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Keywords:

  • Direct laser writing;
  • optical lithography;
  • superresolution;
  • stimulated emission;
  • photoresist

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

Direct laser writing has become a versatile and routine tool for the mask-free fabrication of polymer structures with lateral linewidths down to less than 100 nm. In contrast to its planar counterpart, electron-beam lithography, direct laser writing also allows for the making of three-dimensional structures. However, its spatial resolution has been restricted by diffraction. Clearly, linewidths and resolutions on the scale of few tens of nanometers and below are highly desirable for various applications in nanotechnology. In visible-light far-field fluorescence microscopy, the concept of stimulated emission depletion (STED) introduced in 1994 has led to spectacular record resolutions down to 5.6 nm in 2009. This review addresses approaches aiming at translating this success in optical microscopy to optical lithography. After explaining basic principles and limitations, possible depletion mechanisms and recent lithography experiments by various groups are summarized. Today, Abbe's diffraction barrier as well as the generalized two-photon Sparrow criterion have been broken in far-field optical lithography. For further future progress in resolution, the development of novel tailored photoresists in combination with attractive laser sources is of utmost importance.

1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

A dream of nanoscience is to shape matter from the atomic scale to the macroscopic – in three dimensions. While bottom-up self-assembly approaches have long been expected to eventually take over top-down lithography, the latter remains dominant in many important areas such as computer-chip or photonic-circuitry fabrication. Abbe's famous resolution formula states that the achievable resolution in far-field optical lithography as well as in microscopy is proportional to the wavelength of the (light) waves used. This has led to ultraviolet (UV), deep UV (DUV) or even extreme UV (EUV) planar optical lithography that are used in today's and tomorrow's computer-chip fabrication lines, respectively. The corresponding mask masters are fabricated using electron-beam lithography, which takes advantage of the yet smaller de Broglie wavelength of accelerated electrons. In principle, optical near-field effects can overcome Abbe's barrier in lithography [1]. While interesting demonstrations have been published indeed, such approaches do have fundamental limitations in that the near-field-writing head inherently needs to be in close proximity to the photoresist to be exposed. Moreover, these approaches are intrinsically limited to the surface, i. e., to planar lithography.

The beauty of far-field optics is that it also allows for three-dimensional (3D) lithography, often referred to as 3D direct laser writing (DLW) [2], [3], [4], [5], [6], [8], [9], [10], [7]. In 3D DLW, a (pulsed) laser is tightly focused to a diffraction-limited spot within the volume of a thick-film photoresist. By exploiting two-photon absorption and/or other nonlinearities (e. g., brought about by the photoresist itself), the effectively exposed volume can be restricted to the focal region leading to a volume element, the “voxel”, in analogy to the picture element commonly referred to as pixel. It is important to note that the existence of nonlinearity (precisely, a super-linear behavior) is crucial: Suppose that the photoresist reacted purely linearly and we raster scanned a plane parallel to the substrate deep within the thick-film photoresist. Clearly, the photoresist absorption would have to be very small in order to avoid unwanted intensity gradients into the depth. Thus, every volume element in the bulk photoresist would “see” the same number of photons passing through (independent of the z-position), hence a block of exposed photoresist would result while only a plane was desired. The nonlinearity concentrates the effective dose to the focal volume, especially in the axial direction. Accordingly, nonlinearity is not just a benefit, it is essential in 3D DLW [11].

Such regular 3D DLW is readily commercially available and lateral linewidths down to below 100 nm can routinely be achieved in 3D. However, despite considerable efforts over many years worldwide, no resolution on that scale in the spirit of Abbe has been achieved. In the following section, we will recall Abbe's considerations and point out the crucial difference between linewidth and resolution for parallel as well as serial lithography exposure schemes.

2 Abbe's diffraction limit: linewidth ≠ resolution

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

In the derivation of his famous formula, Ernst Abbe considered a grating with period inline image in the inline image-plane inspected by a microscope lens with finite aperture. The optical axis is along z, a plane wave impinging along this direction serves for illumination. He argued that at least the zeroth and both first diffraction orders of the grating need to be collected by the lens’ aperture in order to retain the information on the grating period. By using the usual Fraunhofer diffraction formula of a grating, it is straightforward to arrive at the Abbe condition

  • display math(1)

where λ is the vacuum wavelength of light, n the refractive index of the material in which the grating and the lens are embedded, α is the half-opening angle of the microscope-lens aperture, and NA the numerical aperture. If we now think of a parallel “single-shot” exposure of a photoresist (see Fig. 1), the resolution criterion stays the same: By reciprocity, i. e., by considering light waves impinging along the direction of the diffraction orders, an intensity grating of the same critical period is formed and can be used to expose a photoresist film. Determining the exposure dose is generally difficult. For the moment, we assume that the local exposure dose is simply proportional to the density of molecules excited by light absorption. For linear (i. e., one-photon) absorption, the exposure dose is thus simply proportional to the light intensity and the exposure time.

image

Figure 1. Diffraction-limited intensity grating (red) applicable to parallel exposures of photoresist films. The squared intensity (purple) is relevant for a parallel two-photon exposure. For a fixed exposure time, the threshold dose translates into a threshold intensity, which determines the width of the exposed lines. The incident vacuum wavelength is 800 nm and the numerical aperture NA = 1.4.

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Would nonlinearity help to improve the resolution defined along these lines? It would not. Suppose we exploit two-photon absorption. Our above reasoning does not change at all, however, the exposure-dose pattern with grating period inline image changes its shape (see Fig. 1). For linear absorption and a fixed exposure time, the inline image intensity pattern results in a corresponding dose pattern. The two-photon absorption probability is proportional to the square of the intensity, thus it follows a inline image pattern. The additional square reduces the width, the “linewidth”, of the grating lines by a factor of roughly 1.4. The maxima of the two-photon exposure dose have a full width at half maximum (FWHM) given by

  • display math(2)

For example, for NA = 1.4, the FWHM is nearly eight times smaller than the free-space wavelength. For yet higher-order processes, the FWHM of the exposure profile would be yet smaller.

So far, we have not addressed the photoresist. The properties of the chemical product (e. g., the cross-linking density) can depend super-linearly on the exposure dose, which, as discussed above, may also depend super-linearly on the intensity of light. While the photochemical processes may be very complex in detail, one can often describe this chemical nonlinearity in the context of a simple digital threshold model. Herein, the photoresist only withstands the development process provided the exposure dose has locally exceeded a certain threshold dose. Reducing the exposure dose towards the threshold dose by decreasing either exposure intensity or exposure time leads to smaller linewidths. In this fashion, arbitrarily small linewidths could be achieved – in principle. However, the grating period, i. e., the resolution, is still limited by the above Abbe condition.

This reasoning has shown that linewidth and resolution are generally not the same. In fact, for the above parallel exposure, the resolution is fundamentally limited by the Abbe criterion, whereas the linewidth is not limited at all. Thus, we have to carefully distinguish between the two notions of linewidth and resolution. To make a claim of resolution, a grating with a certain period has to be demonstrated. Alternatively, we could relax this a bit and ask that at least two lines or features separated by that distance need to be shown (see next section). Claiming a certain linewidth on the other hand can be based on an isolated line or, more generally, on an isolated object.

When aiming at 3D structures, we also have to carefully distinguish between lateral resolution (inline image) and axial resolution (inline image). Abbe's original formula makes no statement on the axial resolution. We can, however, extend Abbe's reasoning in a straightforward fashion by considering four (or more) laser beams with different wave vectors inline image impinging through the microscope objective lens aperture, forming a 3D interference pattern [12], [13]. The minimum axial period is determined by the accessible bandwidth of axial wave-vector components, inline image. The maximum inline image is determined by a beam propagating along the optical axis, the minimum inline image by a beam impinging under the maximum angle compatible with the NA. This leads to a minimum axial period given by

  • display math(3)

The ultimate mathematical limit is obviously reached for inline image which is equivalent to inline image. This axial Abbe limit is only two times larger (i. e., worse) than the lateral Abbe limit. However, for realistic numerical apertures, the axial resolution further deteriorates with respect to the lateral one. For example, for inline image and NA = 1.4 (parameters close to the experiments in the following sections), we obtain inline image. This value is 2.92 times larger than the lateral Abbe limit under the same conditions, i. e., inline image. Another example is inline image and NA = 1.0, for which we obtain inline image. This value is 5.26 times larger than the lateral Abbe limit under the same conditions, i. e., inline image. These examples emphasize that obtaining good axial resolution is even more of a challenge than obtaining good lateral resolution in 3D optical lithography.

As argued above for the lateral Abbe limit, by using a threshold process, the axial linewidth or the axial feature sizes are not fundamentally limited by diffraction at all. This means that a reliable measurement of the axial resolution must likewise study a structure that is periodic along the axial direction or at least study two axially adjacent lines or features (see next section). Measuring just linewidths or axial feature sizes is not sufficient.

In contrast to this thought experiment of parallel interference exposure, DLW is a serial process. In a serial process, nonlinearities can be fully exploited. Let us first assume that doses of sequential exposures simply accumulate linearly (which is a conservative assumption). In this case, the reduced width of a single exposure (e. g., a line) can indeed translate to enhanced resolution. The use of two-photon absorption in a serial scheme therefore improves the resolution by roughly a factor of inline image, as we will argue in Sect. 'The generalized Sparrow criterion in 3D'. Due to the resist's threshold behavior, one might further be tempted to assume that the photoresist “forgets” any below-threshold contributions of a first line's exposure, e. g., due to diffusion exchange.1 In this case, a second line could indeed be located within one linewidth (center-to-center) next to the first line. The gap between the two lines could even be smaller. In fact, nothing would fundamentally limit this gap. Hence, resolution (i. e., minimum period) and linewidth would essentially be the same.

The experiments to be discussed in Sect. 'Review of lithography experiments' are indeed consistent with the resolution improvement by two-photon absorption. We will also see, however, that the reasoning regarding the threshold and the “forgetting photoresist” is highly oversimplified: First, a perfect threshold could allow for arbitrarily small linewidths. In reality, the smallest accessible linewidths are roughly 40% of the two-photon exposure's FWHM. Second, an ideal “forgetting” photoresist would allow for arbitrarily small gaps (i. e., linewidth would equal resolution). However, photoresist‘s usually seem to “remember” a lot. In other words, our above definition of the exposure dose, i. e., the assumption of a linear accumulation of sequential exposures, is often meaningful indeed.

3 The generalized Sparrow criterion in 3D

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

As in optical microscopy, one can arrive at similar definitions of “resolution” in optical lithography by reasonings different from those of Abbe. In fluorescence microscopy, the Abbe criterion nearly coincides with the Sparrow criterion. Sparrow originally investigated the diffraction-limited resolving power of spectroscopes. He found that a spectral line pair (broadened by diffraction) is still resolvable as long as there is a local minimum in the middle of the signal [14]. This condition can easily be translated to fluorescence microscopy. Here, two slightly separated point emitters appear broadened by the microscope's point-spread function. In order to be resolvable, the sum of the shifted point-spread functions must still have a local minimum. This criterion is also relevant to serial lithography schemes like DLW, when we assume that the entire doses of sequential exposures just accumulate, i. e., the photoresist remembers everything. The required local minimum in the sum of two shifted point exposures is then crucial for the separation of the points, even for a perfectly sharp threshold. Translating this criterion to sequential two-photon exposures is achieved by replacing the intensity profiles by their squares. To evaluate the resolution in this sense, one needs detailed knowledge of the laser focus. Here, we complement the above simple analytic considerations by complete numerical calculations of the laser focus using a vector Debye approach following [15]. We chose parameters corresponding to typical experiments, in particular to an exposure wavelength of 800 nm. The scalability of the Maxwell equations allows for translating these results to other exposure wavelengths. The numerical aperture is NA = 1.4, the incident laser light is circularly polarized. The objective lens is illuminated homogeneously, corresponding to a beam diameter that is significantly larger than the pupil diameter.

The resulting distributions of the squared modulus of the (complex) electric-field vector, inline image, and the square of that, inline image, are depicted in Fig. 2.

image

Figure 2. Calculated focal intensity distribution of a typical writing spot. (a) Iso-intensity surfaces. The profiles along the two black lines are depicted in b) and c). (b) Lateral profiles of inline image (red) and inline image (purple) correspond to one-photon exposure and two-photon exposure, respectively. (c) Axial profiles of inline image (red) and inline image (purple). The horizontal lines in b) and c) correspond to the iso-intensity values of the surfaces in a).

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Note that the former quantity is generally distinct from the intensity, i. e., the time-average of the modulus of the Poynting vector (not depicted). For example, for linear polarization of the incident light and for the above tight-focusing conditions, the intensity distribution in the focal plane is rotationally symmetric, whereas that of inline image is elongated along the direction of the incident polarization. Typical photoinitiator molecules have electric-dipole-allowed optical transitions and are hence driven by the electric-field component of the light alone. Thus, inline image is the relevant distribution for one-photon absorption and inline image that for two-photon absorption. (Strictly speaking, this aspect should also be applied to the above considerations regarding the Abbe criterion.) As already expected from our above simple analytic consideration, the axial extent of the profiles in Fig. 2 is significantly larger than the lateral one.

To obtain the resolution according to Sparrow, we add two numerically computed exposure profiles, that are shifted with respect to each other in either the lateral or the axial direction and still yield a local minimum. For one-photon absorption, such a (single) exposure-dose profile is proportional to inline image, where inline image is a fixed exposure time. For two-photon absorption, the exposure-dose profile is proportional to inline image. The results are depicted in Figure 3. For one-photon exposure, we find the critical distances to be inline image in the lateral direction and inline image in the axial direction. The lateral value is very close to the analytic Abbe criterion (inline image). For two-photon exposure, the critical distances are reduced to inline image in the lateral direction and inline image in the axial direction. Assuming Gaussian profiles in lateral as well as in axial direction, one would expect that squaring the profiles would reduce their extent, and hence also their critical distance, by a factor inline image. For the lateral direction, this simple reasoning would lead to a two-photon-modified Abbe formula inline image that nicely resembles the numerical results for the generalized two-photon Sparrow criterion.

image

Figure 3. Critical distances, inline image and inline image, for two point exposures derived from numerical calculations corresponding to the Sparrow criterion. All plots shown use slightly larger values as indicated (i. e., inline image and inline image) such that small local minima are still visible. The exposure-dose profiles along the black lines in the iso-intensity plots (left-hand side of each panel) are plotted separately (right-hand side of each panel). The line plots show the contributions of the single exposures (red) and the sum of both (blue). (a) Critical lateral distance, inline image, for one-photon exposure. (b) Critical axial distance, inline image, for one-photon exposure. (c,d) Same as (a,b), but for two-photon exposure. A typical value for the polymerization threshold in lithography (75% of the peak dose) is used as dose value for the blue iso-surfaces, illustrating that the two point exposures are not separated any more. Parameters are: 800 nm free-space wavelength, NA = 1.4, and circular polarization.

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As expected, the numerical calculations show that the critical distances along the axial direction are significantly larger than the lateral ones, just like the FWHM of the exposure profiles along the two axes. The elongation factors of FWHMs and critical distances for one-photon and two-photon exposure profiles range between 2.45–2.52. Hence, we suggest a further modified Abbe formula inline image for the axial direction, where inline image is the aspect ratio of the exposure volume. Again, this intuitive and handy formula nicely approximates the numerical results for the generalized two-photon Sparrow criterion. However, the aspect ratio depends on the numerical aperture and the refractive index of the photoresist, for which we have taken inline image.

If the photoresist exhibits a threshold behavior, the width of the photoresist voxels is not fundamentally limited by diffraction (in analogy to the discussion in the previous section). However, as long as the resist “remembers” previous below-threshold exposures, the resolution in the sense of Sparrow is fundamentally limited by diffraction.

4 The basic idea of depletion

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

It is obviously desirable to effectively decrease the lateral and/or the axial extent of the exposed volume. Diffraction fundamentally inhibits doing that. It is Stefan Hell's deceptively simple yet ingenious idea of introducing a depletion laser that enables circumventing this limitation [16], [17], [18], [19], [20], [21], [22], [23]. This idea and its derivatives have already revolutionized fluorescence microscopy (see, e. g., the special issue [20] for reviews and state of the art).

In regular DLW, light from a laser excites the photoresist. This excitation eventually leads to an irreversible chemical reaction, e. g., polymerization. For a common negative-tone photoresists, these regions become insoluble whereas the unexposed regions can be removed in a development step. The basic idea of depletion DLW [24], [25], [26], [27], [28] is to access the system at some intermediate state, aiming at inhibiting this chemical reaction, i. e., effectively reducing the photoresist's sensitivity. Only a part of the excited molecules and, hence, only a part of the original exposure dose contributes to the chemical reaction. We will call this part the “effective” exposure dose. The inhibition or switching can be induced by a second laser, which will generally operate at a wavelength different from that of the excitation laser (to avoid excitation by the depletion laser). Clearly, the inhibition is only possible within the lifetime of the intermediate state. It is also important to note that this inhibition needs to be reversible. Otherwise, depleted regions would remain insensitive from thereon. This reversibility must not be confused with our above notion of a “forgetting” photoresist.

This switching alone together with two similarly shaped laser foci does not yet lead to any resolution improvement. However, if the spatial maximum of the excitation profile coincides with a local zero of the depletion profile, only the outer regions of the excitation volume are de-excited, leading to an effectively reduced exposure volume. Upon increasing the depletion power, this effective exposure volume shrinks towards zero. While both the excitation and the depletion profile are governed by diffraction, the exposure-dose profile is not. The diffraction limit is broken by exploiting photoresist switching in combination with tailored foci of light.

In Sect. 'Different depletion mechanisms', we will summarize possible microscopic depletion mechanisms in photoresists suitable for depletion DLW. For now, we assume that the initial local excitation is multiplied with the factor inline image, where Idepl is the local depletion intensity and γ is a photoresist-specific constant containing, e. g., the cross-section of the depletion mechanism and the intermediate-state lifetime. Section 'Stimulated-emission-depletion lithography' will show that this scaling is expected for stimulated emission as well as for other depletion pathways.

4.1 Common depletion modes

Fortunately, the know-how for realizing suitable depletion foci can be copied from fluorescence microscopy (see, e. g., [29]). A well-known and widely used focus is the so-called donut mode illustrated in Fig. 4 a–c. It can be realized by introducing a helical phase mask as shown in Fig. 4 d into the beam. Here, the additionally accumulated optical phase increases from zero to 2π in one turn along the azimuth. The phase mask plane may be imaged onto the back-focal plane of the microscope objective lens. Upon using circular polarization of the correct handedness, a wavelength of 532 nm and again a numerical aperture of NA = 1.4, the intensity distribution shown in Fig. 4 a–c results. The optical intensity on the entire optical axis is strictly zero. Thus, depletion will never occur here. While this focus nicely allows for reducing the lateral extent of the effective exposure profile, it leaves the axial distribution essentially unaffected. This may be useful for planar optical lithography, but is quite undesired for truly 3D optical lithography, where the worst spatial resolution matters for the making of arbitrary complex structures.

image

Figure 4. Typical depletion profiles for depletion DLW. (a–d) Donut depletion focus. (a) Iso-intensity surfaces of the donut depletion focus. The front inline image-quadrant has been removed to reveal the interior. (b) Lateral intensity profile. (c) Axial intensity profile. (d) Phase mask used for the generation of this focus. (f–h) Same as (a–d), but for a bottle depletion focus rather than a donut. (e,j) The anticipated resolution scaling with increasing depletion power is illustrated with the extent of single voxels for each depletion mode ((e) donut, (j) bottle-beam). Parameters are: 532 nm free-space wavelength, NA = 1.4, and circular polarization.

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Thus, the bottle-beam focus shown in Fig. 4 f–h is more attractive for 3D DLW. This focus can be achieved by replacing the helical phase mask by the one shown in Fig. 4 i. Here, a cylindrical disk in the center of the beam introduces a π phase shift. For a large beam, the diameter of the cylinder needs to be inline image of the objective's pupil diameter, such that the cylinder covers half of the relevant beam area. In the resulting bottle-beam focus, the intensity in the center of the focus is strictly zero. In contrast to the donut, however, the intensity not only rises radially but also along the optical axis. In fact, it rises more steeply along the optical axis (where the initial excitation volume is also elongated), resulting in a more pronounced depletion effect in the axial direction. This aspect will lead to a more pronounced axial linewidth improvement compared to the lateral one. The ultimate ratio of axial to lateral voxel extent is given by the shape of the inner iso-intensity surfaces of the depletion focus. Equivalently, this ratio is determined by the ratio of the curvatures of the axial and lateral intensity profiles (compare panels g and h in Fig. 4). For the parameters of Fig. 4, the ultimate aspect ratio is 0.7, i. e., the voxels can be smaller along the axial than along the lateral direction.

The two different phase masks can also be effectively combined by (even coherently) superimposing two beams, one with the helical phase mask and the other with the cylindrical one. This combination allows for controlling the relative steepness of the axial and the lateral intensity minimum via the relative phase and amplitude of the two beams. For many applications aiming at complex isotropic three-dimensional nanostructures, the desired voxel aspect ratio is 1.

4.2 Resolution scaling

Let us get a first impression of what can be expected by using the simple threshold model. Usually, regions with above-threshold excitation will remain in a negative-tone photoresist after the development step. However, if the depletion factor inline image reduces the effective local exposure dose below the threshold, the regions will again wash out in the developer. As a result, the anticipated voxels shrink in size. Strictly speaking, not only the voxel (i. e., the above-threshold region) but also the entire effective exposure profile shrinks. This also includes the below-threshold regions. Therefore, the resolution in the sense of Sparrow is expected to increase. For the donut depletion mode, only the lateral width decreases, whereas lateral and axial extent decrease for the bottle-beam focus. Exemplary calculations for two-photon excitation and depletion with either of the two depletion profiles are depicted in Fig. 4 e and j, respectively. Here, the local effective exposure dose is proportional to inline image. The excitation profile Iexc and the depletion profile Idepl are chosen according to Fig. 2 and Fig. 4, respectively. The threshold of the photoresist is chosen at 75% of the peak exposure dose. Panels e and j can directly be compared, as the same depletion-beam power is used. The different depletion modes have different peak intensities and therefore yield different scales on the horizontal axes. Upon continuously increasing the depletion power, the feature sizes converge to zero (see Fig. 4, right-hand side). There is no fundamental optics limit for the linewidth and the resolution in optical lithography any more.

It is interesting to study the asymptotic behavior. Suppose that the feature size is already strongly reduced and entirely limited by the depletion power. The initial shape of the excitation is not relevant anymore and we can assume a constant exposure profile instead. In this case, the spatial minimum of the depletion profile can be approximated by a parabola. The edge of an exposed feature is given by the condition that the depletion intensity parabola exceeds a certain value, such that the initial (spatially constant) excitation is reduced below the polymerization threshold. Solving for the crossing point immediately leads to a feature size that scales inversely with the square root of the depletion power. Note that this reasoning does not involve the above inline image depletion factor and should therefore apply to all depletion mechanisms alike. Thus, for example, to reduce the feature size by a factor of 10, one needs to increase the depletion power by a factor of 100. This means that undesired but possibly finite one-photon absorption of the depletion beam increases by factor 100, too. Two-photon absorption of the depletion beam increases even by factor 104. This unfavorable scaling with depletion power suggests that parasitic processes may at some point overwhelm the desired depletion benefit. Suppose, for example, a situation in which the two-photon absorption of the depletion beam is the limiting factor. If one aims at further reducing the linewidth by a factor three, the depletion power needs to increase by about a factor ten, hence the two-photon coefficient has to be decreased by two orders of magnitude.

The Figs. 24 refer to a high numerical aperture of NA = 1.4. Using the depletion idea, one can also obtain similarly fine features with lower numerical apertures. This may be desirable in some cases because a lower NA allows for using larger working distances and also for not having to use an immersion liquid (see Sect. 'Review of lithography experiments' or [25]). However, it should be clear from the above that especially the axial linewidths will rapidly deteriorate when decreasing the NA (see Sect. 'Abbe's diffraction limit: linewidth ≠ resolution'). Yet, depletion DLW with air microscope objective lenses may still be interesting for applications in planar optical lithography.

4.3 Noise sensitivity

Another beneficial aspect of depletion DLW is that it tends to substantially reduce the sensitivity of the critical dimensions (minimum feature size attainable) with respect to errors or fluctuations. For example, lithography industry demands for robustness against power fluctuations as large as 5%. The effect of such fluctuations on DLW is studied in Fig. 5 using a hypothetical exposure power with 5% rms noise (Fig. 5 a). When operated at rather high excitation powers (e. g., when the threshold is at the FWHM of the exposure profile), regular DLW is rather insensitive to noise fluctuations (Fig. 5 d). Clearly, the resulting feature sizes are rather large. However, when operated close to the threshold (e. g., when aiming for 100 nm linewidth), the noise translates into terrible linewidth fluctuations – the test line even gets disconnected (Fig. 5 e). Here, the 5% rms power fluctuations (or equivalently about 10% dose or threshold fluctuations) lead to linewidth fluctuations of 42% rms and peak fluctuations of 100%. In sharp contrast, depletion DLW allows for having both at the same time, small linewidths and robustness against fluctuations. This fact is illustrated in Fig. 5 f. Here, we again consider 5% fluctuations of the excitation laser, but additionally also 5% (uncorrelated) fluctuations of the depletion laser. Fairly small edge roughness results. This increased robustness alone may be a major benefit of depletion-mode DLW for many applications. In many scientific applications, however, the excitation-laser fluctuations can typically be controlled to nearly 0.1%, in which case this aspect is only of minor importance. We do emphasize, however, that small spatial inhomogeneities of local photoresist properties (e. g., of the local concentration of photoinitiator and/or inhibiting oxygen), which lead to an effective local threshold variation, would have the same effect and may not be avoidable.

image

Figure 5. Linewidth fluctuations caused by fluctuating laser power. (a) Fluctuating laser powers for excitation and depletion (uncorrelated random numbers with 5% standard deviation). (b) Voxel width and relative voxel-width fluctuations plotted vs. average excitation power for regular DLW. (c) Voxel width and relative voxel-width fluctuations plotted vs. average depletion power in depletion DLW. The excitation power is held constant at 141% of the threshold power. The relative width fluctuations caused by noise of the excitation laser (red) and noise of the depletion laser (green) are plotted separately. Selected working points are marked with circles and illustrated in detail in (d–f). (d) Resulting line shape for regular DLW where the linewidth equals the FWHM of the squared intensity. (e) Shape of a thinner line for regular DLW. The reduction in linewidth is realized by decreasing the excitation power level to 107% of the threshold power. (f) Shape of a thinner line for depletion DLW. Excitation-power level like in d), but the depletion power is increased. The depicted line shape accounts for both lasers’ fluctuations. The upper panels in (d–f) show calculated squared intensity distributions of the excitation focus (red), intensity distributions of the depletion focus (green), the anticipated effective exposure profile (purple) along the a lateral axis. The polymerization threshold is indicated in blue.

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4.4 Time constants matter

So far we have not addressed any time dependence of the depletion process. In reality, depletion will only be possible for a certain time span after (pulsed) excitation of the photoresist. This is essential as it makes the process irreversible after some time. Otherwise, two crossing lines could not be exposed as during the second exposure the first one would be depleted near the crossing point. The relevant linewidth together with this time constant τ of the depletion process imposes a fundamental limitation on the maximum accessible writing speed (other limitations may come in addition). Suppose one wants to write lines with inline image feature size with a certain linear scan velocity v using a common donut mode. Clearly, the depletion process must be completed when the laser foci are separated by one feature size from a first point written on the line. One may even want a certain safety margin to make sure that the process has really become irreversible. Let us consider a conservative margin of a factor of 10. In this case, the writing speed is limited by the inequality

  • display math(4)

For example, for inline image we obtain inline image μm/s, for inline image μs we obtain inline image, and for inline image we obtain inline image. Today, routine DLW writing speeds are in the range of 100 μm/s. The largest speed employed in DLW so far is 190 mm/s using scanning galvanometer mirrors [30]. Future commercial instruments will likely move towards this value. Thus, depletion time-constants in the ms range are clearly undesired, μs time constants are acceptable but may become borderline in the near future, and ns time constants are compatible with very fast writing.

This discussion seems to favor extremely short depletion time-constants. However, there is a trade-off. The intensity required to deposit a certain energy necessary for the depletion process increases like inline image. Thus, larger intensities are required for small τ, which increases the relative weight of undesired two-photon absorption of the depletion beam that will likely occur in any photoresist at high intensities. Furthermore, the intensities required for relatively large values of τ may still be accessible with (quasi-)continuous-wave depletion lasers, whereas short depletion pulses are required for small τ.

5 Different depletion mechanisms

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

The depletion necessary to enhance the resolution in 3D DLW can be accomplished in different ways. Any photo-induced mechanism that is locally prohibiting the formation of an insoluble cross-linked polymer is suitable at first (see Fig. 6 and Fig. 7 for a list of possibilities). Usually, after photoinitiator molecules are excited by light absorption, a major fraction of the molecules undergoes inter-system crossing (ISC) to a long-lived and reactive triplet state. From this triplet state, initiating radicals are generated with a certain yield (e. g., via cleavage or charge transfer to other molecules). These radicals initiate a polymerization reaction, which proceeds in acquiring monomer molecules until the propagating radical chains are terminated or until no monomer is left. As soon as the polymer is sufficiently cross-linked it becomes insoluble for solvents and the exposure has become irreversible. Any process that disturbs this process chain may serve as a depletion mechanism in 3D DLW.

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Figure 6. Schematic diagrams of the molecular states and transitions for the different depletion mechanisms in STED-inspired DLW approaches. (a) STED lithography: Photoinitiator (PI) molecules are excited via two-photon absorption (TPA), relax to the S1 state and are brought back to the ground state via stimulated emission (SE), before they can proceed to the triplet (T1) via intersystem crossing (ISC), generate radicals (R), initiate a propagation polymer chain (RM) and finally yield an irreversibly cross-linked polymer. (b) RAPID lithography: PI molecules are excited via two-photon absorption and generate an active species in a long-lived intermediate state. Upon light excitation, the intermediate state is deactivated and does not lead to a cross-linking polymerization. (c) Two-color photo-initiation/inhibition (2PII) lithography: PI molecules are excited via one-photon absorption (OPA) and generate radicals that can initiate the polymerization. Photoinhibitor molecules are activated via one-photon absorption at a different wavelength. The generated non-initiating radicals (Q) can scavenge initiating radicals and terminate propagating chains (RM).

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Figure 7. Alternative mechanisms for photo-inhibited polymerization. (a) Excited-state absorption: After PI excitation, several intermediate states can absorb the depletion light. From such highly excited states, non-radiative decay to the ground state can occur. (b) Resist heating: Through repeated absorption from an excited-state and non-radiative decay to the same state, the resist can be heated and several resist properties can change with the increased temperature, disturbing the excitation, initiation or polymerization process.

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The following commonly used photoinitiators have been shown to not work in this regard (at least for the experimental conditions of the corresponding papers): Irgacure 369 [26], [24], Irgacure 1800 [26], Irgacure 819 [26], Irgacure Darocur TPO [26], [24], and Irgacure 184 [24]. Less commonly used photoinitiating molecules have been shown to not work either [24]: Brilliant Green, Rose Bengal, and Tris(bipyridine)ruthenium(II) dichloride. Figure 8 summarizes the currently known photoresist compositions discovered by different groups that have the required depletion capabilities. In the following section, we will review several depletion mechanisms (illustrated in Figure 6) that can explain the polymerization inhibition observed in the different photoresists. Moreover, we will shortly discuss possible alternative mechanisms of an effective polymerization inhibition (Figure 7). These alternative mechanisms may also interfere with the above intended mechanisms without being recognized and can either amplify or limit their performance.

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Figure 8. Ingredients of the known photoresist systems that provide a photo-deactivation pathway. The resists contain cross-linkable multifunctional monomer(s), a photoinitiator and in one case a photoinhibitor. The relevant (normalized) spectra of the corresponding photoinitiator (and the photoinhibitor) are plotted on the right hand side. The wavelengths used for excitation and depletion are marked with arrows. The four rows correspond to the photoresists described in (a) [27] (spectra for DETC dissolved in PETTA [36]), (b) [24] (spectrum for MGCB in ethanol), (c) [25] (spectra for photoinitiator and photoinhibitor in CHCl1 [25]), and (d) [26] (spectra for ITX in ethanol [26]). The photoresist used in [28] exploits the same mechanism as the photoresist in panel (c), together with another monomer. Therefore, this resist is not listed separately.

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5.1 Stimulated-emission-depletion lithography

5.1.1 Mechanism and experimental realization

The original idea for diffraction-unlimited lithography is to force photoinitiator molecules to undergo stimulated emission to the ground state after their excitation and before intersystem-crossing takes place (see Fig. 6 a) [17]. This stimulated-emission transition can be induced by the intense light of a depletion laser. The dependence of the depletion efficiency on the depletion power is easily derived when looking at the depopulation of the photoinitiator's S1 state (directly after its population by the excitation pulse). The depopulation rate constant in absence of a depletion beam is inline image, where kfl is the fluorescent rate, kISC is the intersystem-crossing rate, and knr is the combined rate of all non-radiative decay channels. The undisturbed intersystem-crossing quantum-yield is then given by

  • display math(5)

When the depletion laser is switched on, stimulated emission kSTED is added as depopulation channel for the S1, and the depopulation now follows inline image. Now stimulated emission competes with the intersystem-crossing and the intersystem-crossing yield becomes

  • display math(6)

where γ is a photoinitiator-specific constant, Idepl is the depletion laser intensity, and inline image is used. According to this simple model, the intersystem-crossing yield and, hence, the effective exposure dose decreases continuously with increasing depletion intensity.

Usually, the depletion-laser wavelength is chosen at the red end of the fluorescence spectrum. This is a compromise between moving towards the wavelength of maximum fluorescence (and hence towards maximum stimulated-emission cross-section) and avoiding the fundamental absorption band, i. e., limiting one-photon absorption of the depletion laser.

It has been found that common photoresists and photoinitiator molecules are not suited for stimulated emission depletion (STED) [26], [24]. For efficient STED, a large cross-section for stimulated emission is required, which is equivalent to a large oscillator strength between the S0 and the S1 state of the molecule. Common photoinitiator molecules have a inline image type transition with inherently low oscillator strength (e. g., Irgacure 907 [31]), whereas the fluorescent dyes used in STED microscopy have inline image type transitions with large oscillator strengths. Moreover, the excited-state lifetime of photoinitiators is often unfavorably short (around 100 ps) [32], [24]. To drive efficient stimulated emission, one would need to use pulses shorter than 100 ps and additionally increase the pulse energy considerably to compensate for the small cross-sections. Clearly, this would quickly lead to pronounced multi-photon absorption of the depletion beam, limiting the depletion capability. Even more likely, the small cross-section for stimulated emission is overcompensated by a transient absorption from S1 to higher singlet states. Such states are often very reactive and tend to have enhanced intersystem-crossing rates, leading to enhanced exposure instead of depletion [24]. Finally, if excited-state absorption dominates over stimulated emission, repeated excited-state absorptions (followed by non-radiative relaxation to S1) will also increase the temperature of the resist and limit the applicable depletion power.

To overcome these obstacles, “dye-like photoinitiators” [26], [27] with larger oscillator strengths and “photoinitiating dyes” [24], [33] have been explored. However, only recently one photoresist composition based on 7-Diethylamino-3-thenoylcoumarin (DETC) has unambiguously been shown to support STED. DETC belongs to the group of keto-coumarins, which are known as triplet-sensitizers and photoinitiators [34]. Being a coumarin derivative, DETC possesses a large oscillator strength (40550 L/mol/cm [35]) that is comparable to state-of-the-art green-emitting fluorescent dyes (e. g., Atto 425, 45000 L/mol/cm), which are usually coumarin derivatives as well. The additional ketone group in DETC is very common for photoinitiator molecules and promotes the photoinitiating functionality. With fluorescence quantum yields of roughly 2.5% in ethanol [36], 10% in benzene [34], and 27% in the viscous monomer pentaerythritol tetraacrylate (PETTA)[36], DETC is a poor dye, but turns out to be an efficient initiator for two-photon DLW [27]. DETC dissolved in PETTA possesses a one-photon absorption peak at 420 nm wavelength, which is convenient for two-photon excitation with Ti:sapphire oscillator lasers or frequency-doubled Er-doped fiber oscillators (Fig. 8 a). The fluorescence emission of DETC peaks at 480 nm wavelength and decays to 10% at 550 nm. Thus, frequency-doubled Nd or Yb lasers at 532 nm can serve as attractive high-power depletion laser sources. Moreover, keto-coumarins are widely tunable in their absorption and emission wavelengths [34]. This makes other keto-coumarins promising candidates for future optimized STED photoinitiators.

Standard pump-probe experiments on DETC dissolved in ethanol [35] show that stimulated emission overwhelms excited-state absorption for relevant wavelengths within the fluorescence band, including especially 532 nm. This can be seen from the negative change of the optical density in Fig. 9.

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Figure 9. Pump-probe data of DETC in ethanol. Time-dependent change of the optical density (OD), ΔOD (dots), after excitation at 387.5 nm wavelength for different probe wavelengths as indicated. inline image corresponds to increased probe transmittance upon optical pumping. The solid curves result from a global fit of a simple rate-equation model to these data. Negative changes in transient optical density correspond to stimulated emission for wavelengths up to 630 nm. Reproduced from [35].

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From fitting a simple rate-equation model to the measured data, the authors have derived a S1 lifetime of about 100 ps.

However, it is well known that the S1 lifetime of a molecule can depend on the solvent environment. Indeed, the S1 lifetime of DETC dissolved in PETTA increases to about 1 ns [36]. This reference speculates that this increase in the more viscous monomer is due to steric hindering of conformational changes necessary for inter-system crossing. In PETTA, a simple pump-probe experiment is no longer possible, because the intense pump beam leads to irreversible polymerization of the photoresist inside the cuvette. Alternatively, the S1 lifetime can be determined by a lithography experiment with time-delayed excitation and depletion pulses. Such experiments have been performed in [36] and are shown in Fig. 10. These experiments show a temporal decay of the depletion effect composed of an initial rapid decay with about 1 ns time constant and a second slower decay with a time constant between 12.5 ns and 1 μs (Fig. 10 a). The rapid decay has been assigned to stimulated emission [36], the slower one is yet to be determined. The spectral dependence of the fast component nicely follows the gain spectrum of DETC, supporting the interpretation that this depletion channel is indeed stimulated emission (Fig. 10 b). The slow component shows a different spectral dependence, supporting the interpretation that two different depletion mechanisms are at work in this photoresist.

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Figure 10. Temporal (a) and spectral (b) characteristics of the polymerization deactivation with DETC as photoinitiator. The temporal decay in (a) is assigned to the S1 lifetime and corresponds to a fast component of the inhibition due to stimulated emission. The offset is due to another depletion channel with a considerably longer time constant. In (b) the spectral characteristics of the slow and the fast component are plotted vs. the anticipated gain of DETC in PETTA. The fast effect resembles the gain spectrum, consistent with STED being the underlying mechanism. Reproduced from [36].

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5.1.2 Properties and limitations

Compared to other mechanisms to be discussed below, stimulated emission offers the fastest time constant, as the lifetime of the responsible S1 state is typically 0.1 ns - 4 ns. Directly after stimulated emission (and subsequent vibronic relaxation) the photoinitiator molecules are ready for a new exposure. This allows for very fast scan speeds in the range of m/s (see Sect. 'Time constants matter'), but also requires high depletion-laser intensities.

Stimulated emission is also unique among possible depletion mechanisms because it does not inject additional heat into the photoresist, but even ejects energy from the system. Other mechanisms have to be triggered by the absorption of a depletion photon, the energy of which will finally become thermal. In contrast, when using STED, a new photon which contains a major fraction of the initial excitation energy is emitted and leaves the photoresist system.

For efficient stimulated emission, high-peak-power depletion pulses are required – especially if the photoinitiator molecule is not perfectly optimized for the depletion wavelength. The use of stimulated emission comes along with the search for suitable, high-peak-power pulsed laser sources and their temporal alignment. Continuous-wave depletion at relatively high power levels is possible in principle, but might be limited by competing effects like excited-state absorption.

5.2 RAPID lithography

5.2.1 Mechanism and experimental realization

In Resolution Augmentation through Photo-Induced Deactivation (RAPID) lithography [24] special cationic dyes (cationics diarylmethanes, cationic triarylmethanes, cationic rhodamines [33]) are used as photoinitiators. The original implementation used malachite green carbinol base (MGCB). Initially, this molecule was expected to support STED and was chosen due to its very high extinction coefficient. MGCB has its fundamental absorption peak at 620 nm, and another shoulder around 430 nm before the absorption rises strongly towards shorter wavelengths (see Fig. 8 b). Two-photon absorption of femtosecond pulses around 800 nm wavelength is possible and will likely excite the molecule to a higher singlet state inline image followed by non-radiative relaxation to S1. One would expect further red-shifted fluorescence emission around 700 nm wavelength. Hence, a potential STED depletion could also be performed with 800 nm light. Depletion pulse lengths >50 ps would ensure that the depletion pulses do not cause efficient two-photon absorption [24]. However, during the preparation of Fig. 8 we could not detect any luminescence from MGCB in ethanol solution at the anticipated spectral position for excitation wavelengths between 400 nm and 700 nm.

Indeed, activating the depletion laser can induce an effective polymerization inhibition in MGCB-based photoresists [24]. However, the authors have argued that the observed effect can not be caused by stimulated emission, because the depletion effect is insensitive to pulse delays between excitation and depletion pulses up to 13 ns. They assigned the observed effect to the depletion of an intermediate state with longer lifetime (see Fig. 6 b). This allows for the use of a continuous-wave (cw) laser for depletion and eliminates the necessity for a precise timing between excitation and depletion pulses. The exact nature of the intermediate state, however, is yet to be determined [33]. Possible explanations are that after the excitation these molecules generate weakly reactive radical pairs [24] or solvated electrons [33] that can recombine to the parent molecules via photo-induced electron-backtransfer.

5.2.2 Properties and limitations

The photoinitiator MGCB absorbs from 400 nm to 700 nm wavelength, i. e., essentially throughout the entire visible spectrum. This fact has to be considered when handling this photoresist to avoid accidental exposures by ambient light. Moreover, remaining unconsumed photoinitiator molecules in the final polymer structures might render them absorbing for visible light.

Further investigations have shown that not only MGCB but three broad classes of dyes are capable of being depleted by the RAPID scheme [33]. For example, using malachite green carbinol hydrochloride (MGC-HCl) the depletion effect is so sensitive that even the femtosecond excitation pulses themselves lead to a depletion effect. This manifests itself in an unexpected proportional dependence of the resulting polymer linewidth on the writing speed. Usually, increased scan speeds yield decreased linewidths because the local exposure dose is decreased towards the threshold value due to shortened exposure times. In contrast, when using special RAPID photoinitiators, increased scan speeds yield increased linewidths [33]. This is explained as follows [33]: At faster scan speeds, more excited molecules, which are in their vulnerable intermediate state, are left behind the writing spot. These molecules can continue the chemical reaction undisturbed. At slower scan speeds, the same molecules in the intermediate state would have been partially depleted. This means that for faster scan speed the effective dose increases, because the overall depletion is reduced. This contribution overcompensates the expected decrease in dose due to the smaller exposure time. Combining such photoiniators (with proportional linewidth scaling) with common photoinitiators can yield a photoresist with nearly scan-speed-independent linewidths [33].

This highly sensitive depletion mechanism allows for low depletion powers and the use of low-cost cw laser diodes as depletion lasers. Low-power depletion is also beneficial because limiting effects (one-photon absorption, two-photon absorption, and excited-state-absorption of the depletion laser) are less pronounced. Even wide-field parallel exposures with tailored excitation and depletion patterns to reduce linewidths seem to be in reach [33]. With multiple exposures, the diffraction limit could again be circumvented.

Finally, the proportional linewidth scaling intuitively implies that the lifetime of the vulnerable intermediate state is at least on the scale of the effective exposure time used (or even longer). This assumption is in agreement with the numerical modeling in [33]. Therein, a decay time of around 1000 time units and exposure times between 20 and 50 time units (corresponding to 0.05 and 0.02 velocity units) were used to successfully model the observed proportional linewidth scaling. Within this model, the exposure times used in the experiments lead to the conclusion that the depletion time-constant is between 15 ms and 350 ms. (We deduce exposure times of 1–7 ms from Fig. 2j of [33]. These correspond to the used writing speeds of 30 μm/s to 150 μm/s and a diffraction-limited excitation spot with a lateral intensity FWHM of 310 nm.) This implies that RAPID photoinitiators in general or at least the highly sensitive photoinitiator MGC-HCl in particular are not suitable for fast scanning (see Sect. 'Time constants matter') with confinement along the direction of scanning (e. g., with a lateral donut depletion-mode). However, axial confinement with a bottle beam together with lateral scanning is possible and has been demonstrated [24]. Moreover, a less commonly used depletion mode [18] could be used to only improve the resolution in one lateral direction perpendicular to the scan direction.

5.3 Photoinhibitor lithography

5.3.1 Mechanism and experimental realization

A lithography approach based on another depletion mechanism [25] has been named two-color photo-initiation / inhibition lithography (2PII) [37]. 2PII is not based on a direct deactivation of an intermediate excited photoinitiator state but on the activation of a counter-acting photoinhibitor (see Fig. 6 c) [25]. While the photoinitiator system is allowed to generate initiating radicals upon one-photon absorption, the additional photoinhibitor is activated by one-photon absorption at a different wavelength (see Fig. 8 c). The latter cleaves into two weakly reactive radicals which can efficiently scavenge the initiating radicals and also terminate propagating radical polymer chains. Reference [25] has shown that this mechanism can reduce the polymerization rate by up to a factor of 5. Thus, the mechanism can prevent the formation of a cross-linked insoluble polymer network.

The spectra of the compounds have to be chosen such that they can be excited separately with little cross-talk. In the original implementation of 2PII, the photoinitiating system camphorquinone + ethyl 4-(dimethylamino)benzoate is used and excited at 473 nm wavelength near its absorption peak (see Fig. 8 c). The activation of the photoinhibitor (tetraethylthiuram disulfide) is performed with 364 nm radiation, where the photoinitiator has an absorption minimum (see Fig. 8 c). The resulting reduction in polymerization rate under these conditions is shown in Fig. 11 [25].

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Figure 11. Effect of photo-inhibition on photopolymerization rate in 2PII. Initial methacrylate polymerization rate versus UV depletion intensity during constant visible excitation irradiation (15 mW/cm2). Reproduced from [25].

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5.3.2 Properties and limitations

The use of one-photon absorption has distinct advantages and disadvantages. In the original implementation of 2PII, one-photon absorption is used for the excitation of both the initiator and the inhibitor. This results in very low power requirements in the 10 μW range that can easily be delivered by low-cost cw laser diodes. In contrast, two-photon absorption usually demands for 100 fs pulses with < 10 mW average power that can be readily delivered by fs-fiber oscillators, yet at a cost more than ten times higher.

One drawback of one-photon absorption is that it is difficult if not impossible to fabricate complex 3D structures – even if the photoresist offers sufficient nonlinearity to provide 3D operation without two-photon absorption (see Sect. 'Introduction'). When focusing deeper into the photoresist volume, both the excitation and depletion light is attenuated on its way through the absorbing material. Hence, the laser powers to be applied are strongly depth-dependent. Furthermore, this can lead to a consumption of the initiator and/or inhibitor and to a continuous heating of the photoresist inside the complete cone of the focused laser beams. In contrast, using two-photon absorption for excitation, the laser light is only absorbed within the focal volume. In addition, using STED or RAPID, the depletion light is also exclusively absorbed by molecules in their intermediate state (hence, within the focal volume). Thus, the laser powers to be applied are rather depth-independent, the anticipated photoresist heating is much less pronounced, and no consumption of one species is expected.

Applying two-photon absorption to both the photoactivation and the photoinhibition in 2PII would resolve these obstacles and provide full 3D capability. In this case, the depletion laser would likely be centered around 800 nm wavelength. Unfortunately, the shape of the minimum of a donut mode gets much broader (and hence less attractive for depletion DLW) when the intensity profile is squared (see, e. g., Fig. 1 for comparison).

In contrast to the above approaches, 2PII does not only confine the effective excitation but also directly tackles the blurring of the excitation pattern due to diffusion of initiating and propagating radicals. Once those species diffuse (or propagate) out of the anticipated polymerization volume, the probability of their termination increases. Especially in low-viscosity photoresists with pronounced diffusion of the active species, this unique feature can be a major advantage.

The time constant for inhibition with 2PII is (co-) determined by the lifetime of the activated inhibiting radicals. Once the depletion light is switched off, those can recombine and again form the initial parent molecule. The recombination reaction can be very fast, depending on the viscosity of the photoresist formulation (which affects the diffusion speed) and on the concentration of the activated inhibitor (as the recombination is bimolecular). The concentration and, hence, the time constant, changes throughout the depletion profile. For tetraethylthiuram disulfide in low-viscosity acetonitrile, Reference [38] determined a time constant around 2 μs. This value likely provides a lower bound. Reference [39] has estimated an upper bound of 200 ms for the same photoinhibitor in a higher-viscosity photoresist.

5.4 Alternative depletion pathways

Apart from the mechanisms described so far, alternative depletion mechanisms based on excited-state absorption are conceivable and might compete with the above mechanisms. For example, the polymerization-inhibition effect observed for isopropyl thioxantone (ITX) [26] was originally ascribed to stimulated emission. Later it was shown that the transient absorption spectra of ITX are dominated by excited-state absorption [35]. These experiments are analogous to those depicted for DETC in Fig. 9. In contrast to DETC, however, the observed pump-induced change in optical density of ITX in ethanol solution was found to be mainly positive and subsequent analysis showed that both the S1 state and the subsequently occupied T1 state of ITX contribute to this absorption [35].

Historically, some authors had likewise speculated that the fluorescence depletion effect in STED microscopy might actually not be caused by stimulated emission but rather be mediated by excited-state absorption [40]. Although it turned out that STED is the far dominating mechanism in STED microscopy, the proposed processes can still play an important role in depletion lithography. The corresponding processes for lithography are illustrated in Fig. 7. Excited-state absorption might take place directly from the S1 state or, alternatively, from the triplet. Even the generated radicals might absorb depletion light and contribute (not depicted in Fig. 7). Following light absorption, the highly excited molecules might immediately relax non-radiatively to the ground-state (Fig. 7 a) in which case their contribution to the exposure would be lost.

Another conceivable mechanism is that molecules are excited several times from an excited state and quickly relax to the same excited state non-radiatively (see Fig. 7 b). In this case, significant heat might be imposed onto the system and thermal effects could play the dominant role. For example, the two-photon absorption cross-section of a molecule can decrease considerably with increasing temperature (e. g., 50% reduction from 20°C to 110°C for Disperse Red 19 [41]). In this case, the depletion laser might quickly heat up the exposure volume, subsequent excitation pulses would find photoinitiator molecules with reduced two-photon-absorption cross-sections, and the effective exposure dose would drop below threshold. Alternatively, the intersystem-crossing quantum yield might also decrease with increasing temperature due to temperature-dependent non-radiative decay from the S1 state. Further mechanisms are conceivable as well. Such temperature-mediated mechanisms might lead to fairly low depletion-power requirements. However, the corresponding time constants are likely in the range of many μs to ms, which would significantly limit the accessible DLW writing speeds (see Section 'Time constants matter').

Broadly speaking, when aiming at better and better resolutions, large laser intensities will be required. Any sort of absorptive process will eventually introduce heat into the system and may lead to (unwanted) temperature-dependent effects. In contrast, stimulated emission (followed by rapid relaxation from the inline image-state) carries energy out of the system (see Sect. 'Properties and limitations').

6 Review of lithography experiments

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

This section summarizes experimental results obtained by any form of depletion DLW in chronological order. So far, only four groups worldwide (Fourkas [24], McLeod [25], Wegener [26], [27], and Gu [28]) have published corresponding lithography results in journal papers. The papers show systematic improvements in lateral [25], [26], [27], [28] and axial [24], [27] size of single voxels [24], [25], [26], [27], [28] and lines [25], [26], [27], [28]. So far, only one publication has addressed the resolution in the sense of Abbe (see Sect. 'Abbe's diffraction limit: linewidth ≠ resolution') and has broken the Abbe criterion as well as the more appropriate generalized two-photon Sparrow criterion (see Sect. 'The generalized Sparrow criterion in 3D') in the lateral and in the axial direction [27].

Table 1 summarizes experimental results of these publications (first column). The exposure or excitation wavelengths and numerical apertures used are also stated (second and third column) to allow for a fair comparison. Columns four and six show the measured lateral and axial spatial resolutions. For direct comparison, the fifth and seventh columns quote the corresponding generalized Sparrow criteria that have been determined using Debye theory (see Sect. 'The generalized Sparrow criterion in 3D'). For publications using two-photon absorption, the intensity distribution has been squared in these calculations. The refractive index was chosen as inline image for all calculations. The obtained improved feature sizes (columns eight and nine) are not directly relatable to the calculated diffraction-limited critical distances as we have extensively argued in Sect. 'Abbe's diffraction limit: linewidth ≠ resolution'. Finally, the measured reduced aspect ratios, i. e., the ratios of axial to lateral feature size, are summarized in column ten. Where applicable, we have distinguished between results obtained for voxels (V) and lines (L).

Table 1. Summary of recent lithography experiments on depletion-DLW approaches. Gray shaded fields are experimental results. Excitation wavelength λexc and numerical aperture (NA) of the publications are stated and used to determine diffraction-limited critical distances in the lateral and the axial direction. For this purpose, the generalized Sparrow criterion described in Sect. 'The generalized Sparrow criterion in 3D' was numerically evaluated; two-photon absorption was taken into account in cases where it was used. Experimental demonstrations for resolutions can be directly compared to the value of this diffraction limit (diff. limit). Demonstrations of voxels (V) and lines (L) are listed separately. Although feature sizes are not directly limited by diffraction, the reader may relate obtained feature sizes to each other by comparing the corresponding diffraction limits. The aspect ratio is voxel height divided by voxel width
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6.0.0.1 Fourkas group 2009

In 2009, the Fourkas group and the McLeod group simultaneously published their approaches [24], [25]. In [24], the Fourkas group introduced RAPID lithography (Section 'RAPID lithography') and addressed the axial resolution in two-photon DLW by using a bottle-beam for depletion (compare Fig. 4 f–j). The aspect ratio in two-photon DLW is usually between 2.5 and 5 [42], [24]. Consequently, once complex three-dimensional structures are aimed at, the axial resolution is the limiting one. In [24] single voxels were fabricated close to the substrate-photoresist interface and the fallen voxels were characterized by scanning-electron microscopy (SEM) and atomic-force microscopy (AFM) (see Fig. 12). When increasing the depletion power, the aspect ratio of the fabricated voxels decreased systematically from >3 to 0.5 (Fig. 12 a–f and i). The axial extents of the smallest voxels were measured to be 40 nm using AFM (Fig. 12 g), equivalent to inline image. The corresponding voxels fabricated without the depletion laser had an axial extent of 700 nm. Basic three-dimensional operation was demonstrated as well (see Fig. 12 j–k). The axial resolution in the sense of Abbe was not reported.

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Figure 12. Results obtained with RAPID lithography: (a–f) SEM images of voxels created with deactivation beam powers of 0 mW, 17 mW, 34 mW, 50 mW, 84 mW, and 100 mW, respectively. (g) Three-dimensional and contour AFM images of the smallest voxel that have been created with RAPID lithography. (h) Corresponding images of the smallest voxel that could be created with conventional DLW. The x and y dimensions of the voxels in (g) and (h) are exaggerated due to the width of the AFM tip, whereas the z dimension (height) is accurate. (i) Dependence of the height and aspect ratio of voxels on the power of the deactivation beam. The error bars represent ±1 SD based on measurements of four voxels. (j) Tower with rings created with conventional DLW. (k) Tower with rings created with RAPID lithography. Reproduced from [24].

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6.0.0.2 McLeod group 2009

In the second early publication [25], the McLeod group introduced the 2PII scheme (see Sect. 'Photoinhibitor lithography') utilizing a photoinhibitor for spatial confinement. A donut mode (see Fig. 4 a–d) was used to reduce the lateral extent of single voxels fabricated at the substrate-photoresist interface. Using a singlet lens with NA = 0.45, the lateral extent of the fabricated voxels could be reduced from 3.6 μm down to 200 nm (Fig. 13 a). This impressive improvement allows for the use of inexpensive low-NA lenses with large working distances while maintaining the resolution of higher-NA objective lenses. Using a lens with NA = 1.3, even smaller features were fabricated. The smallest voxels had a full width of 110 nm [25] (Fig. 13 b). Scanning the beams at a scan velocity of 0.125 μm/s yielded a connected line with a width of 150–200 nm (Fig. 13 c). The lateral resolution in the sense of Abbe was not reported.

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Figure 13. Results obtained with photoinhibition lithography: Scanning electron micrographs of polymerized features. (a) Voxels polymerized on a microscope slide using a 0.45-NA singlet lens and the coincident Gaussian blue / donut-shaped UV irradiation scheme, observed at 45° and normal to the slide surface. The blue excitation power was held constant at 10 mW while the UV depletion power was progressively increased. The depletion power, from left to right, was 0, 1, 2.5, 10, and 100 mW. The exposure time was 8 s for each dot. Scale bars, 10 μm. (b) Profile of a voxel similarly fabricated but with 10 mW of blue power and 110 mW of UV focused at NA = 1.3, then imaged via SEM at normal incidence. The SEM intensity on the white line (inset) is plotted as squares against the expected polymerization profile (green) obtained by a double-parameter fit of the initiation (blue) and inhibition (violet) rate profiles, as shown. (c) Polymer column fabricated by using the same conditions as Fig. 13 b. The focus was translated normal to the glass slide at a velocity of 0.125 μm/s for 3 μm. Scale bar, 200 nm. Reproduced from [25].

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6.0.0.3 Wegener group 2010

The Wegener group [26] introduced another depletion-DLW approach based on an ITX-containing photoresist (see Sect. 'Alternative depletion pathways'). The observed polymerization suppression was found to be consistent with stimulated emission [26]. Later, it was found that stimulated emission is unlikely to be the dominant mechanism [35]. Nevertheless, the reversible polymerization inhibition could be used to reduce the lateral width of fabricated polymer lines from 155 nm down to 65 nm, again using a donut mode (see Fig. 14). Increasing the depletion power beyond the corresponding optimal value led to increasing feature sizes, probably due to two-photon absorption of the depletion laser. A scan speed of 100 μm/s was used. Moreover, it was shown that the inhibition effect is reversible for a time-delay of 200 ms [26]. This means that the photoresist does completely recover after a depleted exposure and the same regions can be re-exposed without any loss in sensitivity. The lateral resolution in the sense of Abbe was not reported.

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Figure 14. Results obtained with ITX-based depletion DLW: Polymer linewidth versus power of the continuous-wave 532 nm wavelength depletion beam that is focused to a donut-shaped mode. The power of the two-photon excitation beam centered around 810 nm wavelength is fixed to 13.5 mW. The subpanels exhibit electron micrographs illustrating the raw data underlying the data points. A scan speed of 100 μm/s was used. Reproduced from [26].

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6.0.0.4 Wegener group 2011

In [27], the Wegener group published a modified resist formulation based on DETC (see Sect. 'Stimulated-emission-depletion lithography'). Later, they showed [35], [36] that this formulation supports true stimulated-emission depletion as well as another depletion mechanism yet to be determined. Using a cw depletion laser (and hence, triggering both depletion channels simultaneously), increased lateral and axial resolution in the sense of Abbe was demonstrated. A scan speed of 100 μm/s was used throughout this publication.

Using a donut mode for the lateral confinement, gratings with periods down to 175 nm were successfully demonstrated (see Fig. 15). The simple Abbe limit states inline image but is not suited for the sequential two-photon exposure (see Sect. 'Abbe's diffraction limit: linewidth ≠ resolution' and 'The generalized Sparrow criterion in 3D'). The more suitable generalized two-photon Sparrow criterion leads to a lower value of inline image (see Table 1, compare Fig. 3 c). To the best of our knowledge, both criteria were broken for the first time in this publication [27]. All panels in Fig. 15 correspond to best results from a fine excitation-power sweep in 1% steps and a z-position sweep (not shown). Here, depletion DLW was better than the best regular DLW.

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Figure 15. Results obtained with DETC-based depletion DLW: Electron micrographs of simple line gratings fabricated via regular DLW ((a) and (c)) and depletion DLW ((b) and (d)). The center-to-center distance of the lines is inline image and inline image as indicated within the panels. While regular DLW in (a) does not yield a well-defined grating at inline image and suffers from polymer clusters bridging the gaps, the quality of the grating fabricated via depletion DLW shown in (b) is excellent. For inline image, regular DLW does not allow for the fabrication of gratings with lines that are clearly separated from the substrate. Chosing the z-position of the focus within the substrate, a periodic (yet very flat) height variation can be obtained (see (c)). In contrast, using depletion DLW, elevated and simultaneously separated lines are still possible with reasonable quality as shown in (d). The depletion power of the donut mode used is 50 mW in front of the microscope-objective-lens entrance pupil. Reproduced from [27].

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The gratings with inline image and inline image fabricated using regular DLW (Fig. 15 a,c) are still clearly modulated, yet not sufficiently separated. This means, that the generalized two-photon Sparrow criterion – although most suitable – is no sharp fundamental limitation. Otherwise, we would expect to see no modulation at all, as the accumulated exposure dose does not have local minima. Since a “forgetting” photoresist can easily yield gratings below the diffraction limit (see Sect. 'Abbe's diffraction limit: linewidth ≠ resolution') this is not too surprising. Obviously, the resist used in [27] is only “slightly forgetting” and it is not possible to overcome the diffraction limit with regular DLW in a high-quality fashion. To the best of our knowledge, no other “forgetting” photoresist formulation has yet broken the diffraction-limit in regular DLW.

In a second set of experiments, the axial resolution was addressed using a bottle-beam focus for depletion [27]. For this purpose, woodpile photonic crystals illustrated in Fig. 16 have been used as test structures. Cross-sections of fabricated structures are shown in Fig. 17 a–f. Here, the axial as well as the lateral extent decreased with increasing depletion power (also see panel (g)). Furthermore, the aspect ratio of fabricated lines could be reduced from 2.5 to 1.4.

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Figure 16. Scheme of a three-dimensional woodpile photonic crystal [43]. The woodpile is composed of a first layer (gray) of periodically arranged dielectric rods with rod spacing a, a second orthogonal layer (blue), a third layer (red) laterally displaced by half the rod spacing with respect to the first layer, and a fourth layer (green) displaced with respect to the second layer. This unit cell is repeated along the axial direction. For a face-centered-cubic (fcc) woodpile, the resulting axial lattice constant is given by inline image. In a woodpile, the smallest axial distance inline image equals 3/4 of this axial lattice constant.

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image

Figure 17. Improved aspect ratio via DETC-based depletion DLW: (a–f) Oblique-view electron micrographs of ZnO-filled woodpile photonic crystals after focused-ion-beam milling. The viewing angle with respect to the normal is 54°. (g) Width, height and calculated aspect ratio of polymer rods inside the three-dimensional woodpiles ((a)-(f)). Height measurements have been corrected for the viewing angle. The measurements are averaged over 10 rods. The error bars indicate ± one standard deviation of the corresponding ensembles. The bars for height and width in (a–f) correspond to the averaged values shown in (g). Reproduced from [27].

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Instead of using isolated voxels close to the substrate surface [24], polymerized lines inside complex 3D structures were used for the evaluation [27]. This demonstrated the full 3D capability of the approach. Furthermore, shrinkage-based effects were ruled out since lines suffering from heavy shrinkage would not hold complex structures like shown in Fig. 17 a–f. To further ensure that the electron beam did not alter the line shape during imaging, the developed polymer structures were filled with ZnO via standard atomic-layer deposition (ALD) [27]. The resulting composite structures were opened via focused-ion-beam milling. During this step, the initial polymer structures were partly calcined, such that essentially holes in ZnO blocks remained. In Fig. 17, the inner ZnO surfaces were used as a measure for the initial polymer lineshape (see bars in panels (a)-(f)).

The reduced aspect ratio and axial voxel extent were also shown to directly translate to an increased axial resolution in the sense of Abbe. Woodpile photonic crystals [43], [5], [44], [45], [46], [11] with different lateral rod spacings, a, were fabricated using regular DLW (Fig. 18 a,c) and STED-DLW (Fig. 18 b,d). Each square depicted in the reflection-mode optical micrographs (panels a and b) is a woodpile with a footprint of 20 μm × 20 μm and 24 layers in the axial direction. The excitation power was increased along the horizontal direction of the upper panels, to ensure a fair comparison with optimum exposure doses for both approaches. The rod spacing was varied along the vertical axis.

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Figure 18. DETC-based depletion DLW: (a) True-color reflection-mode optical micrographs of woodpile photonic crystals fabricated via regular DLW. (b) Same, but using depletion DLW. All woodpiles have 24 layers and a footprint of 20 μm × 20 μm. The rod spacing is decreased from inline image to inline image along the vertical axis, the exposure power is increased in steps of 1% from left to right. (c) and (d) Selected (see asterisks in (a) and (b)) transmittance (solid) and reflectance (dashed) spectra for DLW and depletion DLW, respectively. Reproduced from [27].

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The smallest axial center-to-center distance between two separated polymer rods in a woodpile photonic crystal is 3 times the layer separation [27], which was chosen as inline image (see Fig. 16). The finest woodpiles successfully fabricated via STED-DLW had inline image, and correspond to an anticipated axial resolution of inline image . However, the actual writing trajectories were pre-compensated for shrinkage along the z-direction and therefore separated by a larger margin. To be conservative, the separation of the voxels during exposure was used as resolution measure, leading to inline image, where inline image is the shrinkage pre-compensation factor. Clearly, this inline image value is below the generalized two-photon Sparrow criterion in the axial direction of inline image (see Table 1, compare Fig. 3 d). This is the first time the axial diffraction-limit was broken.

With the depletion laser switched off, the finest attainable woodpiles had inline image, and hence, inline image. Again, the generalized two-photon Sparrow criterion does not seem to be a sharp limit for regular DLW. However, to our knowledge the presented woodpiles are the finest woodpiles in DLW literature (compare [45], [46], [11]). This implies that high-quality structures below the diffraction-limit are not (yet) attainable with regular DLW and a “forgetting” photoresist.

Moreover, one might be afraid that a photoresist for depletion DLW comes along with unfavorable properties limiting its usability or resolution (e. g., low reactivity, low dynamic range, low mechanical stability of the resulting structures). In this case, depletion DLW would not truly extend state-of-the-art regular DLW but would first have to compensate for the resist's shortcomings before a true improvement in resolution and quality could be expected. The fact, however, that this special DETC-based photoresist was used to demonstrate the finest published woodpiles using regular DLW allays these doubts.

6.0.0.5 Gu group 2011

Recently, the Gu group [28] published systematic experiments on a modified version of the photoresist from [25]. They used the same photoinitiator and photoinhibitor but replaced the original monomer by the bi-functional monomer NK Ester BPE-100 (2.2 Bis[4-(Methacryloxy Ethoxy)Phenyl]Propane). This leads to a higher photosensitivity of the photoresist and higher mechanical stability of the fabricated lines [28]. The lateral extent of single voxels exposed directly at the substrate-photoresist interface could be reduced from 500 nm to 40 nm by using appropriate inhibition laser powers in the range of a few μW. As depicted in Fig. 19 a,

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Figure 19. Results from a modified photoinhibition lithography approach: (a) The obtained lateral voxel sizes are plotted as a function of the depletion power. The voxels were exposed at 200 nW excitation power with exposure times stated in the figure legend. The red curves are corresponding numerical predictions. (b) Voxel size for different exposure parameters (top) and SEM image of a voxel fabricated 200 nW excitation power and 6 μW depletion power at 0.4 s exposure time (bottom). (c) Polymer lines fabricated with different depletion-power levels (top-down): 0 μW, 1.0 μW, 1.5 μW, and 2.0 μW. The scanning speed was 3 μm/s, the excitation power was 200 nW. The scale bar is 200 nm. Reproduced from [28].

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the voxel sizes were also predicted numerically using a non-steady-state kinetic model. Lateral scanning at a velocity of 3 μm/s yielded polymer lines attached to the substrate surface. The width of these lines was reduced from 400 nm down to roughly 130 nm. As in the McLeod work [25], the attainable width of lines was larger than the attainable width of single voxels.

7 Applications in 3D structures

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

Eventually, depletion 3D DLW optical lithography needs to demonstrate more than just interesting principles, small feature sizes, and test structures on spatial resolution – it needs to successfully realize complex functional 3D nanostructures that would be very difficult or even impossible to make with other existing technologies. In particular, depletion DLW obviously needs to be better than the best existing regular DLW (see, e. g., [9], [45]).

Any purely periodic 3D nanostructure can likely be made inexpensively and on a large scale by optical interference lithography. Any simple layer-by-layer structure can be made by standard electron-beam lithography of the individual layers and successive planarization and stacking of layers. Challenges, however, do arise for these and other technologies in case of seemingly simple problems like achieving free-form surfaces in three-dimensional space or for three-dimensional architectures which are intentionally non-periodic. The so-called carpet invisibility cloak to be described in the remainder of this article comprises all of these difficulties at the same time and, hence, represents an interesting and challenging test case with a specific function. Indeed, depletion 3D DLW has enabled the first (and so far also the only) three-dimensional polarization-independent visible-frequency broadband carpet invisibility cloak.

Invisibility cloaking can be viewed as a demanding benchmark example for the much broader and far-reaching ideas of a design approach named transformation optics [47], [48]. Transformation optics connects geometry of curved space and propagation of light in inhomogeneous optical media [47], [48]. Any imaginable distortion of space can be mapped onto spatially inhomogeneous optical materials, which generally need to be anisotropic magneto-dielectrics. A simple yet impressive example is the carpet cloak illustrated in Fig. 20.

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Figure 20. A three-dimensional carpet cloak. Looking through a spatially inhomogeneous region of the woodpile photonic crystal shown here, a bump in the gold film – the carpet – appears as a flat metal mirror. The local refractive-index profile needed to create the illusion is calculated using the laws of transformation optics and can be realized by adjusting the local volume-filling fraction of the polymeric woodpile that leads to locally nearly isotropic optical properties. Reproduced from [49].

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An object can be placed underneath the bump in the metallic floor. Of course, the bump leads to an extreme distortion (or aberration) of the reflection an observer sees from above, which would immediately raise suspicions that something is hidden underneath. These distortions can be approximately reversed or compensated by tailoring the locally isotropic refractive index of the surrounding. The refractive index on top of the bump needs to be higher than in the surrounding to compensate for the shorter optical path length, the refractive index on the two sides needs to be correspondingly lower. The false-color representation in Fig. 20 illustrates the target refractive-index profile, which can be mimicked by locally adjusting the volume filling fraction of a polymer woodpile photonic crystal used in the long-wavelength limit [50]. The performance of the structure can simply be tested by looking at it from the top. Ideally, the structure should appear as a flat hence unsuspicious metal mirror. Most importantly in the context of this review, the structure contains free-form surfaces (the carpet) and intentional complex non-periodicities (the index profile) at the same time. Using regular 3D DLW, operation at 1.4 μm wavelength became possible in 2010, but visible operation wavelengths were out of reach for regular 3D DLW.

Fig. 21 a and b exhibit electron micrographs of a structure fabricated using depletion 3D DLW with the DETC-based photoresist (see Sects. 'Stimulated-emission-depletion lithography' and 'Review of lithography experiments') using a bottle-beam for depletion [51]. (The fabricated structures are oriented upside down compared to Fig. 21.) Along these lines, a miniaturization from a woodpile rod spacing of inline image [50] (by regular 3D DLW) to inline image became possible [51]. At this rod spacing, the volume filling fraction can still be tuned over a considerable range (compare different Bragg-reflection colors for inline image in Fig. 18 b) whereas regular DLW can not realize a single filling fraction in the same photoresist (Fig. 18 a). To realize the refractive-index gradients of the target distribution, the excitation laser power was varied continuously while the depletion power was held constant. This leads to a gradually changing effective refractive index. The resulting 3D structure is so complex that usual characterization techniques such as electron microscopy literally only scratch the surface. However, the invisibility-cloaking performance of the complete 3D device can easily be tested by optical microscopy. We note that the supplementary material of [50] explicitly shows that the performance is very sensitive with respect to both, the high-index and the low-index regions.

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Figure 21. (a) Colored oblique-view electron micrograph of the polymer reference (top) and carpet cloak (bottom) structures (fabricated on glass substrate and coated with 100 nm gold). The scale bar corresponds to 10 μm. (b) Corresponding focused-ion-beam cuts of nominally identical structures. The scale bar corresponds to 2 μm. (c) and (d) are true-color optical micrographs of the structures in (a) taken with an optical microscope under circularly polarized illumination at 700 nm wavelength. Note the identical distortions due to the bump in both structures in (c) when inspected from the air side (serving as a control experiment). When inspected from the glass-substrate side in (d), the reference structure (top) still shows pronounced dark stripes. In sharp contrast, the stripes essentially disappear for the cloaking structure (bottom). Reproduced from [51].

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Fig. 21 c and d show true-color optical micrographs taken at 700 nm wavelength of light. When inspected through the glass substrate (see Fig. 21 a), the bump without cloak (i. e., the homogeneous woodpile) leads to two pronounced dark stripes in the image (Fig. 21 d, top). These aberrations essentially disappear in presence of the cloak (Fig. 21 d, bottom). The device is polarization insensitive [51], works for a large range of angles in three-dimensional space [52], is spectrally broadband from about 600 nm wavelength to about 3 μm, and not only works for the amplitude of the light wave but also for its phase [53]. Some years ago, such cloaking behavior was commonly believed impossible.

8 Conclusions and future challenges

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

In optical microscopy, STED-based and STED-inspired approaches have revolutionized the field and have opened new research possibilities, especially in life-science applications. Fluorescence optical microscopes on this basis have become commercially available. The Abbe diffraction limit is no longer the relevant limit and record spatial resolutions of 5.6 nm have been achieved at visible frequencies. If such spectacular resolutions could be translated from optical microscopy to optical lithography, many further new possibilities would arise. A revolution in nanotechnology might result.

In this review, we have described the underlying principles and have presented a snapshot of the current experimental state of the art. Today, several groups have convincingly demonstrated depletion effects in direct-laser-writing optical lithography as well as reduced feature sizes in the lateral and in the axial direction. However, much less experimental work has actually shown spatial resolutions – in Ernst Abbe's sense of resolving a grating with a certain period – beyond the diffraction limit. For applications aiming at complex 3D nanostructures, nanostructured effective materials, or 3D data storage [37], [54], it is spatial resolution that matters and not just linewidth or feature size. Today, the diffraction limit has been beaten both in the lateral and in the axial direction in optical lithography, too, but only by a margin much smaller than in optical microscopy.

To further progress towards lithographic resolutions of just a few tens of nanometers in three dimensions, new photoresist systems featuring, e. g., reduced radical diffusion and reduced unwanted absorption at the depletion wavelength need to be developed [26], [55].While the optics part still deserves further improvements, it is clear that optics does not impose any fundamental limits – in contrast to what was believed for decades. In this sense, this type of optical laser lithography is “diffraction-unlimited”. Successful photoresist development will likely require interdisciplinary efforts comprising physics, chemical physics, photo-chemistry, and polymer chemistry. Many researchers consider photoresists an issue that has long reached industrial status. However, corresponding basic research regarding diffraction-unlimited optical lithography has just started.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

We thank Tolga Ergin for fruitful discussions and help regarding the figure preparation, Andreas Frölich for the ZnO ALD, Georg von Freymann, Jonathan Müller, Andreas Naber, and Michael Thiel for helpful discussions. We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG), the State of Baden-Württemberg, and the Karlsruhe Institute of Technology (KIT) through the DFG Center for Functional Nanostructures (CFN) within subprojects A1.4 and A1.5. The project METAMAT is supported by the Bundesministerium für Bildung und Forschung (BMBF). The PhD education of J. F. is embedded in the Karlsruhe School of Optics & Photonics (KSOP).

  1. 1

    The Schwarzschild effect found in photographic plates is a similar example for a “forgetting” photosensitive medium and, hence, a deviation from our above simple exposure-dose definition with purely linear accumulation. The Schwarzschild effect corresponds to no darkening of the photographic plate if the incident light intensity is below a certain value – no matter how long the plate is illuminated.

References

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies

Biographies

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Abbe's diffraction limit: linewidth ≠ resolution
  5. 3 The generalized Sparrow criterion in 3D
  6. 4 The basic idea of depletion
  7. 5 Different depletion mechanisms
  8. 6 Review of lithography experiments
  9. 7 Applications in 3D structures
  10. 8 Conclusions and future challenges
  11. Acknowledgements
  12. References
  13. Biographies
  • Image of creator

    Joachim Fischer received his physics diploma in 2008 from the Universität Karlsruhe (TH) in Germany. His diploma thesis describes the fabrication and characterization of three-dimensional flexible micro-scaffolds for cell-culture experiments. Since then, he is working on his PhD project at the Karlsruhe Institute of Technology (KIT). His research interests include three-dimensional super-resolution laser-lithography and its applications.

  • Image of creator

    Martin Wegener After completing his PhD in physics in 1987 at Johann Wolfgang Goethe-Universität Frankfurt (Germany), he spent two years as a postdoc at AT&T Bell Laboratories in Holmdel (USA). From 1990–1995 he was professor at Universität Dortmund, since 1995 he is professor at Universität Karlsruhe (TH), now Karlsruhe Institute of Technology (KIT). Since 2001 he has a joint appointment at Institut für Nanotechnologie. Since 2001 he is also the coordinator of the DFG-Center for Functional Nanostructures (CFN) in Karlsruhe. His research interests comprise ultrafast optics, (extreme) nonlinear optics, photonic crystals, photonic metamaterials, transformation optics, and optical lithography. This research has led to various awards and honors, among which are the Alfried Krupp von Bohlen und Halbach Research Award 1993, the Baden-Württemberg Teaching Award 1998, the DFG Gottfried Wilhelm Leibniz Award 2000, the European Union René Descartes Prize 2005, the Baden-Württemberg Research Award 2005, and the Carl Zeiss Research Award 2006. He is a member of Leopoldina, the German Academy of Sciences (since 2006), Fellow of the Optical Society of America (since 2008), Fellow of the Hector Foundation (since 2008), and adjunct professor at the Optical Sciences Center, Tucson, USA (since 2009).