# Spatio-Temporal Proximity Characteristics in 3D μ-Printing via Multi-Photon Absorption

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

**Setup:**The SLM-based DLW setup differs from the conventional DLW setup by the introduction of an SLM, which is imaged by a 4-f setup onto the entrance pupil of the objective. Details on the SLM-based DLW setup may be found in [6].

**MF pattern:**The algorithm computing the phase pattern, which, in turn, leads to the desired MF is based on a weighted Gerchberg–Saxton algorithm that takes into account high numerical aperture effects. Details on this algorithm may be found in [7].

**Substrate preparation:**170 μm thick round glass substrates with a diameter of $30\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}$ are cleaned in two subsequent ultra-sonic bath steps (each $45\phantom{\rule{3.33333pt}{0ex}}\mathrm{kHz}$, $10\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$), first in aceton, second in isopropanol. Afterwards, substrates are rinsed with water and blow-dried.

**Resist application:**IP-L is drop-cast onto the substrate. IP-G is drop-cast onto the substrate and pre-baked for 1 h at $100{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}\mathrm{C}$. SU-8 50 is spin-coated at $3000\phantom{\rule{3.33333pt}{0ex}}\mathrm{rpm}$ for $30\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ to yield a $40\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}\mathrm{m}$ thick film. It is then soft-baked for $6\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$ at $65{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}\mathrm{C}$ followed by $15\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$ at $95{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}\mathrm{C}$. For SU-8, a post-exposure bake is necessary: $1\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$ at $65{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}\mathrm{C}$ followed by $4\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$ at $95{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}\mathrm{C}$. All bakes are done on a contact hot-plate.

**Development:**IP-L is developed by immersion of the sample in isopropanol for $20\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$ and subsequent rinsing with water. IP-G is developed by immersion in AZ–EBR (AZ Electronic Materials GmbH, Wiesbaden, Germany) for $20\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$. SU-8 is developed by immersion in AZ–EBR for $6\phantom{\rule{3.33333pt}{0ex}}\mathrm{min}$. All samples are gently blow-dried.

**Scanning electron micrographs:**Before taking the micrographs, samples are sputtered with $3\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}$ Iridium. A SEM (SU8000, Hitachi High-Technologies Corporation, Tokyo, Japan) is used to take the micrographs.

**Edge detection and fitting:**From the micrographs, the edges of the lines are automatically determined by Fourier transformation, filtering for edge enhancement and back transformation (also see Figure 1b). The fitting is computed by minimization of the mean-squared error.

## 3. Experimental Results

#### 3.1. Polymerization Reaction

- Photo initiator molecules two-photon absorb incident radiation and subsequently cleave into radicals.
- The generated radicals bind to monomer molecules, thus forming a propagation radical.
- The propagation radical continues to bind to monomer molecules until the chain reaction is terminated by inhibitor molecules (mostly oxygen) or a second radical.

- Photo initiator molecules two-photon absorb incident radiation and subsequently cleave into ions. In case of SU-8, H
^{+}cations are the initiating species. - The generated ions open ring-molecules ionizing the latter.
- The ionized molecule continues to open rings until the reaction is terminated by transfer reactions or bimolecular interaction with other species, e.g., water.

^{+}ion is much smaller than any of the rather complex radicals in radical-based polymerization, and thus more mobile, and second, oxygen does not influence the reaction. Therefore, we expect large differences in the spatio-temporal characteristics of the proximity effect in the two polymerization reactions.

#### 3.2. Proximity in IP-G (Gel-Like, Radical-Initiated)

#### 3.3. Comparison with IP-L (Liquid, Radical-Initiated)

#### 3.4. Comparison with SU-8 (Solid, Cation-Initiated)

#### 3.5. Interpretation

## 4. Numerical Results

#### Diffusion of Radicals

## 5. Discussion

## 6. Conclusions

^{2}/s. Further experiments are necessary to distinguish between radical and oxygen diffusion.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Figure A1.**Oxygen diffusion model fitted to the experimental data. The calculation is done on a discretized grid and no smoothing is applied.

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**Figure 1.**(

**a**) Inset: scheme of the arrangement of the two foci. Displacement of the foci orthogonal to the writing direction by $\Delta x$ and along the writing direction by $\Delta y$. One focus trails the other in time by $\Delta t=\Delta y/v$ with v being the writing speed. Main figure: Exemplary scanning electron micrographs of lines written in alternating writing directions with such a multi foci arrangement (indicated schematically). The linewidths w are defined and labelled according to their relative position (left focus $\to 1$, right focus $\to 2$, trailing along the writing direction $\to \mathrm{t}$ and leading along the writing direction $\to \mathrm{l}$). All linewidths are found by automatic edge detection from micrographs and are individually averaged over a length of several micrometers along the middle of each line (the latter avoids non-steady-state conditions); and (

**b**) edge detection method: scanning electron micrographs (pixel size $7\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm})$ are Fourier transformed, filtered in the Fourier domain and back transformed. Subsequently, remaining noise is removed and edges are detected by a steepest-slope approach.

**Figure 2.**Spatio-temporal characteristics of the broadening $b={w}_{\mathrm{t}}/{w}_{\mathrm{l}}$ in the gel-like, radical based photo resist IP-G. Squares indicate the measured data, the solid line a model fit to the experimental values, and the underlay the corresponding mean-squared error. (

**a**) Spatial characteristics of b for exemplary delays $\Delta t$; (

**b**) temporal characteristics of b for exemplary separations $\Delta x$; (

**c**) comparison of temporal characteristics of b in serial (open squares) and parallel (filled squares) writing mode; and (

**d**) spatio-temporal characteristics of b.

**Figure 3.**Writing power and speed dependence of the broadening $b={w}_{\mathrm{t}}/{w}_{\mathrm{l}}$ in IP-G. Squares indicate the measured data. The solid lines are trend lines given as a guide to the eye. (

**a**) Dependence of b on incident laser power; and (

**b**) dependence of b on writing speed.

**Figure 4.**Spatio-temporal characteristics of the broadening $b={w}_{\mathrm{t}}/{w}_{\mathrm{l}}$ in the liquid, radical based photo resist IP-L. Squares indicate the measured data, the solid line a model fit to the experimental values, and the underlay the corresponding mean-squared error. (

**a**) Spatial characteristics of b for exemplary delays $\Delta t$; (

**b**) temporal characteristics of b for exemplary separations $\Delta x$; (

**c**) spatio-temporal characteristics of b; and (

**d**) comparison of the temporal characteristics of b in SU-8 (open squares) and IP-G (filled squares) for exemplary values of $\Delta x$.

**Figure 5.**Radical diffusion scheme.

**Left**: the leading line affects the trailing line. Radicals diffuse from various positions on the leading line (

**red**circles) to position 1 (marked by the

**black**1). The

**white**lines denote the diffusion distance which changes over time. The lines indicate diffusion prior to the trailing spot reaching position 1. It follows from the figure: ${r}_{\mathrm{lt}}^{2}\left(t\right)=\Delta {x}^{2}+{(\Delta y-vt)}^{2}$ (v is the writing speed). ${t}_{\mathrm{w}}$ is the total writing time.

**Right**: the same as the left but indicating how the trailing line affects the leading line. Here, we find: ${r}_{\mathrm{tl}}^{2}\left(t\right)=\Delta {x}^{2}+{\left(vt\right)}^{2}$.

**Figure 6.**Effective diffusion constant determined from the fits. (

**a**) Dependence of the constant on the line separation in IP-L and IP-G. The

**grey**area indicates the spatial extent (full-width-half-maximum) of the excitation focus; and (

**b**) dependence of the constant on the time delay in IP-G. The

**red**line is an exponential fit to the data excluding the values at $4\phantom{\rule{3.33333pt}{0ex}}\mathrm{ms}$ and $100\phantom{\rule{3.33333pt}{0ex}}\mathrm{ms}$. The inset shows a log-plot of the data.

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**MDPI and ACS Style**

Waller, E.H.; Von Freymann, G. Spatio-Temporal Proximity Characteristics in 3D μ-Printing via Multi-Photon Absorption. *Polymers* **2016**, *8*, 297.
https://doi.org/10.3390/polym8080297

**AMA Style**

Waller EH, Von Freymann G. Spatio-Temporal Proximity Characteristics in 3D μ-Printing via Multi-Photon Absorption. *Polymers*. 2016; 8(8):297.
https://doi.org/10.3390/polym8080297

**Chicago/Turabian Style**

Waller, Erik Hagen, and Georg Von Freymann. 2016. "Spatio-Temporal Proximity Characteristics in 3D μ-Printing via Multi-Photon Absorption" *Polymers* 8, no. 8: 297.
https://doi.org/10.3390/polym8080297