Graphene transistors for interfacing with cells: towards a deeper understanding of liquid gating and sensitivity

This work is focused on the fabrication and analysis of graphene-based, solution-gated field effect transistor arrays (GFETs) on a large scale for bioelectronic measurements. The GFETs fabricated on different substrates, with a variety of gate geometries (width/length) of the graphene channel, reveal a linear relation between the transconductance and the width/length ratio. The area normalised electrolyte-gated transconductance is in the range of 1–2 mS·V−1·□ and does not strongly depend on the substrate. Influence of the ionic strength on the transistor performance is also investigated. Double contacts are found to decrease the effective resistance and the transfer length, but do not improve the transconductance. An electrochemical annealing/cleaning effect is investigated and proposed to originate from the out-of-plane gate leakage current. The devices are used as a proof-of-concept for bioelectronic sensors, recording external potentials from both: ex vivo heart tissue and in vitro cardiomyocyte-like HL-1 cells. The recordings show distinguishable action potentials with a signal to noise ratio over 14 from ex vivo tissue and over 6 from the cardiac-like cell line in vitro. Furthermore, in vitro neuronal signals are recorded by the graphene transistors with distinguishable bursting for the first time.


Supplementary
. A sketch for understanding the geometrical value of □ in the performance of the GFETs.
Supplementary Figure S2. The three consecutive I-V curves recorded consecutively. While the first recording (a) shows some kind of double Dirac behavior, it starts to disappear in the second recording (b) and is completely gone after the third one (c).

Data analysis flow and selection criteria
The complete data processing is depicted in the flowchart ( Supplementary Fig. S3).
Supplementary Figure S3. A Mind diagram for data selection, analysis and calculation.
The set of recorded I-V curves went through two steps of selection before going into complete analysis: 1. Elimination of clearly damaged devices by interpreting the I-V curve shape. See Supplementary Fig. S4a for an example of a clearly damaged GFET that still shows some ambipolar behavior, but will not be considered in the following evaluation; 2. Further selection was done statistically to find out which devices behave normally, but their performance is out of range. The quantity considered for this process was the sheet resistance, or resistance per square, Rs=R0*L/W. This is an inherent property of the graphene and should be equal for every GFET independent of its shape. The values of Rs are plotted in a histogram ( Supplementary Fig. S4b) and fitted with a logarithmic normal . From this fit, the mean value and the standard deviation were extracted ( Supplementary Fig. S4c). For further analysis only values within ξ-σ were considered. As soon as a device is stable, three I-V curves are recorded, then each data point is averaged and a mean characteristics are plotted ( Supplementary Fig. S4d). First, the resistance is simply computed at each data point as = Δ Δ and plotted over VGS ( Supplementary Fig. S4e). The characteristic quantity R0 is the value of RS at VGS = 0 V. Multiplying R0 with the ratio W/L, one gets the sheet resistance RS that was used for the selection of the data. Furthermore, the transconductance can be computed by = .
Since the data of IDS is not smooth enough for numerical derivation, a Savitzki-Golay smoothing algorithm was applied to the data. The polynomial order of the algorithm was set to 3, and the number of considered data points was 21.
The transconductance plot shows two peaks (see Supplementary Fig. S4f). These are the points of maximum transconductance for the hole-and electron conduction with their values (left) and (right) and their positions ( max ), and ( max ). The transconductance graph has a significant dip, which is then used to compute the Dirac Point position. The liquid gate capacitance Ctotal was computed as described below. Since PBS was used as the ionic solution, the n* was set to 10 11 cm -2 , in accordance with the literature, [S1,S2,S3] . The PBS's molarity of 162.7 mM results in a Debye length of 0.754 nm. [S4] If a solution with a different molarity was used, was computed accordingly.The mobility was computed using the following equation: [S5] = • .The points of maximum mobility and are determined similarly to the points of maximum transconductance ( Supplementary Fig. S4g).

Computation of the interface capacitance
The applied voltage shifts the Fermi energy in the graphene area. However, if no VGS is applied, the Fermi energy is still shifted due to the combined chemical potential of the ionic solution and the gate electrode. The application of a gate voltage induces the formation of an electrical double layer at the interface of the graphene and solution. The overall capacitance consists of three parts: quantum capacitance CQ, air gap parallel plate capacitance Cairgap, and EDL parallel plate capacitance CEDL. [S6] It is common to state the capacitance normalized to the area of the capacitor. Therefore all further C values given are capacitances per unit area.
The quantum capacitance is the same for every device and was computed using the formula: [S1] = In this formula, e is the elementary charge, ℏ the reduced Planck constant, ≈ 300 ⁄ the Fermi velocity (c is the speed of light), nG and n* the carrier concentrations induced by gate potential and charged impurities, respectively. The n* is a parameter of the environment and the purity of the graphene. As explored previously, the n* value usually is between 10 11 and 10 12 cm -2 .
The air-gap capacitance was introduced recently and is computed using the standard formula = 0 where is the permittivity of the dielectric, 0 the vacuum permittivity and d the distance between the plates. In the case of the air-gap layer, = 1and = 0.34 . [S7] For the EDL calculation we use, = 78and = − 0.34 , where is the Debye length which can be computed using the formula: [S8] = 0.304 with M being the molarity of the ionic solution used.
The three capacitances are connected in series. Therefore the total capacitance Ctotal is To model the system correctly, for the 10x PBS case, the ionic strength results in a Debye length <0.34nm, which in general indicates a non-physical estimation when ions are too close to the graphene surface. In order to overcome the problem, only and parameters are taken into consideration. [S7] Importance of the n* parameters is also investigated. Below are plots of the capacitances while varying the n* from 10 11 cm -2 to 10 12 cm -2 . Figure S5. (a) The capacitance plot for 10x PBS, varying n* from 1×10 11 to 1×10 12 cm -2 . (b) The capacitance plots for PBS dilutions ≤1 while varying n* from 1×10 11 to 1×10 12 cm -2 (c) The color plot for changes in capacitance with varied ionic strength and the assumed n* probed from 1×10 11 to 1×10 12 cm -2 .

Supplementary
Supplementary Table S1.The changes in mobility for one GFET while varying both the ionic strength and n*. The mobility is given in cm 2 ·V -1 ·s -1 .

An example of a wrong interface capacitance modeling
Here, we would like to present an example of what happens when the Cox is not modeled correctly. We show that the resulting Cox values are several orders of magnitude higher/lower than correct values. In one of the incorrect models ( Supplementary Figs S6a-d) is taken into account, the resulting interface capacitance can be under-/over-estimated up to a factor of 100 (for 0.001x PBS), which will lead to over-/under-estimation of mobility.

Contact resistance and transfer length
The transmission line measurement technique (TLMT) has been used to determine the LT and RC. The resistances, R0, of the transistors are plotted against their channel lengths, L. The data points form groups depending on the channel width W. For each group there is a linear relation between L and R0. A linear regression with slope, a, and intercept, b, yields the following quantities: sheet resistance RS = a*W of the graphene sheet, contact resistance RC = b/2 and transfer length LT = b/2a, which is the average distance that the charge carriers travel under the contacts.
The contact resistance decreases with increasing channel width (see Supplementary Fig. 7 and Supplementary Table 2). This could be expected since the larger W, the larger the overall contact area and the lower the contact resistance. RC multiplied by W a parameter of material, and therefore, these values can be averaged for each wafer: RC, Si-I·W = 8230 ± 1910 Ω·µm, RC, Si-II·W = 5300 ± 1550 Ω·µm.
RC·W is smaller for Si-II than for Si-I. This is most likely due to the double contacted graphene. Figure S7. The TLM plots for wafers with single (Si-I, n=265) and double (Si-II, n=93) contacted graphene.

Supplementary Table S2. Statistical analysis of the contact resistance and transfer length for Si-I and Si-II wafers
The transfer lengths, calculated for both wafers are: LT, Si-I = 8.5±2.2 um, LT, Si-II = 3.6±2.2 um.
This shows that the transfer length could be reduced by more than a factor of 2 using double contacted graphene. The TLMT implies that the sheet resistance, = ( 0 − 2 ) · , is an inherent property of the graphene and should therefore be constant for the devices on one wafer.
If ≪ 0 it can be neglected, leading to * = 0 • .In our case, * ranges from 2 kΩ to 4 kΩ. This is more than double the value of the common sheet resistance, RS = 1.6 kΩ, for graphene on silicon dioxide substrates. [S9] However, if the contact resistance is taken into account, the values for the sheet resistance are RS, Si1 = 1010 ± 380 Ω, RS, Si2·W = 1670 ± 440 Ω. Although the standard deviations are very large, the mean values of RS are much closer to the literature value than of * . This shows that the contact resistance can not be neglected when computing the sheet resistance of a GFET.

Details of transconductance dependency on W/L ratio
For detailed quantification of the transconductance's dependency on W/L ratio, see Supplementary  Fig. S9. Then a linear regression was performed yielding coefficients a and b. The results are summarized in Supplementary Table S3. All wafers have good mean gmax/VDS values, ranging from 0.45 mS·V -1 to 1.1 mS·V -1 .
Supplementary Figure S9. Maximum transconductance, gmax, against the width to length ratio. The two quantities are linearly correlated.

Chip encapsulation for cell culture
To use the graphene transistor arrays for cellular measurements on chips, they have to be prepared for the cell culture environment. That includes contacting the chip to a carrier with standardized contacts and the encapsulation of the chip. Encapsulation is necessary to make sure that the chip is not damaged by liquid and to provide biocompatible material for all surfaces in contact with the cell culture. For contacting the chip to the carrier the so called 'flip chip' procedure is applied. In that procedure, the chip upward facing contacts on chip are soldered to a printed circuit board carrier with downward facing contact pads and all contacts are connected at once.
At first the carrier is tempered at 180°C using a hotplate. Then, soldering paste is applied to the inner contacts of the carrier. The chip is then placed on the carrier with the chip and carrier contacts facing each other. If the chip consists of a transparent substrate (e.g. sapphire), the alignment of the contacts can be done under the microscope. When the substrate is not transparent (e.g. silicon), the surface tension between the gold contacts and the soldering paste has to be used as an indicator of alignment. With the chip aligned, the carrier is removed from the hotplate for the soldering paste to cure. After cooling down, Epoxy (EPO-TEK-302-3M) is applied to glue the chip to the carrier and isolate between solder points. The advantage of this procedure is that the whole chip is contacted to the carrier at once. This saves a lot of time compared to the alternative time-consuming procedure of wire bonding. The soldering part of the flip chip technique only needs five minutes. The downside of the flip chip procedure compared to bonding is the loss of working devices on the chip due to misalignment.
As mentioned above, the encapsulation is done to save the chip from being damaged by liquid and to create a cell-friendly environment. Using PDMS, two glass rings are glued on the carrier (see Fig. 5b). They are later used for holding the cell culture medium. PDMS is also applied to the area of the carrier between the rings that contacts the cell medium. This prevents toxic substances from dissolving from the carrier into the nutrient solution where it can damage the cells.

Neuronal culture
Supplementary Figure S10. (a) and (b) are the DIC and live-dead stained fluorescence image of a chip. In the red circle is depicted the graphene channel that recorded the neuronal action potentials presented in (c). In the live-dead image, it is visible that a bundle of neurites are going through the graphene area of the GFET. In (c) is given the overall timetrace of the recordings. The first three recordings (black, red and blue) are consecutive and around 5 minutes long in total. The pink part of the timetrace is recorded after chip was cleaned (Terg-A-Zyme overnight) in order to eliminate the cells and prove biological origin of the signals. Indeed after the cleaning no APs are visible.

Filters, noise and SNR estimations.
In Supplementary Fig. S11 a timetrace from one HL-1 recording is presented, and the noise and SNR values computed using different methods are presented in Supplementary Table S4. From the table it is visible that the choice of a noise definition influences the level of noise and therefore the final representation of SNR. Choosing RMS instead of 2*MAD one can increase the presented SNR value 3-4 fold. Figure S11. The timetrace of HL-1 activity recorded by a GFET. In the top part, the timetrace is shown without an applied filter, while below the 100Hz low pass filter is applied.  Figure S12. Raman spectra of the CVD grown graphene used in this work.