1. Introduction

In recent years highly efficient diffraction gratings became a key component in many optical devices. For example, they are essential elements in high performance spectrometers, in spectral laser beam combining and in the field of laser pulse manipulation [1, 2]. These so called high performance applications have special demands on various grating characteristics, e.g. diffraction efficiencies higher than 90%, a high spectral dispersion and a broad spectral bandwidth. Furthermore those gratings, especially when they are used in high performance spectrometers or pulse compression set-ups, need to cover a large area in the range of several centimeters [2].

Electron beam lithography (EBL) has been shown to be a versatile method which allows fabricating micro-optical devices like spectrometer gratings with a very high resolution and accuracy [3]. Therefore, EBL allows a reliable fabrication of gratings that fulfill the mentioned demands. However, this technique is restricted to lateral dimensions, in which the grating structure can be fabricated with highest precision. This lateral area of maximum fabrication accuracy is referred to as a “subfield” with lateral dimensions p_sub × p_sub . In order to write a large area grating several single subfields have to be stitched together. In general, this subfield stitching is not executed perfectly and thus is prone to generate deterministic or statistic errors that are periodic with the size of a single subfield.

Therefore, gratings that were fabricated by EBL inherently possess next to their dominating grating period p a super-period p_sub. Such a super-period generates additional spurious diffraction orders at the positions $k_m=m\cdot 2\pi /p_{sub}$ in reciprocal space (m∈ℤ). These undesired artefact in the optical response of the grating appear as distinct stray light peaks in the scattering spectra and are also known as “Rowland ghosts” [4]. Growing demands on spectrometer gratings require an optimized stray light performance [5, 6] concerning in particular the disturbing Rowland ghosts.

In this paper the optimization of the stray light performance regarding the Rowland ghosts of a current spectrometer grating is demonstrated. We will present different approaches for improving the optical performance of the binary grating. As a first approach the technique of the “multi-pass-exposure” and their influence on the Rowland ghosts is investigated. In this technique the sample is exposed multiple times with an accordingly shifted and dose-reduced subarea in each pass. As a second method the direct improvement of the alignment accuracy during the writing process via special calibration parameters is investigated.

For this purpose several gratings were fabricated in different writing regimes and their stray light performance in dispersion direction was measured. The investigated binary grating was designed to have a period p = 667 nm, groove width CD = 237 nm and a depth d = 1639 nm. This grating structure was etched into a fused-silica substrate. The angle resolved scattering (ARS) was measured for a wavelength of 633 nm and an incident angle of 33° which leads solely to the propagation of the −1st and 0th diffraction order. In this mount the grating possesses a diffraction efficiency of ${\eta }_{-1}=84.6\%$.

2. Origin of Rowland ghosts in electron beam lithography

For the fabrication of large area gratings by EBL a special writing strategy is needed to address all regions of the grating by the electron beam. For the sake of illustration, Fig. 1 shows a scheme of the functionality of EBL using the variable shaped beam exposure method [7, 8]. The precise position of the electron beam is controlled by different electro-magnetic deflection systems in the electron column. Additionally, the substrate to be exposed is mounted on a substrate stage moving along x- and y-direction. In EBL the grating grooves are exposed successively and the position of the electron beam can be controlled with a very high accuracy by means of the electrostatic deflection system. Unfortunately, this excellent positioning accuracy can be achieved only within a very restricted area. Hence, in order to fabricate large area gratings the grating area must be divided into several subareas, which are sub-sequentially exposed and stitched together leading to the final full size grating. This division and assembly occur twice and the corresponding subareas are named “subfields” (SUB) and “stripes” (STR). In the standard writing regime of the e-beam writer used for the current grating fabrication experiments, the typical lateral sizes of these subareas amount to p_sub = 35 μm and p_str = 625 μm.

 

Fig. 1 Simplified illustration of the working principle and the stitching process in EBL using the variable shaped beam exposure method.

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Due to a finite alignment accuracy the subareas induce secondary periodic structures that are prone to generate spurious secondary diffraction orders (Rowland ghosts). An ARS measurement of a current grating fabricated by this technology shown in Fig. 2 reveals the undesired Rowland ghosts in vicinity to the grating main diffraction orders around −24° and 33°.

 

Fig. 2 Left: Typical ARS measurement (λ = 633 nm) in transmission around the −1st and 0th diffraction order (DO) of a non-optimized spectrometer grating fabricated by EBL. Right: Illustration of the measurement constellation and the grating geometry.

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The Rowland ghosts that appear in the measurement are typically five orders of magnitude smaller than the −1st diffraction order but, nevertheless, they constrain the optical performance especially of high performance spectrometers, e.g. in Astronomy or Earth observation [6, 9]. Even though this is a very low value and sufficient for a lot of applications, it’s desired to reduce the disturbing Rowland ghosts most effectively or even to make them vanish.

The exact modality of the stitching inaccuracy was profoundly investigated in [10]. The results of this work can now be used to optimize the stray light performance of a high performance spectrometer grating. Following the findings in [10], the Rowland ghosts in the presented ARS measurement (see Fig. 2) mainly arise due to deterministic positioning inaccuracies of the stitched subfields, whereas statistic positioning inaccuracies are negligible.

3. ARS measurement set-up

The ARS in the dispersion direction of the grating was measured by the use of a double circle goniometer stage. The piezo controlled goniometer allows a positioning of the source and the detector with an accuracy of Δθ ≈ 0.001°. As the light source we used a Helium Neon laser with a wavelength of λ = 632.8 nm and a full width half maximum of less than 0.8 nm. Thus, the measured ARS is free of dispersion artefacts of the incident laser beam. Further, the light was coupled into a fiber, which gives an almost perfect Gaussian beam profile and additionally allows a comfortable handling of the incident beam on the goniometer.

The beam was focused by a single lens through the sample onto a slit that is mounted in front of the detector. The slit has dimensions of 50 μm × 2.5 mm and ensures that only signals in a small range around the adjusted scattering angle are measured. The light beam that is impinging onto the grating still has a diameter of about 15 mm. Thus, a large number of subareas and single grating periods is illuminated and the resulting measurement is therefore representative for integrating effects like stray light. Furthermore, this large illumination area allows a distinct propagation of the Rowland ghosts that arise from super periods in the range of p_str = 625 μm.

As detector we used a conventional photodiode-detector, which possesses a dynamic range of 4.5 orders of magnitude. With this set-up the measurement was restricted to an efficiency range of 10⁻⁴…10⁻⁸, stronger signals provoke a detector saturation and weaker signals are covered by thermal noise.

With a measured signal intensity I_S(θ_S) for an adjusted scattering angle θ_S and the reference signal of the incident beam I₀ the corresponding value of the angle resolved scattering (ARS [7],) can be calculated by

4. Optimization of the fabrication process

4.1 Grating design and fabrication

The examined grating was designed in the framework of the FIMAS/FLEX-project of the European Space Agency (ESA) with respect to special demands on the diffraction efficiency. The desired diffraction efficiency of more than 80 % in the −1st diffraction order in a band of λ = [610 nm … 820 nm] can be addressed by a simple binary phase grating. The grating is designed to possess a period p = 667 nm, groove width CD = 237 ± 20 nm and depth d = 1639 ± 50 nm. A typical scanning electron microscope (SEM) image of the cross section of such a grating is depicted in Fig. 3(a). Because of the deep trenches and the high aspect ratios, the geometry of the grating slightly differs from the ideal binary shape. The platinum that surrounds the grating bars was necessary in order to prepare the cross section view. Figure 3(b) also shows a SEM-image of the corresponding resist structure with a groove width of CD ≈ 180 nm.

 

Fig. 3 SEM-image of (a) the cross-section of the fused silica grating (with the platinum necessary for the cross-section preparation) and (b) the resist structure (FEP171) of the examined grating. The scale bars are 250 nm.

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Furthermore, within the project there are special demands on the stray light performance. A first fabricated test grating without stray light optimization also fulfills the requirements that demand Rowland ghosts of a maximum intensity of 10⁻⁴ compared to the useful diffraction order (see Fig. 2). Nevertheless, it is advisable to optimize the parasitic Rowland ghosts further. A successful optimization process requires several stray light measurements on gratings fabricated in different writing-regimes. In order to shorten the time consuming fabrication sequence of e-beam-exposure, resist (FEP171) development, chromium-mask-etching, deep SiO₂-etching and mask removal, most ARS measurements are executed already after the resist development. This shouldn’t affect the results for fully processed deep gratings as the characteristics of the Rowland ghosts do not depend on the state of the sample. This assumption can be deduced from the findings in [10], where it was shown that the effects of alignment errors on the ARS can be described within Fraunhofer approximation. Thus, at least the qualitative characteristics of the Rowland ghosts are independent of the state of the sample and the measurement constellation. Though, the finally fabricated grating with optimized stray light performance is processed completely in order to show explicitly the applicability of the achieved improvements on deep gratings. Thereby, the provided ARS measurements in the resist structure in reflection (see e.g. Figure 4) as well as in the pure fused silica grating in transmission (see Fig. 8) even show a quantitative conformity of the Rowland ghosts.

 

Fig. 4 Left: ARS measurement (λ = 633 nm) in reflection around the −1st DO (at Δθ = 0°) of two gratings that were fabricated in the 1-pass- and 4-pass-regime, respectively. Right: Illustration of the measurement constellation and the grating geometry.

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4.2 Multi-pass-exposure (MPE)

One method to reduce the impact of alignment errors is the already well known technique of the “multi-pass-exposure” [11]. In this approach the sample is exposed multiple times with an accordingly reduced dose in each exposure-pass. Furthermore, each pass is shifted in its lateral position by a fractional amount of the subarea’s size with respect to the previous pass. Thus, the subareas of different passes are overlapping which significantly reduces artifacts at the stitching positions due to an averaging effect. The effects of this method on the stray light performance of a grating is investigated in this section.

For this purpose two gratings were fabricated with different pass numbers N = 1 and N = 4. The corresponding stray light measurement of the 1-pass- and 4-pass-grating is shown in Fig. 4. The ARS measurement in reflection was performed after the resist development with an incident angle of θ_inc = 20°. In the ARS(Δθ)-graph the stray light is measured at ± 6° around the −1st diffraction order and the x-Axis is related to θ₋₁ = −37.4°, hence, Δθ = θ_S − θ₋₁.

The disturbing Rowland ghosts arise as distinct stray light peaks symmetric to the −1st DO. Because of the 2 different super-periods p_sub and p_str we find 2 kinds of Rowland ghosts which we will refer to as SUB- and STR-ghosts, respectively. The black arrows in Fig. 4 indicate the SUB-ghosts whereas the numbered peaks belong to the STR-period. The ARS measurement of the 1-pass-grating reveals an almost perfect match of the −1st DO of the ideal grating with one SUB- and STR-ghosts, respectively. An explanation of this behavior can be found in the chosen writing strategy of the e-beam-writer. Here the SUB-subarea always is an integer multiple of the grating period whereas the STR-period is a multiple of the SUB-period:

As a consequence of the N-pass-exposure strategy, the overlapping subareas of different passes effectively reduce the sizes of the SUB- and STR-subareas to$p_{sub}/N$ and $p_{str}/N$, respectively. In the stray light measurement a reduced super-period should generate less spurious Rowland ghosts. This effect can clearly be seen in the ARS measurement of the 4-pass-grating shown in Fig. 4 as a blue curve. Compared to the ARS-curve of the 1-pass grating only every fourth STR-ghost remains and all the interjacent ghosts disappear almost completely. The same effect can be observed in the occurrence of the SUB-ghosts, but here every third SUB-ghost instead of every fourth remains. This is caused by a more complex algorithm used by the e-beam data generation software in the applied writing strategy. This is not discussed further in this paper as it is not important for the writing process optimization and very specific for the used e-beam writer.

In summary, the Rowland ghosts can be clearly identified and certainly related to the corresponding lithography process features. The MPE reduces the number of the spurious ghosts very effectively. On the other hand, an influence of the pass number N on the strength of the remaining Rowland ghosts was not observed.

4.3 Fine-tuning of the stitching process

A second approach to lower the Rowland ghosts is the direct improvement of the positioning accuracy in the writing process, i.e. the improvement of the stitching of the single subfields and stripes. The e-beam-writer offers several calibration parameters that control the SUB- and STR-alignment. Usually these calibration parameters are monitored regularly by the characterization of coordinate-positions of special test structures and alignment marks, respectively. In this way we tried to optimize the stray light performance of several test gratings, too, but it turned out that this approach was not successful. This is an indication that this method is able to optimize the alignment of adjacent subfields at local positions or very restricted areas very efficiently, but that it is not convenient for improving the overall average alignment accuracy. However, stray light is an integral effect and thus, it is not well indicated by the local marks. Therefore, it turned out that the relevant calibration parameters are much more sensitively determined by performing and evaluating stray light measurements.

Gratings that are fabricated by electron beam lithography possess Rowland ghosts that are mainly caused by deterministic alignment errors during the subfield stitching process. In particular they originate in a constant positioning error of the subareas that results in a gap or an overlap of adjacent subareas whereas statistic positioning errors as well as uniformity errors (of e.g. the CD throughout each subfield) do not have a significant effect onto the scattering spectra [10]. In the used e-beam-writer Vistec 350OS the positioning of the subareas (SUB) is controlled by the micro deflection system which can be tuned by parameter Δ_sub. The STR-positioning is controlled by the macro-deflection-system which is tuned by parameter Δ_str. In the following the influence of these parameters on the stray light performance of several gratings fabricated in the 1-pass-exposure-regime is investigated. The quantity of Δ_sub and Δ_str is given in arbitrary units and their variation is based on the 1-pass grating shown in Fig. 5 which was defined to be the standard according to Δ_sub = 0 and Δ_str = 0.

 

Fig. 5 Left: ARS measurement (λ = 633 nm) in reflection around the −1st DO (at Δθ = 0°) of two gratings fabricated with different STR-overlap. Right: Illustration of the measurement constellation and the grating geometry.

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In order to optimize the STR-stitching several gratings were fabricated with constant parameter Δ_sub and varying Δ_str and their ARS was measured. Figure 5 shows the best and the worst curve regarding the overall stray light performance. We find that the strength of the STR-ghosts can be reduced significantly. In particular in the small angular range of ± 1° around the −1st DO almost all STR-ghosts decrease by actually one order of magnitude. On the other hand, it can be seen that the strength of the SUB-ghosts (marked by black arrows in Fig. 5) remains unaffected.

Instead the strength of the SUB-ghosts can be influenced by turning parameter Δ_sub. The ARS measurements of two gratings fabricated with very different SUB-stitching is depicted in Fig. 6. We find that the strength of the SUB-ghosts can be reduced significantly, e.g. the 1st SUB-ghost next to the −1st diffraction order (at Δθ = 1.3°) decreases by almost 2 orders of magnitude. Furthermore, the measurement reveals also a minor influence of Δ_sub on the strength of the remaining STR-ghosts. Indeed it can be seen that they are reduced slightly. Though, considering the fact that the parameter Δ_sub has been varied strongly its influence on the STR-ghosts can be neglected.

 

Fig. 6 Left: ARS measurement (λ = 633 nm) in reflection around the −1st DO (at Δθ = 0°) of two gratings fabricated with different SUB-overlap. Right: Illustration of the measurement constellation and the grating geometry.

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Although all the Rowland ghosts don’t vanish completely, a best calibration state can be confirmed. As an example in Fig. 7 the strength of the 1st SUB-ghost (at Δθ = 1.3°) is plotted as a function of parameter Δ_sub. The graph shows a parabolic behavior of the strength of the Rowland ghosts on the calibration parameters and the subfield-gap, respectively (cf [10].). By finding the minima of the fitted parabola curve the best calibration state can be determined.

 

Fig. 7 Dependency of the 1st SUB-ghost next to the −1st DO on the parameter Δ_sub.

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It needs to be emphasized that this calibration can only be performed by the shown stray light measurements as the standard method of a microscopic investigation of alignment marks is not suited for optimizing integrating effects that average over a huge number of subfields (e.g. stray light). In summary, the strength of the Rowland ghosts can significantly be influenced by tuning the calibration parameters that are offered by the e-beam-writer. Although it is not possible to make the ghosts vanish completely, they can be reduced by more than one order of magnitude.

4.4 Fine-tuned multi-pass-exposure

In the previous experiments two approaches that are suited for improving the stray light performance of binary spectrometer gratings were presented. So far the results show a significant influence of both approaches on the stray light performance. In particular the MPE is able to reduce the number of Rowland ghosts whereas a fine-tuning is able reduce their strength. Though, both techniques separately still show remaining Rowland ghosts in the stray light spectra.

A combination of both techniques finally allows fabricating gratings with an optimized stray light performance. The corresponding ARS measurement of such a grating is shown in Fig. 8. Now the measurement was performed in transmission on a fully processed fused silica grating with an incident angle of θ_inc = 33°. The measured angular range was $\Delta \theta =\left[-1°,\dots ,10°\right]$ related to the −1st diffraction order (θ₋₁ = −23.8°). Figure 8 also shows a measurement of a non-optimized grating in order to emphasize the improvement of the stray light performance. With the combination of a fine tuned stitching and an 8-pass exposure a conspicuous reduction of the Rowland ghosts was achieved. The Rowland ghosts disappear almost completely. Solely the 8th SUB-ghost remains with a very weak strength and there occurs another tiny peak close to the 3rd SUB-ghost. Unfortunately, a thorough explanation of this peak is not yet available.

 

Fig. 8 Left: Comparison of the ARS measurements (λ = 633 nm) around the −1st transmitted DO (at Δθ = 0°) of two gratings that were fabricated before and after the fabrication process optimization. Right: Illustration of the measurement constellation and the grating geometry.

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5. Conclusion

In this article we demonstrate the successful optimization of the stray light performance of a binary spectrometer grating fabricated by e-beam lithography. The stray light optimization in particular concerns about the spurious Rowland ghosts. As the Rowland ghosts arise from special super periods that have their origin in the writing regime, two different optimization-methods were investigated. On the one hand, the technique of the multi-pass-exposure effectively reduces the number of the propagating Rowland ghosts. On the other hand, a direct improvement of the alignment process of subfields via special calibration parameters influences the strength of the spurious ghosts.

The achieved results show that specific calibration parameters of the e-beam writer combined with an adapted writing regime reduces the peaks significantly. A quantitative reduction of the strength of the Rowland ghosts of almost two orders of magnitude was achieved.