Nanofabrication of graphene field-effect transistors by thermal scanning probe lithography

An important objective of the microelectronics industry is to fabricate high-performance miniaturized devices on a large scale at a low cost and with a high throughput. The exploration of new materials, fabrication methods, and device architectures underpins this objective. Of particular interest in recent years has been the study of electronic devices where the active material is monolayer graphene, due to its intriguing properties, including remarkable carrier transport,¹ high thermal conductivity,² and outstanding mechanical stability.³ These properties have made graphene a promising candidate for a wide range of applications from flexible electronics to high-speed electronics.

The fabrication of graphene functional devices generally requires multiple patterning steps for defining the device active region and patterning metal contacts on graphene. Currently, electron-beam lithography (EBL) is the dominant technique for prototyping high-performance nanoscale devices out of graphene,^4–8 producing better quality devices than photolithography (PL).^9–11 However, the use of a focused electron beam in EBL is a major limitation in terms of cost, the electron beam induced sample damage and potential for parallelization to increase the throughput.

In recent years, novel nano-patterning techniques have been explored for fabricating nanoscale devices.^12–15 Among those, thermal scanning probe lithography (t-SPL) is an attractive choice for multiple reasons.^12,16–20 First, t-SPL is a maskless technique and is capable of patterning nanoscale features with sub-10 nm resolution.^17,21 Second, the entire t-SPL nano-patterning process can take place in atmospheric condition or N₂, which is a considerable advantage for achieving a cost-effective nano-patterning process. Third, t-SPL has a throughput comparable to EBL when using only one probe (∼10⁵ µm² h⁻¹),²² but by multiplexing with thermal nanoprobe arrays,²³ it could reach a much larger throughput. Finally, and more importantly, a recent study has demonstrated that t-SPL can pattern high-performing and low-resistance metal contacts on monolayer MoS₂.²⁴ However, the application of t-SPL for the fabrication of graphene devices remains largely unexplored. The objective of this study is, hence, to study the effectiveness of t-SPL for fabricating graphene devices.

Here, we report the application of t-SPL performed in ambient conditions for the fabrication of graphene field-effect transistors (GFETs). In particular, we study the electrical properties of monolayer graphene using a bottom-gated device structure with no encapsulation layer. In this device structure, monolayer graphene in both channel and contact regions is in direct contact with the t-SPL resist during all the lithographic steps. Despite this, and without the use of contact engineering (see the supplementary material for details), we find that the GFETs fabricated using t-SPL exhibit a relatively low specific contact resistance of 600 Ω·μm. This value is within the typical range of specific contact resistance (100 Ω·μm–800 Ω·μm) for monolayer graphene devices built using EBL, including those employing contact engineering.^4,8,25–28

Our experiments began with the mechanical exfoliation of monolayer graphene from a bulk graphite crystal. Graphene monolayers were exfoliated onto a heavily doped silicon substrate covered with 285 nm of thermally grown SiO₂, which serves as the global back-gate in the final device structure. Monolayer graphene flakes were identified under an optical microscope and then verified using Raman spectroscopy. We then annealed the sample in an Ar/H₂ ambient at 500 °C for 1 h. This annealing step removes the residual tape contaminants on the substrate. The cleanliness of the oxide surface is important for spin-coating the substrate with a uniform resist layer for performing nano-patterning using t-SPL. As we describe below, we used a commercial t-SPL system for all nano-patterning steps in the device fabrication process.

The first step in our device fabrication process was to define and etch the active region within the monolayer graphene flake. Figure 1 shows the schematic illustration and optical images of this processing step. For t-SPL nano-patterning, we used a two-polymer stack resist, consisting of a 210 nm thick PMGI (polymethylglutarimide) layer and a 15 nm thick thermosensitive polymer film, namely, PPA (polyphthalaldehyde). These layers were deposited sequentially onto the substrate through spin coating [Figs. 1(a) and 1(f)]. We then performed t-SPL to define the active region of interest. During the nano-patterning process, a heated nano-probe (typically heated to 200 °C at the probe-resist contact) thermally decomposes and evaporates PPA. The precise movement of the probe transfers a computer-generated pattern into the PPA film [Fig. 1(b)]. The decomposed PPA quickly evaporates without being re-deposited onto the surface of the sample. The pattern was then chemically etched into the underlying PMGI using a diluted TMAH (tetramethylammonium hydroxide) solution, as shown in Figs. 1(c) and 1(g), which exposes the unwanted monolayer graphene regions for removal. We used a brief oxygen plasma treatment (see the experimental method) for removing the exposed graphene regions, resulting in a rectangular active device region [Figs. 1(e) and 1(h)]. The PPA/PMGI stack resist during the oxygen plasma etching process serves as a hard mask for protecting the underneath monolayer graphene in the active region. Hence, it must be sufficiently thick to survive the plasma etch process. However, patterning high-resolution features using t-SPL requires the use of a thin PPA film (see Fig. S1 of the supplementary material), suggesting that the PMGI film must be made thick enough to protect the active device region. In Fig. 1(i), we show how the thickness of PPA and PMGI changes due to exposure to the oxygen plasma. For this experiment, we produced two sample groups. Each sample group consisted of multiple substrates coated with either PPA or PMGI. The initial thickness of the film within each sample group was identical. However, each substrate within the group was subjected to a different etching time. Each data point in Fig. 1(i) represents one substrate. The data show that a thin PPA film (with ∼12 nm initial thickness) withstood less than 15 s of exposure to oxygen plasma. In contrast, only 12 nm of the PMGI film was consumed after 25 s of etching under the same conditions, which is adequately long for etching monolayer graphene. This experiment explains the rationale for choosing the above-mentioned thicknesses for PMGI and PPA when patterning the active region of the graphene device. The resolution of the current pattern-etch transfer process is discussed in the supplementary material, where nanoscale etched graphene nano-ribbons are presented (Figs. S1 and S2).

The second step in device fabrication after defining the active region on monolayer graphene was to pattern the metal electrodes. Figures 2(a)–2(e) show schematic illustrations of the fabrication steps. First, a two-polymer stack of PPA/PMGI (15 nm PPA/210 nm PMGI) was spin-coated on monolayer graphene. Then, we used a heated t-SPL nano-probe to pattern the metal electrode regions in the PPA film. Subsequently, the patterns were transferred into the underlying PMGI through chemical etching in diluted TMAH [see Figs. 2(b) and 2(c)], which also produces the required undercut. In this process, the top thin PPA ensures high-resolution patterning, while the underlying PMGI layer eases the metal lift-off process. Finally, we deposited a stack of Cr/Au (10 nm/20 nm) metals using electron-beam evaporation, followed by the metal lift-off. Figure 2(h) shows an example of the optical image of the final graphene device structure. To demonstrate the capability of t-SPL to fabricate graphene field-effect transistors (GFETs) at the nanoscale, we fabricated metal contacts on graphene with a minimum channel length of 60 nm [Fig. S2(c)]. It is noteworthy that such a small spacing between metal contacts results from the pattern amplification due to the development of PMGI and partial non-line-of-sight metal deposition. With proper optimization of pattern amplification, PPA/PMGI thickness, wet etching duration, RIE etch conditions, probe size, pattern depth, and eventually using a different process without PMGI, sub-10 nm graphene nanoribbons and channel lengths can be obtained using the process described in this work.

The t-SPL technique provides in situ simultaneous patterning and imaging, a capability that distinguishes t-SPL from other fabrication methods such as EBL or PL and provides important benefits, including the fact that there is no need for alignment marks.^29,30 Furthermore, the here-shown graphene devices have been fabricated in the ambient environment without the need for ultra-high vacuum (UHV). Indeed, before nano-patterning, a cold t-SPL probe produces a thermal image of the monolayer graphene active region underneath the resist to determine the target patterning location [Fig. 2(f)]. A second benefit of in situ imaging is the ability to inspect the quality of the patterned features simultaneously with t-SPL nano-patterning, allowing for a true closed feedback loop.¹² Figure 2(g) shows an in situ image of the patterned metal electrodes in the PPA layer.

Next, we studied the electronic properties of the t-SPL fabricated GFETs at room temperature. Figure 3(a) shows the total resistance, R_tot, of three graphene devices as a function of the applied back-gate bias, indicating the increase in the device resistance with the channel length. The total resistance in Fig. 3(a) was calculated by taking the ratio of the drain–source voltage (V_ds) to the current (I_d). These devices [marked as 1–3 in the inset optical image in Fig. 3(a)] have different channel lengths. Note that the shorter length devices were not connected, possibly due to cracks in their channel regions. The Dirac point voltage (V_Dirac) for channels 1, 2, and 3 in Fig. 3(a) are 1.2 V, −1.4 V, and −5.6 V, respectively (Fig. S3). These Dirac voltage shifts correspond to residual carrier densities of 9.1 × 10¹⁰ cm⁻², 10.6 × 10¹⁰ cm⁻², and 4.2 × 10¹¹ cm⁻², which indicate the preservation of the intrinsic state of graphene after the t-SPL GEFT fabrication process.

To analyze the electronic properties of these devices, we first extracted the contact resistance using the transmission-line method (TLM). In particular, the total resistance is the sum of the intrinsic channel resistance and the contact resistance, given by

where R_c is the contact resistance due to one electrode, ρ_ch is the channel resistivity of monolayer graphene, and L and W are the channel length and width, respectively. In this equation, R_tot scales linearly with L, whereas the y-intercept is 2R_c. Moreover, the slope gives information about the intrinsic resistivity of graphene, which depends on the carrier concentration (n) in the graphene channel. In Fig. 3(b), we plot the total resistance of devices 1, 2, and 3 at three different electron carrier densities, giving an estimated total contact resistance (2R_c) of 504 Ω, 403 Ω, and 355 Ω at n = 1.1 × 10¹² cm⁻², 1.9 × 10¹² cm⁻², and 2.6 × 10¹² cm⁻², respectively. Note that we calculated the carrier density n using the following³¹ equation:

where C_ox is the oxide capacitance (1.2 × 10⁻⁸ F/cm²), ℏ is the reduced Planck constant, υ_F is Fermi velocity of graphene (1 × 10⁶ m/s), and $kF=nπ$ is the Fermi wave vector. Figure 3(c) shows the extracted specific contact resistance, ρ_c, plotted against the carrier density for the range of the applied gate bias. The gray shading in this plot marks the region where uncertainty in the intercept of the linear fits to R_tot data is considerably large (>26% of the extracted R_c). This region corresponds to low carrier densities near the charge neutrality point (CNP). At high carrier densities, however, the error in estimated R_c is small, and ρ_c is as low as 600 Ω·μm in the electron branch. These values indicate that the here fabricated contacts to monolayer graphene are of good quality, considering that no supplementary contact engineering strategies were used. Table I compares ρ_c of our graphene devices fabricated by t-SPL in ambient conditions with some of the best results reported in literature for graphene FET fabricated by EBL in UHV and by photolithography with and without different supplementary contact engineering methods. We remark that similar methods of contact engineering can also be implemented together with the t-SPL process to achieve similar reductions of ρ_c (Table I in the supplementary material).

Finally, we calculated the carrier mobility in the as-fabricated monolayer graphene FET. To do so, we extracted the channel resistivity of device 1 from the slope of the linear regressions in Fig. 3(b) at different carrier densities. Figure 3(d) shows the plot of ρ_ch against the carrier density in graphene. The carrier mobility can be estimated by fitting the channel resistivity using $ρch=neμL+σ0−1+ρs$⁠, where μ_L represents the mobility due to long-range scattering, σ₀ is the minimum conductivity at CNP, and ρ_s indicates the contribution from short-range scattering.^32,33 Fitting the data in Fig. 3(d) (pink solid curve) yields μ_L-Fit of ∼4500 cm²/V s and ∼6100 cm²/V s for the electron branch and the hole branch, respectively. These carrier mobilities are within the range of previously reported values for graphene on SiO₂, which is between 2000 cm²/V s and 20 000 cm²/V s.^34–37 

We also employed the theoretical graphene transport study by Adam et al.⁴³ for evaluating the expected carrier mobility in the diffusive limit from the impurity concentration (n_imp) at the graphene–oxide interface. In particular, the transport mobility follows μ = 20e/(hn_imp), where n_imp can be estimated from the residual carrier density (n^*) using n^* ≅ 0.3n_imp. The plot in the inset of Fig. 3(d) shows the double-logarithmic plot of the conductivity vs carrier density, which gives an upper bound estimate of n^* = 2.6 × 10¹¹ cm⁻² from the σ plateau. Using this information, we calculate carrier mobility of ∼5500 cm²/V s. The obtained mobility from the analytical solution is comparable with the fitting results, providing further confidence in the extracted specific contact resistance in Fig. 3(c).

In summary, we demonstrated the application of t-SPL for fabricating GFETs. We showed that it is possible to combine t-SPL with plasma etching for producing graphene structures of desired shapes. More importantly, the t-SPL fabricated metal electrodes resulted in low-resistance contacts on monolayer graphene without contact engineering. Further improvements of the contact resistance require an in-depth study to identify the factors that limit the contact resistance in the t-SPL process. t-SPL is very attractive compared to EBL because it offers in situ simultaneous imaging and patterning capabilities and it operates in ambient conditions, which is a considerable advantage for achieving a cost-effective nano-patterning process. The results presented here establish the prospects of t-SPL for the fabrication of graphene devices.

See the supplementary material for the following analyses and/or descriptions: the high resolution t-SPL pattern in the PPA resist, nanoscale etch-pattern transfer and metal deposition using the t-SPL process, unshifted transfer characteristics of GFET in Fig. 3(a), and the literature review of contact engineering of metal-graphene contacts.