Ion Sensing with Solution-Gated Graphene Field-Effect Sensors in the Frequency Domain

Abstract

Here, we examine the concept of frequency domain sensing with solution-gated graphene field-effect transistors, where a sine wave of primary frequency (1f) was applied at the gate and modulation of the power spectral density (PSD) of the drain-source current at 1f, 2f, and 3f was examined as the salt in the gate electrolyte was switched from KCl to CaCl₂, and their concentrations were varied. The PSD at 1f, 2f, and 3f increased with the concentration of KCl or CaCl₂, with the PSD at 1f being the most sensitive. We further correlated these changes to the shift in Dirac point. Switching the graphene substrate from oxide to hexagonal boron nitride, led to an improved device-to-device reproducibility and a significant reduction of noise, which translated to a higher signal-to-noise ratio and resolution in sensing salt concentrations. The signal-to-noise ratio at 1f was found to be a logarithmic function of KCl or CaCl₂ concentration in the 0.1 to 1000 mM range.

I. Introduction

SOLUTION-GATED field-effect transistors (SGFET) with graphene as the channel material have gained widespread attention over the last decade for a variety of label-free sensing applications including detection of molecules [1]–[4], ions [5]–[10], DNA [11], [12], proteins [13]–[16], and bacteria [17], [18]. Reports to date operate graphene SGFET in DC mode where the source-drain bias (V_DS) is fixed, the gate bias (V_G) is swept and the resulting source-drain current (I_DS) is measured to locate the Dirac voltage (V_Dirac) – a gate bias that results in the lowest source-drain current. The detection of the analyte has been inferred either by the shift in V_Dirac, or change in transconductance (ΔI_DS/ΔV_G) [19].

This paper examines a new modality of sensing with graphene SGFETs in the frequency domain where a sine wave of primary frequency (1f) is applied at the gate and the modulation of I_DS is monitored at 1f as well as second (2f) and third harmonics (3f). This method termed as “frequency-domain sensing” is investigated here as a means to detect changes in concentration of the electrolyte through which it is gated. Higher order harmonics have been proposed to be more sensitive due to high electron mobility, tunable electronic transport polarity and high saturation velocity in graphene [20].

The concept of frequency-domain sensing with graphene SGFETs was inspired by the observation of frequency multiplication with back-gated graphene ribbon by Palacios group [21]. Wang et al. also report similar frequency multiplication with a top-gated insulator-coated graphene ribbon [22]. Joachim-Krause group recently leveraged showed that when a sinusoidal gate-bias (77.77 Hz, 100 mV RMS or 7.777 kHz, 50 mV RMS) was applied through the electrolyte gate the 2f responses yielded more than 95 % of the total output energy with unity gain [23], [24]. In order to sense an analyte, a DC offset applied to the sinusoidal gate bias was swept to locate the V_Dirac; the amplitude of the power spectral density (PSD) was found to increase as the DC offset approached V_Dirac. Their method yield a significant reduction in 1/f noise in locating the V_Dirac. The method proposed in this paper presents a radical departure from the conventional method of locating the V_Dirac in order to infer the analyte concentration in the electrolyte. Instead we examine if the PSD amplitude at 1f, 2f, and 3f can be directly correlated to changes in the analyte concentration.

In this paper, graphene SGFETs such as those shown in Fig. 1a were fabricated using monolayer CVD graphene and gated through solutions with varying concentrations of KCl or CaCl₂ using an Ag/AgCl electrode as shown in Fig. 1b to demonstrate frequency domain sensing of changes in K⁺ and Ca²⁺ concentrations. The V_G was modulated without a DC offset as shown in Fig. 1c in order to operate at lower power without switching the type of majority charge carriers. Identifying the V_Dirac and then modulating the V_G with a DC offset equal to V_Dirac would have caused switching between electrons and holes as the majority charge carriers and reduced the magnitude of modulation in I_DS. Comparatively, neutral gated operation (V_G = 0 V) would result in relatively larger modulation of I_DS. Further, we examine the effect of graphene support on frequency domain sensing; graphene on hexagonal boron nitride (hBN) is compared to when on thermal oxide. Having a wide band gap (5.97 eV), and similar lattice structure (1.7 % mismatch) as graphene, hBN has been considered as an ideal dielectric interface to graphene resulting in improved charge mobility and transconductance [25]–[27]. Multilayer CVD grown hBN (~13 nm thick) was introduced under monolayer CVD graphene to improve frequency domain ion sensing characteristics of the graphene SGFETs.

Fig. 1.

(a) Optical microscope image of the graphene SGFET where the graphene channel (40 m × 10 m) placed on hBN/SiO₂ film can be viewed through the rectangular opening in the SU8 insulation layer. (b) Scheme to test graphene SGFET. The Au/Cr electrodes were used as the source and drain and an Ag/AgCl electrode dipped into the salt solution was used to apply solution-gated gate bias. A PDMS well was used to hold the solutions over the SGFET. (c) Operating point with frequency sensing in transfer curve with varying concentration of KCl: neutral gate point (V_G = 0 V) is chosen for sensing operation to investigate the pure ac signal response from SGFETs.

II. Experimental Methods

A. Device Fabrication

Monolayer graphene or multilayer hBN films grown by the CVD method on copper foils (thickness ~ 20 μm) were obtained from Graphene Labs Inc. With 1–10 μm grain size, these CVD graphene films are mostly monolayer with 10 % to 30 % bilayer islands. The CVD multilayer hBN film was about ~13 nm thick. One side of the copper foil (with graphene or hBN) was spin-coated (1000 rpm for 10 s; 3000 rpm for 30 s) with a PMMA solution (1000 rpm for 10 s; 3000 rpm for 30 s) and baked at 110 °C for 5 min. We found it important to spin coat PMMA twice to keep the PMMA-hBN or the PMMA-graphene film intact after the release. The hBN or graphene film on the opposite side of the copper foil was removed via oxygen plasma ion etching (TECHNICS^® MICRO Series 800 RIE, 100 W, 20 sccm O₂, 20 min for hBN and 30 s for graphene). The PMMA-hBN or the PMMA-graphene film was released by wet etching the copper foil at 60 °C for 2 h. The released PMMA film was rinsed with deionized (DI) water and modified SC-II solution (H₂O:H₂O₂:HCl = 20:1:1, 25 °C, 10 min), and transferred to a Si/SiO₂ substrate. Boron-doped silicon wafers (thickness: 500 ± 25 μm; diameter: 100 mm; oxide thickness: 285 nm) were diced into 1.4 × 1.4 cm² to use as substrates for GFET fabrication. The transferred film was dried and flattened by spinning out the water between the PMMA film and the substrate (200 rpm for 1 min; 500 rpm for 1 min, 1000 rpm for 1 min; 2000 rpm for 10 min) and baking it on a hotplate (60 °C at 5 min; 110 °C for 10 min). PMMA layer was then removed by soaking in a 1:1 solution of methylene chloride and methanol for 1 h at 25 °C. A two-layer resist was used in electrode patterning. The bottom resist layer was a polymethylglutarimide based lift-off resist (LOR 7B; MicroChem^®; spin program: 500 rpm for 20 s; 1000 rpm for 10 s; 3000 rpm for 50 s; soft bake: 180 °C, 7 min) to protect the graphene layer from photo-initiated reactions, undercut the top resist layer during development, and to provide good adhesion and thermal stability. The top resist layer was a positive photoresist (S1813, MICROPOSIT^®, spin program: 1000 rpm for 10 s; 5000 rpm for 50 s; soft bake: 115 °C, 90 s). Patterning of the resist was carried out using a chrome mask and a Süss MicroTec^® MA/BA6 (soft contact mode; 1000 W; 20 s) and development in MF^®-319 (MICROPOSIT^®, 15 s, 25 °C). The metal layers, 25 nm Cr and 200 nm Au were deposited via electron-beam evaporation (CHA^® Industries, BEC-600-RAP) and lift-off was carried out in Remover PG for 15 min at 75 °C. Using similar photolithography process, a layer of S1813 was patterned to protect 40μm × 10μm graphene channels and etch away the remaining graphene. To prevent short-circuiting of the Au electrodes in the solution, a 2 μm thick electrical insulation layer was lithographically patterned using SU-8 2002 (MicroChem^®; 500 rpm for 10 s; 3000 rpm for 30 s).

B. Measurement Setup

Six SGFETs were fabricated with monolayer CVD graphene, three with hBN and three with SiO₂ as the surface beneath graphene. Fig. 1 shows the chip layout and test setup used. A ~5 mm thick polydimethylsiloxane (PDMS) well was punched out to hold the electrolyte over the graphene strip. Aqueous solutions of KCl and CaCl₂ (0.1 mM, 1 mM, 3 mM, 5 mM, 7 mM, 9 mM, 10 mM, 100 mM, and 1000 mM) were used as the gate electrolyte to test ionic sensitivity. First, for each solution, V_Dirac was recorded with a V_DS of 100 mV. All SGFETs had a positive V_Dirac, which implies that the graphene channel is intrinsically p-doped. Then, the frequency domain characteristics were measured by applying a sinusoidal gate potential of 100 mV_RMS and 1400 Hz using a signal generator (HP 33120A). The I_DS measured in the time domain using a source-measurement unit (KEITHLEY 2636A) with a V_DS of 1 mV was converted to PSD using the Welch method where the first three (1f, 2f, 3f) harmonics responses are obtained with different magnitudes for each time-domain sensor current signal. The Welch method is an algorithm used in PDS estimation to determine the signal power magnitude for different frequencies using periodogram spectrum concept.[28]

III. Results and Discussion

A. With Graphene on the Thermal Oxide

As we reported prior,[19] an increase in salt concentration is expected to dope n-carriers in the graphene channel and shift the V_Dirac closer to zero and thus increase the amplitude of PSD at 1f, 2f, and 3f as per [23], [24]. Due to the varying ionic concentration, the double layer capacitance (C-DL) is changing due to the variation in ionic strength and double layer thickness. According to the small signal model of SGFET as shown in Fig. 6, the equivalent impedance and channel current (I_DS) will be affected with the varying ionic concentration. Thus, the PSD amplitudes will vary in harmonic responses. Fig. 2(a-c) shows the increase in PSD amplitude at 1f, 2f and 3f for one of the devices with graphene on SiO₂ and gated through KCl solutions of varying concentrations. Complete PSD data for three such devices is provided in the Supporting Information Fig. S1-S3 and S5-S7 when gated through varying concentrations of KCl and CaCl₂, respectively. Supporting Information Fig. S4 and S8 compare the PSD specifically at 1f, 2f, and 3f for the three different SiO₂ devices. Fig. 2b shows the 2f response was accompanied by additional two peaks of higher amplitude, ~63 Hz above and below the 2f peak, indicating as if the 2f peak was actually split. This is contrary to prior reports, which show a unique response at 2f.[23], [24] We suspect this could be specific to our setup where a loop could be causing an antinode at 2f. As a result, Fig. 2c shows that the 3f response was unique and stronger (in amplitude) than the response at 2f. The response at 3f compared to that at 2f was found to be insignificant below 10 mM KCl; however, over 10 mM KCl, the response at 3f surpassed that at 2f. Overall, the amplitude of 1f, 2f, and 3f was found to increase with an increase in salt concentration; Fig. 2(d-f) shows for increasing KCl concentration and Fig. 2(g-i) shows for increasing CaCl₂ concentration.

Fig. 6.

Small-signal model of graphene solution-gated field-effect transistor (SGFET) with gate to source voltage (ν_g). Debye layer capacitance (C-DL), charge transfer resistance (R-CT), solution resistance (R-Sol), gate-source capacitance (C-GS), gate-source resistance (R-GS), gate-drain capacitance (C-GD), gate-drain resistance (R-GD), voltage-controlled current source (g_mν_g), output resistance (r_o).

Fig. 2.

PSD of I_DS through graphene supported on SiO₂ and gated through KCl or CaCl₂ solutions of varying concentrations. (a) 1f at 1400 Hz, (b) 2f at 2800 Hz, and (c) 3f at 4200 Hz. (a-c) data shown for one of the SGFET on SiO₂. A plot of PSD amplitude at 1f, 2f and 3f versus concentration of KCl (d-f), and CaCl₂ (g-i). Data from three devices is shown as three different series. The dashed lines indicate curves (y = m * x + c) fit to the data and the text close to the line indicates its corresponding slope.

To correlate the observed changes in PSD amplitudes, V_Dirac were also recorded with the different salt solutions using the conventional DC gate approach.[19] PSD amplitudes are recorded for ionic solutions with different molar concentrations and transformed in frequency domain as mentioned in measurement setup section. To demonstrate the changes in PSD amplitudes in frequency domain as a function of DC sensing operation, PSD amplitudes are plotted versus corresponding V_Dirac values reported in our previous study. Fig. 3(a-c) shows that a semi-log plot of the amplitude at 1f, 2f, and 3f versus the V_Dirac when gated through KCl solutions displays a linear sensitivity of −3.09 ± 0.19, −3.91 ± 0.57 and −7.28 ± 0.37, respectively. Similarly, Fig. 3(d-f) shows that a semi-log plot of the amplitude at 1f, 2f, and 3f versus the V_Dirac when gated through CaCl₂ solutions displays a linear sensitivity of −5.74 ± 1.02, −8.90 ± 0.91 and −18.33 ± 2.98, respectively. It can be seen that, for either salts, KCl or CaCl₂, the PSD amplitude at 3f had nearly double the sensitivity to changes in V_Dirac compared to the PSD amplitudes at 1f and 2f. Further, the PSD amplitude at 1f, 2f, and 3f was more sensitive to changes in V_Dirac in Ca²⁺ solutions than in K⁺ solutions. The latter finding is quite contrary to that observed with the use of a DC gate bias where the sensitivity reduces proportionally to the valency of the cation [19], [29].

Fig. 3.

Semi-log plot of PSD amplitude at 1f, 2f and 3f versus V_Dirac measured with solutions of different KCl concentration (a-c), and CaCl₂ concentration (d-f). Data from three devices is shown. Dashed lines indicate a linear fit to the semi-log plot. Color of the dashed lines and the slope value corresponds to the color of the data points. The dashed lines indicate curves (y = m * log10(x) + c) fit to the data and the text in the respective color indicates its corresponding slope.

B. With Graphene on the hBN

Supporting Information Fig. S9-11 shows the complete PSD data for three different SGFETs with graphene on hBN gated through KCl solutions and Fig. S12 compares the response specifically at 1f, 2f, and 3f. Like the SiO₂ devices, peak splitting at 2f was also observed with hBN-based SGFETs as shown in Supporting Information Fig. S12 and S16. Fig. 4(a-f) quantifies the increase in PSD amplitude observed at 1f, 2f and 3f with an increase in salt concentration. Like the SiO₂ devices, overall, the sensitivity of the PSD amplitude to change in salt concentration was highest at 1f. Fig. 4(g-i) shows that a semi-log plot of the amplitude at 1f, 2f, and 3f obtained with KCl solutions versus V_Dirac displays a linear sensitivity of - 3.41 ± 0.13, −2.93 ± 0.20 and −5.39 ± 0.34, respectively. Supporting Information Fig. S13-S15 shows PSD data for the three SGFETs with CaCl₂ solutions of varying concentrations and Fig. S16 compares the response specifically at 1f, 2f, and 3f. Fig. 4(j-l) shows that a semi-log plot of the amplitude at 1f, 2f, and 3f obtained with CaCl₂ solutions versus V_Dirac displays a linear sensitivity of −4.98 ± 0.13, −4.64 ± 0.17 and −11.09 ± 0.82, respectively. Like the SiO₂ devices, for either KCl or CaCl₂, the PSD amplitude at 3f had higher sensitivity to changes in V_Dirac compared to the PSD amplitudes at 1f or 2f. Further, the PSD amplitude at 1f, 2f, and 3f was more sensitive to changes in V_Dirac in Ca²⁺ solutions than in K⁺ solutions.

Fig. 4.

Semi-log plot of PSD amplitude at 1f, 2f and 3f versus V_Dirac measured with solutions of different KCl concentration (a-c), and CaCl₂ concentration (d-f). Data from three devices is shown. Dashed lines indicate a linear fit to the semi-log plot. Color of the dashed lines and the slope value corresponds to the color of the data points. (a-c) The dashed lines indicate curves (y = m * x + c) fit to the data and the text close to the line indicates its corresponding slope. (d-f) The dashed lines indicate curves (y = m * log10(x) + c) fit to the data and the text in the respective color indicates its corresponding slope.

Unlike the SiO₂ devices, the hBN devices had a low coefficient of variation between different devices (ratio of standard deviation to mean). Further, as per a two-tailed t-test, statistically significant reduction in ionic sensitivity of the PSD amplitude at 2f and 3f was noticed, while a statistically insignificant change was seen for sensitivity at 1f. But at the same time a lower noise was observed with hBN devices.

Further performance of SiO₂ and hBN devices were compared in terms of signal-to-noise ratio (SNR), which was calculated as the ratio of signal power (P_signal) to noise power (P_noise). P_signal was calculated as the PSD amplitude at 1f, 2f, or 3 f. P_noise for a given electrolyte at a given concentration was calculated as the average PSD amplitude in the frequency range of 1500 Hz to 2500 Hz, which excludes the 1f, 2f, or 3f signal.

The benefits of reduced P_noise resulting from the use of hBN can be seen in the SNR values calculated in Fig. 5. Fig. 5(a) shows that the SNR at 1f for SiO₂ and hBN device plot against KCl concentration fit a logarithmic trend. By introducing hBN in place of SiO₂, 18 to 53 times higher SNR was achieved in addition to a two order of magnitude higher ionic sensitivity (slope) to KCl concentration. Fig. 5b shows the SNR at 2f plot against the KCl concentration; the 0.1 mM to 10 mM range exhibited a linear trend and the 10 mM to 1000 mM range showed a (natural) logarithmic trend. In either range, use of hBN provided 60 to 124 times higher SNR along with four-time higher ionic sensitivity between 0.1 mM to 10 mM and three order magnitude better between 10 mM to 1000 mM. Fig. 5c shows the SNR at 3f plot against salt concentration, like 2f, the 0.1 mM to 10 mM range showed a linear curve (inset chart), while the 10 mM to 1000 mM range exhibited a logarithmic trend. In either range, the use of hBN provided 196 to 364 times higher SNR along with 189 times higher ionic sensitivity between 0.1 mM to 10 mM and 354 times higher between 10 mM to 1000 mM.

Fig. 5.

SNR calculated in frequency domain for graphene supported on SiO₂ (sensor 1 of Fig. 3) and hBN (sensor 1 of Fig. 4) at (a,d) f = 1400 Hz, (b,e) f = 2800 Hz, and (c,f) f = 4200 Hz, gated through KCl (a-c) or CaCl₂ (d-f) solutions of varying concentrations. Further description of the curve fitting provided in the main text. The insets in (c) and (f) show a magnified view of the graph at lower salt concentration. S_lin indicates the slope.

Fig. 5d shows that the SNR at 1f for SiO₂ and hBN device plot against CaCl₂ concentration fit a logarithmic trend. By introducing hBN in place of SiO₂, 13 to 85 times higher SNR was achieved in addition to a two order of magnitude higher ionic sensitivity (slope) to CaCl₂ concentration. Fig. 5e shows the SNR at 2f plot against the CaCl₂ concentration; the 0.1 mM to 10 mM range exhibited a linear trend and the 10 mM to 1000 mM range showed a (natural) logarithmic trend. In either range, use of hBN provided 200 to 338 times higher SNR along with four-time higher ionic sensitivity between 0.1 mM to 10 mM and three order magnitude better between 10 mM to 1000 mM. Fig. 5f shows the SNR at 3f plot against salt concentration, like 2f, the 0.1 mM to 10 mM range showed a linear curve (inset chart), while the 10 mM to 1000 mM range exhibited a logarithmic trend. In either range, use of hBN provided 128 to 225 times higher SNR along with 166 times higher ionic sensitivity between 0.1 mM to 10 mM and almost three orders in magnitude higher sensitivity between 10 mM to 1000 mM.

Overall, the SNR analysis shows that only the PSD amplitude at 1f provides the means to measure KCl and CaCl₂ concentration continuously from 0.1 to 1000 mM range. It is notable to mention that a monotonic change is obtained in SNR trend with salt concentration at its fundamental frequency (1f) though at higher harmonics (2f, 3f), the SNR trends are no longer monotonic. At fundamental frequency, the PSD signal amplitudes are comparatively higher than those at its higher harmonics (2f, 3f). Hence, the SNR trend overcomes the noise power trend and follows the signal power’s monotonic trend. At higher harmonics (2f, 3f), the noise power amplitudes are comparable to the signal power amplitudes and the noise power non-monotonic trends are exposed in the SNR trends.

C. Resolution Limit With Frequency Domain Sensing Compared to DC Mode

The slopes of the PSD amplitude plot against the salt concentration as shown in Fig. S5, and Fig. S14 gave us the ionic sensitivity of SGFETs fabricated on SiO₂ and hBN. The resolution limit (R_AC) at a given harmonic (1f, 2f or 3f) was calculated as the ratio of the minimum detectable signal to the ionic sensitivity. The minimum detectable signal was calculated as three times the standard deviation of the PSD amplitude recorded at 1f, 2f or 3f during 30 trials with 10 mM KCl. The resolution limit (R) values are shown in Table I.

TABLE I.

The Resolution Limit Determined for Sensing Changes in KCl or CaCl₂ Concentrations Using PSD Amplitudes at 1f, 2f, and 3f.

Frequency	Device	Electrolyte	Salt Concentration Range (mM)	Ionic sensitivity (A2/Hz/mM)	Minimum Signal Level (A2/Hz)	Resolution Limit (mM)
1f	G/SiO2	KCl	0.1 - 10	~1×10−15	9.7×10−16	0.97
			10 - 1000	1×10−17		97
1f	G/SiO2	CaCl2	0.1 - 10	1×10−15	9.7×10−16	0.97
			10 - 1000	1×10−17		97
2f	G/SiO2	KCl	0.1 - 10	1×10−17	7.6×10−17	7.6
			10 - 1000	1×10−19		760
2f	G/SiO2	CaCl2	0.1 - 10	1×10−18	7.6×10−17	76
			10 - 1000	1×10−20		7630
3f	G/SiO2	KCl	0.1 - 10	1×10−18	1.6×10−17	16
			10 - 1000	1×10−18		16
3f	G/SiO2	CaCl2	0.1 - 10	1×10−17	1.6×10−17	1.63
			10 - 1000	1×10−18		16
1f	G/hBN	KCl	0.1 - 10	1×10−15	7.2×10−16	0.72
			10 - 1000	1×10−16		7.2
1f	G/hBN	CaCl2	0.1 - 10	1×10−15	7.2×10−16	0.72
			10 - 1000	1×10−16		7.2
2f	G/hBN	KCl	0.1 - 10	1×10−17	5.6×10−17	5.66
			10 - 1000	1×10−18		57
2f	G/hBN	CaCl2	0.1 - 10	1×10−17	5.6×10−17	5.66
			10 - 1000	1×10−19		566
3f	G/hBN	KCl	0.1 - 10	1×10−16	1.5×10−17	0.16
			10 - 1000	1×10−17		1.56
3f	G/hBN	CaCl2	0.1 - 10	1×10−16	1.5×10−17	0.16
			10 - 1000	1×10−17		1.56

To compare, the resolution limit in DC mode (R_DC) was also calculated as per the method of Fu et al. [30] Normalized transconductance (g) was calculated as,

$$g=\frac{1}{V_{DS}}\frac{\Delta I_{DS}}{\Delta V_G}$$ (1)

where V_DS is the drain-to-source voltage, ΔI_DS is the change in channel current for the corresponding change in gate voltage, ΔV_G. The conductance at the Dirac point (G_S) was calculated as the ratio of the drain-to-source current at the Dirac point (I_Dirac) to V_DS. The current noise spectral density (S_I) at 100 Hz was chosen from a power spectral density recorded with a V_DS of 0.1 V. The noise equivalent Dirac voltage shift (δV_Dirac) was calculated as,

$$\delta V_{\mathit{Dirac}}=\frac{\sqrt{S_I∕I_{DS}^2}}{g∕G_S}$$ (2)

The R_DC values tabulated in Table II were calculated as the ratio of δV_Dirac to ionic sensitivity. The ionic sensitivity in DC mode was obtained from the plot of the shift in Dirac point (V_Dirac) versus ion concentration reported in our prior work.[19] A lower resolution limit for sensing was observed for sensing in the frequency domain.

TABLE II.

The Resolution Limit Determined for Sensing Changes in KCl or CaCl₂ Concentrations Using V_Dirac*

Salt	Device	Ionic Sensitivity (V / decade)	SI (A2/Hz)	Channel Current, IDS2 (A2)	Trans-conductance, g(A/V2)	Conductance at Dirac Point, GS (S)	δVCNP (V/Hz1/2)	Resolution Limit (mM)
KCl	G/SiO2	0.164	5.2×10−17	1.6×10−07	2.1×10−05	1.2×10−04	1.0×10−04	1.0×10−04
	G/hBN	0.198	4.9×10−18	8.7×10−08	6.4×10−05	5.9×10−05	6.9×10−06	6.3×10−06
CaCl2	G/SiO2	0.057	5.0×10−17	1.8×10−07	6.2×10−06	1.7×10−04	4.6×10−04	1.3×10−02
	G/hBN	0.110	4.8×10−18	9.1×10−08	6.2×10−05	6.7×10−05	7.9×10−06	8.8×10−06

Overall, we find that the method of using PSD amplitudes as a gauge to measure salt concentration does hold advantages and disadvantages. The advantages of the AC gate method compared to the DC gate method were found to be: (1) Low measurement time and no need for an dual source measurement unit (complex instrumentation) as V_G sweep was not necessary as in the case of conventional DC gate method where the V_Dirac must be first located in order to interpret a salt concentration, and (2) Similar sensitivity noticed at 1f for a monovalent and a divalent cation as opposed to the DC gate method where the sensitivity drops proportionally to the valency of the cation being sensed. The main disadvantage of the AC gate method was found to be the low sensitivity to changes in KCl or CaCl₂ concentrations compared to the DC gate method.

Graphene exhibits normal modes of phonon as well as layer breathing modes (LBMs) due to the movement between two consecutive layers (shear modes) and compression and expansion (compression-expansion modes).[31] When a sinusoidal signal is applied at the gate of a solution-gated transistor, graphene channel acts like a nonlinear electrical load due to the interaction between the electrons and the quantized lattice vibrations.[32] The electron-phonon interaction in graphene channel draws a non-sinusoidal wave form (as shown in Supporting Information Figure S17) from the sinusoidal electric field applied at the gate. Thus, the PSD of the current through the graphene channel exhibits multiple harmonics of the principal frequency applied at the gate.

Fig. 6 represents the small signal model equivalent circuit of SGFET with gate, drain and source terminals. The graphene channel is modeled as the voltage-controlled current source (g_m v_g) in parallel with output resistance (r_o). The model accounts for the charge transfer resistance (R-CT) and Debye layer capacitance (C-DL). The change in concentration of gate electrolytes (KCl, CaCl₂) is expected to change the ionic strength (I) in the solution bulk and the Debye layer thickness (κ⁻¹) at the solid-electrolyte interface. This in-turn leads to the change in Debye layer capacitance (C-DL), which alters the level of coupling between the gate bias and the phonon modes of the graphene channel, and subsequently the current passing through the graphene channel.[32]–[34] As a result, the amplitudes at 1f, 2f, and 3f in the PSD change as a function of varying electrolyte concentration in AC mode operation, analogous to the Dirac point shift with electrolyte concentration in DC mode operation.

IV. Conclusion

In summary, we demonstrate the concept of operating graphene SGFETs with a sinusoidal signal (1400 Hz) applied to the gate with zero DC offset and report the changes observed in the drain-source current as the salt in the gate electrolyte was switched from KCl to CaCl₂, and their concentrations were varied. We find a unique peak in the PSD of the current at 1f and 3f, but a peak splitting was noted at 2f. The PSD amplitudes at 1f, 2f, and 3f increased with the concentration of KCl or CaCl₂, with the PSD amplitude at 1f showing the most sensitivity. However, when correlated with the shift in Dirac point, the PSD amplitude at 3f showed a larger change for a given change in V_Dirac compared to the PSD amplitudes at 2f and 3f. Further, the PSD amplitudes at 1f, 2f, and 3f were much more sensitive to changes in V_Dirac in CaCl₂ solutions than in KCl solutions, with the PSD amplitude at 3f to be the most sensitive. Switching the graphene substrate from SiO₂ to hBN, led to improvements in device-to-device variation of performance, significant reduction of noise and thus improved SNR and resolution in sensing salt concentration. The SNR at 1f provided the best means to measure KCl or CaCl₂ concentration with similar sensitivity continuously from 0.1 to 1000 mM range through a logarithmic relation.

Biography

Nowzesh Hasan received the Ph.D. degree in engineering with concentration in micro and nanoscale system from Louisiana Tech University, USA in 2018. His research interest comprises of microfabrication process development, 2D materials characterization, biosensor and bioelectronic device performance enhancement, testing, and modeling. He received the M.S. degree in engineering with microsystem engineering concentration from Louisiana Tech University, USA in 2018 and the B.S. degree in electrical and electronic engineering from Bangladesh University of Engineering and Technology (BUET), Bangladesh in 2007.

Bo Hou received the B.S. degree in electrical engineering from the Guilin University of Electronic Technology in 2007, the M.S. degree in Microsystems Engineering and the Ph.D. degree in Engineering with a concentration in micro and nano-scale systems from Louisiana Tech University, in 2013 and 2017, respectively.

From 2017, she is a Post-doctoral Research Associate with Prof. Adarsh Radadia’s laboratory at Louisiana Tech University. She is the author of 3 peer-reviewed journal articles. Her research interests include microfabrication of electrical sensors.

Adarsh D. Radadia received the B.S. degree in chemical engineering from the University of Michigan, Ann Arbor, in 2002 and the MS and Ph.D. degrees in chemical engineering from the University of Illinois at Urbana-Champaign, IL, in 2006 and 2009, respectively.

From 2009 to 2011, he was a Post-doctoral Research Associate with Prof. Rashid Bashir’s laboratory at the University of Illinois. Since 2011, he was an Assistant Professor with the Chemical Engineering Program, Louisiana Tech University, Ruston, and in 2017 promoted to an Associate Professor. He is currently endowed with the Frank Earl Hogan Family Professorship. He is the author of 21 peer-reviewed journal articles and 2 US patents. His research interests include the application of surface machining, surface chemical modification, and surface characterization.