1. Introduction

The advent of commercially available nanoscale 3D direct laser writing (3D-DLW) systems has led to a rapid expansion of the application space available to researchers employing additive manufacturing techniques for the fabrication of 2D and 3D structures with features ranging from the nanometer to millimeter scale. Initially, the fields of structural and acoustic mechanics were the central focus of publications reporting on the properties of materials produced by 3D-DLW processes. A representative example of this initial effort is the work by Bückmann et al. where it has been shown that 3D-DLW of polymer structures can lead to materials which can cloak mechanical motion [1]. Recently it has been demonstrated that two photon polymerization can provide base elements from which materials exhibiting mechanical strengths that approach the theoretical maximum of the constituent materials can be created [2].

Interestingly, the characteristic feature scales that make the 3D-DLW processes attractive for mechanics and acoustics also lend themselves to the design of long wavelength optical components such as printable optoelectronics, THz imaging and sensors, infrared optical devices, etc. This relatively new application of additive manufacturing processes for the fabrication of designed optical materials may have significant impact as early works have already demonstrated that printable optical interconnects exhibit performance that is suitable for industrial telecommunications applications [3, 4]. More recent works have shown very encouraging results on materials and devices for the mid-infrared spectral range for instance broadband dichroic circular polarizers and photonic crystals with measurable band gaps [5, 6]. Such photonic crystal structures rely upon polymer scaffolding and removal processes that exceed the material space accessible through 3D-DLW alone in their complexity.

In addition to the advancement of optical components in the infrared spectral range, it has been demonstrated that with care two photon lithography can be extended toward the realization of components intended to work in the visible spectrum. One example is the use of structures fabricated by 3D-DLW in order to realize a plasmonic control of liquid crystals [7].

Although there is a rapidly growing effort to apply 3D-DLW techniques to fabricate materials for THz and infrared applications, accurate infrared dielectric function data on the some of the most commonly used monomers have not yet been reported. This hinders both the understanding of the scattered fields from structures designed to operate in the infrared in measurement and simulation as well as the simulation-based design of materials with novel properties.

In this paper we report on the first mid-infrared ellipsometry experiments to determine the complex dielectric function of two polymerized monomers which are frequently used in the Nanoscribe 3D-DLW process named IP-Dip and IP-L [8]. These monomers have different viscosities, indices of refraction, and intended uses. IP-Dip is recommended for use in standard and inverted 3D-DLW configuration. IP-L can be used in an inverted oil immersion configuration wherein the laser beam writes through a transparent substrate into the IP-L. A parameterized model dielectric function is derived and discussed.

2. Experiment

2.1. Sample preparation

The samples investigated here were prepared by means of spin coating IP-DIP and IP-L onto their respective substrates at 5000 rpm for 4 minutes. Highly-doped (ρ ≃ 0.003 Ω·cm), 4 inch < 100 > silicon wafers were used as substrates according to the best practices detailed in [9]. Prior to the spin coating, the substrates were carefully cleaned by immersion in CMOS grade acetone for 5 minutes followed by a DI rinse and 5 minutes of immersion in CMOS grade methanol. Afterward, each substrate was dried manually with nitrogen, cleaned in a 3:2 mixture of 96% sulfuric acid and 30% hydrogen peroxide for 20 minutes, and then thoroughly rinsed in DI water. After the spin coating the adhered monomers were polymerized in a UV oven over the course of 30 minutes. It can be expected that the linear displacement of the voxel during 3D-DLW will induce differences relative to the measured optical properties presented herein due to localized polymerization and induced strain resulting from the small but non-negligible volume changes during polymerization. This induced anisotropy has been observed but not quantified from 3D-DLW structures. The sample preparation was carried out in a class 100 clean room to ensure purity of the films.

2.2. Data acquisition and analysis

The cured IP-Dip and IP-L polymer film samples were measured on a commercial infrared ellipsometer (Mark I IR-VASE^®, J.A. Woollam Company). The instrument is equipped with a Boman FTIR source and a DTGS detector and operates in a classical rotating polarizer - sample - rotating compensator - rotating analyzer configuration as is detailed in [10]. Ellipsometric Ψ and Δ data were acquired over the spectral range from 250 to 6000 cm⁻¹ with a resolution of 2 cm⁻¹ at three angles of incidence: Φ_a = 60°, 65°, and 70°. The measurements were carried out under normal ambient conditions while the room temperature was kept at approximately 21°C.

The optical modeling and data analysis was carried out using a commercial ellipsometry data analysis software package (WVASE32™, J.A. Woollam Company). The complete ellipsometric data set obtained for each sample was fit to a stratified layer optical model. The optical model consists of ambient/polymer thin film/Si substrate. Separate parameterized dielectric function models were employed to describe the infrared optical response of IP-DIP, IP-L, and the doped Si substrate.

The infrared dielectric functions of both IP-Dip and IP-L are described here using a mixed oscillator model method which was first introduced by Synowicki and Tiwald [11]. Synowicki and Tiwald demonstrated that combinations of oscillators with Gaussian and Lorentzian broadening can be combined with Tauc-Lorentz oscillators in order to describe the dielectric response of different materials over a wide spectral range from the infrared to the vacuum ultraviolet [11] using functions with physically relevant parameters. The mixed oscillator model used to produce the dielectric response of IP-Dip and IP-L uses no previously existing data, however. The advantage of phenomenological mixed oscillator models is that typically a reduced number of parameters is required in order to accurately describe the experimentally observed optical response. Here we employ a combination of oscillators with Gaussian and Lorentzian broadening to describe the infrared dielectric function of IP-Dip and IP-L monomers after polymerization:

Equations (2) and (3) show the Lorentzian and Gaussian forms for the imaginary part ${\epsilon }_2^{\text{Lor}}\left(\omega \right)$ and ${\epsilon }_2^{\text{Gau}}\left(\omega \right)$ of the complex dielectric function ε(ω), respectively:

The infrared dielectric function of the doped Si substrates is described using a classical Drude response where the resistivity ρ and the scattering time τ are accessible fit parameters. For the Si substrate which was used for the IP-Dip sample we obtained ρ = (0.0031 ± 0.0001) Ω·cm and τ = (13.7 ± 0.2) fs. For the Si substrate which was used for the IP-L sample we obtained ρ = (0.0032 ± 0.0001) Ω·cm and τ = (13.1 ± 0.1) fs.

3. Results and discussion

Figure 1 depicts the experimental (dashed green lines) and best-model calculated (solid red lines) for Ψ (shown in (A) for IP-Dip and (C) for IP-L) as well as for Δ (shown in (B) and (D)) of polymerized IP-Dip and IP-L obtained at Φ_a = 65°. Note that while the data obtained at all three angles of incidence were analyzed simultaneously only the data for Φ_a = 65° are shown here for clarity. An excellent agreement is found between the experimental and best-model calculated data, which are virtually indistinguishable in Fig. 1. The combination of a low mean square error and a correlation matrix with low off-diagonal values allows the determination of the provided material parameters within a 90% confidence limit. This isotropic model of the bulk optical properties may be used to describe form-induced birefringence which may be present in 3D-DLW structures very similar to the effective medium models developed for sculptured thin films in the visible and THz spectral range [12–14].

 

Fig. 1 (A) and (C) Experimental (dashed green line) and best-model calculated Ψ data (solid red line) for the monomer IP-Dip (A) and IP-L (C) obtained at Φ_a = 65°. Vertical dash marks in (A) and (C) indicate the oscillator center energies listed in Tab. 1 and Tab. 2 below. (B) and (D) Experimental (dashed green line) and best-model calculated Δ data (solid red line) for IP-Dip (B) and IP-L (D) obtained at Φ_a = 65°.

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Both IP-Dip and IP-L show a very similar infrared optical response where strong absorption bands are found in the range from 500 to 2000 cm⁻¹. The oscillator center energies are indicated as vertical dashes in Fig. 1. Tab. 1 and Tab. 2 show the best-fit mixed oscillator parameters for the dielectric response of IP-Dip and IP-L from 250 to 6000 cm⁻¹. The oscillator energy ω₀, amplitude A, and broadening Γ are given in units of cm⁻¹. The letters ‘G’ and ‘L’ next to the oscillator number indicate whether the oscillator is Gaussian or Lorentzian. The best-fit value for ε_∞ is ε_∞ = 2.37 ± 0.01 for IP-Dip and ε_∞ = 2.22 ± 0.01 for IP-L. Error bars in parentheses [last digit(s)] represent the 90% confidence limits of the oscillator parameters shown above. The range from ω = 2000 to 6000 cm⁻¹ is transparent for both polymerized monomers as can be easily observed by the Fabry-Perot oscillations generated in the transparent films seen in Fig. 1. Note that the frequency of these oscillations is significantly higher for the IP-Dip. IP-Dip has a higher viscosity compared to IP-L. This results in a significantly larger film thickness for IP-Dip d_IP-Dip =7.474±0.002 μm while the thickness for IP-L is d_IP-L =4.448±.001 μm when fabricated at the same spin speed during the deposition process described in section 2. A few very weak absorption features can be identified in both polymerized monomers at approximately 3000 cm⁻¹ and 3500 cm⁻¹.

Table 1. IP-Dip best-fit oscillator parameters

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Table 2. IP-L best-fit oscillator parameters

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The real and imaginary parts of the best-fit model complex dielectric function are depicted in Fig. 2 for both IP-Dip and IP-L. The black dashed lines in Fig. 2 indicate the dielectric response of SU-8, which is provided for comparative purposes. The data from SU-8 was digitally reproduced from [15]. The infrared dielectric response of both polymerized monomers is dominated by two strong absorption lines around 1200 and 1600 cm⁻¹. However, comparing Fig. 2(B) and Fig. 2(D) it is readily apparent that while IP-L shows a relatively simple structure, IP-Dip shows a large number of narrow resonances. In fact, the dielectric function for IP-Dip gives evidence of a more complex chemistry than IP-L, as it takes nearly twice as many oscillators to fit IP-Dip compared to IP-L such that a good match between the experimental and best-model calculated data is obtained as shown in Fig. 1.

 

Fig. 2 Best-model calculated real (ε₁(ω)) and imaginary (ε₂(ω)) part of the complex dielectric function ε(ω) for IP-Dip are shown in panels (A) and (B), respectively. Similarly, (C) and (D) depict ε₁(ω) and ε₂(ω) for IP-L. Dashed lines in black represent the dielectric response of SU-8 for comparison. The major contributions to the dispersive behavior of both IP-Dip and IP-L occur between 1000 and 2000 cm⁻¹. The best-model parameters are given in Tab. 1 and Tab. 2.

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4. Summary and conclusion

In this work we have determined the complex dielectric function of polymerized IP-Dip and IP-L, two monomers which are frequently used in two photon polymerization with commercial direct laser writing tools. A mixed oscillator model composed of oscillators with Gaussian and Lorentzian broadening was found to appropriately render the dielectric response. Comparing the dielectric functions of IP-Dip and IP-L shows that IP-Dip exhibits almost twice as many discrete resonances which is interpreted here as an indication a more complex chemistry. We anticipate that the parameterized dielectric function reported here will help to improve first-principle calculations of the infrared optical response of 2D and 3D structures composed of these materials.