3.1.

Photoresist and Substrate

The photoresist used in the experiments is a SU-8-based epoxy resin formulation called mr-X (micro resist technology GmbH) with additives to improve stability, sensitivity, and adhesion properties. Two versions, namely mr-X 10 and mr-X 50, are used actually in deep x-ray lithography to fabricate microstructures. The mr-X 10 resist has more solvent content compared to the mr-X 50 and is de facto more applicable for structuring thin resist layers, which is the case here. A standard characterization of these formulations is performed by the method described in Ref. 14, which is used to determine the contrast. The contrast will be translated here as dose threshold; higher contrast corresponding to a higher threshold. The wafers used are 4-in. silicon substrates with a thickness of 200 or $525\mu \mathrm{m}$ and coated with an oxidized $2.5\text{-}\mu \mathrm{m}$ titanium layer. The samples are spin-coated with $10\mu \mathrm{m}$ resist and stored for 4 to 5 days before exposure to allow the coated resist layer to settle.

3.2.

Exposure and Postprocess

The x-ray irradiations are performed at the LIGA-1 beamline of the ANKA/KARA synchrotron facility (KIT, Germany). The synchrotron has electron beam energy of 2.5 GeV and the beamlines are situated on a bending magnet (1.5T). The LIGA-1 beamline is equipped with a chromium single mirror; a grazing incidence angle of 15.4 mrad is used, cutting off x-ray photons with energies larger than $5{\mathrm{keV}}^3$. A $7.5\text{-}\mu \mathrm{m}$ thin film of polyimide is used between the mask and resist (sample) to absorb the photoelectrons from the titanium mask membrane. The standard bottom-dose used is $140\mathrm{J}/{\mathrm{cm}}^3$ as it has been identified in x-ray gratings fabrication (LIGA-1) with the mr-X resist. The required exposure dose (in mA.min/cm) for the specific parameters is calculated using the DoseSim¹² program. The exposure parameters are summarized in Table 1. A postexposure bake (PEB) is done at 65°C for the final curing of the samples. For the samples development, the freeze drying technique is used.¹⁵

Table 1

Exposure parameters for analysis of sub-μm periodic structures.

4.1.

Spectrum Discretization and Fresnel Diffraction

The low x-ray energy spectrum (2 to 4 keV) at the ANKA LIGA-1 beamline is most suitable for the fabrication of sub-$\mu \mathrm{m}$ periodic microstructures with periods smaller than $2\mu \mathrm{m}$ and with heights of several $10\mu \mathrm{m}$ owing to the high energy photons cut-off by the installed mirror optics. DoseSim uses a discrete spectrum, which is a function of the resist unit cell size ($10\mathrm{nm}\times 10\mathrm{nm}$ or $100\mathrm{nm}\times 100\mathrm{nm}$). For our purpose, only the 100-nm unit cell size could be employed. The discretization of the spectrum used in the simulation, after the mask and filter, is presented in Fig. 2. For the resist material, the data for the positive resist PMMA have been used; the data calculations for the negative resist are still in progress. Nevertheless, first calculations show that the point spread function of the dose deposition is comparable.

Fig. 2

Discretization of ANKA LIGA-1 spectrum ($100\mathrm{nm}\times 100\mathrm{nm}$ unit cells).

In Fig. 3, a comparison of the contribution of Fresnel diffraction in the case of the proximity in the order of $20\mu \mathrm{m}$ is shown. For simplicity, the simulation has been done for 3-keV monoenergetic source (majority of photons with this energy, see Fig. 2), $10\text{-}\mu \mathrm{m}$ thick resist, $10\text{-}\mu \mathrm{m}$ proximity between mask and resist layer and $1\text{-}\mu \mathrm{m}$ Au absorber thickness. A sideview of part of the dose distribution (width) is shown for the $10\text{-}\mu \mathrm{m}$ resist thickness (depth) when exposed from the top. The dose spreads out decreasingly from the exposed region (right) to the shadowed region (left). The white lines are the iso-dosis-lines labeled with the actual dose values in $\mathrm{J}/{\mathrm{cm}}^3$. Two iso-dosis-lines are represented (35 and $10\mathrm{J}/{\mathrm{cm}}^3$); these values represent the threshold between completely developed and undeveloped photoresist (mr-X-10). The difference in position is less than 3%, resulting in comparable widths achieved after exposure. Therefore, in the following simulation results, the effect of Fresnel diffraction has been ignored due to its negligible contribution in the final microstructure dimensions.

Fig. 3

Comparison of the effect of Fresnel diffraction on structural widths by simulation (3-keV monoenergetic source, $10\text{-}\mu \mathrm{m}$ resist, $10\text{-}\mu \mathrm{m}$ proximity, and $10\text{-}\mu \mathrm{m}$ Au absorber) (a) with diffraction and (b) without diffraction.

4.2.

Results

As an example, the simulation results of the influence of the photoelectrons generated in the resist on the dose deposition for a $1.4\text{-}\mu \mathrm{m}$ periodic structure are presented in Fig. 4. A simple periodic structure, where an absorbing region (metal) is present in between two nonabsorbing regions (resist) is simulated. The iso-dosis-line values are decreasing while spreading outward from the exposed region to the region underneath the absorber, with maximum dose at the center of the exposed areas. Due to the secondary effects, the increased dose underneath the absorber could initiate unwanted crosslinking of the resist in the shadowed region, which is intended to be developed completely for subsequent electroforming of metals. The iso-dosis-lines are labeled with the actual dose values in $0.01\mathrm{J}/{\mathrm{cm}}^3$.

Fig. 4

Iso-dosis-lines of $1.4\mu \mathrm{m}$ periodic structure with DC of 0.5. The values on the iso-dosis-lines indicate the actual dose in $0.01\mathrm{J}/{\mathrm{cm}}^3$. The Au absorber thickness is $1\mu \mathrm{m}$. The calculated bottom dose is $140\mathrm{J}/{\mathrm{cm}}^3$.

By choosing a crosslinking threshold of $35\mathrm{J}/{\mathrm{cm}}^3$, the opening region width decreases by 100 nm (700 to 600 nm). Decreasing the threshold to $10\mathrm{J}/{\mathrm{cm}}^3$, the simulated width is 300 nm smaller. Therefore, it should be possible to fabricate gratings with such periods, without having residual resist in the unexposed region. However, the width of the unexposed region is decreasing as a function of the resist contrast, and thus a duty cycle (DC) of 0.4 and 0.3 compared to the design value of 0.5, will be obtained for the threshold 35 and $10\mathrm{J}/{\mathrm{cm}}^3$, respectively.

To obtain a DC of 0.5 for the copy of the mask, the DC of the mask should be increased. In Fig. 5, a simulation of a DC 0.64 (absorber width is $0.9\mu \mathrm{m}$) is presented. In this case, a DC of 0.43 will be matched for the threshold $10\mathrm{J}/{\mathrm{cm}}^3$.

Fig. 5

Iso-dosis-lines of $1.4\mu \mathrm{m}$ periodic structure with DC of 0.64. The values on the iso-dosis-lines indicate the actual dose in $0.01\mathrm{J}/{\mathrm{cm}}^3$. The Au absorber thickness is $1\mu \mathrm{m}$. The calculated bottom dose is $140\mathrm{J}/{\mathrm{cm}}^3$.

One important fact is that the decrease of the width is constant (100 and 300 nm), and it is independent of the width of the absorber. This will be true until the dose deposition can reach a plateau; using LIGA-1 this plateau is reached for a width of $0.4\mu \mathrm{m}$. Below this value, the decrease will increase until the difference will be 0. By reducing the bottom-dose, the resist opening width will be increased for a given threshold. For example, by reducing the bottom-dose from 140 to $100\mathrm{J}/{\mathrm{cm}}^3$, the width is increased by 20 and 30 nm in the case of the $1.4\text{-}\mu \mathrm{m}$ period with DC 0.5 (see Fig. 6).

Fig. 6

Iso-dosis-lines of $1.4\mu \mathrm{m}$ periodic structure with DC of 0.5. The values on the iso-dosis-lines indicate the actual dose in $0.01\mathrm{J}/{\mathrm{cm}}^3$. The Au absorber thickness is $1\mu \mathrm{m}$. The calculated bottom dose is $100\mathrm{J}/{\mathrm{cm}}^3$.

As a summary, in Fig. 7, the simulated results for the two different thresholds are plotted, with $140\mathrm{J}/{\mathrm{cm}}^3$ as bottom-dose. The Au absorber width versus resist opening width is linear; this quality is not anymore present when the absorber mask width is so small that the deposited dose in the two irradiated parts overlaps. From these results, the minimum period will be in the range of 0.6 to $1.2\mu \mathrm{m}$ (DC: 0.5 for the mask), by using the two different thresholds. By reducing the exposure dose, this minimum period could be slightly reduced.

Fig. 7

Simulation of resist opening width against mask Au absorber width. The calculated bottom dose is $140\mathrm{J}/{\mathrm{cm}}^3$.

5.1.

Test Microstructures

To compare/validate the simulated results and experimentally realize the possibilities to fabricate sub-$\mu \mathrm{m}$ structures, at first, a $2.5\text{-}\mu \mathrm{m}$ titanium membrane mask was fabricated using E-beam lithography. The thickness of gold absorber structures is in the range of 0.65 to $1\mu \mathrm{m}$. The design includes 1-D grating fields ($2.5\mathrm{mm}\times 2.5\mathrm{mm}$) with periods from $2.4\mu \mathrm{m}$ down to $1.0\mu \mathrm{m}$ in $0.1\mu \mathrm{m}$ steps. There were seven fields for each period; each field presenting a different ratio between metal/resist opening and period of structures (DC), between 0.4 and 0.8. The image in Fig. 8 shows the arrangement of the various fields, with an example scanning electron microscope (SEM) image showing the Au structures. The lines are $20\mu \mathrm{m}$ long, with gaps/breaks in between (equal to the width of the line). These gaps act as support bridges for stability of the resist lamellae.

Fig. 8

Test fields arrangement for experimental realization of sub-$\mu \mathrm{m}$ microstructures using deep x-ray lithography (the missing structure fields in the top-left could not be fabricated by E-beam lithography due to their low DC and period).

5.2.

Results

Several aspects throughout the x-ray lithography process can influence the final quality of the microstructures. These include the mechanical stability and adhesion of the photoresist on a particular surface, the exposure dose that is applied during x-ray lithography, the adhesion promoting seed layer used between the photoresist and the substrate, the process of electroforming related to the desired metal to deposit, etc.

The parameters investigated concern one type of layer (TiOx) and one thickness ($10\mu \mathrm{m}$); the experiment is completed after the development process (no electroforming).

The characterization is performed using a SEM and the lateral measurements executed using an in-house developed program for the period and DC. The samples are sputtered with 20-nm gold layer for better imaging.

5.2.1.

Quality criteria of 1-D grating microstructures

The mechanical stability of the microstructures is an important innate characteristic of the formulation of the photoresist. It depends on the level of adhesion that is achieved on a specific layer or wafer surface, on the dose gradient, and the stresses induced during the PEB.

The resist lamellae should be straight as in Fig. 9(a). When all the parameters are not well chosen, the microstructures can undergo defects such as sticking, waviness, and crosslinking in the shadowed regions. Waviness could be due to inadequate resist crosslinking and/or poor adhesion [Fig. 9(b)]. Sticking may arise from the same conditions plus due to improper development and drying of the samples [Fig. 9(c)]. Crosslinking in the shadowed regions may be due to overexposure of the samples [Fig. 9(d)]. Any shifts in the sensitivity/contrast of the photoresist also mean incorrect estimation of the required dose for resist crosslinking and therefore introduces defects in the final microstructures.

Fig. 9

Quality criteria of test microstructures using deep X-ray lithography including (a) ideal quality, (b) sticking, (c) waviness, and (d) crosslinking in the unexposed part and cracks in the resist lamellae.

5.2.2.

Variation of bottom dose and contrast

The influence of the exposure dose (different doses) applied during x-ray lithography on the gratings quality is analyzed by applying different doses, while the other process parameters are kept the same (resist coating, baking, development, etc.). In addition, samples prepared with the same photoresist formulation (mr-X 10) but different supplied batches (batch-1 and -2) were also compared. Table 2 lists the samples with the variable parameters used.

Table 2

List of samples with the variable parameters of bottom-dose and resist batches.

Sample	Bottom-dose, BD (J/cm3)	mr-X 10 batch
Sample-1	140	Batch-1
Sample-2	140	Batch-2
Sample-3	140	Batch-2
Sample-4	100	Batch-1
Sample-5	100	Batch-2

Exemplarily, an overview of the fields from sample-2 for 1.6, 1.4, and $1.2\mu \mathrm{m}$ periods with different DC (five for each period) is shown in Fig. 10. The defects seen in field ($k$) are due to mask defects. Some random sticking of lamellae is seen in few fields as (j), (l), and (o). With a minimum period of $1.2\mu \mathrm{m}$, resist structural width of $\sim 450\mathrm{nm}$ (AR 22) is achieved, which is almost at the limit of being mechanically stable [Fig. 10(o)].

Fig. 10

Overview of SEM images of periodic microstructures with period (a)–(e) $1.6\mu \mathrm{m}$with increasing DC, (f)–(j) $1.4\mu \mathrm{m}$ with increasing DC, and (k)–(o) $1.2\mu \mathrm{m}$ with increasing DC; for resist thickness of $~10\mu \mathrm{m}$ (sample-2). Defects from the mask transferred to resist in (k). Random sticking of resist lamellae in (j), (l), and (o)

In Figs. 11 and 12, the relation between the mask absorber widths and the resulting resist opening widths on the sample is plotted for various periodic fields from sample-1 and sample-2 (same bottom-dose $140\mathrm{J}/{\mathrm{cm}}^3$). The relationship is relatively linear and independent of the period, as it was pointed out in the simulation for the same exposure parameters.

Fig. 11

Graphical representation of resist opening widths achieved from corresponding absorber widths on the mask from sample-1.

Fig. 12

Graphical representation of resist opening widths achieved from corresponding absorber widths on the mask from sample-2.

However, for the samples prepared from different resist batches, a change in the resist contrast can be observed. In Fig. 13, a comparison concerning the $1.4\text{-}\mu \mathrm{m}$ period for sample-1, sample-2, and sample-3 shows clearly this difference between batch-1 (sample-1) and batch-2 (sample-2 and sample-3). Sample-1 presents a lower contrast, which results in a higher crosslinking in the unexposed part, producing thicker resist lamellae (smaller openings). The difference in structural widths due to difference in resist contrast of batch-1 and batch-2 is between 7% and 16%.

Fig. 13

Graphical comparison of resist opening widths achieved from corresponding absorber widths on the mask for period $1.4\mu \mathrm{m}$ fields between sample-1, sample-2, and sample-3 prepared from two resist batches (batch-1 and batch-2).

Two bottom-doses 100 and $140\mathrm{J}/{\mathrm{cm}}^3$ are tested in case of two sets of samples prepared with different batches. Figure 14 presents the $1.4\text{-}\mu \mathrm{m}$ period measurement comparison of sample-1 (BD $140\mathrm{J}/{\mathrm{cm}}^3$) and sample-4 (BD $100\mathrm{J}/{\mathrm{cm}}^3$) using batch-1 and in Fig. 15 the comparison of sample-2 (BD $140\mathrm{J}/{\mathrm{cm}}^3$) and sample-5 (BD $100\mathrm{J}/{\mathrm{cm}}^3$) using batch-2.

Fig. 14

Graphical comparison of resist opening widths achieved from corresponding absorber widths on the mask for period $1.4\mu \mathrm{m}$ with two bottom-doses 100 and $140\mathrm{J}/{\mathrm{cm}}^3$ between sample-1 and sample-4.

Fig. 15

Graphical comparison of resist opening widths achieved from corresponding absorber widths on the mask for period $1.4\mu \mathrm{m}$ with two bottom-doses 100 and $140\mathrm{J}/{\mathrm{cm}}^3$ between sample-2 and sample-5.

In both cases (batch-1 and batch-2), as expected, a lower bottom-dose of $100\mathrm{J}/{\mathrm{cm}}^3$ (sample-4 and sample-5) produces wider resist openings. The difference observed is not linear: $\sim 16\%$ larger resist opening (110 nm) is achieved for smaller mask absorber width; the value is $\sim 6\%$ (50 nm) for larger absorber width. Using a lower bottom-dose seems to be more appropriate to obtain the desirable structure dimensions similar to the mask. Using a smaller bottom-dose also minimizes the possibilities of having residual resist at the bottom of the structures in the unexposed regions. In contrast, for thicker resist layers (larger than the $10\mu \mathrm{m}$ used here), the smaller bottom-dose could introduce instability.