6.2 Properties of Flexible Molds
6.2.2 Lateral Stability of PDMS Molds
In contrast to roof collapse, the deformation mechanism discussed here is not based on the interaction of the mold with the surface of a substrate. Instead, the elastic behavior of the mold material in combination with the adhesive forces between the protrusions causes the imprinted profile to differ from the one of the rigid master. The lateral collapse of the mold protrusions is depicted schematically in Fig. 6.5. As soon as their strain energy is sufficiently low to be overcome by adhesion, neighboring protrusions spontaneously jump into contact. For this to happen, the lateral collapse requires thathmbe at least on the order ofw. Therefore, this effect is not observed on the molds with indentations on the micrometer scale (cf. Chapter 6.1.1).
w
hm
PDMS-mold
s
Figure 6.5: Schematic diagram of laterally collapsed line patterns of an elastic mold (cross-sectional view). The collapse is induced by the adhesive interaction of neighboring protrusions.
A quantitative stability criterion has been derived by Hui et al. based on a model of two isolated plates clamped at one end.[197] According to their theory, lateral collapse of line patterns occurs for cavity widthsw<w˜crit, with
˜ wcrit= 5
sγsh4m
Eζ3 (6.2)
andζ =s/w.
on the nanometer scale from the NIL-Technology master were carried out with the PDMS polymers Elastosil®601 and Sylgard®184. The surface energy γsof PDMS is on the or-der of 20 mJ m−2.[196,198]By inserting a typical modulus ofEElastosil=1.4MPa and a height of hm =100nm into Eq. (6.2), one obtains ˜wcrit=68nm for ζ =1 (type I pattern) and
˜
wcrit=45nm for ζ =2 (type II pattern). Young’s modulus is chosen to be the one of Elastosil®601, which is lower than that of Sylgard®184 (ESylgard≈1.8MPa).[195,199]From the above results, lateral collapse is not expected to occur for any of the line patterns on the molds prepared from both PDMS polymers.
However, while the 150 and 300 nm line patterns kept their lateral line profile after re-lease from the master, the 100 nm line patterns were found to collapse for both polymers.
These values denote the cavity width w and are valid for both type I and II molds. The deformation caused by lateral collapse is illustrated in Fig. 6.6 a) and 6.6 b) for 100 and 300 nm line patterns of type I molds prepared from Elastosil®601, respectively. For de-creasing values of w, the periodic arrangement of parallel lines transforms into a compli-cated Y-branched pattern. Consequently, the true value of ˜wcrit turns out to be in the range 100nm<w˜crit<150nm.
a) b) c)
Figure 6.6: AFM pictures of line patterns of molds prepared from different UV-curable polymers.
a) Laterally collapsed 100 nm line pattern prepared from Elastosil®601 (type I). b) 300 nm line pattern prepared from Elastosil®601 (type I). c) 100 nm line pattern prepared from EVG® (type II).
Deviations from theory can be attributed to the fact that the stability criterion in Eq. (6.2) is based on the assumption that two isolated plates protrude perpendicularly from a rigid substrate. Obviously, this applies here only partially, since the protrusions are located on a flexible underground which can bend itself. The derivation of Eq. (6.2) then overestimates the strain energy required to deform the structures and ˜wcritis predicted to be smaller than the measured value. Nevertheless, Eq. (6.2) yields valuable information about the influence of changes in specific mold parameters on the lateral stability.
The absence of Y branches for 150 nm line patterns suggests that even a slight increase in Young’s modulus of the polymers may be sufficient to prevent lateral collapse. For PDMS polymers, E is known to be almost doubled if curing is performed at elevated tempera-tures.[193] Thus, Elastosil®601 and Sylgard®184 molds were cast from the master under different curing conditions. In procedure 1 (P1), curing was performed overnight at room temperature and, subsequently, the polymer was stored at 80◦C for 14 h. For molds prepared according to procedure 2 (P2), the resin was heated up to 150◦C within 20 min immediately after it had wet the master and was kept at this temperature for 12 h. The latter preparation method is expected to increase Young’s modulus of the PDMS polymers as a consequence of a higher degree of cross-linking caused by the higher curing temperature.
6.2 PROPERTIES OF FLEXIBLE MOLDS 55 First, the profiles of line patterns of type I and II molds withw=300nm prepared from the two PDMS polymers under the above curing conditions were investigated. Three re-presentative profiles measured with AFM are shown in Fig. 6.7. After release, the surface tension deforms the elastic PDMS molds, until an equilibrium state is reached. Thus, flex-ible molds generally develop rounded corners at their edges, even if cast from a perfectly rectangular shaped master. A lower limit for the radius of curvature isR≈γs/E, which is on the order of 50 nm in PDMS.[196] Since the Elastosil®601 molds have the lowest Young’s modulus, their profiles show the strongest deviations from the rectangular profile. The pro-file of an Elastosil®601 mold with 1 : 1 spacing prepared withP1looks almost sinusoidal due to the spatial proximity of the protrusions (Fig. 6.7, bottom). The higher curing tem-perature ofP2produces line patterns with slightly sharper edges although the profile of the investigated mold with 2 : 1 spacing reveals slanted sidewalls (Fig. 6.7, middle). Preparing Sylgard®184 molds withP2results in a significantly improved reproduction of the edges (Fig. 6.7, top). As compared to Elastosil®601 molds, however, the transferred cavities are clearly narrower. In sum, adjustment of the annealing procedure has a much smaller influ-ence on the mold quality than varying the polymer type.
0
Figure 6.7: AFM profiles of 300 nm line patterns of PDMS molds prepared under different curing conditions. Bottom: Profile of an Elastosil®601 mold (type I) prepared fromP1. Middle:
Profile of an Elastosil®601 mold (type II) prepared from P2. Top: Profile of a Sylgard®184 mold (type II) prepared fromP2.
The lateral collapse of the 100 nm structures could not be avoided, neither by curing the molds at higher temperatures nor by preparing them from Sylgard®184. Unlike roof collapse, the shape of the mold does not change during imprinting. Instead, the Y-branched patterns are transferred to the azobenzene resist material. Laterally stable line patterns with w=100nm for type I and II molds were obtained only after changing the mold material to the EVG® polymer and applying the preparation method discussed in Chapter 6.1.2. The reason is that the cured EVG®polymer features an increased Young’s modulus. In addition it is functionalized with fluorine, whereby its surface energy is significantly lower than that of PDMS. The profile of a 100 nm EVG®line pattern (type II) is shown in the AFM image of Fig. 6.6 c), revealing homogenous, uncollapsed lines. As a drawback, adhesion of an EVG®mold to an arbitrary substrate decreases as well, which affects the imprinting speed.
nanometer-sized structures should preferably consist of the same material. Hence, using Elastosil®601 molds is reasonable for imprinting uncollapsed 150 and 300 nm line patterns as well as for rectangular and hexagonal arrangements of punches.
7
Experimental Section
7.1 Holographic Setup
Inscription of holographic gratings was performed with the setup shown in Fig. 7.1. It has been built and improved during several PhD works.[85,184,200,201]
P
λ/2 P
λ/2 P BS
PD PD
sample λr
λw
EOM
PD PD L
Figure 7.1: Setup for the inscription of plane-wave holographic gratings. BS: beam splitter, λ/2: half-wave plate, P: polarizer, PD: photodiode, EOM: electro-optical modulator, L: lens.
Coherent light for the inscription of the holographic gratings is provided by an argon-ion laser (Coherent Innova 307) at a wavelength ofλw=488nm or by an optically pumped semiconductor laser (Coherent Genesis™ MX SLM Series) atλw=489.2nm. Owing to the system change during the PhD work, the wavelengths of the two laser systems differ slightly. The influence on the efficiency of the azobenzene isomerization, however, is neg-ligible. In both cases, the n→π∗ transition of the azobenzene-functionalized samples is excited, giving rise to atrans-rich state during illumination. Since this reduces the num-ber of randomly relaxingcisisomers after the inscription process, the long-term stability of volume holograms is fostered. The writing beam first passes a lens (see discussion below).
Subsequently, it is divided into two beams by a beam splitter. Either of them is deflected by a mirror, such that they interfere at the sample position. Their intensity and polarization can be adjusted individually by an arrangement of a half-wave plate and a polarizer. Unless
57
was eitherpporss, depending on whether SRG formation was desired or not. In both cases, sinusoidal intensity gratings are generated at the interference region.
The temporal evolution of a grating is monitored with ans-polarized diode laser (Laser 2000 PMT24). Since its peak wavelength ofλr=685nm is outside the azobenzene absorp-tion band, it does not affect the development of the grating. The reading laser is adjusted to hit the center of the grating with an optical power of 87 µW. The intensities of the 0th and 1st diffracted order emerging behind the sample are measured with photodiodes (Thorlabs PDA-55). Their signals are processed with lock-in amplifiers (Stanford Research Systems SR830) operating with an integration time of 10 ms. For this purpose, the intensity of the reading laser is modulated at a frequency of 10 kHz. This measurement method results in a high signal-to-noise ratio with the lower detection limit of the diffraction efficiency as low as 1×10−6.
To generate gratings with constant periodicity throughout the entire interference region, the wave fronts of the writing beams have to be highly planar. For a laser with Gaussian intensity profile this requirement is best fulfilled near its beam waist. Hence, the writing beams are focused onto the sample surface by placing a lens (f=150cm) between the laser head and the beam splitter. Depending on the laser system used for inscription, the resulting beam diameter at the sample position is 1.4 mm (488 nm) or 1.1 mm (489.2 nm). Grating diffraction theory further assumes that the probing light be a plane wave. Focusing of the reading beam onto the sample is achieved by adjusting a lens integrated in the laser module.
Samples are mounted on a rotational stage. It is used to vary the angle of incidence of the reading beam for either angular multiplexing or the determination of critical diffraction angles (cf. Chapter 9). The stage is driven by a stepper motor which provides an angular resolution of 1×10−2degrees.
The angle between the writing beams is 28.30° in air, resulting in a grating period of approximately 1µm. During grating inscription, the angle of incidence of the reading wave isθr=19.85°. It is adjusted such that the Bragg condition is fulfilled for thick holograms.
To calculate the refractive-index or surface modulation from the diffraction efficiency of Raman-Nath and Bragg-selective gratings, the angle of incidence of the readout beam inside the medium has to be determined. It can be derived from Snellius’s law if the refractive index of the photo-active material is known. Assuming thatn0is about 1.5, the angle of the reading beam inside the medium becomes 13.2°.
An extension of the plane-wave setup has been implemented by installing an electro-optic modulator (EOM, Gsänger LM0202) in the object beam path. The EOM is oriented such that the phase of the object beam shifts proportionally to an externally applied DC voltage. Thus, it can be used to spatially shift the intensity grating relative to a previously inscribed grating. In standard holographic experiments, the EOM is switched off and has no effect. The phase shift between the light intensity and the refractive-index grating man-ifests itself in a difference of the intensities of the writing beams behind the sample, also referred to as “photo-refractive effect” or “asymmetric two-beam coupling”.[202,203]In thick azobenzene-based polymer samples, this energy transfer can be observed even without the EOM. To measure the intensities of the writing beams behind the sample, two additional preamplified photodiodes (Thorlabs PDA-55) are used. Conversion to a digital voltage sig-nal is achieved by processing their output with a DAQ computer card (Keithley DAS-1700 Series).
Holography requires interferometric stability to warrant a constant phase relationship between object and reference beam. To protect the experimental setup from external vibra-tions or air draft, it is mounted on an optical table with air suspension and is surrounded
7.2 IMPRINTING SETUP FOR AZO-NIL 59