Specification
Description:FIELD OF INVENTION
The present invention generally relates to material fabrication. More specifically, the present invention relates development of a bi-layer material having controlled wrinkles over surface.
BACKGROUND
Nano and microstructures enhance light-matter interactions, enabling the manipulation of electromagnetic radiation properties essential for creating customized photonic devices. Such customized photonic devices find applications across various fields, including healthcare, energy harvesting, smart displays, computation, communication, and wearable technology. Different conventional methods are available for development of these customized photonic devices.
One conventional fabrication method includes usage of lithography and precise etching. Such method is complex, time-consuming, and costly, and thus restricts its scalability and cost-effectiveness. Moreover, the structures developed using this method lack dynamic tunability. Hence, redesigning and re-fabrication of structures to meet different device requirements is often required.
Non-lithographic methods involving exfoliation techniques, microfluidics, and nanoimprint lithography, also encounter fabrication challenges. Mechanical exfoliation requires meticulous peeling of thin films without causing damage, while microfluidics necessitates fabrication of complex channel designs over large areas. Nanoimprint lithography frequently faces defects stemming from material inconsistencies and alignment problems. To address these issues, there is a demand for photonic devices that can be produced using self-ordered surface morphologies such as spikes, wrinkles, and folds.
Wrinkles have been formed through various techniques such as photoinduced methods like LASER and UV treatments, chemical swelling, mechanical pre-straining and thermal annealing. While methods like mechanical straining and thermal annealing can cover large areas, they often lead to cracks that disrupt the uniformity and order of wrinkles, making them unsuitable for development of large-scale photonic devices. On the other hand, LASER treatments and chemical swelling produce fewer defects but are limited in area and often yield disorganized patterns. Existing research has primarily focused on irregular structures or methods constrained by area or plagued by defects.
Therefore, an efficient method of developing a material having controlled wrinkled surface is required.
OBJECTS OF THE INVENTION
An object of the present invention is to provide a method of controlled thermal processing for development of wrinkle patterns on surface of a variety of materials including metals, semiconductors, and polymers.
Another object of the present invention is to provide a method of precisely tuning parameters such as temperature variations, thermal expansion coefficients, surface energy, Young’s modulus, and thin film thickness for development of tailored wrinkle patterns.
Yet another object of the present invention is to develop wrinkled materials for use as visible camouflage, tunable diffraction gratings, tunable optical diffusers, device for increasing out-coupling efficiency of encapsulated light sources and photovoltaics, flexible and washable reflective displays, and mechanochromic sensors.
SUMMARY OF THE INVENTION
The summary is provided to introduce aspects related to a method of development of a bi-layer material having controlled wrinkles over surface, and the aspects are further described below in the detailed description. This summary is not intended to identify essential features of the claimed subject matter nor is it intended for use in determining or limiting the scope of the claimed subject matter.
In one aspect, a scalable thermal processing technique is described for producing large-area, dynamically tunable, customized 1D, 2D, and 3D wrinkles. By carefully adjusting the thermal expansion coefficient mismatch between the film and substrate, along with controlling the film thickness, surface energy, and system temperature, the structure, orientation, and periodicity of wrinkles can be effectively customized. A universal mathematical model is also introduced for validating experimental results and calibrating the process for achieving specific wrinkle characteristics.
The effectiveness and versatility of proposed method is showcased through prototypes of various photonic devices, such as tunable temperature-controlled diffraction gratings, optical diffusers, temperature-controlled camouflage and body-motion sensors, all of which have applications in healthcare and smart displays. Tunability of these devices is reversible and repeatable for 100s of cycles, demonstrating the reliability and durability of the samples. Furthermore, these samples exhibit promising results for improved outcoupling efficiencies in encapsulated light sources, making them ideal for use in energy harvesting devices like solar cells.
In one embodiment, a method of developing a wrinkled bi-layer material comprises preparing a Polydimethylsiloxane (PDMS) substrate by mixing a predefined concentration of liquid PDMS base with 1 part of curing agent in a weight ratio to form a mixture. The method further comprises desiccating the mixture to remove bubbles, pouring the mixture onto a silicon mould, and curing the mixture at a predefined temperature for a predefined time period. The method further comprises peeling a layer of cured PDMS substrate containing ridges from the silicon mould. The method further comprises depositing a thin film of a material onto the layer of cured PDMS substrate via physical means. The method further comprises subjecting the thin film deposited over the layer of cured PDMS substrate to thermal processing to create a wrinkled surface of the thin film. The thermal processing involves heating and subsequent cooling down to a room temperature.
In one aspect, the predefined concentration of liquid PDMS base ranges from PDMS 3 to PDMS 10.
In one aspect, the thin film is made using one of chalcogenide, a metal, and a polymer.
In one aspect, the silicon mould contains grooves pre-etched through photolithography and Reactive Ion Etching (RIE)-F.
In one aspect, the physical means used for depositing the film onto the layer of cured PDMS substrate include one of thermal evaporation, sputtering, and spin-coating.
In one aspect, the wrinkled surface includes one of 1D sinusoidal, 2D zig-zag, and 3D wrinkles.
In one aspect, a structure, orientation, and periodicity of the wrinkles is customizable by adjusting one or more of thermal expansion coefficient mismatch between the film and substrate, thickness of the thin film, surface energy, and system temperature.
In one aspect, the predefined temperature ranges from 80ᵒC to 120ᵒC and the predefined time period is 3-6 hours, for curing the PDMS mixture.
Other aspects and advantages of the invention will become apparent from the following description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings constitute a part of the description and are used to provide further understanding of the present invention. Such accompanying drawings illustrate the embodiments of the present invention which are used to describe the principles of the present invention. The embodiments are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings in which like references indicate similar elements. It should be noted that references to “an” or “one” embodiment in this invention are not necessarily to the same embodiment, and they mean at least one. In the drawings:
Figs. 1a and 1b cumulatively illustrate a method of controlled thermal processing for development of wrinkle patterns on surface of a material;
Figs. 2a to 2e illustrate Atomic Force Microscopy (AFM) images of various morphologies attained through the proposed method;
Figs. 3a to 3d illustrate Scanning Electron Microscope (SEM) images of wrinkles achieved on various materials through the proposed method;
Fig. 3e illustrates a large area, defect free ordered wrinkled structure;
Figs. 4a and 4b illustrate comparison matrix of SEM images depicting dependence of wrinkle wavelength on film thickness, substrate softness and heating temperature;
Fig. 5a illustrates experimental data of the SEM images shown in Fig. 4a vs. plots obtained from the wavelength equation under similar parameters;
Fig. 5b illustrates a plot showing dependence of wrinkle wavelength on thermal expansion coefficient mismatch between film and substrate of the material;
Fig. 6a illustrates a schematic of bi-layer material;
Fig. 6b illustrates a schematic of stress formation in the film and the substrate during cooling;
Fig. 6c illustrates a schematic of the forces and moments acting on the film and the substrate during cooling;
Fig. 6d illustrates a schematic of a free-standing film under compressive force;
Fig. 7a illustrates an AFM image of a first sample having a film of As2Se3 deposited over PDMS 5 substrate;
Fig. 7b illustrates a line plot showing a surface profile of the film across a line drawn over the AFM image shown in Fig. 7a;
Fig. 7c illustrates an AFM image of a second sample having a film of As2Se3 deposited over PDMS 5 substrate;
Fig. 7d illustrates a line plot showing a surface profile of the film across a line drawn over the AFM image shown in Fig. 7c;
Fig. 8 illustrates a schematic of an array of wrinkles considered for mathematical modelling;
Figs. 9a, 9b, and 9c illustrate SEM images of samples of different films of As2Se3, PMMA, and Al;
Fig. 10 illustrates a table confirming the alignment of proposed wavelength equation with experimental data shown in Figs. 9a, 9b, 9c for different thin film materials;
Fig. 11a illustrates SEM images showing wrinkle formation in thin films of different materials;
Fig. 11b illustrates a table providing values of the thermal expansion coefficients of different thin films;
Fig. 12 illustrates the effect of PDMS curing time on the wavelength of the wrinkles
Fig. 13 illustrates through the SEM image the existence of a critical stress for a given bilayer system for the development of 1D wrinkles and its transition into 2D wrinkles;
Fig. 14 illustrates, through SEM images of different bilayer systems, the effect of different parameters like thermal expansion coefficient mismatch between the thin film and the substrate, temperature change within the system, and surface energy of the thin film on the orientation of the wrinkles;
Fig. 15 illustrates the absence of wrinkles when the bilayer system is heated to lower temperatures;
Fig. 16 illustrates the role of heating temperature and PDMS curing time on the orientation of the wrinkles;
Figs. 17a, 17b, and 17c illustrate schematic images showing different orientations of incident beam plane relative to the direction of the wrinkles;
Figs. 17d through 17i illustrate experimental images of diffraction spots obtained from green and red incident beams (experimental images on the left and corresponding simulation images on the right) as per the orientations illustrated in Figs. 17a, 17b, and 17c;
Fig. 18a illustrates reflectivity spectrum obtained experimentally when the sample is stretched uniaxially along the direction of wrinkles;
Fig. 18b illustrates images of samples shown in Fig. 18a, captured with a detector/camera;
Fig. 18c illustrates a plot between peak wavelength of reflection vs. strain% from the experimental data obtained from Fig.18a;
Fig. 18d illustrates repeatability and reversibility of spectral change obtained in Fig. 18a over 400 cycles of applied periodic strain of maximum 30% on the sample;
Fig. 19a illustrates the change in peak position of the reflected spectra when the wrinkled sample undergoes Joule heating followed by subsequent cooling;
Fig. 19b illustrates the peak reflection wavelength vs. Current-Voltage plot for Joule heating experiment shown in Fig.19a;
Fig. 20 illustrates different diffraction orders generated upon heating the sample to different temperatures and cooled down subsequently;
Fig. 21a illustrates an increase in out-coupling efficiency of encapsulated light sources;
Fig. 21b illustrates simulation result for the arrangements illustrated in Fig. 21a;
Fig. 22 illustrates diffraction patterns formed by controlling cooling temperature of a wrinkled bi-layer material for use as a tunable optical diffuser;
Fig. 23a illustrates a prototype of a body motion sensor mounted on a finger;
Fig. 23b illustrates hue vs. finger position plot observed while using the body motion sensor mounted on the finger;
Fig. 24 illustrates a large area, angle-dependent and washable reflective display developed using the material; and
Fig. 25 illustrates that the obtained bilayer materials can be used for dynamically tuneable camouflage.
DETAILED DESCRIPTION OF THE INVENTION
The detailed description set forth below in connection with the appended drawings is intended as a description of various embodiments of the present invention and is not intended to represent the only embodiments in which the present invention may be practiced. Each embodiment described in this invention is provided merely as an example or illustration of the present invention, and should not necessarily be construed as preferred or advantageous over other embodiments. The detailed description includes specific details for the purpose of providing a thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without these specific details.
Present disclosure describes a method of controlled thermal processing for fabricating large-area, dynamically tunable 1D, 2D, and 3D wrinkle patterns across a variety of materials including metals, semiconductors, and polymers. By precisely tuning parameters such as temperature variations, thermal expansion coefficients, surface energy, Young’s modulus, and thin film thickness, robust, uniform, and periodic structures are formed over extensive areas (10s of cm2) on soft substrates.
Figs. 1a and 1b cumulatively illustrate a method of controlled thermal processing for development of wrinkle patterns on surface of a material. The method includes preparing soft and flexible Polydimethylsiloxane (PDMS) substrates by mixing X parts of liquid PDMS base (Sylgard 184, Dow Corning) with 1 part of curing agent in weight ratio to form a mixture (PDMSx). Substrate softness increases with increase in proportion of the liquid PDMS base and also by reducing the curing time. For instance, PDMS 10 is softer than PDMS 5, and PDMS 5 is softer than PDMS 3. The softness is determined in terms of Young’s modulus. The mixture is stirred thoroughly and desiccated to remove all bubbles. The mixture is then poured onto Silicon (Si) moulds and cured at 80ᵒC for different times(1 hour/3hours/6 hours) to get PDMS substrates of different softness. The Si moulds contain grooves pre-etched through photolithography and Reactive Ion Etching (RIE)-F. A layer of cured PDMS substrate containing ridges is peeled off from the Si moulds. A thin film of chalcogenide (As2Se3), metal (Ag or Al), or polymer (Polymethyl Methacrylate (PMMA)) is then deposited onto the layer of cured PDMS substrate via physical means, such as thermal evaporation, sputtering, or spin-coating. Successively, the thin film deposited over the layer of cured PDMS substrate is subjected to thermal processing, involving heating and subsequent cooling down to a room temperature, to create an ordered structure.
Scanning electron microscopy and atomic force microscopy were done for determining structural characterisation of different ordered structures obtained through the proposed method. Figs. 2a to 2e illustrate Atomic Force Microscopy (AFM) images of various morphologies attained through the proposed method. Such morphologies were attained using the material As2Se3 on a PDMS substrate. Specifically, Fig. 2a illustrates nanocones, Fig. 2b illustrates 1D sinusoidal wrinkles, Fig. 2c illustrates 2D zigzag wrinkles, Fig. 2d illustrates isotropic labyrinth wrinkles on 1D sinusoidal wrinkles, and Fig. 2e illustrates checkerboard wrinkles. Therefore, various thin film surface morphologies can be achieved and controlled through the proposed method.
Figs. 3a to 3e illustrate Scanning Electron Microscope (SEM) images of wrinkles achieved on various materials through the proposed method. Fig. 3a illustrates wrinkles on As2Se3, Fig. 3b illustrates wrinkles on Aluminium, Fig. 3c illustrates wrinkles on Silver, and Fig. 3d illustrates wrinkles on PMMA. Fig. 3e illustrates SEM image of a large area (about 1200µm×1200µm) ordered 1D sinusoidal wrinkles of As2Se3 on PDMS substrate. Therefore, proposed method is compatible with a wide range of materials, including chalcogenides, metals, and polymers, resulting in well-ordered sinusoidal wrinkles.
Figs. 4a and 4b illustrate comparison matrix of SEM images depicting dependence of wrinkle wavelength on film thickness and heating temperature. Specifically, Fig. 4a illustrates the comparison matrix of SEM images for As2Se3 as the thin film material and PDMS 5 as the substrate; and Fig. 5a illustrates experimental data of the SEM images shown in Fig. 4a vs. plots obtained from the wavelength equation under similar parameters. Fig. 4b illustrates the comparison matrix of SEM images for As2Se3 as the thin film material and PDMS 10 and PDMS 5 as the substrate. Heating temperature was varied from 80ᵒC to 120ᵒC, in intervals of 10ᵒC and room temperature was kept as 25ᵒC. The film thickness ranges from 100nm to 200nm, in intervals of 50nm. It could be observed that with increase in the film thickness and heating temperature, the wrinkle wavelength(d) also increases.
Role of substrate properties like thermal expansion coefficient and refractive index on development of the wrinkles for obtaining photonic devices is explained successively. Formation of the wrinkles necessitates substrates with an ideal thermal expansion coefficient. Solid substrates such as glass and silicon, which possess low coefficients of thermal expansion, experience minimal expansion and contraction during heating and cooling, respectively. Consequently, the solid substrates lack capacity to induce necessary level of contraction in thin films crucial for wrinkle formation. Conversely, substrates such as PDMS 15 and above, which have extremely high coefficients of thermal expansion expand significantly, resulting in the cracking and subsequent dewetting of thin films deposited atop them. PDMS 3, 5, and 10, cured for 3-6 hours at 80ᵒC have been found to possess the optimum thermal expansion coefficient required for the wrinkle formation. Fig. 5b illustrates a plot showing dependence of wrinkle wavelength on thermal expansion coefficient mismatch between film and substrate of the material.
Additionally, the substrates must have a minimum thickness such that they can act as a semi-infinite wrinkled bi-layer material. Below the minimum thickness, the substrates undergo global buckling upon thermal treatment, thereby hampering formation of uniform wrinkles. Transparency and non-absorption of PDMS within the visible and Near Infrared (NIR) spectra render it highly promising for photonic applications.
Role of thin film properties like thermal expansion coefficient, film thickness, and surface energy on development of the wrinkles for obtaining photonic devices is explained successively. Formation of the wrinkles also depend on an ideal thermal expansion coefficient of deposited thin film. If such ideal thermal expansion coefficient is similar to that of the ideal thermal expansion coefficient of the substrate, contraction force experienced during cooling is not adequate for wrinkle formation. Conversely, if the ideal thermal expansion coefficient of the deposited thin film is excessively lower than the ideal thermal expansion coefficient of the substrate, the thin film will experience very high tensile stress during heating which will lead to formation of cracks, ultimately favouring dewetting over wrinkle formation in achieving equilibrium. High difference between thermal expansion coefficients of the substrate and the thin film results in formation of the wrinkles with large wavelengths. For a given substrate and thin film material, wrinkle formation requires a minimum film thickness, contingent upon temperature change within the wrinkled bi-layer material and surface energy of the thin film. The lower the surface energy, lower is the required minimum film thickness.
Temperature also plays a crucial role in formation of the wrinkles. Formation of large area, uniform, ordered wrinkles requires a uniform force acting on the film. The uniform force can only be achieved within an optimal temperature range. Lack of wrinkle formation at temperatures much below this range is attributed to insufficient generation of compressive stress on the film. Conversely, when the wrinkled bi-layer material is heated to temperatures exceeding this range by a large extent, disorderness starts in the thin films. At temperatures just below the optimal range, wrinkle formation is not uniform over the entire thin film area due to the non-uniformity of force acting on the film. The force is highest near center of the film and gradually diminishes towards both sides. Similarly, at temperatures just above the optimal range, the wrinkled bi-layer material experiences non-uniform forces leading to disorderness. By performing several experiments, an optimal temperature range of 90ᵒC to 120ᵒC was determined for development of the wrinkles.
Fig. 6a illustrates a schematic of a wrinkled bi-layer material with film thickness ‘h’ and substrate thickness ‘H’. Fig. 6b illustrates a schematic of stress formation in the film and the substrate during cooling. Arrows shown in Fig. 6b indicate direction of stress. When the film-substrate bilayer starts to cool down, the PDMS substrate, owing to its higher thermal expansion coefficient than that of the film deposited atop, contracts faster than the film. In order to maintain compatibility between the film and the substrate, the substrate experiences a tensile stress whereas the film experiences compressive stress as depicted in Fig. 6b. Fig. 6c illustrates a schematic representing resultant stress and moment acting on the film and the substrate. In Fig. 6c, interfacial set of stresses are replaced by a single force and moment for each of the film and the substrate, F_f and M_f for the film and F_s and M_s for the substrate. The wrinkled bi-layer material will bend to counteract the unbalanced moments. Fig. 6d illustrates a schematic showing stress formation on the film of width ‘w’ and radius of curvature ‘R’, due to the compressive stress acting over the film.
When the wrinkled bi-layer material is heated, the substrate expands more than the film, thereby exerting tensile stress over the film. If the substrate expansion is too high, for instance in case of PDMS 15, 20, and above, tensile stress acting on the film is so high that cracks are formed in it. As the wrinkled bi-layer material cools, the substrate contracts more than the film, resulting in a compressive stress on the film. To maintain equilibrium, wrinkles with appropriate wavelength form in the film. The size of these wrinkles directly correlates with the stress on the film. A greater mismatch in thermal expansion coefficients between the film and substrate leads to increased stress on the film, resulting in wrinkles with larger wavelength. Similarly, cooling the wrinkled bi-layer material from a higher temperature increases the stress on the film, resulting into enlargement of the wrinkles' wavelength.
Fig. 7a illustrates an AFM image of a first sample having a film of As2Se3 deposited over PDMS 5 substrate, and Fig. 7b illustrates a line plot showing a surface profile of the film across a line drawn over the AFM image shown in Fig. 7a. It illustrates that the amplitude of wrinkles is much lesser than their periodicity. The first sample had a film thickness of 150nm, and was obtained at a change in temperature of 95ᵒC. Wavelength and amplitude of the wrinkles in the first sample are around 7.5µm and 700nm respectively. The table provided below gives Δx and Δy values of the cursor pairs in the line plot shown in Fig. 6b, where Δx denotes a half value of the wavelength of the wrinkles and Δy denotes the amplitude of the wrinkles.
Cursor Δx(µm) Δy(nm)
Red 3.633 690.164
Green 3.865 604.846
Blue 3.668 816.852
Fig. 7c illustrates an AFM image of a second sample having a film of As2Se3 deposited over PDMS 5 substrate, and Fig. 7d illustrates a line plot showing a surface profile of the film across a line drawn over the AFM image shown in Fig. 7c. It could be observed from Fig. 7d that the amplitude of wrinkles is much lesser than their periodicity. The second sample had a film thickness of 200nm, and was obtained at a change in temperature of 75ᵒC. Wavelength and amplitude of the wrinkles in the first sample are around 6µm and 200nm respectively. The table provided below gives Δx and Δy values of the cursor pairs in the line plot shown in Fig. 7d.
Cursor Δx(µm) Δy(nm)
Red 2.900 272.959
Green 3.096 252.585
Blue 2.900 159.937
From the above provided details, it could be observed that the wavelength of the wrinkles is much greater than their amplitude.
Mathematical modelling of wrinkled thin film formation on PDMS substrate is successively described. Considering the film to be a longitudinal beam, strain acting over the film can be represented using below provided equation (1).
Strain=({ Rθ-(R-h)θ})/Rθ (1)
Therefore, stress acting over the film can be represented using below provided equation (2).
σ_f=(Y_f { Rθ-(R-h)θ})/Rθ 〖⟹σ〗_f=(Y_f h)/R (2)
In above equation (2), σ_f denotes the stress acting on the film, Y_f denotes Young’s modulus of the film, R denotes radius of curvature of the film, θ denotes angle of curvature of the film, and h denotes the film thickness. Thus, for a given film stiffness and radius of curvature, higher the film thickness higher is the stress experienced by it. Due to such reason, wrinkles of larger wavelengths are developed for higher film thicknesses and wrinkle formation also becomes easier with increase in film thickness.
For mathematical modelling, it could be considered that stress energy U leads to formation of ‘n’ number of wrinkles.
U= ∫_0^U▒dU =∫_0^l▒fdx (3)
In above equation, f denotes the compressive force acting on the film at an instant, dx denotes contraction in the film along the direction of the compressive force at that instant, and l denotes the total contraction that should occur in the film due to the total stress energy U.
Fig. 8 illustrates a schematic of an array of wrinkles considered for the mathematical modelling. For modelling purpose, the wrinkles are considered to be of triangular shape. In Fig. 8, w denotes width, a denotes amplitude, and d denotes periodicity/wavelength of the wrinkles.
The compressive force f acting on the film at an instant can be represented using below equation.
f=Y_f (α_s-α_f)∆Twh (4)
In above equation, Y_f denotes the Young’s modulus of the film, and α_s and α_f denote the thermal expansion coefficients of the substrate and the film, respectively. ∆T signifies the temperature change of the wrinkled bi-layer material and w,h denote the width and the thickness of the film, respectively.
Utilizing equations 3 and 4, the stress energy U can be defined using below equation
U= ∫_0^l▒〖Y_f (α_s-α_f ) 〗 ∆T(wh)dx
= Y_f (α_s-α_f )∆Twhl (5)
For the triangular wrinkles, total surface area of a wrinkle can be defined using Pythagoras theorem, as represented using below equation.
A=2× 2w√(d^2/4+a^2 ) (6)
In above equation, first numeral 2 is used for a top and a bottom surface of the wrinkle, and a second numeral 2 (used in 2w) is for both faces of the triangle. Only the bottom surface of the wrinkle is newly formed surface during wrinkle formation.
At verge of wrinkle formation, the stress energy gets converted into surface energy of newly formed surfaces of the wrinkles. Thus, from energy conservation, below equation is obtained.
〖 Y〗_f (α_s-α_f )∆Twhl=Cn2w√(d^2/4+a^2 ) γ_f (7)
In above equation, γ_f denotes the surface energy of the thin film and C is a proportionality constant, greater than 1, which accounts for the disparity in surface area between a sinusoidal and a triangular wrinkle. The surface area of a sinusoidal wrinkle is greater than that of a triangular wrinkle
Since d≫a, below equation could be derived using Binomial expansion.
Y_f (α_s-α_f )∆Twhl=〖Cγ〗_f nwd (8)
d= C (Y_f (α_s-α_f)∆Thl)/(nγ_f ) (9)
Strain acting on the film is defined using below equation.
∈ = l/L= (α_s-α_f)∆T (10)
In above equation, l denotes a total change in length of the film, perpendicular to the direction of the compressive stress. L denotes total expanded length of the film after heating, along which the compressive stress starts acting when the wrinkled bi-layer material starts cooling down from the maximum temperature.
From equation (10), below mentioned equation could be derived.
l=L(α_s-α_f)∆T (11)
Using equations (9) and (11), below mentioned wavelength equation could be obtained.
d= C (Y_f 〖[(α_s-α_f )∆T]〗^2 hL)/(nγ_f ) (12)
Ascertaining the maximum length L of the film directly isn't feasible. Ascertaining the maximum length L of the film (i.e. the length of the film after heating) and the proportionality constant C directly isn't feasible. Therefore, (L/Cn) has been replaced by a proportionality constant C_w. It is a dimensional constant with units of length (i.e. meter when SI units are used for all other parameters).Thus, below mentioned final wavelength equation can be obtained.
d=C_w (Y_f 〖[(α_s-α_f )∆T]〗^2 h)/γ_f (13)
From the final wavelength equation (13), it is determined that an increase in Young’s modulus and a decrease in the surface energy and thermal expansion coefficient of the film results into increase in the wavelength.
The proportionality constant C_w depends on the following parameters
More the thermal expansion coefficient of the substrate more is the tensile stress exerted by it on the film during heating. L is directly proportional to the tensile stress acting on the film. In case of PDMS, the thermal expansion coefficient varies with the curing temperature and also the duration of curing.
More the thermal expansion coefficient of the film more is its expansion during heating, and more is the value of L. In case of thin films, the thermal expansion coefficient of a given material can also vary with the film thickness.
Lower the surface energy of a film, the higher the surface area required to balance out a given stress. Thus, to balance out a given stress during heating, the expansion in length L will be more for a thin film material having lower surface energy. Thus, L is inversely proportional to surface energy.
The higher the tensile force acting on the film while heating, higher is the expansion in it. Thus L is directly proportional to the tensile force acting on the thin film. The tensile force is dependent on the Young’s modulus (Y_f), width (w), and thickness of the film (h), change in temperature of the system (∆T), and the thermal expansion coefficient mismatch between the film and the substrate (α_s-α_f). (Refer SI equation 3).
L also depends on the initial length of the sample. Higher the initial length, higher is the expanded length L. However, it has been experimentally seen that beyond a critical length L_c, keeping other parameters constant, as L increases, n also increases such that the wrinkle periodicity doesn’t change significantly. Below the critical length wrinkle formation does not take place.
Figs. 9a, 9b, and 9c illustrate SEM images of samples of different films of As2Se3, PMMA, and Al. The films were deposited on PDMS 5 substrates having α_s≈210×〖10〗^(-6) K^(-1). Fig. 10 illustrates a table of results obtained using the wavelength equation. It could be observed that outcomes generated by the wavelength equation (shown in Fig. 10) closely match with the experimental findings (shown in Figs. 9a through 9c).
From the wavelength equation (13), it could be understood that an increase in film thickness and/or ∆T leads to an increase in the wavelength of the wrinkles. As the film thickness increases, the stress acting on the film during the cooling process also increases, thereby increasing the wavelength. Similarly, as the heating temperature increases, the compression in the substrate while cooling down to room temperature also increases, thereby increasing the compressive stress on the film during the cooling process.
Fig. 4a already illustrates the comparison matrix of SEM images depicting the dependence of wrinkle wavelength on the film thickness and the heating temperature for PDMS 5 substrate. Fig. 5a illustrates experimental plots of the SEM images shown in Fig. 4a vs. plots obtained from the wavelength equation (13) under similar parameters and the corresponding values that have been considered for C_w in the Wavelength Equation in order to align with the data obtained.
Fig. 4b already illustrates the comparison matrix of SEM images depicting the dependence of wrinkle wavelength on the film thickness and the heating temperature for PDMS 10 substrate. Fig. 5b illustrates, through experimental plots of the SEM images shown in Fig. 4b, a dependence of the wrinkle wavelength on the thermal expansion coefficient mismatch between the film and the substrate. Solid dots represent experimental data plots, and dashed lines are obtained from the wavelength equation using similar parameters. The substrates used are PDMS5 and PDMS 10 and the thin film material is As2Se3. Together, Figs. 4a,4b and 5a,5b illustrate compatibility of the wavelength equation with the experimental results.
As the difference in thermal expansion coefficients between the substrate and the rigid film deposited on the substrate increases, disparity in their thermal expansion also increases. Consequently, as the wrinkled bi-layer material cools, the mismatch in contraction between the substrate and the film intensifies, leading to greater compressive stress on the film. For such reason, larger wrinkles form when there's a higher thermal expansion coefficient mismatch between the film and the substrate. PDMS10 has a higher thermal expansion coefficient than PDMS5, hence the wrinkles formed on the film deposited atop PDMS10 have higher wavelength than the film deposited on PDMS5, for the same film material and film thickness, as evident from Fig. 5b. It is to be noted that some deviation between the theoretical and experimental values arises because all the thin film and substrate parameters have been assumed to be constant with respect to change in film thickness and system temperature. Also, in the theoretical model the sinusoidal wrinkles have been assumed to be triangular.
Compressive stress acting on a thin film is directly proportional to the thickness and Young’s modulus of the film, as evident from the Equation 3. Wrinkles manifest in a film when the stress energy due to a compressive force is balanced by the surface energy generated due to the formation of new surfaces. Consequently, a thin film with a higher surface energy will require a higher compressive stress for wrinkle formation. For instance, when being cooled down from 80℃ to 25℃, As2Se3, having a Young’s modulus of 〖10〗^10 Pa, and surface energy of 0.2 J/m^2 requires a critical thickness exceeding 70nm for wrinkle formation, while materials like Ag and Al, having a Young’s modulus of approximately 5×〖10〗^10 Pa, and surface energy around 0.05J/m^2 exhibit a critical thickness of around 15 nm. This could be seen in Fig. 11a illustrating SEM images showing wrinkle formation in thin films of different materials. Specifically, wrinkles form in 15nm Al and Ag thin films and do not form in 60nm As2Se3 thin films. All the thin films were deposited on PDMS5, were heated to 80ᵒC for 5 minutes, and cooled down to 25ᵒC, before capturing the SEM images shown in Fig. 11a.
The wavelength equation (13) could be used for determining thermal expansion coefficients of the thin films by considering appropriate values for the proportionality constant C_w. A table providing values of the thermal expansion coefficients of different thin films is shown in Fig. 11b. From the table, it could be understood that proposed wavelength equation can correctly predict the values of the thermal expansion coefficient of different thin film materials. The values obtained using the wavelength equation matches with the experimental values obtained from the wrinkled surfaces.
As the curing time of PDMS increases, the cross-linking between the PDMS base and the curing agent increases, thereby decreasing its thermal expansion coefficient (α_s). This in turn decreases the difference in thermal expansion coefficient (α_s-α_f), which leads to a decrease in the wavelength d, as shown in Fig.12.
By combining Equations 5 and 11, below mentioned equation defining the stress energy can be obtained.
U= Y_f [(〖α_s-α_f)∆T]〗^2 whL (14)
Here L is the length along which the compressive stress is acting. To overcome the critical stress required for wrinkle formation, the compressive stress should act along a length that is greater than the critical length required for the wrinkled bi-layer material. When the distance between the grooves increases, the 1D wrinkles give way to 2D wrinkles because then both the lateral and longitudinal stress are greater than the critical stress required by the bi-layer material for wrinkle formation, as shown in Fig. 13.
From equations 8 and 12 it could be concluded that, if
L
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202441100464-STATEMENT OF UNDERTAKING (FORM 3) [18-12-2024(online)].pdf |
2024-12-18 |
| 2 |
202441100464-PROOF OF RIGHT [18-12-2024(online)].pdf |
2024-12-18 |
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202441100464-FORM FOR SMALL ENTITY(FORM-28) [18-12-2024(online)].pdf |
2024-12-18 |
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202441100464-FORM 1 [18-12-2024(online)].pdf |
2024-12-18 |
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202441100464-EVIDENCE FOR REGISTRATION UNDER SSI(FORM-28) [18-12-2024(online)].pdf |
2024-12-18 |
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202441100464-EVIDENCE FOR REGISTRATION UNDER SSI [18-12-2024(online)].pdf |
2024-12-18 |
| 7 |
202441100464-EDUCATIONAL INSTITUTION(S) [18-12-2024(online)].pdf |
2024-12-18 |
| 8 |
202441100464-DRAWINGS [18-12-2024(online)].pdf |
2024-12-18 |
| 9 |
202441100464-DECLARATION OF INVENTORSHIP (FORM 5) [18-12-2024(online)].pdf |
2024-12-18 |
| 10 |
202441100464-COMPLETE SPECIFICATION [18-12-2024(online)].pdf |
2024-12-18 |
| 11 |
202441100464-FORM-9 [02-01-2025(online)].pdf |
2025-01-02 |
| 12 |
202441100464-FORM-8 [02-01-2025(online)].pdf |
2025-01-02 |
| 13 |
202441100464-FORM 18A [02-01-2025(online)].pdf |
2025-01-02 |
| 14 |
202441100464-EVIDENCE OF ELIGIBILTY RULE 24C1f [02-01-2025(online)].pdf |
2025-01-02 |
| 15 |
202441100464-FORM-26 [11-03-2025(online)].pdf |
2025-03-11 |
| 16 |
202441100464-FER.pdf |
2025-04-16 |
| 17 |
202441100464-FORM 3 [16-06-2025(online)].pdf |
2025-06-16 |
| 18 |
202441100464-Proof of Right [18-06-2025(online)].pdf |
2025-06-18 |
| 19 |
202441100464-OTHERS [24-06-2025(online)].pdf |
2025-06-24 |
| 20 |
202441100464-FER_SER_REPLY [24-06-2025(online)].pdf |
2025-06-24 |
| 21 |
202441100464-COMPLETE SPECIFICATION [24-06-2025(online)].pdf |
2025-06-24 |
| 22 |
202441100464-CLAIMS [24-06-2025(online)].pdf |
2025-06-24 |
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202441100464-ABSTRACT [24-06-2025(online)].pdf |
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202441100464-SER.pdf |
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202441100464-OTHERS [15-10-2025(online)].pdf |
2025-10-15 |
| 26 |
202441100464-FER_SER_REPLY [15-10-2025(online)].pdf |
2025-10-15 |
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202441100464-CLAIMS [15-10-2025(online)].pdf |
2025-10-15 |
| 28 |
202441100464-ABSTRACT [15-10-2025(online)].pdf |
2025-10-15 |
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