Highly doped graphene on ion-exchanged glass

Graphene holds great potential in the future of optoelectronic device applications, owing to its unique transport [1–3], optical [4–6], and mechanical properties [7–9]. However, the expected high performance of graphene is often hindered by the substrate, with, for instance, a relatively high sheet resistance (R_s )  ∼ 1 kΩ sq⁻¹ for graphene on conventional substrates such as SiO₂/Si. Much lower values in the order of a few 100 Ω sq⁻¹ are required for industrial touchscreen [10] and transparent conductor [11–14] applications. Ongoing research thus continuously tries to find methods to reduce the resistance of graphene. One method is to increase, through doping, the low charge carrier density (n_s ) ∼1–2 × 10¹² cm⁻² [15–17], that determines, along with the carrier mobility, the resistance of graphene [18].

Graphene doping techniques can be broadly classified in three categories: (i) substitutional, (ii) chemical and (iii) electrostatic. With substitutional doping techniques, the number of heteroatoms incorporated into the graphene lattice is difficult to control which can compromise the accuracy and repeatability of doping level achievable by this method. Meanwhile, chemical doping techniques can suffer from a lack of control over the surface coverage and reactivity of the chemical species adsorbed onto the graphene which can compromise the doping stability and repeatability. Additionally, the incorporation of heteroatoms or chemical dopants can induce lattice stain effects and structural defects, which may compromise the conductivity of graphene thus limiting its use in electronic devices [19]. On the other hand, electrostatic doping, where graphene n- or p- doping is induced by the application of a gate voltage, allows for a degree of reversible and accurate control of the doping. The main issue, however, is the relatively low reachable n_S due to the limited capacitance of the available solid-state thin film or electrolyte capacitors (e.g. 300 nm-thick SiO₂ grown on Si) and limitations due to the host substrates.

In light of these limitations, several works have demonstrated graphene doping after its transfer onto appropriately treated substrates. For example, the deposition of ammonia or aluminum on the surface onto SiO₂ substrates led to formation of positive (NSiO⁺) and negative (AlSiO^-) surface charge layers on the substrate which were shown to induce the electrostatic n- and p-doping of graphene, with n_S of −8.62 × 10¹² and 2.17 × 10¹² cm⁻², respectively [20].

More recently, n-doping of graphene has been demonstrated on multicomponent glass where the mobility of the ions was exploited to n-dope graphene to a level sufficient to reverse environmental and process related p-doping [21]. Similarly, soda lime glass (SLG) has been used to obtain highly n-doped graphene, in the order of −1.33 × 10¹³ cm⁻², where it was proposed that the high surface density of Na in SLG dopes the graphene via electron transfer [22].

In this work we describe, for the first time, a method to obtain highly n-doped graphene with a n_s of the order of −10¹³ to −10¹⁴ cm⁻² by transferring graphene (e.g. pristine graphene) onto ion-exchanged (IOX) Corning^® Gorilla^® glass. This glass, depicted schematically in figure 1(a), contains potassium ions (K⁺) from an ion-exchange process in which some of the sodium ions (Na⁺) near the glass surface are replaced by K⁺. The depth of the exchange layer (referred to herein with a subscript) can be modified in the range of 1–50 μm.

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Two types of devices were fabricated on IOX Corning^® Gorilla^® glass, fused silica (FS) and Si/SiO₂ substrates for electrical measurements. van-der-Pauw devices, shown in figure S1(a) in supplement 1, features four identical devices (D1–D4) with the typical cloverleaf geometry for performing sheet resistance measurements. Hall bar devices, shown in supplemental figure S1(b), features two identical devices (D1 and D2) with Hall bar geometry for performing transport measurements. To allow for statistical descriptions, multiple samples of each design were fabricated. Both devices follow the same fabrication procedure outlined below, with the addition of Al₂O₃ device encapsulation for the Hall bar structures. The fabrication procedure is shown schematically in supplemental figure S2.

All experiments have been carried out with graphene grown by chemical vapor deposition (CVD) purchased from Graphenea. The graphene sheets were transferred using a wet-transfer technique [23] onto FS, Si/SiO₂ or IOX Corning^® Gorilla^® glass substrates. Prior to graphene transfer, the substrates were cut to a size of 1 cm² and cleaned in an ultrasonic bath using acetone and isopropyl alcohol for 5 min in each solvent. Then, Ti/Au (3/50 nm) contacts were fabricated with van-der-Pauw or Hall bar geometry by photolithography and lift-off processes. CVD graphene was transferred to the metallized substrates which were subsequently dried under atmospheric conditions for 12 h and later immersed in a bath of acetone to remove the PMMA residues. A photolithography process and subsequent argon/oxygen etching step was performed to reduce the area of the graphene to a 300 μm diameter cloverleaf in van-der-Pauw devices and a 140 × 300 μm rectangle in the Hall bar devices, respectively. Remaining photoresist was removed by immersing the samples in acetone for 2 min. Finally, the Hall bar devices were encapsulated with 40 nm Al₂O₃ by atomic layer deposition, A final photolithography and subsequent etching process was performed to remove the excess the Al₂O₃. The etching was performed by dipping the samples in a buffered HF oxide etchant solution (BOE, HF: NH₄F, 1:7) for 1 min.

The four-point R_s of all van-der-Pauw devices (comprising 16 on IOX and 16 on FS) have been measured in a probe station equipped with two precision source-meter units (Keysight B2901). For each device, the I–V curve was measured several times to ensure repeatability, sampling at 1 mV steps, which were subsequently averaged. A linear fit was applied to the I–V curves collected for all devices on each substrate, from which the average R_s was obtained from the slope according to equation (1), which considers the geometric factor ($\pi$/ln(2)) for the cloverleaf geometry to calculate R_s [24, 25].

The R_s, n_s and μ of the Hall bar devices (comprising 16 on IOX_{20 μm} and 2 on Si/SiO₂) was carried out at 300 K in a physical property measurement system by quantum design. A constant DC current of 1 μA was injected into the sample via probes 1–2 whilst probes 3–4 and 3–5 measured the longitudinal (V₃₄) and transverse (V_{35 (Hall)}) voltage, respectively, during a perpendicular magnetic field sweep (−5 T to 5 T) at 300 K. The subscripts indicate the contact pads shown in figure 2(a). From the longitudinal voltage (V₃₄), the sheet resistance (R_s ) was determined at zero magnetic field by Ohms law according to equation (2), where 'W' and 'L' correspond to the width (140 μm) and length (300 μm) of the graphene area, respectively. The charge carrier density (n_s ) was obtained from the slope of the linear fit between the transversal voltage (V_Hall), and the magnetic field (B), according to equation (3) where q_e is the electron charge (1.6 × 10⁻¹⁹ °C) and I_DC is the constant DC current, (1 μA). Assuming the Drude model of conductivity [26], the mobility (μ) was calculated by equation (4). Finally, the Fermi level, E_F, was calculated from the n_s according to equation (5), where ħ is reduced planks constant, v_F is the Fermi velocity, k_F is Fermi wave vector which is equal to $\sqrt {{{\pi }}{n_s}}$ and n_s = number of additional charge carriers

$$\begin{align}\kern-30.4pt {R_s} = \frac{{\text{V}}}{I}\frac{\pi }{{{\text{ln}}\left( 2 \right)}}\,\end{align} \tag{ 1 }$$

$$\begin{align}\kern-36.6pt{R_s} = \frac{{{V_{34}}}}{{{I_{12}}}}\frac{{\text{W}}}{L}\end{align} \tag{ 2 }$$

$$\begin{align}{{\textrm{n}}_s} = {I_{DC}}/{q_e}\left( {{V_{Hall}}/B} \right)\end{align} \tag{ 3 }$$

$$\begin{align}\mu = 1/1{{\textrm{q}}_e}{{\textrm{n}}_s}{{\textrm{R}}_s}\end{align} \tag{ 4 }$$

$$\begin{align}\kern-43.2pt{E_F} = { }\hbar {v_F}{k_F}.\end{align} \tag{ 5 }$$

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Figure 1(c) compares the I–V characteristics for van-der-Pauw devices prepared on IOX_{20 μm} Corning^® Gorilla^® glass and FS substrates, where the difference in slope confirms the strong influence of the supporting substrate on the sheet resistance of graphene. The corresponding average R_s (obtained from the slope of the linear fit according to equation (1)) of the graphene/FS devices was 1.22 ± 0.353 kΩ sq⁻¹ which is similar to those values previously reported [12], thus confirming the reliability of our transfer technique and characterization method. On the other hand, the R_s for the graphene/IOX_{20 μm} devices was consistently 3–5 times lower with an average of 0.245 ± 0.069 kΩ sq⁻¹. The results were quite repeatable across all devices fabricated by independent runs.

R_s measurements were also performed on graphene transferred onto bare (i.e. with no pre-defined Au contacts) IOX_{20 μm} Corning^® Gorilla^® glass and FS substrates. Interestingly, and in contrast to Au-contacted graphene devices (figure 1(c)), no difference in R_s was found, irrespective of the underlying substrate with both IOX and FS systems measuring between 1–2 kΩ sq⁻¹ (figure S3 in supplement 1). This result was repeated several times by independent fabrication processes.

Eight samples on IOX_{1−43 μm} were fabricated with a hall bar design, figure S1(b) in supplement 1, where each sample contains two identical devices (D1 and D2) for gathering statistics. Figures 2(a) and (b) show the measurement scheme and the evolution of Hall voltage (V_Hall) as a function of perpendicular magnetic field sweep (B) between −5 and 5 Tesla at 300 K.

A negative slope indicates n-type doping (excess of electrons), while a positive slope indicates p-type doping (excess of holes) where the magnitude of the gradient correlates to the strength of the doping. Comparing the slope of the devices fabricated on IOX_{1−43 µm} to that of the Si/SiO₂ reference, it is found that V_Hall induced by the charge carriers in the graphene on IOX substrates is lower in amplitude and of opposite sign, for a fixed current and magnetic field.

Figures 3(a)–(c) shows the evolution of R_s, µ_H and n_s respectively, for the eight graphene/IOX samples, comprising of IOX thicknesses: 1 × 1 µm, 1 × 5 µm, 2 × 10 µm, 2 × 20 µm and 2 × 43 µm. Each marker and corresponding error bar represent the average and standard deviation of D1 and D2. Identical measurements on the Si/SiO₂ reference sample are indicated with blue markers. Note that the low R_s (and high n_s) is reproduced with a comparable magnitude irrespective of the IOX thickness.

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The sheet resistance measurements shown in figure 3(a) show an average R_s values 0.318 ± 0.078 kΩ sq⁻¹ for the of the graphene/IOX_{1−43 µm} devices. This is in close agreement with the R_s statistics obtained with the van-der-Pauw structures (0.245 ± 0.069 kΩ sq⁻¹) and confirms that the effect of the underlying substrate is significant and independent of the slight processing differences between the two designs e.g. encapsulation with Al₂O₃. Furthermore, the R_s for the Si/SiO₂ reference, 2.32 ± 0.690 kΩ sq⁻¹, is of the same order of that for graphene/FS devices fabricated with van-der-Pauw geometry (1.22 ± 0.353 kΩ sq⁻¹).

The room temperature (RT) carrier mobility (µ) measurements, in figure 3(b), show a mobility between 80–800 and 150–160 cm² V⁻¹ S⁻¹ for graphene on IOX and Si/SiO₂ substrates, respectively. Graphene wet-transferred onto Si/SiO₂ substrates typically produce mobility values in the range of 10²–10³ cm² V⁻¹ s⁻¹ at 300 K for a carrier concentration, n_s ∼ 10¹²cm⁻² [12, 16, 27]. In the future, we will perform studies and evaluate previous techniques to reduce the spread of the mobility we have observed toward the highest values observed in the literature for glass [28–30].

The carrier density measurements (n_s ) shown in figure 3(c) show a moderate p-doping (average n_s +3.9 × 10¹³ cm⁻² ± 1.3 × 10¹³ cm⁻²) for the graphene/Si/SiO₂ devices (blue marker). The doping may depend on processing conditions and is consistent with data previously reported in graphene − silica systems [17, 31–36]. In contrast, the graphene/IOX_{1−43 µm} devices, indicated with red markers, show a strong n-doping within range −1.7 × 10¹⁴ to −4.5 × 10¹⁴ cm⁻², with an average of −1.9 × 10¹⁴ ± −9.8 × 10¹³ cm⁻² which validates the effect of the IOX layer on the graphene doping. Substituting the average n_s value into equation (5) returns a Fermi level (E_F) of −1.61±0.4 eV for the graphene/IOX_{1−43 µm} devices.

The observed high n_s might be related to a local surface density of positive charge present in the IOX glass layer in which the graphene is in direct contact. A positive surface charge might originate from the excess of K⁺ after the ion-exchange process [37, 38]. When the graphene is contacted, electrons are drawn into graphene to neutralize the excess surface charge due to IOX process. Similar examples have been reported in literature where it is demonstrated that a charged substrate surface induces the doping of graphene [20, 39]. Although it is clear that the IOX glass is a key element to achieve doping, additional experiments are needed to confirm the doping mechanism and the interplay between the processing steps to make the devices and the substrate composition [17, 40–42].

To evaluate the stability of the doping, the R_s of several IOX and Si/SiO₂ devices was measured again after being kept for five months in a dry box. The IOX devices (purple markers in figure 3(a)) reveal an increase between 0.100–0.160 kΩ sq⁻¹ corresponding to a 42% average increase as compared to the initial R_s . The Si/SiO₂ devices reveal a similar increase of $\sim$0.100 kΩ sq⁻¹, corresponding to a 5% average increase compared to the initial R_s . Given that the increase in R_s after 5 months is of a similar magnitude for both IOX and Si/SiO₂ devices, we understand that the 42% increase for the IOX is only large in the context that the initial starting R_s was low. We believe that the increase in R_s after 5 months is probably not due to the IOX substrate, but more likely related with a combination of atmospheric exposure, which is known to degrade the graphene, and degradation induced by the Al₂O₃ encapsulation layer. In this regard, future work should consider alternative encapsulation techniques, that maintain an effective moisture barrier and the initial quality of the transferred graphene over time.

3.1. Applications

As described herein, IOX Corning^® Gorilla^® glass was found to naturally modify graphene doping without the need of additional post-treatment (e.g. thermal poling under applied potential). Sheet resistance and Hall measurements performed at RT demonstrate high and reproducible doping levels of graphene placed in direct contact with IOX glass leading to graphene with an unexpectedly high n_S (−10¹³ cm⁻² or higher). The negative values obtained with IOX glass were found to be 1–2 orders of magnitude larger than the positive values on undoped silica glass substrate.

The authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the 'Severo Ochoa' Programme for Centres of Excellence in R&D (CEX2019-000910-S) [MCIN/ AEI/10.13039/501100011033] and the project TUNA-SURF (PID2019-106892RB-I00), from Fundació Privada Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya through the CERCA programme. This project was also funded by the Agència de Gestió d'Ajuts Universitaris i de Recerca (2021 SGR 01458). This project also received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 754510.

The authors would like to thank the Low Temperatures and Magnetometry Service of ICMAB-CSIC for assisting and performing the transport measurements under magnetic field on the Physical Properties Measurement System PPMS. We also thank Dr Xiaoju Guo for help with samples.

All data that support the findings of this study are included within the article (and any supplementary files).