeneous doping of graphene transistors. Carriers and baseband harmonic distortion. Crosstalk modelling. DAQ noise. (PDF) AUTHOR INFORMATION Corresponding Author * joseantonio.garrido@icn2.cat (Jose A. Garrido) and anton.guimera@imb-cnm.csic.es (Anton Guimerà Brunet) Author Contributions R.G.C. Contributed to the design and fabrication of the neural sensor arrays. He characterized the devices and contributed to the software development and in-vivo experiments. N.S. Contributed to the design of the sensor arrays, DAQ system design and in-vivo experiments. J.C. Designed the front-end and contributed to the characterization of the DAQ system. L.R. Contributed to the software development and devices characterization. X.I. Contributed to the design and fabrication of the neural sensor arrays. G.S. Did the surgery for the acute experiment. A.M. Developed the inkjet printing procedure to evaluate the crosstalk. S.S. and G.G. Developed the polyelectrolytes used for crosstalk determination. A.S. Led the team for the in-vivo proof of concept. F.S.G. Contributed to the concept of frequency-division multiplexing of graphene sensor arrays and the design of the front-end. R.V. Provided support for the development of the software and harware. 20 A.G.B. Contributed to the experimental design, development of the software and hardware as well as in-vivo proof of concept. J.A.G. Led the team for development of the graphene sensor arrays and contributed to the experimental design. R.G.C., A.G.B. and J.A.G. wrote the manuscript. ∇ R.G.C. and N.S contributed equally to this work. Notes Patent application (no. EP18382593) filled by UAB, CSIC and ICN2; entitled “Circuit for the multiplexing and read-out of variable-resistance sensor arrays” (pending); inventors who are co- authors in the present article are AGB, FSG and JAG. ACKNOWLEDGMENT This work has been funded by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 732032 (BrainCom) and Grant Agreement No 785219 (Graphene Flagship). The ICN2 is supported by the Severo Ochoa Centres of Excellence programme, funded by the Spanish Research Agency (AEI, grant no. SEV-2017-0706), and by the CERCA Programme / Generalitat de Catalunya. R.G.C. and N.S. acknowledge that this work has been done in the framework of the PhD in Electrical and Telecommunication Engineering at the Universitat Autònoma de Barcelona. R.G.C is supported by the International PhD Programme La Caixa - Severo Ochoa (Programa Internacional de Becas "la Caixa"-Severo Ochoa). This work has made use of the Spanish ICTS Network MICRONANOFABS partially supported by MICINN and the ICTS ‘NANBIOSIS’, more specifically by the Micro-NanoTechnology Unit of the CIBER in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN) at the IMB-CNM. This work is within the project FIS2017-85787-R funded by the “Ministerio de Ciencia, Innovación y 21 Universidades” of Spain, the “Agencia Estatal de Investigación (AEI)” and the “Fondo Europeo de Desarrollo Regional (FEDER/UE)”. REFERENCES: (1) Jeannerod, M. Motor Cognition : What Actions Tell the Self; Oxford University Press, 2006. (2) Georgopoulos, A. P.; Kettner, R. E.; Schwartz, A. B. 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