Generating smooth potential landscapes with thermal scanning-probe lithography

Scanning probe microscopy (SPM) uses a sharp tip to interrogate surfaces with atomic precision. Inputs such as mechanical, electrical, or thermal energy can activate highly localized interactions, providing a powerful class of instruments for manipulating materials on small length scales. Thermal scanning-probe lithography (tSPL) is an advanced SPM variant that uses a silicon tip on a heated cantilever to locally sublimate polymer resist, acting as a high-resolution lithography tool and a scanning probe microscope simultaneously. The main advantage of tSPL is the ability to electrically control the temperature and applied force of the tip, which can produce smooth topographical surfaces that are unattainable with conventional nanofabrication techniques. Recent investigations have exploited these surfaces to generate potential landscapes for enhanced control of photons, electrons, excitons, and nanoparticles, demonstrating a broad range of experimental possibilities. This paper outlines the principles, procedures, and limitations of tSPL for generating smooth potentials and discusses the prospective impact in photonics, electronics, and nanomaterials science.


Introduction
Recording information on surfaces has been vital to human civilization for thousands of years.The hieroglyphs in ancient Egypt and the printing press in Europe represent significant milestones in surface patterning for their respective time periods, each having major societal impact [1,2].More recently, our digital society was built on computer chips containing tiny transistors by patterning semiconductor surfaces at nanometer length scales [3].This effort sparked a push for miniaturization, which reached the ultimate limit with the invention of the scanning tunneling microscope (STM) in 1982 at IBM Zurich [4,5] as a tool that could image individual atoms, an achievement that was awarded the Nobel Prize in 1986.The atomic force microscope (AFM) was introduced shortly after as a powerful generalization of STM that no longer required conductive samples [6], enhancing the versatility of scanning probe techniques.Together, the STM and AFM laid the foundation for a more general class of instruments-scanning probe microscopes (SPMs)-that scan a sharp tip over a surface to generate images with high (or even atomic) resolution through tip-sample interactions.Beyond imaging, the capabilities of SPM were expanded to a lithographic tool-scanning probe lithography (SPL)-that can add, remove, or modify small amounts of material.An example of the precision offered by scanning probes was demonstrated by using a STM to arrange individual atoms on a surface and measure electronic states with an astonishing level of control [7].The capabilities and applications of SPL have evolved over the past few decades, providing a toolbox of instruments for patterning materials on small length scales [8,9].
The success of SPM and SPL motivated researchers at IBM to explore the use of heated probes-thermal scanning-probe lithography (tSPL) [10]-to pattern and read small volumes of material as a means of high-density data storage, in an effort known as the Millipede Project [11].The technology did not become commercially viable as a data storage medium, however, it found a valuable application pivot to a high-resolution nanolithography tool [12][13][14][15], which is now sold as a commercial instrument under the Rendering of a tSPL cantilever and a smooth topographical landscape.tSPL is comprised of a cantilever (grey) and a sharp silicon tip (glowing orange), which can produce a smooth topographical landscape in polymer resist (blue).The cantilever is heated by passing current through the 'writer' junction (faint orange/red), resulting in a hot tip.For patterning, the tip is translated by piezo scanners and a voltage bias is applied between the cantilever and substrate to produce an attractive force that pulls the cantilever towards the surface at each pixel in the pattern.Thus, the temperature and applied downward force of the tip can be accurately controlled to produce a smooth topographical landscape.The cantilever also reads the surface topography while patterning, providing instant characterization and a feedback loop to generate precise surface profiles.Relative dimensions are approximately to scale, and the thermal glow is a simplified representation of temperature distribution.trade name NanoFrazor.In this paper, tSPL is discussed in the context of the commercial NanoFrazor implementation.tSPL uses a hot tip to simultaneously pattern and measure the topography of a polymer surface, providing a combined SPM-SPL tool, visualized in figure 1.The tip-based approach provides high-resolution structures that are comparable with feature sizes produced by standard nanofabrication techniques, such as electron beam lithography (EBL).Additionally, the unique advantage of tSPL is the ability to control the temperature and applied force of the tip, which can be used to produce smooth topographical surfaces that are unattainable with conventional nanofabrication techniques.Furthermore, these surfaces can be produced with nanometer precision in minutes under ambient conditions on a standard lab benchtop, enabling rapid prototyping at the nanoscale [13].
Recent investigations have shown that these smooth topographical surfaces (patterned in a polymer layer) can be transferred to a variety of materials to produce potential landscapes to manipulate photons [16][17][18][19], surface-plasmon polaritons [16], electrons [17], excitons [20], and nanoparticles [21].In this paper, 'potential landscape' is used as a general term to describe the influence of the surface topography on the band-structure, confinement, or trajectories of waves/particles such as photons, electrons, excitons, or nanoparticles.The benefit of this approach is the direct link between theory and experiment, where mathematically precise potentials offer previously unattainable possibilities [19][20][21][22].After a decade of research as a commercially available tool, the tSPL community is growing and exploring new ideas [13].This paper serves as a guide to researchers entering the field by establishing the procedures, possibilities, and limitations of tSPL for generating smooth potential landscapes, and discusses applications in photonics, electronics, and nanomaterials science.

Working principle and limitations
tSPL works by pressing a hot silicon tip with controlled downward force into a film of polymer resist.The applied thermal and mechanical energy locally sublimates a volume of the resist, producing an indent that resembles the shape of the tip [23].A single indent can be used as a pixel in a two-dimensional (2D) array in the x-y plane, where the depth of each pixel can be varied in z to map out a topographical surface with a range of height values.The shape of the tip sets limitations on the minimum feature size and maximum topographic slope for a patterned surface (figure 2).
At shallow depths (d < 100 nm) the tip can be simply approximated as having a conical shape with an opening half-angle between 15 and 30 degrees, and a tip width typically between 6 and 12 nm at the apex [23], where random differences can be expected between each tip due to fabrication variance.For depths greater than 100 nm, the width of the tip no longer varies linearly, where the exact profile can be seen in [24].A patterning event occurs when a volume of material is sublimated, where a fraction leaves as volatile compounds and another fraction re-deposits on the tip.The re-deposited material is generally referred to as tip contamination.This is one of the most severe limitations for tSPL as it increases the effective size and changes shape of the tip while the pattern is being generated, complicating the fabrication and measurement process.The shape of the tip can be described as a cone with a finite tip width at the apex, w 0 , and a width w that varies as a function of the indent depth d, given by: where θ is the opening half-angle of the tip, and ∆w is a term that captures broadening of the pattern relative to the tip shape.The broadening can be defined as the sum of two quantities, ∆w = w tm + w c , where w tm is the spatial extent of thermo-mechanical interactions in the resist, and w c is additional broadening from tip contamination during the patterning process (figure 2(a)).It should be noted that the realistic shape of a contaminated tip is typically more complex than the simple model described here.A detailed discussion of the tip and high-resolution patterning is presented in [23].
For some applications periodic structures are required [16][17][18], where the minimum periodicity can be described as two indents separated by their width, Λ min (d) = 2w (d), which is governed by the tip shape and pattern depth, plotted in figure 2(b).The plot is calculated for realistic experimental values of w 0 = 10 nm, θ = 22 • , w tm = 1 nm, and w c ranges from 0 to 20 nm during the patterning process.Periodicities above the lines are possible to pattern, where the top left inset illustrates a pair of resolved indents, and the bottom right inset shows a loss of resolution between the indents.
The width at the tip apex w 0 ≈ 10 nm sets the lower limit for the physical size of a pixel during the patterning process, where any smaller assigned pixel size will be broadened by the tip shape due to convolution.The resolution limit has important consequences for the smooth topographies that can be realized.For example, patterns on electronic length scales require Λ ≈ 10-50 nm, where the periodicity approaches the minimum feature size set by the tip (Λ min ⩾ 2w 0 ).The effect of the tip shape on the spatial frequencies that can be patterned is visualized in figure 2(c) by plotting the analytical function: where g = g (x) = g 0 + mx is the local spatial frequency of the pattern, g 0 = 2π Λ0 is the initial spatial frequency of a pattern with local wavelength Λ 0 , which changes as a function of x, where the rate of change is governed by the slope m.This function is chosen as a convenient way to generate a range of spatial frequencies, which can be used to analyze patterning limitations.The digitized version of this function is plotted in figures 2(d) and (e), where the function on the left (figure 2(d)) has a small slope relative to the tip, and the function on the right (figure 2(e)) has a relatively large slope.The tip geometry therefore sets the resolution limits and maximum surface slope for smooth topographic landscapes.

Fabrication process
The process begins with mathematical design, where analytical functions are typically used to define smooth topographical landscapes that will be patterned by tSPL (figure 3(a)).The analytical functions are then digitized into a greyscale image format, such as a bitmap, which can contain up to 8 bits (256 depth levels) of height information (figure 3(b)).The pixel size is dictated by the tip as described in section 2, where a value of 20 nm × 20 nm is typically used.There is some flexibility in the choice of pixel size, depending on the pattern, where a larger pixel size (up to ∼50 nm) can be used for deep patterns with lower resolution to decrease the patterning time.However if the pixel size is too large, the indents become too sparse and the patterns will no longer match the design.For high-resolution patterning, the pixel size can be decreased to below 10 nm.When the pixel size is set, the bitmap is then ready to be imported into the tSPL tool for patterning.
The second step is to choose the resist layer(s) that are best suited for the specific fabrication requirements of a given process.The choice of resist is important because it is directly patterned with the thermal probe to contain topographic information, which is then modified by further process steps such as etching or templating.The resist should therefore have the desired chemical, mechanical, and thermal properties for the specific process requirements.The resist should also wet the sample surface and form a uniform film during spin coating, a simple detail that is critical for precision patterning and processing.The two most common resists for greyscale tSPL patterning are poly (phthalaldehyde) (PPA) [15,18,21,23] and poly (methyl methacrylate-co-methacrylic acid) (PMMA/MA) [16,17].PPA is the 'gold standard' for tSPL because it decomposes efficiently and shows reduced tip contamination, minimizing errors and increasing patterning throughput and reliability [13].However, PPA is a specialized polymer that does not always interface well with other materials and process parameters.An alternative is to use a standard EBL resist, PMMA/MA, as a stable and reliable option besides PPA [16,17].The downside of PMMA/MA is that it contaminates the tip quicker and more severely than PPA, resulting in increased patterning difficulty and a shorter tip lifetime.Despite the limitations of each resist, they have both been used successfully for a broad range of materials and processes [13,[16][17][18].The chosen resist is then spin-coated on the sample surface, ideally generating a uniform film with a desired thickness (figure 3(c)).The sample is baked to remove residual solvent and form a solid resist film, where it is ready for patterning by tSPL [25].
The sample is then placed on the tSPL stage and aligned under a built-in optical microscope with a digital camera, such that the region of interest is visible in the corresponding software image.A cantilever is loaded into the cantilever holder, which is then magnetically attached to the scan unit such that the cantilever is sitting a few millimeters above the sample surface, where it is brought down to within ∼100 µm of the surface using a coarse approach.An automated fine approach is run by the software until the tip contacts the sample surface (approach), and then the cantilever is lifted away from the surface until the tip snaps out of contact (retract).An approach-retract curve can be generated, where the difference between the height value for the snap-in and snap-out of contact for the tip can be measured, known as the 'adhesion length' , providing information about the state of the tip and contamination.A fresh tip shows relatively little adhesion to the surface, while a tip with contamination has increased contact area between the tip and surface, increasing the adhesion and therefore the measured adhesion length.The adhesion length can be monitored throughout the process and provide information on when a change to a fresh tip is necessary.The system also checks electrical connectivity and calibrates the temperature response by passing current through the reader and writer 'arms' of the cantilever.The two 'arms' of the cantilever can be seen in figure 1, where the tip is on the 'writer' arm, and the other is the 'reader' arm, where both connect to the middle plane of the cantilever.Finally, the probe measures orthogonal line scans along the x-y plane to calibrate tilt in the sample plane.2b 2 cos (gx)] 2 describing the desired topographic landscape in the resist, where g is the spatial frequency for a surface with periodicity Λ given by g = 2π Λ , and b is a parameter that describes the width of the Gaussian envelope (b).Digitized mathematical function (c).Polymer resist is spin-coated onto the sample and baked to remove residual solvent and form a solid film.(d).The resist is patterned using tSPL (e).Top view of the patterning process, indicating the fast axis (along x) for writing and reading, and the slow axis (along y), along which the scan proceeds.The blue-to-black colour gradient represents the height of the surface along the z-axis (f).The measured surface profile (blue dots are simulated topography data) is compared with the desired profile (red line), providing instant characterization and a feedback loop (g).After patterning, the topographic landscape can be transferred to other materials through deposition, etching, or templating.
Next, the desired pattern is imported as an image file to the software.The pixel size, depth range, temperature, applied forces, feedback settings, and other parameters are all set to the desired values for the process [13].If necessary, the cantilever can first read the surface topography, where the pattern can then be laterally aligned to an existing feature on the surface, with alignment accuracy on the order of the pixel size.
Patterning (figure 3(d)) is started by passing a current through the 'write' arm to heat the cantilever to a constant temperature, typically ∼950 • C for PPA and ∼1100 • C for PMMA/MA.It is important to note that the set temperature corresponds to the temperature of the cantilever at the base of the tip, and the temperature at the tip apex is not exactly known, but it will be less than that of the cantilever [23].The hot tip is raster scanned over the patterning region at a constant speed.At each write pixel the tip is actuated to form an indent by applying a voltage bias between the cantilever and the substrate.The electrostatic potential attracts the cantilever, acting like a spring, towards the surface with a controlled downward force [15].Each pixel has a typical patterning time of 25 microseconds, allowing surfaces on the order of ∼100 µm 2 to be patterned in minutes.The surface is patterned pixel by pixel along x for each line.The scan proceeds along y until every line is patterned.The surface topography is measured during patterning by scanning the probe in contact mode along the retrace direction of a line, providing topography data similar to contact-mode AFM [26] (figure 3(e)).Reading the surface during patterning allows for a real-time comparison between the target and measured depth profile (figure 3(f)), providing instant topographic characterization.Furthermore, this comparison can be used to generate a feedback loop, providing real-time error compensation that generally results in a more accurate topographic landscape.
An important limitation for tSPL is the maximum size of a single write field, which is restricted by the ∼50 µm × 50 µm piezo scanner range.However, the read function of tSPL can be used to align additional write fields to an existing pattern, allowing large-area patterns to be created by stitching separate fields together.There is no upper limit on how large a pattern can be using this approach.However, tSPL is a serial writing technique, so the upper limit to the pattern area will be dictated by the time available for the pattern.Tip contamination will further complicate the patterning process eventually, imposing another practical limitation on the achievable area for a high-quality pattern.
The patterning process results in a smooth topographic landscape in polymer, which can be used to directly generate potential landscapes for some experiments [20,21].However, most applications require that the pattern is transferred to another material of interest, such as a metal, semiconductor, or dielectric.In general, this can be done in 3 ways (figure 3(g)): by adding material to the surface (deposition), by transferring the pattern into the substrate below (etching), or by making copies of the same pattern through  [18] (b).Plasmonic potential landscape on a silver surface [16], where the topography modulates the boundary h of the dielectric function across the metal-air interface (c).Electronic potential landscape for a graphene layer encapsulated in structured hBN [17].The topography modulates the electric potential V at the graphene layer, gated by a voltage bias between the gold and silicon layers.The top hBN and gold are cut for visualization.The horizontal axis for all insets represents space (line cut through the horizontal plane).multiple rounds of deposition and removal (templating/imprinting).These techniques have been used to generate smooth potential landscapes in various materials for several applications [13,[16][17][18].

Smooth potential landscapes
The diverse set of fabrication pathways available for tSPL can be used to generate potential landscapes, for example, in optics [16][17][18][19], integrated photonics [18], plasmonics [16], or electronics [17].Studies have also shown that smooth potential landscapes can be used to strain 2D materials [20,24], to sort nanoparticles [21], and to mimic biological surface textures [27].This section briefly outlines some possible experimental configurations that can be used to generate smooth potential landscapes.
The spatial resolution and topographic control of tSPL is ideally suited for making wavy diffractive surfaces with periodicities comparable to optical wavelengths, known as optical Fourier surfaces [16,22].In a photonic slab-waveguide system, such as the silicon-on-insulator (SOI) platform shown in figure 4(a), thickness variations lead to a modulation of the effective refractive index n eff of a waveguide mode.When the wavelength of the modulation is on the order of the wavelength of the guided photon, diffraction effects can be used to shape the electromagnetic field inside or outside the waveguide [18].Based on this general principle, optical materials can be sculpted to form diffractive structures such as grating couplers, photonic quasicrystals, and distributed-feedback cavities [18,22].These structures show potential for holography [28], gradient-index waveguide optics [29], beam shaping [30], nonlinear photonics [31], and more.
Plasmonic surfaces support bound electromagnetic fields at optical frequencies, providing nanoscale confinement and enhanced light-matter interactions [32].Wavy silver interfaces like the layer stack shown in figure 4(b) provide exact mathematical control over plasmonic band structure, generating fresh opportunities to manipulate flat bands [16], dark modes [33], and lasing modes in distributed-feedback cavities [34].Similar silver surfaces can be used to form high-efficiency diffraction gratings [16], providing a general route to precise optical diffraction in the near-and far-field.
2D electronics is a rapidly growing field that continues to produce surprising discoveries [35] and technological innovation [36].2D electron optics investigates the flow of electrons through potential landscapes in graphene layers, where the electric potential is analogous to refractive index, and thus optical principles can describe electrons in graphene [37][38][39].To manipulate the flow of electrons, artificial lattices have been used as electrostatic diffraction gratings to influence band structure [40][41][42][43], which may benefit from tSPL.However, one major difficulty is to scale patterns down to electronic length scales [17], where moiré periodicities on the order of ∼10 nm are commonly desired.Nevertheless, lithographically defined lattices on the order of ∼30-50 nm have shown the ability to manipulate electronic bandstructure [40][41][42][43], which are possible to fabricate with tSPL [17].One of the experimental configurations in literature [17,[40][41][42][43] could be used to generate electronic Fourier surfaces [17,22] (figure 4(c)), which may provide opportunities for tailoring electron flow through artificial lattices in 2D materials.

Outlook
After a decade of research as a commercially available tool, tSPL has enabled several unique experiments for a broad range of applications.The number of tSPL researchers is growing and new ideas are being identified and explored at an increasing rate.Further advances will face challenges with upscaling and reliability, however, tSPL remains a powerful scientific instrument that allows smooth topographical surfaces on the nanoscale to be fabricated quickly and accurately for research purposes.Further progress will require tSPL to be integrated with established fabrication processes, as required by each application.Upscaling tSPL patterns to large areas will require reduced tip contamination, reliable automated stitching procedures, and likely a replication process based on templating [16] and/or imprinting [24].For control of electron systems at the quantum level, smaller periodicities would allow artificial lattices to be introduced at twisted-moiré length scales, providing a route to enhanced control over electronic band structure.In addition to standard polymer resists, tSPL may provide opportunities to pattern topographical landscapes in a variety of thermally decomposable materials on the nanoscale.Beyond the applications mentioned here, tSPL may provide unforeseen possibilities for a broad range of investigations.

Figure 1 .
Figure 1.Rendering of a tSPL cantilever and a smooth topographical landscape.tSPL is comprised of a cantilever (grey) and a sharp silicon tip (glowing orange), which can produce a smooth topographical landscape in polymer resist (blue).The cantilever is heated by passing current through the 'writer' junction (faint orange/red), resulting in a hot tip.For patterning, the tip is translated by piezo scanners and a voltage bias is applied between the cantilever and substrate to produce an attractive force that pulls the cantilever towards the surface at each pixel in the pattern.Thus, the temperature and applied downward force of the tip can be accurately controlled to produce a smooth topographical landscape.The cantilever also reads the surface topography while patterning, providing instant characterization and a feedback loop to generate precise surface profiles.Relative dimensions are approximately to scale, and the thermal glow is a simplified representation of temperature distribution.

Figure 2 .
Figure 2. Principles and limitations for patterning smooth topographical landscapes (a).Indent width w as a function of depth d in the resist formed by a tip with apex width w 0 and opening half-angle θ, broadened by ∆w (b).Minimum periodicity Λ min between two or more indents as a function of pattern depth d, plotted for increasing tip contamination wc from 0 to 20 nm.Points below the line are not possible to pattern, while points above the line are possible.The top-left inset shows resolved indents, the bottom-right inset shows a loss of resolution between two indents.(c).Analytical function representing a sine wave with a range of spatial frequencies, described by f (x) = cos (gx), where g = g (x) = g 0 + mx (d).Digitized portion of the function (dashed green box in c) where the slope is small relative to the tip slope and therefore possible to pattern.(e).Digitized portion of the function (dashed red box in c) where the slope is large relative to the tip slope and not possible to pattern.

Figure 4 .
Figure 4. Examples of smooth potential landscapes (a).Photonic potential landscape in a SOI waveguide, where the topography modulates the effective refractive index n eff[18] (b).Plasmonic potential landscape on a silver surface[16], where the topography modulates the boundary h of the dielectric function across the metal-air interface (c).Electronic potential landscape for a graphene layer encapsulated in structured hBN[17].The topography modulates the electric potential V at the graphene layer, gated by a voltage bias between the gold and silicon layers.The top hBN and gold are cut for visualization.The horizontal axis for all insets represents space (line cut through the horizontal plane).