# Impact of interdigitated electrodes design on the low frequency and random telegraph noise of single-layer graphene micro ribbons

Georgia Samara, Christoforos Theodorou, Alexandros Mavropoulis, Nikolaos Vasileiadis, Konstantinos Papagelis, Panagiotis Dimitrakis

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Georgia Samara, Christoforos Theodorou, Alexandros Mavropoulis, Nikolaos Vasileiadis, Konstantinos Papagelis, et al. Impact of interdigitated electrodes design on the low frequency and random telegraph noise of single-layer graphene micro ribbons. Applied Surface Science, 2025, 715, pp.164567. 10.1016/j.apsusc.2025.164567. hal-05406740

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# Impact of Interdigitated Electrodes design on the Low Frequency and Random Telegraph Noise of Single-Layer Graphene Micro Ribbons

**Authors:** Georgia Samara<sup>a,b</sup>, Christoforos Theodorou<sup>c</sup>, Alexandros Mavropoulis<sup>a</sup>, Nikolaos Vasileiadis<sup>a</sup>, Konstantinos Papagelis<sup>b</sup>, Panagiotis Dimitrakis<sup>a,d</sup>

<sup>a</sup> Institute of Nanoscience and Nanotechnology, NCSR "Demokritos", Ag. Paraskevi, Greece

<sup>b</sup> Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

<sup>c</sup> Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, CROMA, Grenoble, France

<sup>d</sup> Institute of Quantum Computing and Quantum Technology, NCSR "Demokritos", Ag. Paraskevi, Greece

Keywords: Single-layer graphene, CVD, Interdigitated electrodes, Low frequency noise, Random telegraph noise, surface traps

## Abstract

High performance devices consisting of interdigitated electrodes (IDE) on top of single layer graphene (SLG) are candidates with favorable prospects for sensing applications. Graphene micro ribbon (GMR) of various widths and IDE design geometries were fabricated and experimentally examined regarding their low frequency noise (LFN) behavior. Measurements revealed a 1/f behavior and different kinds of trap activity behind it, which was studied through the analysis of Random telegraph noise (RTN) signals.
Our investigation suggests that adjusting the geometrical characteristics of either the GMR width or the IDE topology can significantly influence the SNR ratio of SLG-based electronics. On the bright side, the results of our study can help orientate fabrication decisions for the maximization of the SNR.

# I.Introduction

On top of the impressive development of classic semiconductors, like Si, over the past decade, two-dimensional (2D) materials have captured the scientific interest due to the excellent merging of downscaled dimensions and enhanced material properties in order to enable applications in the More than Moore technology direction. Boehm et al [1], were the pioneers of graphene investigation and isolation in 1961, as well as its definition through graphite lattice in 1994. In 2004, graphene was the cornerstone for in-depth research, initially in atomically thin carbon sheets through its isolation utilizing the exfoliation method [2] and then in other materials with similar outstanding properties in atomic scale. SLG is a zero bandgap semiconductor whose structure resembles a honeycomb planar lattice of carbon atoms linked via π-π* bonds [3], [4], [5]. Moreover, it has been characterized as supreme material due to its exceptionally high electron mobility at room temperature (highest theoretical limit at $200,000 \text{ cm}^2\text{V}^{-1}\text{s}^{-1}$), absorbance of white light equal to 2,3 %, thermal conductivity ranging from 4.84 to $5.30 \times 10^3 \text{ Wm}^{-1}\text{K}^{-1}$[6], breaking strength 200 times higher than that of steel, Young modulus 1TPa and low fabrication cost [7], [8], [9], [10]. Thus, a lot of research effort was directed towards SLG because it has potential for a wide spectrum on electronic and sensing applications [11].

Electrical noise measurements can serve as a diagnostic tool for thermal, shot, burst, generation-recombination, $1/f$ and $1/f^2$ noise, providing insight about the relation between the noise in a device and its reliability, or its intrinsic properties such as interface trap density [12].
The first statements on LFN measured in graphene devices were addressed in 2007 and 2008, respectively [13], [14]. A comprehensive investigation on LFN in SLG devices was performed in 2013 by Balandin's group [15], demonstrating 1/f spectral dependence. Following, in 2022 Nah et al. combined various IDE topologies on top of functionalized SLG sheets and examined their resistive nature for sensing applications [16]. However, the noise behavior of such different IDE topologies is not examined yet. In this research work, different IDE configurations on top of different pristine SLG micro-ribbons were manufactured, and the samples were thoroughly examined through Current-Voltage (I-V) characteristics, LFN and RTN measurements. The possibility of a direct dependence between the measured electronic properties and the geometrical characteristics of the IDE is investigated. The aim of this study is to use these topologies as sensing devices. The most critical aspect is to investigate the trade-off between GMR width and the distance among IDE in order to maximize the signal-to-noise ratio (SNR).

## II. Materials and Methods

### A. Device fabrication process

IDE-GMR devices were fabricated following the experimental steps depicted in Fig. 1. Chemical Vapor Deposition (CVD) technique was employed for SLG growth on Cu foil and covered by Poly (methyl methacrylate) (PMMA). Cu foil was etched in Ammonium Persulfate solution and then a wet-transfer process was utilized to transfer SLG/PMMA on top of 300nm SiO₂/Si substrate. PMMA was removed by UV exposure (325nm) and then development in Methyl Isobutyl Ketone MIBK: IPA (3:1) solution. The last step before graphene patterning was furnace annealing in hydrogen contributing in PMMA residuals removal. Following, spin coating and electron beam lithography (EBL) and Oxygen plasma (dry) etching techniques were applied in order to pattern the GMR strips (Fig. 1). Different topologies of IDE, meaning IDE with various
electrode interspace distance or gap G (8, 15, and 25µm) on top of GMR having different widths
W (50, 100, and 200 µm) were fabricated by Aluminum lift-off process. A total number of nine
devices were fabricated following the combinations among the different gaps and widths.

<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Optical microscope image and (b) electrical equivalent circuit of a typical IDE-GMR device. (c) Definition of the geometric parameters of IDE-GMR architecture. Here, G=25µm, W=50µm, L=25µm</figcaption></figure>

Typical optical microscope image of the final IDE (11 electrode pairs with interspace distance 25µm) and GMR (50 µm width) topology is presented in Fig. 1(a). Also, the electrical equivalent
circuit is shown in Fig. 1(b) where R<sub>ch</sub> and R<sub>c/2</sub> are the SLG and the contact resistances respectively.

## B. Electrical Characterization Methods

A HP4155A Semiconductor Parameter Analyzer connected to a wafer prober was used to perform Current -Voltage (I-V) measurements. For RTN measurements, the instrumentation set up of Fig.2 was formed by connecting the device under test (DUT) on wafer prober with a low-noise current amplifier SR570, a Keysight B2902A source measure units and a Keysight DSO7104A digital oscilloscope.

<figure><img src="image_3.png" /><figcaption>Figure 2: Final set up for RTN measurements.</figcaption></figure>

# III. Results and Discussion

## A. Current-Voltage Measurements

All the fabricated IDE-GMR devices were tested through I-V measurements, which were performed by applying current logarithmic sweeps in the range 1 to 100 µA and measuring the voltage. It should be stressed that no bias on the back side of the sample was applied. The experimental results for different G gaps are shown in Fig.3 with parameter the GMR width W. The work function value between GMR and Aluminum (Al) electrodes is of great importance because it controls the Ohmic behavior of the contacts. In accordance with measurements in Fig. 3, the experimental data within the range 1-20µA fit excellent to the relation $ln(V)=ln(R) +$
$n \cdot \ln(I)$, with $0.98 \le n \le 1$, revealing Ohmic conduction. For higher current values, 20-100µA, experimental data deviate from linear behavior, that may be attributed to self-heating effect of GMR and/or conduction through grain boundaries. This effect becomes stronger as $W$ is decreasing. Furthermore, as expected, devices with higher W/G ratio exhibit lower resistance. Indeed, the resistance $R$ of thin film material of resistivity $\rho$, length $L$, width $W$ and thickness $t$ is given by the well-known formula $R=\rho L/Wt$. In our case $L=G$ and for the same GMR, resistivity and thickness can be considered constant, hence $R=R_{\text{sheet}}[G/W(N_{\text{IDE}}-1)]$, where $R_{\text{sheet}}$ is the sheet resistance of the GMR in $\Omega$/c. The calculated resistance values from the measured data after linear fitting, as shown in Fig. 3, are presented in Table 1. The estimated error in resistance is lower than 1 %. Obviously, the resistance values shown in Table 1 are relatively high compared to the values of pristine SLG in the literature[17]. This should be attribute mainly to the high contact resistance of Al on SLG[18], [19].

<figure><img src="image_4.png" /><figcaption>Figure 3: Current -Voltage characteristics of IDE- GMR devices with different graphene ribbon width $W$ and electrode interspace distance $G$.</figcaption></figure>
Where N<sub>IDE</sub> is the number of interdigitated electrodes.

<table><caption>Table 1. The extracted resistance values after linear fitting on data shown in Fig. 3.</caption><thead><tr><th rowspan="2">G(μm)</th><th colspan="3">W50<br>(W=50μm)</th><th colspan="3">W100<br>(W=100μm)</th><th colspan="3">W200<br>(W=200μm)</th></tr><tr><th>W(N<sub>IDE-1</sub>)/G</th><th>R (kΩ)</th><th>R<sub>sheet</sub><br>(kΩ/□)</th><th>W(N<sub>IDE-1</sub>)/G</th><th>R (kΩ)</th><th>R<sub>sheet</sub><br>(kΩ/□)</th><th>W(N<sub>IDE-1</sub>)/G</th><th>R(kΩ)</th><th>R<sub>sheet</sub><br>(kΩ/□)</th></tr></thead><tbody><tr><td>8</td><td>194</td><td>38</td><td>7372</td><td>388</td><td>11</td><td>4268</td><td>775</td><td>6</td><td>4650</td></tr><tr><td>15</td><td>117</td><td>29</td><td>3393</td><td>233</td><td>7</td><td>1631</td><td>467</td><td>5</td><td>2335</td></tr><tr><td>25</td><td>42</td><td>25</td><td>1050</td><td>84</td><td>13</td><td>1092</td><td>168</td><td>5</td><td>840</td></tr></tbody></table>
## B. Low Frequency Noise characteristics and 1/f' behavior

LFN measurements were performed for all of the different topologies applying bias voltage between the electrodes in the range $0.1V \le V \le 0.6V$ with floating bottom gate. For each bias voltage, the current was recorded for 100s with sampling frequency 80kHz. Following, the Power Spectral Density (PSD) was obtained through Fast Fourier Transform (FFT) (Welch method) of all I-t recordings (Fig. 4(a)).

The PSD spectra for all applied voltages is shown in Fig. 4(a). It is evident that 1/f' dependence of the PSD is observed any bias voltage with $1 \le \gamma \le 2$. Following, figures 4 (b), (c) and (d) depict the log-log plots of the normalized PSD ($S_I/I^2$) vs f in the range 10 Hz to 20 kHz, organized and studied in triplets with fixed electrode distance. Obviously, all spectra show the 1/f' dependence. Specifically, under different bias voltages, PSD spectra plots exhibited various slopes, $\gamma$, in log-log scale, from $\gamma=0.5$ to and $\gamma=2$, depending on the measured sample and bias condition, which indicates the presence of Lorentzian spectrum contributions, commonly related to isolated traps. In addition, the PSD is decreased by almost one order of magnitude for GMR width greater than 50µm. To discover the origin of 1/f' noise, all measured $S_I$ values in a defined range of constant applied bias ($0.1V \le V \le 0.6V$) and across various topologies, were extracted at a specific frequency value set to 20 Hz. Furthermore, plots of $S_I^{1/2}$ (at 20Hz) vs voltage were generated and presented in Fig.5(a) indicating that the 1/f' noise amplitude is linearly dependent on the applied voltage.
<figure><img src="image_5.png" /><figcaption>Figure 4: (a) Typical PSD spectra for IDE-GMR with G=8µm and W=100µm with the theoretical $1/f$ and $1/f^2$ lines plotted. (b), (c), (d) Normalized PSD spectra $S_I/I^2$ vs. $f$ for all tested devices. I-t measurements scrutinized for different constant bias ranging 0.1 to 0.6 V.</figcaption></figure>

The observed dependence indicates that the measured noise originates from GMR's conductance fluctuations due to traps (variation of $\gamma$ with frequency) and not from contact-related defects. Almost identical trends were observed in all studied triplets. Following, based on equation (1)
the normalized square root resistance noise, $S_R^{1/2}/R^2$, term was calculated from the data depicted in Fig.5(a).

$$ \frac{S_I}{I^2} = \frac{S_R}{R^2} \Rightarrow \frac{\sqrt{S_I}}{I} = \frac{\sqrt{S_R}}{R} \Rightarrow \frac{\sqrt{S_I}}{V} = \frac{\sqrt{S_R}}{R^2} \Rightarrow \sqrt{S_I} = \frac{\sqrt{S_R}}{R^2} V \quad (1) $$

where $R=V/I$ is the total resistance of the tested device (see Table 1), $S_I$ and $S_R$ are the current and resistance noise, respectively.

According to McWhorter and Van der Ziel [20], the carrier number fluctuations PSD, $S_N$, due to trapping/de-trapping in slow oxide traps near the interface can be described by:

$$ \frac{S_N}{N^2} = \frac{S_{Nt}}{N^2} = \frac{AN_t kT}{N^2 f} \quad (2) $$

where N the total number of carriers in the conductive volume, $A_G$ the active graphene surface area

$A_G= G \cdot W \cdot (N_{IDE}-1)$ and $N_t$ the trap density in cm$^{-2}$eV$^{-1}$. Assuming a constant GMR mobility, $\mu$, with the applied voltage bias V, and that the current for low V is equal to

$$ I = \frac{W(N_f - 1)}{G} qn\mu V = \frac{W(N_f - 1)}{G} q \frac{N}{W(N_f - 1)G} \mu V = q \frac{N}{G^2} \mu V \quad (3) $$
<figure><img src="image_6.png" /><figcaption>Figure 5: (a) $S_I^{1/2}$ vs Voltage at 20Hz, (b) $S_R^{1/2}/R^2$ vs $1/A_G$ and (c) $S_R^{1/2}/R^2$ vs $1/A_C$ for all tested IDE-GMR devices where $A_G$ and $A_C$ denote the area of free graphene and contact regions respectively. Linear fit among experimental data is plotted when necessary.</figcaption></figure>

where n the GMR carrier density in cm⁻², one can write:
$$ \frac{S_I}{I^2} = \frac{S_N \left( \frac{q\mu V}{G^2} \right)^2}{N^2 \left( \frac{q\mu V}{G^2} \right)^2} = \frac{S_N}{N^2} \quad (4) $$

Combining (2) and (4) we obtain:

$$ \frac{S_I}{I^2} = \frac{AN_t kT}{N^2 f} = \frac{AN_t kT}{n^2 A^2 f} = \frac{N_t kT}{n^2 A f} \quad (5) $$

which reveals a potential scaling of the normalized PSD with the reciprocal of area, assuming a constant carrier density, n. Based on (5), we plotted the normalized resistance noise, $S_R/R^2$, as a function of $1/A_G$ where $N_{IDE}$ is the number of the IDE as defined in Fig.5(b) [21], to verify if any linear dependence is observed. Each combination of symbol and color corresponds to a device with a specific G and W topology. Indeed, a linear fit was successfully applied to these data, with the exception of two outlier devices (G15W50 and G25W100) which deviate from the linear regression. This may be attributed to the presence of wrinkles or graphene sheet abnormality issues as well as to the contribution of contact resistance noise, $S_{RC}$. Under severe impact of contact resistance $R_C$, the measured LFN spectra would be dominated by $S_{RC}$. In that case, according to (5), the normalized PSD would be proportional to $1/A_C$, where $A_C=W\cdot(N_{IDE}-1)/L$ [22], [23].

To examine this hypothesis, the $S_R/R^2$ is plotted as a function of the inverse contact area $1/A_C$, in Fig.5(c). Evidently, there is no clear correlation or linear dependence between these data, not even for the two outliers. Summarizing, Fig. 5 indicates that LFN results mainly from the SLG conductance fluctuations, as opposed to contact region noise. In addition, Fig. 5(b) also provides insights into the noise performance with regards to the IDE topology, indicating that an
augmentation in the active GMR area results in a decreased SNR value. Thus, geometrical characteristics of the devices have a critical impact on LFN and consequently on device performance.

### C. Characterization of Random Telegraph Noise

Apart from frequency-domain noise analysis for each device, time-domain noise analysis provides also significant information. In Fig.6, a typical example of current amplitude distribution is shown for G8W100 device under six different constant applied voltages. The experimental current distributions fit perfectly to single and multi-Gaussians (0.4 and 0.5V), revealing the presence of RTN signals. Typical examples of RTN are depicted in Fig. 7. Specifically, RTN time windows are demonstrated together with the corresponding histograms with multi-gauss distribution. For G8W100 topology, the I-t waveform captured under constant voltage bias of 0.5V more than one switching events were found at different time windows, as shown in Fig.7 (b), and (c) for example. The different number of RTN levels suggest the presence of one or more traps [24]. Specifically, Fig. 7(a), (c) and (e) present two-level RTN signals, while in Fig. 7(b), (d) and (f) three level RTN are shown. Three level RTN seems to suggest that during the certain time window, electrons are captured and emitted by two traps, while a two level RTN signal corresponds to the presence of a single trap. This is also represented in corresponding Weighted Time Lag Plots (WTLP) (see Supplementary).
<figure><img src="image_7.png" /><figcaption>Figure 6: Histograms as extracted from the statistical analysis of the recorded I-t waveforms of G8W100 device at various constant applied voltages. Gaussian curve fitting approach was used in most cases except 0.4 and 0.5V where multi-Gauss fitting was applied.</figcaption></figure>

In all time domain noise illustrations, high and low current levels of RTN noise are denoted with (blue) dotted lines and named $I_H$ and $I_L$, respectively. In three level noise recordings, such as in Fig. 7 (b) (d) and (f), there is one more intermediate level (pink dotted line) that is named $I_{H0}$.

The final objective of this study was to identify the origin of RTN events between traps at the channel/dielectric and/or channel/metal contacts interfaces, where channel is considered the material where electrons are flowing. In the examined devices, there are two possible interfaces: the SLG/SiO₂ (channel and bottom dielectric region) and the SLG/Al (contact regions).

As discussed in section B, the analysis of normalized noise resistance revealed that LFN is attributed to resistance fluctuations in graphene layer and not to series resistance at the contacts.
The ΔI/I<sub>H</sub> (%) ratio, where ΔI is the difference between the current mean values of two sequential RTN levels, e.g., I<sub>H</sub> and I<sub>L</sub>, was extracted for all detected RTN signal levels.

<figure><img src="image_8.png" /><figcaption>Figure 7: (a) - (f) Typical Illustrations of RTN signals as detected in *I-t* waveforms along with the corresponding histograms( vertical) plots after statistical analysis.</figcaption></figure>
To distinguish whether the RTN originates from SLG/SiO₂ or SLG/Al, we plotted ΔI/I<sub>H</sub> versus the inverse of the total graphene channel area, A<sub>G</sub> (Fig. 8(a)), and versus the inverse of the contact region area, A<sub>C</sub> (Fig. 8(b)). This was done because, based on (3), and considering no mobility change due to the trapping, a single electron trapping which introduces a ΔN change equal to 1 would yield a ΔI/I equal to:

$$ \frac{\Delta I}{I} = \frac{1}{nA_{G,C}} \quad (6) $$

For each IDE-GMR device, usually more than one RTN levels were detected, therefore the extracted ΔI/I<sub>H</sub> values were categorized and studied in three regions: RTN-1 ranging from 0 to 0.03, RTN-2 from 0.03 to 0.05 and RTN-3 for values greater than 0.05, depicted with black, red and blue color, respectively. Since the examined factor 1/A<sub>G</sub> in Fig. 8(a) includes both G and W variables it was not clear enough whether the traps are related to the contact region or the free graphene area ΔI/I<sub>H</sub> (%) -1/A<sub>C</sub>. After linear fitting in RTN-1 and RTN-2 regions of Fig. 8(a) we find the slope values are 0.9 and 0.79, respectively. However, in the same regions of Fig 8(b) the slope values were equal to 0.38 (RTN-1) and 0.91 (RTN-2). Hence, it can be claimed that the RTN-1 (low amplitude) traps originate from SiO₂/SLG interface while RTN-2 (medium amplitude) traps are located within the contact region, either SiO₂/SLG, or SLG/Al. However, since trapping at SLG/Al would mean not only the presence of dangling bonds in the graphene layer but also much faster traps due to the huge free carrier concentration in the ohmic contact and in our case (Fig. 7) the capture/emission times are in the millisecond range, we conclude that all RTN levels are generated by SiO₂ interface traps, in both channel and contact regions, with contact regions resulting in higher amplitudes. Interestingly, G15W50 is an outlier in all RTN regions in both illustrations. This result in conjunction with Fig.5(b) (1/f noise analysis) indicates
that the quality of SLG of this device is lower than the rest, which may result during the fabrication process.

It is significant to mention that, in both plots Fig.8(a) and (b), RTN-3 group does not exhibit any direct dependence between ΔI/I<sub>H</sub> (%) and the geometrical characteristics of the device. We assess that this behavior can be attributed to non-uniformities or percolation effects in the graphene conduction area, acting as a single trap that is strong enough to reduce significantly the current in the conduction path, leading to RTN amplitudes much more important than the ones expected by (6).

Moreover, Fig. 8(c) was constructed to examine whether the RTN amplitudes scale with the inverse of the total measured conductance, G<sub>tot</sub>=dI/dV, calculated from the derivatives of the I-V plots of Fig.3. The reason is that whatever the physical source of fluctuation behind the RTN, i.e. carrier number fluctuations or induced mobility fluctuations or series resistance fluctuations, all of it is reflected in the total conductance fluctuation [25], because:

$$I = G_{tot}V \Rightarrow dI = dG_{tot}V = \frac{I}{G_{tot}} dG_{tot} \Rightarrow \frac{\Delta I}{I} = \frac{\Delta G_{tot}}{G_{tot}} (7)$$

Firstly, the illustration of ΔI/I<sub>H</sub> (%) compared to 1/G<sub>tot</sub> suggests a direct correlation between the width of SLG and the total conductance. Even without knowing how n or μ are varying between different devices or regions, the experimental results of Fig.8(c) suggest that the higher the width of graphene micro-ribbon, the higher the total channel conductance. Second, it is worth mentioning that the variation in conductance values is greatest among the devices of 50μm SLG width. This variability decreases as the SLG width increases to 100μm and ultimately reaches zero for SLG width equal to 200μm. The latter observation suggests that sensors based on SLG with IDE are less prone to graphene inhomogeneity for widths above 100μm.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

Figure 8: Plots of (a) $\Delta I/I_H - 1/G_{tot}$ reveals that high free graphene areas have the greatest amount of charge carriers. Moreover, the high variability in conductance values indicates that electron mobility is not the same in graphene area near to nanoscale. (b) $\Delta I/I_H (\%) - 1/A_G$ for three different trap regions RTN-1, RTN-2 and RTN-3. (c) $\Delta I/I_H (\%) - 1/A_C$ was created to distinguish the impact of metal regions from the impact of free graphene among IDEs in the detected RTN events. (d) $\langle \Delta I/I_H \rangle - 1/G_{tot}$ suggests a clear correlation between conductance and the mean values of $\Delta I/I_H (\%)$.

This conductance variability in devices of 50µm SLG width probably originates from changes in electron mobility due to the limited number of current pathways (percolation effect). Another
factor that may affect conductance is the increasing effect of SLG edges (armchair, zigzag) as
the free graphene micro-ribbon size approaches nanoscale. Finally, despite the spread of points
in Fig.8(c) and no clear linear correlation, Fig 8(d) reveals a clear linear correlation (R²=0.92)
between the mean value of ΔI/I<sub>H</sub> (%) from each device versus 1/G<sub>tot</sub>, regardless the exact device
geometry. Black vertical lines denote the standard deviation of ΔI/I<sub>H</sub> (%) for each device. To
conclude, we assess that this final plot reveals that even in cases of micro- or nano-scale graphene
sheets, where both carrier density and mobility can vary a lot from region to region or from
device to device, the total measured conductance can function as a metric for the expected
amplitudes of RTN. This means that, in general, a device with higher conductance levels (not
necessarily achieved through geometry characteristics) would exhibit RTN of lower normalized
amplitudes. This information is valuable for the reduction of the SNR in the graphene sensor
performance, or, in the opposite way, be used in noise-enhanced sensing[26] [27], where RTN is
used as a sensing tool and needs to be high.

IV. Conclusions

A thorough investigation has been conducted in IDE-GMR devices having different geometric topologies. Initially, I-V characteristics reveal Ohmic behavior for current that do not exceed 20 µA and self-heating effect for higher current values. Through statistical analysis of specific time domain windows from noise signals, up to three RTN levels revealed and originated from different regions of the IDE-GMR. Specifically, it was proved that the generation of different RTN levels is due to traps lying either at SiO2/SLG or SLG/Al interface. Finally, the correlation between the GMR width and the electron density were investigated.
# Acknowledgements

This work was supported in part by the research project "LIMA-chip" (Proj. No. 2748) which is funded by the Hellenic Foundation of Research and Innovation (HFRI) respectively.

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# Supplementary Information

## Appendix A: Current amplitude histograms of all the examined Devices

G8W50

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>
G8W200

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

G15W100

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>
G15W200

<figure><img src="image_31.png" /></figure>

Current (μA)

<figure><img src="image_32.png" /></figure>

Current (μA)

<figure><img src="image_33.png" /></figure>

Current (μA)

<figure><img src="image_34.png" /></figure>

Current (μA)

<figure><img src="image_35.png" /></figure>

Current (μA)

<figure><img src="image_36.png" /></figure>

Current (μA)

G25W50

<figure><img src="image_37.png" /></figure>

Current (μA)

<figure><img src="image_38.png" /></figure>

Current (μA)

<figure><img src="image_39.png" /></figure>

Current (μA)

<figure><img src="image_40.png" /></figure>

Current (μA)

<figure><img src="image_41.png" /></figure>

Current (μA)

<figure><img src="image_42.png" /></figure>

Current (μA)
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>
Appendix B: Weighted -Time Lag Plots

<figure><img src="image_49.png" /><figcaption>(b) G8W100-0.5V</figcaption></figure>

<figure><img src="image_50.png" /><figcaption>(c) G8W100-0.5V</figcaption></figure>

<figure><img src="image_51.png" /><figcaption>(d) G15W100-0.2V</figcaption></figure>

<figure><img src="image_52.png" /><figcaption>(e) G25W200-0.5V</figcaption></figure>

<figure><img src="image_53.png" /><figcaption>(f) G25W200-0.6V</figcaption></figure>

<figure><img src="image_54.png" /></figure>
Appendix C: Tables from $\gamma_1$ and $\gamma_2$

<table><caption>G8W50</caption><thead><tr><th>Bias (V)</th><th>Current (µA)</th><th>γ<sub>1</sub></th><th>Gauss</th></tr></thead><tbody><tr><td>0.1</td><td>0.31</td><td>1.20</td><td>1</td></tr><tr><td>0.2</td><td>0.7</td><td>1.12</td><td>1</td></tr><tr><td>0.3</td><td>1</td><td>0.91</td><td>1</td></tr><tr><td>0.4</td><td>1.4</td><td>1.06</td><td>1</td></tr><tr><td>0.5</td><td>1.71</td><td>0.9</td><td>1</td></tr><tr><td>0.6</td><td>2.04</td><td>0.91</td><td>1</td></tr></tbody></table>

<table><caption>G8W100</caption><thead><tr><th>Bias (V)</th><th>Current (µA)</th><th>γ<sub>1</sub></th><th>γ<sub>2</sub></th><th>Gauss</th></tr></thead><tbody><tr><td>0.1</td><td>1.95</td><td>1.22</td><td></td><td>1</td></tr><tr><td>0.2</td><td>4.14</td><td>1.21</td><td></td><td>1</td></tr><tr><td>0.3</td><td>6.3</td><td>1.23</td><td></td><td>1</td></tr><tr><td>0.4</td><td>8.75</td><td>1.02</td><td>1.50</td><td>2</td></tr><tr><td>0.5</td><td>11.43</td><td>1.08</td><td>1.44</td><td>2</td></tr><tr><td>0.6</td><td>14.58</td><td>1.29</td><td></td><td>1</td></tr></tbody></table>
G8W200

<table><thead><tr><td>Bias (V)</td><td>Current (μA)</td><td>γ<sub>1</sub></td><td>Gauss</td></tr></thead><tbody><tr><td>0.1</td><td>3.27</td><td>1.16</td><td>1</td></tr><tr><td>0.2</td><td>7</td><td>1.10</td><td>1</td></tr><tr><td>0.3</td><td>11</td><td>1.09</td><td>1</td></tr><tr><td>0.4</td><td>15</td><td>1.19</td><td>1</td></tr><tr><td>0.5</td><td>20</td><td>1.10</td><td>1</td></tr><tr><td>0.6</td><td>25</td><td>1.13</td><td>1</td></tr></tbody></table>

G15W200

<table><thead><tr><td>Bias (V)</td><td>Current (μA)</td><td>γ<sub>1</sub></td><td>Gauss</td></tr></thead><tbody><tr><td>0.1</td><td>4.36</td><td>1.24</td><td>1</td></tr><tr><td>0.2</td><td>8.89</td><td>1.26</td><td>1</td></tr><tr><td>0.3</td><td>13.82</td><td>1.27</td><td>1</td></tr><tr><td>0.4</td><td>19.6</td><td>1.32</td><td>1</td></tr><tr><td>0.5</td><td>25</td><td>1.31</td><td>1</td></tr><tr><td>0.6</td><td>31.9</td><td>1.30</td><td>1</td></tr></tbody></table>
G25W50

<table><thead><tr><td>Bias (V)</td><td>Current (μA)</td><td>γ<sub>1</sub></td><td>Gauss</td></tr></thead><tbody><tr><td>0.1</td><td>0.56</td><td>0.80</td><td>1</td></tr><tr><td>0.2</td><td>0.95</td><td>0.85</td><td>1</td></tr><tr><td>0.3</td><td>1.7</td><td>1.02</td><td>1</td></tr><tr><td>0.4</td><td>2.17</td><td>0.98</td><td>1</td></tr><tr><td>0.5</td><td>2.94</td><td>0.96</td><td>1</td></tr><tr><td>0.6</td><td>4.05</td><td>0.94</td><td>1</td></tr></tbody></table>

G25W200

<table><thead><tr><td>Bias (V)</td><td>Current (μA)</td><td>γ<sub>1</sub></td><td>γ<sub>2</sub></td><td>Gauss</td></tr></thead><tbody><tr><td>0.1</td><td>2.64</td><td>1</td><td></td><td>1</td></tr><tr><td>0.2</td><td>5.71</td><td>1.03</td><td></td><td>1</td></tr><tr><td>0.3</td><td>9.39</td><td>0.97</td><td></td><td>1</td></tr><tr><td>0.4</td><td>13.59</td><td>1.03</td><td></td><td>1</td></tr><tr><td>0.5</td><td>18.14</td><td>1</td><td>1.51</td><td>2</td></tr><tr><td>0.6</td><td>24</td><td>0.89</td><td>1.54</td><td>2</td></tr></tbody></table>