Reversible Switching of the Dirac Point in Graphene Field-Effect Transistors Functionalized with Responsive Polymer Brushes

The reversible control of the graphene Dirac point using external chemical stimuli is of major interest in the development of advanced electronic devices such as sensors and smart logic gates. Here, we report the coupling of chemoresponsive polymer brushes to reduced graphene oxide (rGO)-based field-effect transistors to modulate the graphene Dirac point in the presence of specific divalent cations. Poly[2-(methacryloyloxy)ethyl] phosphate (PMEP) brushes were grown on the transistor channel by atom transfer radical polymerization initiated from amine-pyrene linkers noncovalently attached to rGO surfaces. Our results show an increase in the Dirac point voltage due to electrostatic gating effects upon the specific binding of Ca and Mg to the PMEP brushes. We demonstrate that the electrostatic gating is reversibly controlled by the charge density of the polymer brushes, which depends on the divalent cation concentration. Moreover, a theoretical formalism based on the Grahame equation and a Langmuir-type binding isotherm is presented to obtain the PMEP−cation association constant from the experimental data.


■ INTRODUCTION
Graphene, a two-dimensional semiconducting material, is one of the most promising materials for post-silicon electronics due to its outstanding physical and electronic properties. 1−3 Due to its great sensitivity, graphene can be used as the chemo-toelectrical signal transducing material in field-effect transistors (FETs) for the generation of high-performance responsive devices, such as advanced sensors and smart logic gates. 4−7 For these applications, the reversible modulation of the graphene electronic properties (i.e., the doping level) by a specific external (bio)chemical stimulus represents a key feature. 8,9 The chemoelectrical signal transduction in graphene FETs is based on various mechanisms, including charge transfer, charge scattering, and capacitive and electrostatic field effects. 10 Among them, the electrostatic field effect (also referred to as electrostatic gating) is widely regarded as the most reliable sensing mechanism 11 and consists of the modulation of the Fermi level by means of an external electric field, for example, the local electric field induced by the adsorption of charged macromolecules. 12,13 The modulation of the Fermi level by electrostatic gating is observed as a shift in the Dirac point voltage.
To confer specificity to the transducer, recognition elements need to be anchored on the graphene surface. For instance, the use of monoclonal antibodies or enzymes as recognition elements has led to FET sensors with low limits of detection and high sensitivity. 14−17 Unfortunately, the biomolecule activity is affected by changes in temperature, pH, ionic strength, and the presence of inhibitors. Furthermore, irreversible denaturation of the biomolecule structure with complete loss of its functional activity can occur in harsh conditions. 18 This issue is an important limitation for the development of FET devices for sensing applications. 19 To solve this problem, synthetic and robust "recognition elements" anchored on the transducer surface should be used.
Regarding the electrostatic gating sensing mechanism, the synthetic receptors have to display controllable charge density as a function of specific target concentration and be located directly onto graphene. In this sense, chemoresponsive polyelectrolytes seem to be an ideal "recognition element" because they display high charge density that is controllable via chemical means. 20,21 Hence, the use of polymer brushes 22,23 is an attractive alternative to generate synthetic and robust responsive interfaces 24−31 for FET sensing devices. 32−35 As an example, Hess et al. 35 reported the covalent functionalization of graphene with polymer brushes containing weak cation monomer units (N,N-dimethylaminoethyl methacrylate, DMAEMA). Due to the polymer brush's nature, the pH sensing range of the graphene FETs has been modified, enhancing the enzymatic detection of acetylcholine. 35 Since graphene FETs present the inherent property of sensing pH changes, 36 the DMAEMA monomer units do not confer on the graphene FETs a new recognition function, but they act as an enhancer of the one already present. Therefore, the use of stimuli-responsive polyelectrolytes to confer on the graphene interface a new selective interaction is still a challenging task. In this regard, polymer brushes containing phosphate monomer units turn out to be a promising system to be studied because on the one hand, they present high charge density, and on the other hand, they can form strong complexes with some divalent cations (e.g., Ca 2+ and Mg 2+ ). 37,38 In this work, we report the polymerization of poly[2-(methacryloyloxy)ethyl] phosphate (PMEP) brushes on reduced graphene oxide (rGO) FETs to confer on them a cation selective response (Ca 2+ and Mg 2+ ). The growth of responsive PMEP polymer brushes was accomplished via surface-initiated atom transfer radical polymerization (SI-ATRP), a powerful approach to tune/adapt the chemical and physical properties of surfaces. 39−41 Surface modification with PMEP brushes was characterized by X-ray photoelectron spectroscopy (XPS), ellipsometry, atomic force microscopy (AFM), and contact angle goniometry. Then, the field-effect properties of the PMEP-modified graphene transistors, in particular the Dirac point voltage, were studied in the presence of different types of cations. Finally, a theoretical formalism was introduced to obtain the PMEP−cation association constant from the experimental values of the Dirac point voltage at different Ca 2+ concentrations. Our results show a strong influence of the PMEP brushes on the rGO FET response provided that the presence of divalent ions Ca 2+ and Mg 2+ promotes significant changes in the Dirac point of graphene. We believe that these results further broaden the scope of action of polymer brushes to emerging technological areas, namely, graphene-based field-effect transistors.
1. rGO-FET modification with amine-pyrene: rGO-FET chips were incubated in 2 mM amine-pyrene solution prepared in dimethylformamide (DMF) for 4 h, rinsed with DMF and Milli-Q water, and finally dried with N 2 .
2. Acylation of amine-modified rGO-FETs with α-bromoisobutyryl bromide to obtain ATRP initiator sites: 43 amine-modified rGO-FET substrates were immersed in an Erlenmeyer containing 40 mL of dry THF and 2 mL of triethylamine under N 2 . After this, the reaction solution was placed in an ice bath, and 2 mL of α-bromoisobutyryl bromide was added slowly using a pressure-equalizing dropping funnel. After 3 h, the transistors were removed and washed with acetone, ethanol, and Milli-Q water.
3. Growth of PMEP brushes from immobilized initiators: ATRP was carried out according to the method described by Zhou et al. 44 MEP (12.5 g) was dissolved in 20 mL of water and neutralized with NaOH solution to produce the disodium salt. Then, 0.4 g of 2,2′bipyridyl and 0.011 g of CuBr 2 were added, and the solution was degassed by N 2 bubbling for 1 h. Then, 0.144 g of CuBr was added, and the mixture was left for 15 min under N 2 . Simultaneously, ATRP initiator-modified rGO-FETs were sealed in Schlenk tubes and degassed through vacuum/N 2 cycles. Then, the reaction mixture was syringed into these Schlenk tubes, adding enough to cover the samples completely. The mixture was left overnight under N 2 at 60°C , and then the substrates were removed, washed with deionized water, and dried with N 2 .
Field-Effect Transistor Characterization. Liquid-gated graphene FETs were measured using the batch cell from Micrux Technologies. Electrical measurements were performed by applying a 100 mV source−drain bias and sweeping the gate potential (V g ) while monitoring the current between the drain and the source (I ds ) using a Teq4 bipotensiostat (nanoTeq, Buenos Aires, Argentina). A Ag/AgCl reference electrode from BASi (Indiana, USA) was used as a gate electrode.
X-ray Photoelectron Spectroscopy. An SPECS SAGE HR 100 X-ray photoelectron (XPS) spectrometer was used. A Mg Kα (1253.6 eV) X-ray source was employed operating at 12.5 kV and 10 mA. Quantitative analysis of spectra was carried out by using the Casa XPS software, employing Shirley baselines and Gaussian\Lorentzian functions. Surface-charging effects were corrected by setting the binding energy of the main component of the C1s core level at 284.6 eV.
Contact Angle Goniometry. A Rame−Hart contact angle system (model 290) at 25°C was used using 1 μL drops. The average contact angle value was obtained at three different locations of the same sample.
Atomic Force Microscopy (AFM). A Veeco Multimode AFM connected to a NanoScope V controller was used to image the polymer brushes. AFM measurements were performed in tapping mode with a sample scan size of 2.5 μm × 2.5 μm. Nonconductive sharpened silicon nitride probes (Bruker, K = 0.12 Nm −1 ) were used.
Ellipsometry. For the PMEP film thickness estimation, an alpha-SE ellipsometer from Woollam Co. Inc. was used. The ellipsometric measurements were conducted using a wavelength range from 550 to 900 nm and incidence angle of 70°in high-precision mode. A multilayer model taking into account the layers of different materials (i.e., APTES, rGO, amine-pyrene, and PMEP) was used. All the layers were treated as Cauchy materials having the following wavelengthdependent refractive index: , where A, B, and C are the fitting coefficients and λ is the wavelength. To obtain the A, B, and C coefficients for each layer, ellipsometric measurements were performed after each modification step and fitted with the CompleteEASE software.

■ RESULTS AND DISCUSSION
A set of interdigitated gold electrodes as source and drain electrodes, connected via a very narrow channel (10 μm) of rGO, was used for the preparation of the transistors ( Figure  1a). The interdigitated arrangement together with the liquid gate configuration leads to FETs with an extremely high transconductance and a charge carrier mobility of 30 and 15 cm 2 V −1 s −1 for holes and electrons, respectively, as described in previous works. 16 molecules on graphene disrupts the π-conjugation structure, 45−47 a polymerization method that does not alter the semiconducting properties of graphene needs to be chosen. It has been shown that the self-assembly of aromatic compounds on graphene surfaces via π−π stacking has no deleterious effects on the exceptional electronic quality of this material. 48 With this in mind, we propose an SI-ATRP approach initiated from an amine-pyrene linker previously assembled on the rGO surface ( Figure 1b). The surface functionalization was confirmed using X-ray photoelectron spectroscopy (XPS). The first two spectra in Figure 2a show the successful reduction of GO to rGO using hydrazine as the intensity of the C−O peak decreases in the presence of signals corresponding to other functional groups on the rGO surface. After the PMEP modification, the signal corresponding to OCO groups increased in intensity, which is consistent with the additional ester groups of PMEP. Further, the effective functionalization of the rGO surface by PMEP is evidenced by the presence of P 2s and P 2p XPS signals (Figure 2b). In another experiment, Ca and P spectra were recorded after incubation of a PMEP-modified rGO in 1 mM CaCl 2 and subsequent rinsing with deionized water to remove the salt excess. The resulting Ca/P ratio was determined to be 0.4 (Figure 2c) instead of 1. We attribute this observation to two plausible effects: (i) the presence of counterion gradients within the film or (ii) the coexistence of mono-and dibasic phosphate species, instead of the sole presence of dibasic species in the brush layer. Surface modification was also proven by contact angle measurements (see Figure S1 in the Supporting Information). Further, the PMEP thickness was studied by ellipsometry ( Figure S2), showing a film thickness of 19 ± 3 nm. This value is in agreement with the thickness of PMEP brushes polymerized on gold and silicon wafers using also the ATRP approach. 44 The AFM topography image of an rGO substrate modified with PMEP ( Figure 1c) reveals a continuous and uniform film with a roughness (in terms of the root mean square height) of 3.3 nm (additional scanning electron microscopy characterization is included in Supporting Information, Figure S3).
To assess the chemoresponsive properties of the PMEP brushes, the contact angle was measured with solutions containing monovalent (K + ) or divalent cations (Ca 2+ ). Figure  3a shows contact angles of PMEP brushes prior to and after coordination with Ca 2+ . A marked increase in hydrophobicity was observed in the presence of the divalent cation, which is a result of a surface charge density decrease due to the PMEP coordination with Ca 2+ ions. 38 Sweeping the gate potential (V g ) while monitoring the current between the drain and the source (I ds ) results in transfer characteristics with a minimum conductance, corresponding to the minimum concentration of charge carriers (the so-called Dirac point). The left and right branches from this charge neutrality point represent the hole and electron conductivity regimes, respectively. 49 We should note that after the MEP polymerization, a slight decrease in the FET transconductance was observed ( Figure S4), which could be attributed to desorption of the rGO sheets not so strongly attached to the substrate surface. The negative charge of the PMEP brushes induces an electric field that generates positive charges in the graphene channel (i.e., holes into the valence band) and shifts the Fermi level below the Dirac point ( Figure  3b). When Ca 2+ ions bind to the phosphate groups in the polymer brushes, the surface charge is neutralized, and the transfer characteristics shift to more negative gate values. This  phenomenon can be observed by comparing the transfer characteristics in the presence and in the absence of Ca +2 (Figure 3c). For the PMEP-modified FET, the Dirac point (V i ) clearly shifts to more negative values upon binding of the divalent cations (right), whereas no signal is observed in the control measurement using nonmodified rGO FETs (left). Figure 4a shows that the binding of the analyte to the polymer brushes can be reversed by complexing the Ca 2+ ions using 10 mM EDTA for 20 min. This treatment regenerates the negative charge of the brush and shifts the Dirac point (left) and the contact angle (right) back to the dissociated PMEP values. On the other hand, in the case of Ca 2+ binding, we have observed that the signal reaches a stable value after 1 min exposure. Measuring the Dirac point shift (ΔV i ) at different concentrations of Ca 2+ gives a response curve with a Langmuir-like adsorption behavior, where the polymer brush reaches a binding saturation close to 10 mM Ca +2 (Figure 4b).
According to the experimental data taken from the linear regime, the sensitivity of the PMEP-modified FET device is 17 mV per decade. For the sake of comparison, current Ca 2+ sensors employing more sophisticated sensing configurations exhibit sensitivities close to 25 mV per decade. In principle, we assumed that all the monomer units are exposed to Ca 2+ ions. In previous studies, it has been demonstrated that in the case of thin polymer brushes (thickness <100 nm), counterions fully penetrate the inner environment of the polymer layer. 50−53 In our experiments, the thickness of the polymer brushes is ∼20 nm; hence, we can infer that cations penetrate through the whole thickness of the macromolecular layer.
A formalism based on the Langmuir−Freundlich binding isotherm and the Grahame equation was proposed to obtain the degree of PMEP coordination (i.e., the surface coverage) from the change in the Dirac point (ΔV i ). The modification of the graphene surface with very thin polymer brushes facilitates the use and application of this isotherm to describe the binding process. However, we recognize that above a critical thickness value, this isotherm is no longer applicable and a more detailed analysis would be needed to describe the experiments.
The binding equilibrium of Ca 2+ to the phosphate groups of the polymer brushes can be described as follows where parentheses are used to designate surface species and K 1 , K 2 , and K 3 represent the respective equilibrium constants, which are described in the Supporting Information. As we worked at pH 10, 54 [(RO−HPO 3 −1 )] ≈ [(RO−H 2 PO 3 )] ≈ 0, and it is possible to assume that the divalent cation coordination is described by the K 1 equilibrium. Therefore, the PMEP-Ca surface coverage expression (θ) simplifies to   The surface charge density (σ) is a function of the concentration of phosphate charged groups and can be expressed as follows: As phosphate groups are neutralized by the coordination to Ca 2+ , the surface coverage can be written in terms of the surface charge density: θ = (σ i − σ)/σ i , where σ i is the surface charge density of completely dissociated PMEP (i.e., in the absence of Ca 2+ ).
On the other hand, the Grahame equation relates the surface charge density to the electrostatic potential at the interface of the polymer brush (ψ s ): The relation can be simplified for low ψ s to σ = ϵϵ 0 ψ s /λ D where λ D is the Debye length. As the Dirac point (V i ) is proportional to the electrostatic potential, 12 the surface coverage can finally be expressed as follows where ΔV i, max is the change of the Dirac point obtained upon saturation of Ca 2+ . The dependence of the surface coverage (calculated using eq 4) as a function of [Ca 2+ ] 0 was fitted with eq 1 to determine K 1 and m. Values corresponding to K 1 = 301 ± 42 M −1 and m = 1 ± 0.2 were obtained. These values are consistent with previously reported association constants of calcium with other (RO−PO 3 2− ) molecules such as phosphatidylinositol (10 M −1 ) and phosphatidylinositol 4,5-bisphosphate (500 M −1 ). 56 Moreover, the value obtained for m evidences a very low degree of heterogeneity of the binding sites.
It was also observed that the transconductance of the PMEP-modified rGO FET diminishes when Ca 2+ binds to the polymer brush with respect to measurements in KCl ( Figure  S5). This effect may be attributed to the collapse of the polymer brush upon binding of the divalent cation. 4,38 A similar effect was observed for Mg 2+ . The maximum Dirac point shift upon binding of Mg 2+ ions was found to be −2 mV (see the Supporting Information for more details). This lower shift compared to the measurements performed with Ca 2+ is expected since the affinity between phosphate and calcium is higher than that corresponding to phosphate and magnesium. 56,57 ■ CONCLUSIONS In summary, an ion-responsive negatively charged polymer brush was grown on the graphene surface via atom transfer radical polymerization (ATRP) of poly[2-(methacryloyloxy)ethyl] phosphate (PMEP). The resulting chemoresponsive graphene-based transistor responds to the presence of the divalent ions Ca 2+ and Mg 2+ . Our results show a reversible modulation of the Dirac point voltage (by electrostatic gating effects) due to the divalent PMEP−cation coordination. The binding of Ca 2+ showed a Langmuir-type binding behavior with an affinity constant of 301 M −1 . This functionalization approach, initiated from amine-pyrene linkers noncovalently attached to the rGO surface, represents a powerful tool to combine functional polymer brushes and rGO-based FETs to develop chemoresponsive devices with responsive interfacial architectures. Since our polymerization approach could be extended to a wide variety of stimuli-responsive monomers, we believe that these results will have profound implications for the development of advanced sensors and smart logic gates.