Measurement of high carrier mobility in graphene in an aqueous electrolyte environment

Electrolyte-gated graphene is used for electronic biosensing applications,¹ supercapacitor applications,² and fundamental measurements of graphene properties at high carrier concentration.³ The electrolyte environment likely affects the mobility of charge carriers in graphene. Of particular concern is the case of graphene biosensors (typically operated in an aqueous electrolyte), for which carrier mobility is critical to device performance.

A significant effort has been made to optimize the carrier mobility in dry graphene devices that are supported by a silicon oxide substrate. Benchmark mobility values for graphene derived from chemical vapor deposition (CVD) are ∼7000 cm²/Vs,⁴ and slightly higher values are sometimes found with mechanically exfoliated graphene (∼10 000 cm²/Vs).⁵ When an SiO₂-supported graphene device is placed into an aqueous electrolyte, however, we lack clear expectations for the carrier mobility, as the presence of salt ions in the liquid introduces an additional mechanism for Coulomb scattering. Previous work related to this question was performed by Newaz et al., who investigated the effect of salted, non-aqueous liquids on the carrier mobility of suspended graphene devices.⁶ Additional insight comes from transconductance measurements of graphene field effect transistors (FETs) contacted by two probes and gated by an aqueous electrolyte.^7–11 For example, Hess et al. used FET measurements of two-point conductance as a function of liquid gate voltage to estimate the relationship between sheet conductivity, $σs$⁠, and sheet carrier density, n_s.¹¹ Surprisingly, there have been no direct measurements of $σs$ as a function of n_s for graphene gated by an aqueous electrolyte, and therefore no direct measurement of carrier mobility, $μ$⁠, in this system.

Measuring carrier mobility in electrolyte-gated graphene is more challenging than the equivalent measurement of dry, back-gated graphene. First, n_s is not simply the product of the gate voltage and a constant gate capacitance. The gate capacitance changes with gate voltage due to quantum capacitance effects.¹² Moreover, the double-layer capacitance between the electrolyte-graphene interface has not been well established. Second, if the electrolyte environment contacts the metal electrodes, the electrolyte gate interferes with the voltage measurements that are required to establish n_s and $σs$⁠.

In this work, we overcome the challenges of measuring carrier mobility in an aqueous electrolyte. Graphene electrodes are capped with an insulating layer of SiO₂ to minimize the interference between the electrolyte gate and the voltage measurements. The Hall effect is used to measure sheet carrier density as a function of electrolyte gate voltage. We find a peak carrier mobility greater than 7000 cm²/Vs, comparable to the benchmark values for dry graphene on SiO₂.

Graphene on copper foil was produced in our chemical vapor deposition system. Copper foil (25 μm thickness, Alfa Aesar) was cleaned with dilute nitric acid (5%) followed by acetic acid.¹³ The foil was annealed for 60 min in H₂ gas at 1070 °C, before starting graphene deposition (30 min at 1070 °C, 20 sccm H₂, 30 sccm CH₄, pressure 50 Pa).¹⁴ A wet transfer process was used to place the graphene on an Si/SiO₂ substrate (300 nm thermally-grown oxide).¹⁵ The graphene was patterned using a two-layer photolithography process (Shipley S1813 photoresist over a base layer of MicroChem LOR) and O₂ plasma. A second photolithography step was used to create metal electrodes encapsulated by SiO₂ (5 nm Cr, 30 nm Au, 70 nm SiO₂). The electrode materials were deposited via e-beam evaporation. After device fabrication, the graphene was characterized using microRaman spectroscopy (see supplementary material). Figure 1 shows a completed device, in which L = w = 40 μm.

All experiments were performed with the graphene device submerged in an NaCl aqueous solution (100 mM) with phosphate buffer (10 mM) to stabilize the pH at 7.2. The electrostatic potential of the liquid gate, V_lg, was controlled using a tungsten wire immersed in the electrolyte (see Fig. S2 in the supplementary material). A current source (Keithley 2400 Source meter) was used to supply a dc current, I = 5 μA. The magnetic field, B, was applied perpendicular to the graphene using a variable-field electromagnet (±0.5 T). Gate voltage sweeps were performed at a rate of 10 mV/s.

Figure 2 shows the Hall voltage, V_H, measured when B = ±0.5 T. The measurement procedure is as follows. First, V₁₃ is measured at B = 0 to establish the gate-dependent background voltage. This background voltage (of the order 0.1 mV) is related to the spatial inhomogeneity in the electrolyte gate potential. Next, V₁₃ is measured at B = ±0.5 T. The Hall voltage is then V_H = V₁₃(B = ±0.5 T) − V₁₃(B = 0).

When B > 0 (red line), V_H is positive for hole-type transport and negative for electron transport. When B < 0 (black), the sign of V_H reverses. The transition from hole transport to electron transport occurs at the Dirac point, V_D ∼ 0.03 V, with respect to the tungsten electrode.

The sheet carrier density is inversely proportional to the Hall voltage

We calculate n_s as a function of V_g using Eq. (1) (Fig. 2(b), black dots).

To understand the relationship between n_s and V_lg (Fig. 2(b)), we consider both the graphene density of states and the double-layer capacitance between the electrolyte gate and carriers in the graphene, C_dl. Assuming a tight binding model for the graphene dispersion relation, n_s scales as E_F², where E_F is the Fermi energy measured relative to the Dirac point

where the Fermi velocity is v_F ∼ 10⁶ ms⁻¹ and $ℏ$ is the reduced Plank constant. The quantum capacitance of graphene, C_q = e²(dn_s/dE_F), approaches zero as E_F approaches zero. If C_dl ≫ C_q, C_q limits $ns$ such that $ns≈(1014 cm−2V−2)⋅Vlg2$ (grey line on Fig. 2(b)).

To account for C_dl, we model the system as two capacitors in series. The sheet charge density on C_dl and C_q is equal, and the voltage across each capacitor adds to V_lg. n_s is found by solving

Equation (3) fits our experimental data when C_dl = 5 μF/cm² (red dashed line). The value of C_dl that we determine from fitting our measurements is consistent with a model developed by Dankerl et al. for the spatial charge and electrostatic potential distributions at a graphene/electrolyte interface.¹⁶ The measured n_s values deviate from Eq. (3) at small V_lg. In this low-doping regime, n_s is dominated by electrostatic disorder in the graphene. We find a disorder-induced carrier concentration, n_s,disorder ∼0.4 × 10¹² cm⁻², which is typical for SiO₂-supported graphene.¹⁷ 

After establishing n_s(V_lg), we turn to the sheet conductivity, σ_s(V_lg). Figure 3(a) shows the sheet conductivity, σ_s = I/V₁₂, which is calculated from the voltage drop V₁₂ (see Fig. 1). The sheet conductivity is smallest at the Dirac point, V_D, and increases almost linearly with |V_lg − V_D|. The linearity of σ_s(V_lg) is described well by a Boltzmann transport model (red dashed line), as discussed further below. The transconductance, dσ_s/dV_lg, is a useful figure of merit for biosensor sensitivity. We observe a peak transconductance of 4.5 mS/V. This is higher than previous reports for graphene in an aqueous environment and is indicative of high mobility.

The commonly used framework for interpreting $σs$ is the Drude model: $σs=μens$⁠, where $μ$ is the Drude mobility. Figure 3(b) shows the calculated $μ$ values for electrons and holes based on the measurements of n_s and $σs$⁠. The maximum mobility exceeds 7000 cm²/Vs, matching the typical benchmark for dry GFET devices on SiO₂ substrates.

Our measurements of $σs$ and $μ$ (Fig. 3) give insight into the effect of the aqueous electrolyte on graphene's electronic properties. The mobility-limiting factor in graphene is thought to be Coulomb scattering caused by charged impurities.¹⁸ There are at least two roles that the aqueous electrolyte could play in Coulomb scattering. First, dissolved ions could act as charged impurities, thereby decreasing $μ$⁠. Second, the dielectric constant of the water may screen charged impurities, thereby increasing $μ$⁠. The effectiveness of dielectric screening would depend on the location of the charged impurities. For example, dielectric liquid above the graphene cannot effectively screen charge traps located in the SiO₂ underneath the graphene.

We tested the possibility that dissolved ions reduce $μ$ by measuring $μ$ in a variety of salt concentrations. Figure S3 (supplementary material) shows that $μ$ is unchanged by varying the salt concentration from 1 mM to 100 mM. To explore the second possibility (dielectric screening increases $μ$⁠), we compare our measurements to previous work on dry, SiO₂-supported CVD graphene in which $μ$ ∼ 7000 cm²/Vs.⁴ Since we find a similar $μ$ for our water-gated, SiO₂-supported graphene, we postulate that charge traps buried in the SiO₂ substrate are likely the limiting factor in both a dry environment and an aqueous electrolyte environment.

A recent experiment by Newaz et al.⁶ corroborates our claim that the SiO₂ substrate has a much greater effect on $μ$ than the salt ions in the aqueous electrolyte. Newaz et al. investigated the effect of submerging suspended graphene devices in a non-aqueous solution (anisole) with dissolved salt (tetrabutylammonium tetraphenylborate). In a low-salt solution, mobility was enhanced due to the dielectric screening properties of anisole. Increasing the salt concentration from 0.01 mM to 100 mM reduced $μ$ from 50 000 cm²/Vs to 20 000 cm²/Vs. A mobility of 20 000 cm²/Vs is significantly higher than $μ$ in SiO₂-supported graphene. Therefore, Newaz's result suggests that our measurement of $μ$ ∼ 7000 cm²/Vs is more likely attributable to the SiO₂ substrate than to dissolved salt ions.

Figure 3(a) includes a fitting curve based on Boltzmann transport theory. Unlike the Drude model, the Boltzmann transport model accounts for the Pauli-exclusion principle and the distribution of electrons in k-space. For a 2d material with relativistic dispersion, Boltzmann transport theory predicts¹⁸ 

where τ is the energy-averaged carrier scattering time. Combining Equations (3) and (4) yields a good fit to the measured data when τv_F = 70 ± 5 nm (dashed line in Figure 3(a)).

It is interesting that Boltzmann transport describes the sheet conductivity with a single fit parameter, τv_F, in contrast to the Drude model, which is fit by allowing $μ$ to change as a function of n_s. Previous reports of graphene's electronic properties have favored the Drude model over the Boltzmann transport model (Eq. (4)), perhaps because τ varies with n_s for dry graphene devices.¹⁹ However, it appears that τ is insensitive to n_s when screening is provided by a dielectric fluid. In future work, it will be interesting to explore the application of the Boltzmann transport theory for electrolyte-gated graphene.

In conclusion, we have measured the carrier mobility for graphene submerged in an aqueous electrolyte. The measured room-temperature mobility is significantly higher than traditional semiconductors such as silicon, and is comparable to the benchmark values reported for dry graphene on SiO₂ substrates. Our results demonstrate that graphene's superb electrical properties are robust, even in an aqueous electrolyte environment. Future experiments on suspended graphene, or graphene on hexagonal boron nitride, may demonstrate even higher mobilities in the aqueous electrolyte. Graphene's high carrier mobility in aqueous electrolytes, together with mechanical strength/flexibility, chemical stability, and biocompatibility, suggests an exciting future for graphene biosensor applications.

See supplementary material for characterization of graphene quality, chip carrier design and the liquid-gate electrode, relationship between salt concentration and graphene carrier mobility.

Funding for this research was provided by the National Science Foundation under Award No. DBI-1450967. M.R.L. and Y.B.Q. would like to thank funding from the Energy Materials and Surface Sciences Unit of the Okinawa Institute of Science and Technology Graduate University to support the synthesis of graphene samples, which was performed at OIST. We thank Michael Reynolds and Paul McEuen for valuable discussions. Device fabrication was performed at the MaSC Facility at Oregon State University.