Burger Model as the Best Option for Modeling of Viscoelastic Behavior of Resists for Nanoimprint Lithography

At a Glance

Metadata	Details
Publication Date	2021-11-04
Journal	Materials
Authors	Hubert Grzywacz, Piotr Jenczyk, Michał Milczarek, Marcin Michałowski, Dariusz M. Jarząbek
Institutions	Polish Academy of Sciences, Warsaw University of Technology
Citations	9
Analysis	Full AI Review Included

Executive Summary

This research utilizes Atomic Force Microscopy (AFM) nanoindentation to characterize the viscoelastic behavior of Poly(methyl methacrylate) (PMMA) thin films, aiming to accelerate the selection of optimal resists for thermal Nanoimprint Lithography (NIL).

Viscoelastic Modeling Validation: The Burger model was identified as the most suitable constitutive model for representing the creep compliance of PMMA thin films, consistently providing the best fit (highest R²) across various temperatures and loads compared to SLS Maxwell and SLS Kelvin models.
Proposed NIL Suitability Parameter: A simple, fast-to-determine parameter is introduced for predicting resist suitability: the ratio of Hardness (measured at demolding temperature, 20 °C) to Viscosity (measured at molding temperature, 80 °C).
Temperature Dependence: Hardness and Young’s Modulus exhibit a sharp decrease between 20 °C and 40 °C, indicating a threshold temperature where polymer chain mobility significantly increases, crucial for determining molding conditions.
Film Thickness Effect: The thinner PMMA film (235 nm) generally exhibited higher hardness and a better tentative NIL suitability ratio (0.51) compared to the thicker film (513 nm, ratio 0.32).
Oliver-Pharr (OP) Correction: King’s method was applied to the OP and Burger model results to correct for the influence of the Si substrate, with corrections ranging up to 28% of the measured Young’s modulus value.
Hardness Dependence: Hardness was found to decrease non-linearly with increasing penetration depth and linearly with increasing normal load, confirming that hardness is not an intrinsic property for these thin polymer films.

Technical Specifications

Parameter	Value	Unit	Context
PMMA Film Thickness (Thin)	235 ± 5	nm	PMMA-235 sample
PMMA Film Thickness (Thick)	513 ± 4	nm	PMMA-513 sample
PMMA Molecular Weight	950	K	Both films
Film Roughness R_a (Thin)	0.328 ± 0.032	nm	PMMA-235
Film Roughness R_a (Thick)	0.259 ± 0.033	nm	PMMA-513
Test Temperature Range	20, 40, 60, 80	°C	Controlled by heating stage (Accuracy ± 2 °C)
Relative Air Humidity (RH)	25 ± 5	%	Maintained environment
Indentation Load Range	200 to 500	nN	Applied during nano-indentation
Loading/Unloading Rate	40	nN/s	Constant rate for all measurements
Creep Dwell Time	40	s	Used for viscoelastic analysis
Cantilever Tip Material	DLC (Diamond-Like-Carbon)	N/A	NSC14/Hard/ALBS cantilever
DLC Tip Young’s Modulus	1147	GPa	Tip material property
Cantilever Stiffness	3.4162 ± 2%	N/m	Measured using Sader method
NIL Suitability Ratio (Thin)	0.51	N/A	Hardness (20 °C) / Viscosity (80 °C) for PMMA-235
NIL Suitability Ratio (Thick)	0.32	N/A	Hardness (20 °C) / Viscosity (80 °C) for PMMA-513

Key Methodologies

Sample Preparation: PMMA thin films (235 nm and 513 nm) were prepared by spin-coating the e-beam resist (AR-P 672.045, 950 K MW) onto Si wafers.
AFM Nano-indentation Setup: A Flex-Axiom AFM equipped with a vibration-isolation stage was used. Tests employed a DLC-coated cantilever (NSC14/Hard/ALBS).
Environmental Control: Experiments were conducted under controlled temperature conditions (20 °C to 80 °C) and constant relative air humidity (25 ± 5%).
Mechanical Testing: Nano-indentation tests were performed using loads between 200 nN and 500 nN, with a loading/unloading rate of 40 nN/s. Creep behavior was measured using a 40 s dwell time at maximum load.
Calibration: Cantilever stiffness (3.4162 N/m) was determined using the Sader method. Sensitivity (photodetector constant) was measured on a sapphire substrate (75.5 nm/V).
Hardness and Modulus Calculation (Oliver-Pharr): The Oliver-Pharr (OP) method was applied to the indentation curves to calculate hardness and Young’s modulus.
Substrate Correction: King’s method was used to correct the measured Young’s modulus values, accounting for the effect of the underlying Si substrate on the thin polymer films.
Viscoelastic Modeling: Creep compliance curves were fitted using three Standard Linear Solid (SLS) models: Maxwell, Kelvin, and Burger. The Burger model was selected for further analysis due to its superior fit (R²) and inclusion of both viscoelastic and viscoplastic dashpots, which are critical for modeling NIL resists.

Commercial Applications

The findings directly support the optimization and material selection processes for high-resolution manufacturing technologies, particularly those relying on polymer deformation.

Thermal Nanoimprint Lithography (NIL): The primary application is the rapid screening and selection of thermoplastic resists (like PMMA) based on the proposed Hardness/Viscosity ratio, significantly accelerating process optimization.
Micro- and Nano-Electromechanical Systems (MEMS/NEMS): NIL is a key fabrication technique for creating high-aspect-ratio structures used in sensors, actuators, and microfluidic devices.
Optical Device Manufacturing: Fabrication of periodic structures such as diffraction gratings, waveguides, and anti-reflective surfaces requiring precise pattern transfer and minimal demolding defects.
Flexible and Printed Electronics: Utilizing NIL to pattern conductive polymers or dielectrics on flexible substrates, where understanding temperature-dependent viscoelasticity is essential for reliable processing.
Advanced Polymer Rheology: Providing validated constitutive models (Burger model) for predicting the time- and temperature-dependent mechanical response of thin polymer films at the nanoscale, relevant for coating and film stability studies.

View Original Abstract

In this study, Atomic Force Microscopy-based nanoindentation (AFM-NI) with diamond-like carbon (DLC) coated tip was used to analyze the mechanical response of poly(methyl methacrylate) (PMMA) thin films (thicknesses: 235 and 513 nm) on a silicon substrate. Then, Oliver and Pharr (OP) model was used to calculate hardness and Young’s modulus, while three different Static Linear Solid models were used to fit the creep curve and measure creep compliance, Young’s modulus, and viscosity. Values were compared with each other, and the best-suited method was suggested. The impact of four temperatures below the glass transition temperature and varied indentation depth on the mechanical properties has been analyzed. The results show high sensitivity on experiment parameters and there is a clear difference between thin and thick film. According to the requirements in the nanoimprint lithography (NIL), the ratio of hardness at demolding temperature to viscosity at molding temperature was introduced as a simple parameter for prediction of resist suitability for NIL. Finally, thinner PMMA film was tentatively attributed as more suitable for NIL.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma14216639

References

2016 - Next generation lithography—The rise of unconventional methods? [Crossref]
2021 - Friction-Induced Nanofabrication: A Review [Crossref]
2008 - The effect of temperature on the nanoscale adhesion and friction behaviors of thermoplastic polymer films [Crossref]
2010 - Tribology issues in nanoimprint lithography [Crossref]
2021 - Demolding force dependence on mold surface modifications in UV nanoimprint lithography [Crossref]
2006 - AFM characterization of anti-sticking layers used in nanoimprint [Crossref]
2011 - Thermomechanical properties of polymer nanolithography using atomic force microscopy [Crossref]
2017 - Investigation of the anti-adhesion layers for nanoimprint molding [Crossref]
2016 - Alternative nano-structured thin-film materials used as durable thermal nanoimprint lithography templates [Crossref]