Reflow of supported sub-100 nm polymer films as a characterization process for Nano Imprint lithography

In this paper, we address the reﬂow behavior of polymer thin ﬁlms, focusing our effort on the accuracy of surface shape recognition. Although much work was already performed to control resist reﬂow during lens manufacturing for instance, our approach is signiﬁcantly different since no contact line (substrate/ polymer/atmosphere) needs to be considered. Here, a linear stability approach is successfully developed to describe the thin ﬁlm evolution which is also compared with experiments. Polystyrene ﬁlms, with thickness ranging from few tens of nanometers up to several hundred of nanometers were patterned with NanoImprint lithography technique. Atomic force microscopy measurements were used to characterize smooth or steep shapes, respectively. Mechanical measurements of earlier stages of pattern reﬂow were directly accessible without any assumption, contrary to the diffraction method usually employed. We show that by controlling the reﬂow process of any complex surface shape during the course of time, measurements of material parameters such as thin ﬁlm viscosity, surface tension, or even Hamaker constant can be made possible.


Introduction
Surface dynamics of viscous polymer films have been widely studied for fundamental purposes [1] and microelectronics applications as well [2,3]. Ultra-thin film manufacturing appears to be a key point of nanotechnology engineering and numerous studies have been recently led in order to exhibit driving parameters of viscous smoothing dynamics of a nanopatterned thin film. Characterization of flow properties of polymer melts at macroscopic scale is easily performed by classical measurement devices devoted to volume rheology. In NanoImprint Lithography (NIL) processes, resist film thickness is ranging from several tens of nanometer up to several hundred of nanometer. In such configuration, surface phenomena increasingly play a decisive role which induces significant deviation for viscous-driven flows properties. Several experimental approaches, mainly based on scattering correlation methods onto iso-dense patterns (line width = space width), have been carried out [3][4][5][6]. These techniques provide a very high time resolution, but data on shape evolution depends on ab initio geometrical models used for the diffraction analysis. To our knowledge, up to now, no study had associated detailed theoretical aspects and specific nanoscale experiments.
In this paper, we address the reflow behavior of thin polymer films, focusing our attention on the accurate detection of surface shape during the course of time. Although a large amount of work was already performed to understand and control resist reflow for lens manufacturing [7], our approach distinguishes itself from existing state of art since dynamics of the contact line (substrate/ resist/atmosphere) does not need to be considered in order to model our system based on a supported thin film. An analytical solution describing the system evolution is proposed in this paper and compared with experiments. Although this work was performed on polystyrene two-dimensional patterns, our approach may be extended to any kind of viscous material and feature shapes.

Experiments
A low molecular weight ðM w ¼ 27:5 kg mol À1 Þ monodisperse ðM w =M n < 1:06Þ polystyrene (PS) solution is spin-coated onto 8 in. silicon substrates. The glass transition temperature ðT g ¼ 102 AE 1 CÞ is measured by Differential Scanning Calorimetry (DSC). The thickness of coated polystyrene films ranges from h 0 ¼ 27 nm up to 237 nm and is measured by ellipsometry. Polystyrene films are subsequently patterned with NIL technique [8,9] (Fig. 1 NIL processes, the residual layer is not removed by plasma etching and resist features as-imprinted will be used in this study. Given the mold design (printed line size = spacing between two lines), the residual layer thickness is ranging from 12 nm (for h 0 ¼ 27 nm) up to 222 nm (for h 0 ¼ 237 nm). PS features are then annealed above T g and cooled down to room temperature in less than one second. Patterns are further characterized by Atomic Force Microscopy (AFM) measurements performed at a spatial resolution lower than 1 nm. As previously shown [2], for the temperature range considered in this work, pattern shapes are not significantly modified by a quench. Both usual conic and flared tips [10,2] are used to characterize smooth or steep shapes, respectively ( Fig. 1). Therefore, mechanical measurements of earlier stages of pattern reflow are directly made possible without any assumption, contrary to diffraction method usually employed [3].

Model
Pattern reflow may be seen as a process driven by a minimization of the surface free energy slowed down by the viscous shear across the polymer film [4,11]. Assuming a two dimensional pattern with a mean thickness h 0 and a surface topography characterized by the local instantaneous surface elevation hðx; tÞ¼h 0 þ hðx; tÞ, the reflow can be described from momentum equation completed by mass conservation equation. As shown by Oron et al. [1], due to the creeping kinetic of flow at large viscosity and the small angles thin film geometry, the momentum and mass conservation equations reduce to the Reynolds lubrication equation: where @ x p is the pressure gradient and g is the Newtonian viscosity.
For nanoscopic isothermal thin films, the pressure gradient is usually created by two types of forces: the van der Waals forces (long-range molecular forces) and the surface tension [1]. It can be written as: where A is the Hamaker constant related to the van der Waals forces in the system Si-PS-Air and c is the surface tension. Using this expression for the pressure gradient into Eq. (1), we get: The resulting evolution equation for the thickness h is a non-linear equation which generally cannot be solved analytically. In order to obtain an analytical expression for h at any time, given any initial shape, we must linearized the evolution equation under the assumption thath ( h 0 . We get: The solving of Eq. (3) by a spectral approach is then straightforward. The thickness is expressed as a Fourier series in space whose coefficients depend on time: hðx; tÞ¼ X þ1 À1 a n ðtÞ exp in 2p k x where k is the period of the imprinted grating (or in the case of a non-periodic patterns, it is the length of the whole sample) and a n ðtÞ is the complex amplitude of the mode n. According to Eq.
(3), each Fourier mode of order n follows an exponential decay whose relaxation time s n is given by: Finally, the evolution of the film is described by: hðx; tÞ¼ X þ1 À1 a n ð0Þ exp À t The coefficients a n ð0Þ are given by the Fourier transform of the initial thickness. From Eq. (4) we can state that if the dimensionless ratio Ak 2 =ð8p 3 ch 4 0 Þ is much smaller than 1, the van der Waals forces can be clearly neglected. If we consider a typical order of magnitude for the Hamaker energy, A ¼À10 À19 J [12], and for the PS free surface tension c ¼ 34 mN m À1 [13], then in our experimental layout van der Waals forces have an insignificant contribution to the flow except for the largest pattern ðk ¼ 8 lmÞ imprinted in the thinnest film ðh 0 ¼ 27 nmÞ.
Provided that the van der Waals forces can be neglected, Eq. (4) reduces to: Eq. (5) clearly points out the fact that the flow smoothes the high wavelengths of the film geometry. Fig. 2 shows AFM views of typical imprinted patterns used in this study. Fig. 3a reports the surface profile reflow at an annealing temperature of T g þ 43 Co fak ¼ 2 lm iso-dense imprinted line array and confirms that surface effects tend to smooth the film. Iso-dense pattern is a special case where high spatial frequencies quickly disappear in favor of a monochromatic topography. It is possible to plot the decrease of the pattern height versus the annealing time (Fig. 3b). That decrease is consistent with the law of Eq. (6), and the decay time s 1 can be extracted and the viscosity finally computed. We get s 1 ¼ 369 s, and with c ¼ 34 mN m À1 it follows that g ¼ 3:0 Â 10 4 Pa s.

Results and discussion
The decay time s 1 was easily determined from a significant height decrease of reflowed patterns. However, even for larger period and shorter corresponding annealing times, height evolution may be used to determine characteristic reflowing time more precisely. Indeed, neglecting van der Waals contribution, and using simplified Eq. (6), knowing the relaxation time s n , for a given profile of the initial pattern k, it is possible to calculate the relaxation time s 0 n for any other geometry of spatial periodicity k 0 , because the temporal and spatial scales are directly connected. Since all arrays are iso-dense line grating, there are described by the same a n ðtÞ coefficients. All arrays of different periods will go through the same reflowing shapes during annealing, but with different velocities. In order to compare different geometries, the time scale may be thus renormalized using the following ratio:   amplitude evolution is well described by our spectral approach with a correlation coefficient of 0.97 over the whole profile. This demonstrates that our approach allows us to describe any reflowing shapes even at early annealing time, which was not possible with previous works. The viscosity of polymer melts can be extracted using the previously described technique at various temperatures. A similar experiment was performed at T g þ 15 C and exhibits a much higher viscosity. This thermodependence of viscosity corresponds to a well-known behavior of a polymer material validated at macroscopic scale (polymer bulks). Extensively studied by William et al. [14], these authors proposed a constitutive law well adapted to describe thermal behavior for most of amorphous polymers: with c 1 and c 2 two parameters and g s the dynamic viscosity at the temperature T s . Results are summed up in Fig. 5 and are consistent with data from previous authors.

Conclusion
In this paper, we proposed a new and accurate approach for direct polymer thin film viscosity measurement. We monitor pattern reflow manufactured by NanoImprint lithography to extract the PS viscosity from relaxation kinetic. Using PS films thick enough compared to pattern height, low molecular weight and low imprint-induced stresses, we demonstrated that even the first-stages of reflow were faithfully described by a dedicated viscous model. Our results clearly demonstrate that the whole reflow process is dominated by viscous damping. With the spectral analysis of the reflow dynamics proposed in this paper, we show that this approach provides two main advantages: first, whatever the initial surface shape is, the spectral decomposition of topography can be computed; and then, whatever the pattern wavelength and film thickness are, the decay time of the reflow process can be deduced from the quasi-ideal configuration of long-time reflow of iso-dense patterns. As a consequence, viscous reflow of organic or mineral material may be rigorously computed and profile evolutions can be predicted with a very high precision within an error less than 3%. As a way to validate this new methodology, we determine the viscosity of a low molecular weight (27.5 kg/mol) thin PS film (from 27 up to 237 nm) at a different temperature and we find good agreement with WLF law and data in literature.