Influence of electron-beam lithography exposure current level on the transport characteristics of graphene field effect transistors

The potential for using high mobility graphene channel field-effect transistors (FETs) for high-frequency applications¹ has driven an immense amount of research in the field. However, in reality, many factors limit the mobilities that can be practically obtained. Without addressing these issues, the potential advantages of employing graphene may be greatly reduced. Several of these factors that degrade the electrical transport characteristics, especially the carrier mobility, of graphene FETs have been identified. These include the type of substrate that is used, condition of the substrate in terms of physical corrugations and charged impurities, other extraneous impurities, and polymer residues introduced during the fabrication process. Techniques such as using ultra-smooth hexagonal boron-nitride (hBN) as a substrate material,² removing the substrate to obtain suspended structures,³ pre-exfoliation surface treatment of the substrate,⁴ post-fabrication annealing,^5,6 and chemical treatment of the device⁷ have all been shown to be effective in mitigating these effects. In addition to these factors, some have reported that the electron-beam lithography (EBL) process, which is commonly used to pattern the graphene active region and source/drain contacts, has a negative impact on the electrical characteristics of the device.^8–10 Several studies have been conducted to investigate the effect of electron beam irradiation on mobility.^11–14 Some have argued that irradiation of the device after fabrication causes defects in the graphene lattice, which shows up as an increase in the Raman D-peak intensity, and a consequent degradation of the mobility.¹¹ They also showed that this degradation becomes more severe with an increase in the cumulative exposure dose.^11,12 However, more recently, it has been pointed out that crystalline defects cannot be the cause of degradation when the EBL acceleration voltage is too low to generate defects.¹⁴ Instead, they argued that degradation could be due to hydrogen containing radicals that are generated by a depolymerization of the poly-methyl-methacrylate (PMMA) resist layer when the device is subjected to EBL processes. It was suggested that these radicals cause hydrogenation of graphene, resulting in device degradation.

However, all of these prior reports considered direct bombardment of electrons onto the channel region and examined the effects thereof. This is not representative of EBL employed for device fabrication, since in the latter case, the channel region is not directly bombarded, but rather areas of the graphene where it is ultimately removed through plasma etching. Hence, we argue that the experimental setups used in these previous studies are insufficient for explaining the effects of EBL on device characteristics. In this report, we show that even for EBL exposure energies that are low enough (<80 keV) to not directly displace carbon atoms from the graphene lattice,¹⁵ and for electron beams not directly targeted on the channel region, EBL can still cause degradation in the mobility. We give evidence that this degradation is, indeed, caused by resist depolymerization, and that the extent of depolymerization is dependent on the level of resist heating, which, in turn, is dependent on the EBL current level. This heating, which is greater for higher exposure currents, causes the PMMA to more readily generate radicals that get trapped between the graphene and resist interface. Electrical measurements and model fitting¹⁶ reveal that a lower exposure current results in higher mobility, decreased variation in the charge neutrality point (CNP), and lower residual carrier density (RCD). By controlling the exposure current level used during the EBL patterning, we were able to obtain very high mobility in excess of 18 000 cm²/V s, approaching the reported record for graphene on a silicon dioxide (SiO₂) substrate.¹⁷ 

The process flow and specific conditions used for the fabrication of the devices used in this study are as follows. A 280 nm SiO₂ layer is grown by means of dry thermal oxidation on a degenerately doped n-type Si (100) wafer. The highly doped silicon substrate functions as the back gate for the final graphene FET. Monolayer graphene flakes are then prepared by mechanical exfoliation from graphite crystals onto this substrate and verified using a combination of optical contrast, and Raman spectroscopy. A resist layer of poly-methyl-methacrylate (PMMA, 950 K 6% dissolved in anisole, supplied by MicroChem Corp.) is spin-coated at a rate of 4000 rpm for 60 s to obtain a 470 nm film and is subsequently baked at 140 °C for 120 s to remove any residual solvent. EBL is performed using a Zeiss Neon 40 scanning electron microscope (SEM) equipped with a Raith Elphy Quantum Pattern Generator system with the exposure current ranging from 10 pA to 125 pA, while keeping the energy, dose, and step size fixed at 20 keV, 320 μC/cm², and 4 nm, respectively. The resist is then developed in a 1:3 solution of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) for 20 s and rinsed in IPA for 30 s. The sample is then exposed to O₂ plasma in a reactive ion etching (RIE) chamber (Plasma-Therm 790 Series) for 10 s at a power of 100 W, a gas flow rate of 15 sccm, and chamber pressure of 50 mTorr to pattern the graphene into a Hall bar geometry. Subsequently, another layer of PMMA is spin coated using the same conditions given above, and EBL is performed to pattern the metal contacts. Finally, a combination of 5 nm chromium and 25 nm gold is deposited onto the sample in a thermal evaporator (Denton Vacuum Inc.) and then submersed in acetone for 24 h to strip away the PMMA and lift-off the metal. Measurement of the device was performed in ambient immediately after retrieval from acetone on a Cascade probe station using an Agilent B1500A parameter analyzer. A 4-point probe configuration was used to eliminate effects of the contact resistance. The measured results were then fitted with a simple model to extract the mobility, CNP, and RCD.¹⁶ An optical micrograph of a typical device used in this study is shown in Fig. 1(a), and its electrical characteristics, along with the model fit results, are shown in Fig. 1(b). It should also be mentioned that we maintained uniform channel dimensions of around 1.5–2 μm width, and 10–15 μm length for all of our devices in order to minimize the effects of device geometry.¹⁸ Only devices showing a good fit (R²> 0.99) were used in the following discussion.

Our main observation is summarized in Fig. 2. The mobility of the final devices shows a correlation with the exposure current level used during the active EBL step. In particular, the mobility is significantly lower at higher exposure currents. The CNP and RCD are also correlated with the exposure current level, albeit to a lesser extent. The CNP and RCD both increase with exposure current, as is evident in the device characteristics shown in Fig. 3(a). Furthermore, the device-to-device variation is also found to increase with exposure current. Raman spectroscopy results are shown in Fig. 3(b) for low, moderate, and high exposure current devices. As the exposure current is increased, there is a red shift in the G and 2D peaks and a decrease in the 2D-to-G peak intensity ratio, indicating that the graphene is more heavily doped.¹⁹ It should also be noted that there is no significant D peak present in any of the devices, which points to there being no structural defects in the graphene nor any hydrogenation of graphene.

Although there have been several reports on the degradation of mobility due to post-fabrication direct electron beam exposure of graphene FETs, suggesting a similar explanation for mobility degradation from EBL processes,¹² the connection was unclear. This is because during the actual device fabrication process, when using a positive resist such as PMMA, the graphene channel area is not directly exposed to the electron beam whether there is a resist layer present on top or not. Although Woo and Teizer¹⁴ added a PMMA resist layer on top of the graphene, here also the entire active region was exposed to the electron beam. Moreover, the exposure dose used in the experiments was well in excess of values that are used for EBL during typical FET fabrication, and unlike our results, there was a significant D-peak in the Raman signature after irradiation.¹⁴ In our experiments, which itself is a standard procedure for fabricating graphene FETs, with commonly used dose for PMMA resist, the electron beam is irradiated onto regions of the graphene where it is ultimately removed by plasma etching, and none of the active graphene channel region is directly exposed to the electron beam. Although the electron beam is directly exposed onto the resist on top of the graphene layer for the contact EBL step, it is limited to a relatively small portion of the contact regions, and the effects of which, if any, are eliminated when using a 4-point probe measurement setup. Even after the elimination of any contact effects, we observe a correlation between the mobility and electron beam exposure current. Moreover, previous reports only showed dependence on the electron energy and dose, and not the exposure current. Our results show that the extent of degradation is dependent on the rate at which electrons are irradiated onto the sample and suggests that resist heating—which is known to be highly dependent on the exposure current—could be playing a role.

This is apparent when considering the results shown in Fig. 4. In Fig. 4(a), a graphene flake after PMMA coating and bake is shown, and the shaded region is where the electrons are exposed during EBL. Right after the EBL step and before development with MIBK, it can be seen in Fig. 4(b) that the graphene flake has curled up. This is similar to the case of Figs. 4(c) and 4(d) where the graphene flake is curled up after an excessive baking step of 220 °C for 2 min. In other words, it is likely that the graphene curling up during EBL is caused by excessive resist heating and the resulting stress caused by the mismatch in the thermal expansion coefficient of PMMA and graphene.^20,21 It should also be noted that the discoloration of PMMA in the exposed region seems to be dependent on the type of substrate. There is more change in color where the graphene was present compared to bare SiO₂, as marked by solid and broken arrows in Fig. 4(b), respectively. This could be due to the spreading of the resist heating through the highly conductive graphene layer as discussed below.

Here, we show that the difference in the level of resist heating originating from the difference in exposure currents used in our experiment is sufficient to explain the observed correlation. A general model based on a multi-layer Green's function solution for the heat diffusion equation for EBL induced resist heating effects has been previously reported for the case of direct writing onto various substrates.^22–26 Its validity was experimentally verified using thermocouple measurements.^21,23 It was shown that even for a relatively low beam current density of 100 A/cm² and a low dose of 100 μC/cm², the temperature on the surface of the resist can reach up to 750 °C at a depth of 0.4 μm—which is approximately the thickness of the PMMA resist layer in our experiments.²⁵ 

The general solution for the resist heating problem is given as a four dimensional integration of a Green's function over the heat source region

where G is the Green's function, g represents the heat generation distribution due to the electron beam, ρ is the mass density, and C_p is the specific heat of the resist. The x, y, z, and t coordinates represent the temperature evaluation field, and the prime coordinates represent the heat source region. Assuming a Gaussian beam, the heat generation function g can be approximated by

Here, V is the acceleration voltage, Q is the dose, λ is the Everhart-Hoff function representing the energy-loss distribution perpendicular to the surface, R_g is the Grün range, θ is the dwell time, and r_b is the beam radius.²² 

Using this model, we calculated the temperature rise for two different exposure current levels with all other parameters held constant. Parameters such as the acceleration voltage, dose, and beam size used in the simulation were identical to those used in the experiments. Our simulation results, shown in Fig. 5, clearly illustrate the difference in resist heating that can result from the difference in EBL current level. Due to computational limits, we were not able to directly simulate real situations where a typical process would require roughly 10⁸ such exposures in continuous sequence. However, it can be noted from Fig. 5 that an order of magnitude difference in the exposure current results in roughly an order of magnitude difference in the rise of temperature. Moreover, it should be emphasized that since graphene has a very high thermal conductivity compared to the underlying SiO₂ layer,²⁷ once this heat is transferred to the graphene layer, it can quickly spread across the whole flake. The transferred heat causes the resist on top of it near the interface to heat up and release alkyl, methyl, and formyl group radicals.^23,28,29 This occurs not only at the directly exposed regions but also at the interface between the active channel region of the graphene and PMMA where the electron beam is not exposed. It has been suggested that in the case of ion bombardment, the depolymerization temperature of PMMA is significantly reduced from 360 °C to 115 °C.^30,31 In other words, due to the combined effect of resist heating and the spreading of this heat through the graphene layer, a local depolymerization process can be initiated at the graphene and PMMA interface even where the electron beam is not directly exposed. This is in addition to the regular molecular weight reducing main-chain scissions and side group modifications that create radicals where the PMMA is directly exposed to electron beams.^32,33 This depolymerization process can be further assisted by mobile radicals that are generated in the electron beam exposed regions. This means that even a relatively moderate temperature increase at the graphene active channel and PMMA interface can result in the release of radicals and accumulation of various polymer species generated by these radicals in this region. It should also be noted that exposing electron beams to PMMA has been found to result in a large yield of negatively charged radicals,³³ and this may be a reason why we observe a large positive shift in the CNP at higher exposure currents as shown in Fig. 3(a).

These radicals, generated through resist heating during EBL, could otherwise dissolve and be eliminated when subjected to solvents such as IPA or acetone used during subsequent fabrication steps. However, as depicted in Fig. 6, the O₂ plasma etch step produces non-volatile carbonyl and carbonate residuals on the top surface of the PMMA.³⁴ When the second PMMA layer is spin coated onto the substrate for metal contact EBL, these residuals are swept underneath the first PMMA layer. During subsequent baking step, they are solidified and locked in place on top of the graphene, thereby trapping the radicals that were generated during the EBL process earlier. The presence of this solidified residual layer is shown in the AFM image of Fig. 7(a). When compared to a control group shown in Fig. 7(b), where a cleaning process is introduced after the O₂ plasma etch and before the second PMMA layer coating in order to remove the residuals on top of the PMMA, it can be noted that these residuals form a roughly 5 nm thick layer on top of the graphene active region as well as other edges of the exposed region. PMMA, when spin coated onto a substrate, is hydrophobic and forms roughly a 70° contact angle with de-ionized water.³⁵ Though this is somewhat reduced when subjected to oxygen plasma, for low power and short durations, it is not significantly reduced.³⁵ Although in a strict sense, a contact angle of 70° would not be considered hydrophobic, it has been shown that even for this level of hydrophobicity, the same effect on the device characteristics as for a 90° contact angle substrate can be obtained.⁴ Also, this is significantly larger than for the thermally oxidized SiO₂ substrate which water contact angle is close to 0° for thicknesses beyond 30 Å.³⁶ Therefore, this polymer residual layer acts as a screening layer for moisture induced ambient effects during measurement from influencing the electrical characteristics, as has been demonstrated with other hydrophobic materials.^4,37,38 It has also been shown that coating graphene FETs with a hydrophobic layer can increase the mobility by a factor of 100%, which matches the gain we observe in low exposure current devices with only the effects of the hydrophobic layer present.³⁹ In addition, this layer effectively traps any radicals that were generated by the EBL process and allows the device characteristics to be determined by the amount of these trapped radicals, free from ambient effects. We have also confirmed that this layer is not removable by vacuum or forming gas anneal processes even at temperatures as high as 400 °C.

In order to further confirm our hypothesis, we performed three control experiments. In the first experiment, O₂ plasma etch time was increased to 60 s with all other conditions being unaltered. For this group, the correlation between exposure current and mobility, CNP, and RCD all disappear and the mobility is relatively constant in a range of 2000–3000 cm²/V s, regardless of the exposure current, as can be seen in Fig. 8. This is because when the etch time is increased, more radicals are generated by the plasma process on top of the PMMA and subsequently swept underneath the existing PMMA layer.³⁴ This effect overshadows the radicals introduced by the EBL process and dominates the electrical characteristics of the device. In a second control experiment, an electron beam evaporator (CHA Industries) with an acceleration voltage of 10 keV is used instead of thermal evaporation for the metal deposition process, with all other conditions held constant. Here, the baseline correlation between EBL current and mobility disappears at low EBL exposure currents as is shown in Fig. 8, and the mobility is in the range of 4000–5000 cm²/V s. E-beam evaporation is known to have effects such as secondary electron scattering and X-ray emission which can potentially degrade the PMMA layer and release radicals.⁴⁰ Thus, the radicals from the EBL process dominate when EBL exposure current is large, while at low EBL exposure current levels, the radicals generated by the electron beam evaporation process degrade the graphene mobilities. In the final control experiment, a cleaning process involving a 5 min dip of the sample in IPA is introduced after the plasma etch and before the second PMMA layer coating, with other conditions being constant. In this case also, the devices show no correlation between their electrical characteristics and exposure current, and the mobility is relatively constant in a range of 6000–8000 cm²/V s. Since the hydrophobic residual layer created by the plasma process is removed by the IPA rinse, there are no residuals on top of the graphene to either protect the device from ambient effects or hold down the radicals that are generated during the EBL process. Thus, the characteristics are determined by the ambient and substrate condition and show a relatively constant mobility value that is typically reported in the literature for graphene FETs on SiO₂.

Although there have been numerous reports on the effects of electron beam exposure on the transport properties of graphene FETs, the experimental setups were not representative of actual device fabrication processes, and therefore had limited explanatory power. Most of the experiments involved direct exposure of electron beams onto graphene FET channel regions without any resist layer present. Even when a resist layer was introduced, the electron beam was exposed onto the channel regions, which is not the case in actual graphene FET fabrication process using a positive resist such as PMMA. In this report, we provide direct evidence of exposure current dependent resist heating induced depolymerization of PMMA during the EBL process commonly used for graphene patterning. When a high exposure current is used, the resist heating is severe, leading to an enhanced release of radicals near the graphene and resist interface. Subsequently, when the sample is processed with O₂ plasma etch for active patterning, a hydrophobic residual layer forms on top of the PMMA. Upon spin coating of the second PMMA layer for metal contact patterning, this residual layer is swept underneath the existing PMMA and on top of the graphene active region. Radicals that are released from the previous EBL process get stuck at the interface between the graphene and residual layer, which ultimately determines the electrical characteristics. We performed resist heating calculations to show that an order of magnitude difference in the exposure current level roughly translates to an order of magnitude difference in the temperature rise. In other words, we found that the use of a higher exposure current leads to increased radical release, which get trapped at the residual layer and graphene interface, resulting in lower mobilities, positively shifted CNPs, and higher RCDs. Furthermore, we give evidence for this hypothesis through three control experiments where more radicals were intentionally introduced by an increase in O₂ plasma etch time, employing e-beam evaporation for the contact metal deposition, and also by removing the residual layer to obtain devices without any trapped radicals. By minimizing the exposure current for the EBL process, minimizing the plasma etch time, and using thermal evaporation for the metal deposition, trapped radicals can be minimized to obtain enhanced electrical characteristics. As a result of our findings, we were able to demonstrate mobility of up to 18 000 cm²/V s on SiO₂ substrates.

We believe that our findings can be generalized to other 2D material based devices and other nanoscale devices, other resist materials or polymers, and other heat inducing lithography processes in general, provided that the generated radicals can get trapped at various interfaces. In the case of electron beam induced resist heating, we think that whenever the resist material is not sensitive and requires a high enough dose to cause sufficient resist heating for depolymerization to occur, as is the case for PMMA, our findings should be taken into consideration. In addition to these lithography processes, care must be taken in order to prevent excessive heating of PMMA resist, or any other polymer, above its depolymerization temperature, in order to avoid the effects of trapped radicals. In the case of PMMA, depolymerization occurs at roughly 360 °C without any assistance from electron or ion beams, and at 115 °C in the presence thereof.^30,31 We also note that it is possible that variations in the reported mobility of many 2D FETs might be caused by differences in the EBL process condition and that further study of this effect in such devices will be worthwhile.

This work was supported by the NRI SWAN center and NSF NNCI program.