## Abstract

Electric-field-assisted atomic force microscope (E-AFM) nanolithography is a novel polymer-patterning technique that has diverse applications. E-AFM uses a biased atomic force microscope (AFM) tip with conductive coatings to make patterns with little probe–sample interaction, which thereby avoids the tip wear that is a major issue for contact-mode AFM-based lithography, which usually requires a high probe–sample contact force to fabricate nanopatterns; however, the relatively large tip radius and large tip-sample separation limit its capacity to fabricate high-resolution nanopatterns. In this paper, we developed a contact mode E-AFM nanolithography approach to achieve high-resolution nanolithography of poly (methyl methacrylate) (PMMA) using a conductive AFM probe with a low stiffness (∼0.16 N/m). The nanolithography process generates features by biasing the AFM probe across a thin polymer film on a metal substrate. A small constant force (0.5–1 nN) applied on the AFM tip helps engage the tip-film contact, which enhances nanomachining resolution. This E-AFM nanolithography approach enables high-resolution nanopatterning with feature width down to ∼16 nm, which is less than one half of the nominal tip radius of the employed conductive AFM probes.

## Introduction

For decades, the scaling theory in semiconductor and integrated circuit technology development requires novel nanolithographic methods and strategies to overcome existing resolution limitations in nanodevice manufacturing [1]. Current nanolithography can be classified into masked lithography and maskless lithography. The masked lithography, such as photolithography and nano-imprint lithography [24], transfers patterns using lithographic masks in high throughput. The maskless lithography, which includes electron beam lithography [5], focused ion beam milling [6], direct laser writing [7], and scanning probe lithography (SPL) [8], fabricates masks for masked lithography or directly produces prototypes or products. Electron-beam lithography is developed to pattern the electron-sensitive resist layer on a substrate by emitting a beam of accelerated electrons. Similarly, focused ion beam milling uses a focused beam of ions to strike the sample and modify the surface structure. Both the electron-beam lithography and focused ion beam milling processes are capable of creating fine features, but are costly and have low fabrication yields [9]. In contrast to these electron and ion beam-based techniques, SPL techniques, which are based mostly on atomic force microscope (AFM) and scanning tunneling microscopy techniques, have shown great potential to fabricate high-resolution features with unprecedented technical capabilities. They have been applied to many scientific and potential industrial applications [10,11].

Compared with other nanolithography technologies mentioned above, the cost-effective AFM lithography exhibits many advantages in process simplicity and resolution [12], and can be used to make patterns on a variety of materials [13], thanks to the unique combined scanning, manipulating and imaging capabilities of ultrasharp AFM probes with a typical tip radius below 10 nm [14,15]. It can be applied to achieve nanoscale features such as nanodots [16], nanowire [17], nanofluidics [18], and two-dimensional (2D)/three-dimensional (3D) nanopatterns [1923] on a variety of materials, which includes polymers [24], silicon [25], metals [26], and 2D materials [27,28]. Meanwhile, the wide usage of polymers in diverse applications such as opto/micro-electronics, sensors, and data storage has promoted the innovation of polymer nanolithography [16]. Nanopatterns fabricated on the polymer film can be transferred to different substrate materials through reactive ion etching while using the patterned polymer film as a mask [29].

Atomic force microscope-based nanolithography processes rely on the interaction of AFM tips with sample substrates [30]. AFM tip-sample interactions in nanopatterning processes include mechanical-, thermal-, chemical-, and electric-induced interactions [13]. The mechanical interactions are utilized in dynamic plowing [31], direct machining [32], and vibration-assisted lithography [33,34]. Thermal-assisted AFM lithography includes thermal writing that uses a heated AFM probe [35], and a sample heating method by using a softened sample under elevated temperatures [34]. Electric-field-assisted AFM lithography, or the so-called bias-assisted AFM lithography process, involves highly confined joule heating, local oxidation, field emission, and electrostatic interactions [14,3640].

Two typical electric-field-assisted AFM nanolithography techniques for patterning polymers are AFM-assisted electrostatic lithography (AFMEN) and field-emission-SPL [36,41,42]. AFMEN generates features through biasing a conductive AFM probe above a thin polymer film that rests on a grounded conductive film on silicon substrate. Features are formed by joule heating from the current flow between AFM tip and conductive substrate. Depending on the applied voltage, either raised features (by the effect of nonuniform electric field gradient on polarizable softened polymer) or depressed features (by polymer ablation) can be generated by AFMEN, which has an initial gap distance between an AFM tip and a sample [41]. Studies show that feature size of SPL-based electrostatic lithography is influenced by a number of factors, such as tip radius, current magnitude, and material characteristics of polymers [43]. In addition, AFM tip-polymer film separation is one of the critical factors that leads to the control of polymer dielectric breakdown [16]. As the distance between tip–polymer surface increases, larger-size pattern features are fabricated [44]. Similarly, the amplitude-modulated AFMEN (AM-AFMEN) process includes an oscillating conductive AFM tip. This process can be applied to make nanodots with smaller dimensions due to variant tip-sample interaction distance and better control of the heat generation. Field-emission-SPL process also applies bias between a sharp AFM tip (with 7–15-nm tip radius) and the sample, which generates a Fowler–Nordheim (FN) field emission of low energy electrons and leads to the cross-linking or scission of the polymer resist sample [36]. A feedback control can be incorporated in this technique to maintain both a constant emission current through controlling tip-sample distance in the lithography process and a constant tip oscillation amplitude in regular scanning [45].

A larger distance between tip–polymer surface leads to the formation of wider nanostructures because tip-film separation acts as one of the governing factors that affect the polymer dielectric breakdown and fabricated feature size [16,44] (see Supplemental Materials on the ASME Digital Collection for further details). Much of the existing literature reported electric-field-assisted AFM lithography experiments under tapping mode (or amplitude-modulated mode), in which tip-sample distance is within a large range due to the tip oscillation. Among studies that use similar nanolithography techniques, AFMEN was conducted with no tip-film contact and a tip-sample separation possibly due to condensed water meniscus between the AFM tip and the polymer film. The fabricated nanopits and nanogrooves typically have large feature width of around 500 nm [41]. AM-AFMEN fabricates nanopatterns with finer resolution; however, this process requires a more complex and precise control of cantilever oscillation amplitude, applied AFM tip bias, and tip-sample interactions. Except for the tip-sample distance, the patterning speed is another important indicator when evaluating the lithography techniques [46,47]. One of the existing SPL technologies has reached a very high patterning speed at meters per second [48].

In this study, we developed a contact mode electric-field-assisted AFM lithography process that generates high-resolution nanofeatures on polymer substrates using a soft probe. Constant force of 0.5–1 nN was applied to the AFM tip to secure the tip-film contact, in which localized electric breakdown took place inside the polymer film produced nanoholes and nanopatterns with adjustable feature dimensions. Nanostructures with feature widths down to ∼16 nm were fabricated on a 15 nm-thick poly (methyl methacrylate) (PMMA) film, which was coated on a gold layer. Moreover, we studied the effects of applied bias voltage, contact force, and bias duration time on the lithographic feature dimensions. We also simulated the tip-induced electric field strength distributions in the polymer layer using finite element analysis. This study demonstrates a new method of fabricating high-resolution nanopatterns using contact mode electric-field-assisted AFM with a small contact force.

## Methods

The contact mode electric-field-assisted AFM lithography experiments were performed inside a commercial AFM (XE7, Park Systems Corporation, Suwon-si, South Korea) with a high voltage toolkit. A schematic of the electric-field-assisted AFM lithography setup is shown in Fig. 1 (see Supplemental Materials on the ASME Digital Collection for the actual experimental setup). The entire setup was placed inside an acoustic enclosure, which had a humidity of ∼15%. The sample is prepared by first e-beam evaporation of an Au layer (100 nm thickness) on a silicon substrate. Subsequently, a 15-nm PMMA layer was spin-coated on the Au layer, followed by a postbaking at 180 °C for 90 s. A conductive AFM probe (CSG10/Au) with conductive Au coatings on both the tip side and the back side was used in contact mode lithography, which applied small constant contact forces (1 nN) between the AFM tip and sample. A sharp AFM probe (MCNT-500 12 deg) was used in noncontact (tapping) mode to image the lithography results (see Supplemental Materials on the ASME Digital Collection for specifications of the AFM probes).

Fig. 1
Fig. 1
Close modal

Numerical simulations were conducted using ansysmaxwell 3D to simulate the electric-field-assisted AFM lithography process and to generate the distributions of electric field strength in the polymer film.

## Experimental and Simulation Results

With the electric-field-assisted AFM lithography setup mentioned in the previous chapter, multiple nanopatterns with different feature dimensions were fabricated on the 15 nm-thick PMMA film. The lithography speed was set at 0.5 μm/s.

One of the most important factors in the electric-field-assisted lithography process is tip bias. Figure 2 shows results of several experiments that were conducted to analyze the voltage effect on lithography feature dimensions. Figure 2(a) shows three trenches fabricated with bias voltage of 32.4 V, 33.3 V, 34.1 V, which correspond to input voltages of 1.85 V, 1.90 V, 1.95 V before amplification, respectively. As shown in the z profile of the topography image in Fig. 2(b), the depth of the three lines is around 3.0, 4.0, and 5.0 nm, respectively. Nanopatterns in Fig. 2(d) also exhibit similar results in which the trench depth increases as the voltage increases. The voltage applied from left to right trenches is 22.93 V, 21.18 V, 23.10 V, 21.35 V, 23.28 V, 21.53 V, 23.45 V, 21.7 V, 23.63 V, 21.88 V, 23.8 V, 22.05 V, 23.98 V, and 22.23 V, respectively. Note that the force applied on the AFM tip during lithography was set as 1 nN for all the tests. Measurement results of topography images in Figs. 2(a) and 2(d) are shown in Figs. 2(b) and 2(e), respectively. Figures 2(c) and 2(f) show a summary of the fabricated trench width and depth versus applied voltage for the nanotrenches shown in in Figs. 2(a) and 2(d). Based on the height profiles, we measured trench depths and widths in five random spots along each trench and took the average value. In Fig. 2(c), for voltage applied between 32.4 and 34.1 V, trench depth ranged between 3.3 and 4.7 nm, and trench width ranged between 26 and 33 nm. In Fig. 2(f), for voltage applied between 21.18 and 23.98 V, trench depth ranged between 1.1 and 3.0 nm, and trench widths ranged between 25 and 36 nm.

Fig. 2
Fig. 2
Close modal

In addition, we investigated the effect of tip bias hold time on the lithography dimensions. Figure 3(a) shows the 2D image of holes fabricated in electric-field-assisted contact mode AFM-based nanolithography, in which the tip bias hold time was set as 100 ms, 160 ms, 220 ms, respectively, with 1 nN contact force and 24 V tip bias applied for all three holes. Figure 3(b) is a depth-profile view of the fabricated holes, which shows the depth differences of the three holes. Depths of holes increase from 5.3 nm to 11.0 nm, and widths increase from ∼27 nm to ∼33 nm, as the tip bias duration increases from 100 ms to 220 ms, as shown in Fig. 3(c). The results demonstrate the effect of bias hold time on the dimensions of holes.

Fig. 3
Fig. 3
Close modal

We conducted another experiment to investigate the effect of normal force applied by the AFM tip on the dimensions of features in the lithography process. As shown below in Fig. 4(a), the designed pattern includes two National Science Foundation (NSF) logos, in which the characters of NSF are inside an ellipse. We set the contact force of the NSF characters in the left circle to be 1 nN, which is a very small load force simply to ensure the contact between AFM tip and sample. To make a better comparison of different forces, we applied 8 nN to NSF characters in the right circle. The tip was applied with an 8 nN contact force in drawing the two circles.

Fig. 4
Fig. 4
Close modal

As shown in Fig. 4(b), height profiles of the left and right NSF logos show similar patterns but with different feature depths. The maximum depth of the left NSF characters fabricated with 1 nN force was about 2.5 nm, while it was about 8.0 nm for the right NSF characters fabricated with 8 nN force. Therefore, the contact force has a substantial influence on the size of the feature patterned by using electric-field-assisted contact mode AFM-based nanolithography. An increase in the contact force results in an increase in feature width. However, as the contact force between the tip and sample becomes larger, it leads to larger tip wear. The resulting tip apex dimension change and reduction of the conductive coating on the AFM tip might negatively affect the lithographic performance.

Figure 5 shows several nanopatterns that include snowflake shapes and Systems Science and Industrial Engineering characters. The two snowflake patterns are fabricated with 1 nN setpoint force and a tip bias of 17.50 and 26.25 V, respectively, which correspond to input voltages of 1.0 and 1.5 V, respectively. Patterns in Fig. 5(a) have a feature depth around 0.5–1 nm and a trench width around 16–30 nm. Feature depths for the nanopatterns in (b) and (c) are around 1–2 nm.

Fig. 5
Fig. 5
Close modal

Because the applied mechanical force in our E-AFM lithography is small, the observed debris along the side of fabricated features is assumed to be produced mainly by the effect of electrostatic force from a nonuniform electric field gradient on softened or melted polymer, which is on the outside of the sublimated polymer. The direction of the electrostatic force on the polarized softened or melted polymer is toward the tip end; therefore, raised debris on the trench side appears. Even so, the debris alongside the fabricated patterns is much less than that produced by other mechanical force-based AFM lithography techniques.

As it is an important parameter to evaluate the lithography performance, we also studied the effect of lithography speed on the patterning results. We designed four lines with 400 nm interval between each other. The patterns were fabricated with different lithography speeds (50, 10, 5, 0.5 μm/s from left to right, respectively), as shown in Fig. 6. Measurement shows the trench width of the four lines from left to right are 0, ∼25, ∼28, ∼32 nm, and the trench depths are 0, 1.35, 1.79, 2.95 nm, respectively. The results show that feature depth gradually increases as patterning speed decreases. As the results in Fig. 2 indicate that deeper trenches can be fabricated through the increase of tip bias voltage, we could potentially achieve higher nanopatterning speed by applying higher voltages to compensate the reduced feature depths of higher machining speed.

Fig. 6
Fig. 6
Close modal

To understand the effect of the electric field strength on the nanolithography results, we developed a simulation model in ansys electronics and performed some quantitative analysis on the electric-field-assisted contact mode AFM-based nanolithography, as shown in Fig. 7(a). The model is composed of a gold sphere with 35 nm radius, which is the size of the AFM tip end. The gold sphere is in contact with a 15-nm thick PMMA film, which is on the top of a 100-nm thick gold layer. To better study the distribution of electric field strength in the polymer layer, we inserted six lines (line 0, 1, 2, 3, 5, and 6) on the Y–Z plane inside the PMMA film, which has z values equal to 0, −3, −6, −9, and −12 nm, respectively. These lines evenly divided the polymer film into five 3 nm regions on the Y–Z plane. Line 6 was designed as a line on Z-axis in the PMMA film to show the electric-field changes in the z-direction. We set the simulation temperature as 22 °C, which is close to the actual temperature. Tip bias was defined by assigning a voltage excitation on the sphere, while the voltage applied to the gold layer was 0 V.

Fig. 7
Fig. 7
Close modal

Figure 7(b) shows the electric field distribution on the YZ plane in the PMMA film with an applied 20 V tip bias, where the maximum electric field strength is around $2×109$V/m, which is located at the tip-film interface right under the AFM tip. With the same applied tip bias, Fig. 7(c) shows the electric field strength distribution on lines 1–5 designed in Fig. 7(a). Each of them has a bell-shaped curve, the maximum electric field strength increases from $1×109$ V/m to $2.5×109$V/m as the line gets closer to the XY plane. Based on the simulation results, for the experiments that generate features with 16 nm width, the relative electric field strength is around $1.63×109 V/m$ (plotted Fig. 7(c) in dash lines). Figure 7(d) shows the electric field strength distribution on line 6 (along the Z-axis). As the distance from the tip-film interface increases, the electric field strength gradually decreases.

To explore the potential of fabricating sub-10 nm feature sizes, we changed two major factors in the simulation model that may affect the nanolithography resolution: tip radius and PMMA film thickness. Figure 8 shows the simulation results with the same tip bias of 20 V while changing the tip radius and PMMA film thickness. In Fig. 8(a), we show the electric field strength distributions on the tip-sample interface along the Y-axis for the cases of four different tip radii (20, 10, 5, and 3 nm), while the PMMA film thickness was 15 nm. According to our previous experimental and simulation results in Fig. 7(c), features with 16 nm width corresponds to the electric field strength of $1.63×109 V/m$. Using this value as the threshold to fabricate nanopatterns, the simulation results in Fig. 8(a) indicate that the feature width can be reduced to sub-10 nm (9.2 nm) if we use an AFM tip with 3 nm radius. A tip with 20 nm radius results in a feature width of 14.8 nm. Results show that feature width decreases along with the decrease of tip radius, which indicates a great potential to fabricate nanopatterns with sub-10 nm resolution if a sharp tip in the electric-field-assisted contact mode AFM-based nanolithography is used.

Fig. 8
Fig. 8
Close modal

Figure 8(b) shows electric field strength distributions along the Y-axis for the cases of different film thickness, which are 10, 15, 20, and 30 nm, while the tip radius is 35 nm and tip bias is 20 V. Results show the minimum feature width is 6 nm when the thick PMMA film thickness is 30 nm, and the feature width is 20.6 nm when the thin PMMA film thickness is 10 nm. Results indicate that finer features could be fabricated on thicker PMMA film if other factors remain the same. The reason is that the critical electric field strength crosses a short distance on the thicker film compared to that on the thinner film. However, the electric field strength shows a greater slop on the thin film, which could be beneficial to the edge sharpness of fabricated nanopatterns. The tip bias can be set at a lower level in experiments to reach the critical electric field strength if on thinner films. Therefore, thinner film thickness is preferred in nanolithography processes that aim to fabricate nanopatterns with sharper edges.

Comparing the effects of two factors, tip radius and film thickness, on the nanolithography resolution, reducing tip radius has greater potential to improve the nanolithography resolution and quality. A sharp increase in the electric field strength distribution using a tip with a small radius could greatly lower the needed tip bias and could potentially sharpen the edges of nanopatterns, which leads to high-resolution and high-quality nanopatterns.

## Conclusions

In summary, we demonstrated a novel method of fabricating high-resolution nanopatterns using contact mode electric-field-assisted AFM lithography, which fabricates fine features with little debris on a thin polymer film using very small contact force. The experiments were conducted with direct gentle tip-sample contact. Through the application of a different tip bias, contact force applied on the tip, and tip bias hold time, we fabricated high-resolution nanofeatures that included holes, trenches, and other nanopatterns with feature widths down to ∼16 nm. We studied the effects of several process parameters, which included tip bias, contact force, and bias hold time on the dimensions of nanopatterns to better control the lithography performance in the actual experiments. Moreover, we developed a numerical simulation model to analyze the tip bias-induced electric field strength distribution in the polymer film. The simulation results provided more quantitative insights into the process mechanism and the future research directions to enhance the resolution and quality of nanopatterns. The contact mode electric-field-assisted AFM-based nanopatterning process developed in this paper shows great potential in fabricating nanopatterns with sub-10 nm resolution, which can advance nanomanufacturing fields and nano-enabled scientific and industrial applications.

## Funding Data

• National Science Foundation (Grant No. CMMI-2006127; Funder ID: 10.13039/100000084).

• Small Scale Systems Integration and Packaging (S3IP) Center of Excellence, funded by the New York Empire State Development’s Division of Science, Technology, and Innovation.

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