1 Introduction

In the last decades, two-photon absorption (2PA) has become a very promising tool for three-dimensional micro- and nanofabrication [2]. In this fabrication technique, a tightly focused ultrashort pulsed laser beam is used to induce energetic transitions in a photosensitive material [7]. Due to the high spatial and temporal focusing, the needed energy \(\varDelta E\) for the transition can be provided by the simultaneous absorption of two photons with the energy \(\frac {\varDelta E}{2}\) instead of one photon with the energy \(\varDelta E\). In contrast to one-photon absorption, which follows the Beer–Lambert law, the 2PA processes only takes place in the focal region [7]. Hence, by a relative movement between the focal spot and the photosensitive material, a three-dimensional structure can be created [2, 4]. Several artistical, medical, and optical applications were demonstrated in the last years [8,9,10]. The lithographic resolution is given with around 100 nm for line with constant width [11], even though certain suspended lines with thinnest parts down to 25 nm could be achieved [3]. Super-resolution techniques like stimulated emission depletion STED-DLW or SLM-assisted DLW (SLM, spatial light modulator) decrease the dimension of constantly written lines to 55 nm [12]. Due to the behavior of light, some groups predict the validation of a modified diffraction limit, even though the writing is a serial process [13]. The reason is motivated in a threshold behavior in combination with a memory of the photoresist, which sums up the induced illumination doses below the threshold [13]. In consequence, the fabrication of structures and trenches between these structures could only be realized by super-resolution DLW techniques [13].

Besides the lithographic resolution, the positioning resolution and the repeatability are limiting factors in processing precise structures [4]. The positioning resolution depends on the scanning mode and therewith on the applied positioning systems [14]. The most precise positioning systems that are used for STED-DLW offer repeatabilities of around 10 nm [15]. Nevertheless, if extended areas should be addressed with the positioning systems, the drawbacks in precision must be taken into account. One of the large area fabrication systems addresses a positioning volume of \(150\,\hbox {mm} \times 150\,\hbox {mm} \times 4\,\hbox {mm}\) with a resolution of 0.5 nm per direction, but the repeatability is given with 75 nm for the linear stages in x- and y- direction and 200 nm in z-direction [14]. Accordingly, the precision of the positioning systems is in the same range or even worse than the lithographic resolution of the DLW technique. To improve the precision of two-photon processes by means of positioning, nanopositioning and nanomeasuring machines are very promising.

2 Experimental Setup

The experimental setup for two-photon DLW with the use of the nanopositioning and nanomeasuring machine NMM-1 is depicted in Fig. 1. The main part for the 2PA-processes in the photosensitive material is a Ti:sapphire oscillator (Spectra Physics) with a central wavelength of 801 nm, a repetition rate of 85 MHz, and a pulse duration of approximately 43 fs. The beam passes a half waveplate and a polarizing beam splitter cube, which enables adjusting the polarization on the one hand and attenuating the power of the laser beam on the other hand. Subsequently, an acousto-optical modulator (Pegasus Optik GmbH) is used to shutter the laser beam by guiding the first diffraction order of the beam to mirrors. Finally, the beam enters the objective and is focused onto the sample stage of the NMM-1.

Fig. 1
figure 1

Setup for two-photon DLW with the nanopositioning and nanomeasuring machine

Full size image

The distance between the focal spot and the sample with the photosensitive material is measured and controlled by a laser focus sensor that was developed for the use with nanopositioning and nanomeasuring machines [16]. This laser focus sensor works contact free with a wavelength of 650 nm to avoid an influence on the photosensitive material, which is typically designed for shorter wavelengths in the range of 400 nm or less. Due to the sensor’s optical properties, the numerical aperture for the used objective is determined, which leads to a reduced \(N\!A\) for the used femtosecond laser beam of only 0.16. The sensor’s measuring velocity goes up to 6 mm/s with a reproducibility of 2 nm [16]. Such a high precision is achieved by a consequent compliance of the Abbe Comparator Principle, which is not only implemented for the laser focus sensor but also for the movement of the sample stage.

2.1 Principle of Nanopositioning

For the precise positioning, a resolution of 0.1 nm and a repeatability of less than 1 nm [17], over a large measuring volume of \(25\,\hbox {mm} \times 25\,\hbox {mm} \times 5\,\hbox {mm}\) [5, 6] are the center pieces of the hole setup. The basic measurement approach is, like mentioned above, the Abbe Comparator Principle, which says that the measuring apparatus is to be arranged in such a way that the distance to be measured is a straight-line extension of the graduation used as a scale [18]. To realize this highest precision, it is necessary to apply the Abbe Comparator Principle in all three coordinate axes. The Abbe error in three dimensions can be described as

$$\begin{aligned} \varDelta l_{i} = l_{\text {off},i} \cdot \sin (\alpha _{i}) \quad i \in x,y,z \end{aligned}$$
(1)

and is minimized in the measuring setup.

Mostly for nanopositioning, piezoelectrical devices are used. Even if the positioning with these piezoelectrical devices is comparably precise, they can just address a small range. In order to achieve larger positioning ranges, so-called stitching methods must be used. A different actuation was chosen for the NMM-1. For the realization of the positioning, voice coils in combination with anti-friction bearings are integrated [19].

The NMM-1 combines a complex interferometric length and angle measurement, with a three-dimensional platform positioning. For the supply and measurement acquisition, as well as the measurement evaluation of the various components, four different units are integrated: the laser unit with frequency stabilized laser, the interferometer unit for the acquisition and evaluation of the input signals from the interferometers, the digital signal processor (DSP) for all processed laser signals as well as the environmental signals and the calculated position signals, and the motor unit to generate the input signals for the voice coils.

The central module of the measured value acquisition and processing is the DSP. It is responsible for the measuring sequence control, the position and angle control, as well as for the manipulated variables control. For the positioning of the sample table, the enormous amounts of measurement and positioning data must be recorded and processed in real time. For this purpose, the measurement data acquisition is at 6.25 kHz. The movement of the sample stage occurs in a closed-loop controlled manner [16]. In order to achieve a high resolution despite the real-time capability of the system by using high-precision fiber coupled planar interferometers for the measurement system [20, 21], a combination with 13-bit AD converters has been used [22].

3 Theory of Diffraction Limit for 2PA

Regarding a limit for the resolution of resist lines and trenches fabricated by means of DLW, Fischer et al. [13] predict a modified Abbe Criterion as diffraction limit for 2PA. As for 2PA, the squared Gaussian intensity profile has to be taken into account, the Abbe criterion is extended by the narrowing factor \(\sqrt{2}\) compared to the regular Gaussian intensity. A DLW process for two or more lines is hardly comparable with the diffraction produced by a grid, but more like a two adjacent objects, the Rayleigh criterion seems to be more convenient to describe the process. The modified 2PA-Rayleigh diffraction limit is then given by

$$\begin{aligned} d = 0.61 \cdot \frac{\lambda }{\sqrt{2}\cdot N\!A} \, \end{aligned}$$
(2)

whereas d is the minimum distance between the two objects, which means in this case the center-to-center distance between the illuminated lines, \(\lambda \) is the wavelength and \(N\!A\) is the numerical aperture. Their motivation is a threshold behavior of photoresist during the illumination process so that a certain amount of illumination dose is needed to start a reaction [23]. This threshold behavior defines the line width for a given illumination time, laser power, and focal spot size (see Fig. 2). When the dose is below this threshold, the amount of energy is stored in the photoresist and subsequent illumination processes add on this amount of energy. Fischer et al. [13] call this effect the resist memory. For the given setup, the 2PA Rayleigh diffraction limit is determined by \(d = 2.16\,\upmu \hbox {m}\).

Fig. 2
figure 2

Normalized absorption profile for one-photon absorption (solid line) and the squared intensity profile for two-photon absorption (dashed line) for a Gaussian beam with an arbitrary focal spot size in lateral dimension. The threshold for a reaction in the photoresist is exemplarily given by 0.4 of the total amount of laser power (dash-dotted line), which leads to a line width indicated by the dotted lines and the gray rectangle

Full size image

4 Fabrication of Small Resist Lines

To prove the 2PA diffraction limit, samples were prepared as followed: a \(130\,\upmu \hbox {m}\) thin borosilicate glass was treated with hexamethyldisilazane for adhesion promotion and then spin-coated with AZ1505 (MicroChemicals GmbH, Ulm, Germany). A prebake for 1 min at \(115\,^{\circ }\hbox {C}\) was applied. In first experiments, the center-to-center distance between illuminated lines was systematically reduced from \(10\,\upmu \hbox {m}\) to \(1\,\upmu \hbox {m}\) in steps of \(1\,\upmu \hbox {m}\). The diameter of the femtosecond laser spot at the sample surface was measured to be \(4.6\,\upmu \hbox {m}\). The illumination dose was chosen in the way that the achieved trenches in the positive resist after development have a width of \(1.655\,\upmu \hbox {m}\) to assure less line edge roughness. Assuming that the diffraction limit is valid for the process, the trenches that occur in positive resist AZ1505 at the illuminated lines should be separated by resist lines for bigger distances between the illuminated regions. For trenches resulting from illuminated lines with a distance of \(2\,\upmu \hbox {m}\) and less, the diffraction limit predicts that no separation could be observed and the trenches should overlap resulting in one big trench in the resist without separation of a resist line.

Fig. 3
figure 3

a Trenches written in AZ1505 with a nominal distance between illuminated lines that was systematically reduced from 10 \(\upmu \hbox {m}\) to \(1\,\upmu \hbox {m}\) in steps of \(1\,\upmu \hbox {m}\). The resist lines between the trenches decrease down to \(385\,\hbox {nm}\) for a center-to-center distance of \(2\,\upmu \hbox {m}\). For a nominal distance between the illuminated lines of \(2\,\upmu \hbox {m}\), just one broad trench is visible. b Detailed view of the resist lines for nominal distances of \(3\,\upmu \hbox {m}\) and \(2\,\upmu \hbox {m}\) with resulting resist lines of \(1.376\,\upmu \hbox {m}\) and \(385\,\hbox {nm}\)

Full size image
Fig. 4
figure 4

a Written trenches with nominal distances from \(1.72\,\upmu \hbox {m}\) to \(1.69\,\upmu \hbox {m}\) decreasing 5 nm per illuminated line. The resulting resist lines are shown in detail in b with a 38-nm resist line for a center-to-center distance of \(1.695\,\upmu \hbox {m}\) and c with a 30-nm resist line for a center-to-center distance of \(1.690\,\upmu \hbox {m}\)

Full size image

In Fig. 3, the achieved trenches and resist lines are shown. The combination of two-photon DLW with the NMM-1 offers best conditions for a precise positioning and therefore for further very exact investigation regarding the smallest possible distances between the illuminated lines. The nominal distance between the illuminated lines, which means the distance between the coordinates of the trajectories for the lines, was decreased successively.

In the used setup, the very precise positioning of the NMM-1 allows to reduce the center-to-center distance in much finer steps. For further investigations on possible limits regarding the distance between illuminated lines, a step size of 5 nm was chosen. The results can be seen in Fig. 4 that shows resist lines between the trenches that are further decreased. The tiniest resist line that could be achieved without any discontinuities was realized with a width of 38 nm for a nominal distance of \(1.695\,\upmu \hbox {m}\). Even a 30-nm resist line was found, but it exhibits some discontinuities.

5 Discussion

Obviously, the experimental results show that achieved trenches and resist lines and thereby the associated nominal distances are below the predicted diffraction limit for two-photon processes. If the resist has a memory for illuminations below the threshold, the absorption profiles corresponding to Fig. 2 would sum up according to the superposition principle for the illumination of two adjacent lines. In Fig. 5, the normalized two-photon absorption profiles for the DLW process with maintained Rayleigh distance are shown. The normalization of the profiles facilitates the comparison to the theory and focuses on the essential information. The superposed absorption profile resulting from both individual illuminations is calculated and the absorption threshold for the process is derived from the achieved width of the illuminated trenches. In this case, the superposition absorption profile exhibits a dip, but in the range between the illuminated regions it is completely above the reaction threshold. In consequence, following the theory of resist memory, this would illuminate the resist in the blue, red, and gray area with enough energy for the absorption process remaining in one broad trench in the resist.

Fig. 5
figure 5

Normalized absorption profiles for two illuminated lines for two-photon DLW (blue and red line) that are written with the theoretical Rayleigh distance of \(2.16\,\upmu \hbox {m}\). The width of \(1.655\,\upmu \hbox {m}\) for each of the resulting trenches is indicated by the blue and red dotted lines and rectangles. The threshold (dotted line) is determined by the measured width of the experimentally achieved trenches of \(1.655\,\upmu \hbox {m}\). The superposition of both absorption profiles is shown by the dash-dotted line and the theoretically achieved trench is indicated by the overlaying gray rectangle

Full size image

For a distance of around \(2.55\,\upmu \hbox {m}\) between the center of the illuminated lines, the simulations show separated resulting trenches due to a superposition profile that falls below the threshold in a small region (see Fig. 6). The simulation also shows that in this case the width of the resulting trenches (indicated by the red and blue rectangle) in the resist would be broadened (indicated by the gray rectangles) compared to lines that are written with a bigger distance to each other. Such a broadening in the linewidth was not obtained in the experimental part of this work (see Figs. 3 and 4). At this point, it is obvious that the theory of the remembering resist should be reviewed. In Fig. 7, the normalized two-photon absorption profiles for the experimentally shown illumination with a resulting resist line of 38 nm (according to Fig. 4) are shown. As in Fig. 5, again the whole range from the left edge of the blue indicated illumination line up to the right edge of the red indicated illumination line is induced by energy above the threshold if the superposition is assumed. However, as shown experimentally, even though the illuminated lines are quite close to each other, two well-defined trenches with a separation resist line with a width of 38 nm appear after development of the sample. The distance at threshold level between the indicated trenches in the simulation is 41 nm, which is considerably conforming with the experimental results. With these results, we could show that a conventional 2PA-DLW process is able to create trenches and resist lines beyond the diffraction limit. Up to now, the diffraction limit was only broken by STED-DLW [13, 24].

Fig. 6
figure 6

Normalized absorption profiles for two illuminated lines for two-photon DLW (blue and red line) that are written with a distance of \(2.16\,\upmu \hbox {m}\). The dotted lines and the red and blue rectangles show the width of the resulting trenches of \(1.655\,\upmu \hbox {m}\). The gray rectangles indicate the broadening of the lines by assuming an illumination according to the superposition (dash-dotted line) and the threshold (dotted line)

Full size image
Fig. 7
figure 7

Normalized absorption profiles for two illuminated lines for two-photon DLW (blue and red line) that are written with a distance of \(1.695\,\upmu \hbox {m}\) as shown in 4b. The dotted lines and the red and blue rectangles show the width of the resulting trenches of \(1.655\,\upmu \hbox {m}\). The superposition of both profiles is shown by the dash-dotted line and the threshold by the dotted line. The distance between the red and the blue dotted line in the simulation is \(41\,\upmu \hbox {m}\)

Full size image

6 Conclusions and Outlook

In conclusion, it was experimentally shown that by means of two-photon laser direct writing structures beyond the diffraction limit were realized. With the current setup, we should have a diffraction limit of \(2.16\,\upmu \hbox {m}\). Nevertheless, it was possible to write two adjacent illuminated lines with a distance of \(1.695\,\upmu \hbox {m}\), resulting in resist lines between the written trenches down to 30 nm. This also leads to the result that the theory of the remembering resist should be reviewed. Theoretically, the smallest possible center-to-center distance should be given by the least dip in the superposition absorption profile according to Sparrow criteria [13], which should be investigated in future experiments. In this work, the illuminated regions and therefore the width of the resulting trenches in the positive resist, are comparably big caused by the low effective numerical aperture. A setup with an integrated beam expander promises line widths in the regime of the state of the art. As it can be seen in Fig. 4, discontinuities in the resist lines arised for smaller distances between the illuminated lines. To prevent the influences of fluctuating laser power on the width of the trenches and therefore the discontinuities, a new controlling concept should be investigated for the setup. Additionally, with a controlled laser power, the threshold for the illumination processes (see Fig. 2) can be adjusted finer, so that very small trenches would be possible by only using the peak of the absorption profile.

To push the linewidth to its minimum, the absorption profile has to be shaped by adjustments of the laser power and illumination time in order that the peak is slightly over the threshold. Shaping the absorption profile can be theoretically equalized with adjusting the threshold height. Therewith the lateral dimension of the reactive area on the resist is thinner (see Fig. 8). However, going closer to the threshold has the drawback that the writing process gets more sensitive to laser fluctuations [13]. Further, in the given setup, there are relative uncertainties of the laser power of around \({\pm }7\%\) in dependence of the applied voltage at the acousto-optical modulator. Thus, for writing at the threshold, some trenches would occurs due to enough illumination dose, others are illuminated below the threshold. To counteract this, the development of a control concept for the laser power is the next necessary step. At last, the design of more complex structures with DLW should be enabled by a controlled laser power, depending on the writing velocity.

Fig. 8
figure 8

Normalized absorption profiles by adjusting the threshold (dash-dotted lines) to a higher percentage, the resulting linewidth (gray rectangle and red rectangle, respectively) for the two-photon absorption profile (dashed line) can be reduced

Full size image