Modelling the deformation process of flexible stamps for nanoimprint lithography

The present thesis is devoted to numerical modelling of the deformation process of flexible stamps for nanoimprint lithography (NIL). The purpose of those models is to be able to predict the deformation and stretch of the flexixble stamps in order to take that into account when designing the planar 2D silicon master used in the NIL process.

Two different manufacturing processes are investigated; (i) Embossing of an electroplated nickel foil into a hydrogen silsesquioxane (HSQ) polymer resist on a double-curved surface, (ii) NIL of a flexible polytetrafluoroethylene (PTFE) stamps into a polymethyl methacrylate (PMMA) resist. Challenges comprise several non-linear phenomena.

First of all geometrical non-linearities arising from the inherent large strains and deformations during the process are modelled. Then, the constitutive behaviors of the nickel foil and the PTFE polymer during deformation are addressed. This is achieved by a general elasto-plastic description for the nickel foil and a viscoelastic-viscoplastic model for the PTFE material, in which the material parameters are found.

Last, the contact conditions between the deforming stamp and the injection moulding tool insert are adressed. The different modelling phenomena for simulating the deformation process of the flexible foils are in this thesis added through a progression in complexity. The importance of including non-linear geometry in the numerical models for simulation of nanoimprint lithography on curved surfaces is first investigated through a simple beam model, where a Timoshenko beam is deformed from 1D to 2D.

Comparison with analytical solutions shows, that by including non-linear geometry, the deformations are in general smaller as compared to the linear theory for the same applied load. It is found, that for large deformations non-linear geometry has to be taken into account in order to accurately calculate the displacements of the loaded geometry.

A 2D axisymmetric numerical model for simulating the deformation of the nickel foil during embosing into HSQ on a double-curved surface is developed, utilizing non-linear material and geometrical behaviour. A nanostructure consisting of sinusoidal cross-gratings with a period of 426 nm is in an experiment successfully transferred to hemispheres with three different radii of 500 µm, 1000 µm and 2000 µm, respectively.

Good agreement between measured and numerically calculated stretch ratios on the surface of the deformed nickel foil is found, and from the model it is also possible to predict the limits of the nanostructures on the curved surfaces, with decreasing radii. A combination of proper constitutive and frictional models for simulating the deformation of PTFE against steel on micro-scale is presented.

The 2D axisymmetric model is verified through an experiment, in which a PTFE sheet with a predefined square grid pattern on the surface is deformed by a steel sphere mounted in a uniaxial tensile test machine. Good agreement between simulations and experimental results are found, both regarding force-displacement and principal strain measurements.

The rheological representation of the constitutive model with a combination of a viscoelastic Zener-body and Johnson-Cook plasticity can be used to model the mechanical behavior of PTFE. Inclusion of the frictional behavior between the PTFE stamp and steel tool on micro-scale in the numerical model is shown to be of major importance in order to best simulate the strain field in the deformed PTFE sheet.

Simulations in 3D of the deformation process of PTFE flexible stamps used for NIL on double-curved surfaces are presented. The constitutive model is implemented in ABAQUS through a user material subroutine. In order to take the large strains and deformations during the imprinting manufacturing process into account, non-linear geometry is applied in the simulations.

The model is first verified through a series of experiments, where NIL on a curved tool insert for injection moulding is performed with various process parameters such as temperature, imprinting pressure and flexible stamp thickness. Good agreement between simulations and experimental results is found.

The optimum process parameters are then used in the final application, where nanoimprint of a nanostructure giving a color effect is performed numerically and experimentally. Both experiment and simulation show a mismatch between the defined and measured nanostructures as a result of stretching of the flexible stamp.

The model is shown to predict the stretch of the nanostructures with a maximum error of 0.5%, indicating that the model is able to capture the physics of this manufacturing process. The 3D model for simulating the imprint of the nanostructure giving a color effect is then used as the global model in the coupling to a local 2D model.

The coupling between global and local model is performed defining the displacements at the edges of an element from the global model as boundary conditions for the local model. This was implemented in the subroutine DISP in ABAQUS. Both experiment and simulation show a mismatch also on nanoscale between the defined and measured nanostructures as a result of stretching of the flexible stamp.

Comparison with profiles extracted from the atomic force microscopy (AFM) scans shows good agreement with the local model in terms of predicted wavelength. A mismatch between the actual shape of the deformed flexible stamp from the simulation and the measured nanostructures on the final injection moulded plastic part, suggestes that the subsequent etching and injection moulding manufacturing steps may also have an influence on the final shape of the nanostructures.