Description:FIELD OF INVENTION:

The present invention is related to a method for forming electrically conductive Ga film on Styrene-Ethylene-Butylene-Styrene (SEBS) substrate. More particularly, the present invention is related to a method in which SEBS substrate is exposed to plasma and liquid Ga is thermally evaporated on said substrate to form electrically conductive Ga film on SEBS substrate. The SEBS substrate with electrically conductive Ga film have applications in stretchable and flexible electronics.

BACKGROUND OF INVENTION:

[2] The stretchable and flexible electronics has attracted considerable attention in recent times, primarily owing to its wide-ranging applications in consumer electronic displays, wearable devices, interfacing of biosensors with humans, and soft robotics. Stretchable electronic devices are mainly prepared by either developing new structural layouts with conventional materials or by employing new materials in conventional layouts.

[3] Conventional materials such as gold and silver are often used as thin films generally relies on wrinkling, in-plane and out-of-plane buckling, and bending-induced deformations in stretchable electronics. However, said conventional materials tend to fail under excessive stretching, especially when the difference between applied and pre-strain exceeds 10% or when they are sharply bended. In view of said limitations, there is an excessive demand for materials with greater stretchability, driving research into inherently soft materials as a promising alternative.

[4] Soft polymers are combined with conducting materials such as carbon nanotubes, rigid nanoparticles, or nanorods made of silver, gold, and copper in order to achieve both stretchability and conductivity. However, the effectiveness of said soft polymer could be restricted by the filling fraction. In contrast, liquid metals have emerged as a highly promising alternative due to their exceptional blend of fluidity and conductivity. However, the use of mercury, a well-known room-temperature liquid metal, is mainly limited due to its toxic nature. Hence, Gallium and its alloys, which are nearly room-temperature liquid metals, offer a promising alternative to enable the development of flexible and stretchable electronic devices.

[5] Liquid metal Gallium offers multiple advantages such as viscosity just twice that of water at room temperature, good conductivity of 3.86×104 S/cm, a low vapour pressure and a melting point of around 28° C. Despite these advantages, high surface energy of Gallium and the formation of native oxide layer limits the Gallium to wet the surfaces, thus resulting in the formation of discrete droplets and non-continuous films or surfaces.

[6] Researchers have extensively explored various techniques to integrate Gallium (Ga)-based liquid metal (LM) into diverse materials and structures for soft electronics applications. These methods include additive processing techniques such as inkjet printing, microcontact printing, and stencil or screen printing, as well as subtractive processing approaches like lift-off and laser ablation. Other approaches involve the wetting and sintering of droplets formed through sonication and the creation of polymer composites. However, all of these methods have largely been constrained to produce Ga films, droplets, or structures at the scale of 10 µm, primarily due to the high surface tension of Ga and the formation of oxide layers. Therefore, achieving the desired functionalities with reduced material consumption remains a critical challenge when moving to thin films with sub-micron range of thickness.

[7] Physical vapor deposition (PVD) is a well-established process for creating thin films in fabrication of integrated circuits with high accuracy. However, PVD process when applied to deposit Ga results in isolated spherical droplets, instead of films due to its high surface tension. Researchers have attempted to overcome the high surface tension of Ga by depositing on top of microstructures covered with thin film of gold or during deposition, oxygen is purged inside the deposition chamber to react with Ga and form bigger size droplets. However, these works are either limited by the size of the substrate due to lithographic process or doesn’t form a mono layer of Ga which could prevent the theoretical analysis of conducting pathways. Nevertheless, developing a monolayer of Ga-based thin-film devices with sub-100 nm thicknesses and scalable to a large area, that demonstrate innovative applications could unlock vast potential in the soft electronics domain, offering new pathways for highly efficient, flexible, and stretchable technologies.

[8] For instance, reference is made to EP1090159B1 which discloses plasma-enhanced, chemical vapor deposition of coatings and, more particularly, to the use of an atmospheric-pressure, plasma discharge jet for deposition of films on substrates. However, it requires application of high deposition temperature.

[9] Reference is further made to A. Hirsch et al. in A Method to Form Smooth Films of Liquid Metal Supported by Elastomeric Substrate, Adv. Sci. 2018, 5, 1800256, which discloses method to produce smooth film of liquid gallium (Ga) on extended surface areas with controlled thickness and electrical properties. The surface chemistry and topography of silicone rubber (poly(dimethylsiloxane)) is engineered with microstructured pillars and gold precoating layer to produce Ga superlyophilic substrates. Physical vapor deposition of Ga on such substrates leads to the formation of smooth and homogeneous films by imbibition of the surface topography rather than coalescence and formation of Ga drops. By capillarity, Ga accumulates in between the pillars up to their top surface, forming a smooth film with a root mean square roughness (Rq) smaller than 100 nm. However, said method suffers from drawback of precoating with gold in order to form a Ga layer. Further, said method requires nanopatterning which is time consuming and not scalable to large area.

Therefore, there is a crucial need for simple and efficient method for forming electrically conductive Ga film on substrate that addresses all of the major challenges associated with the existing methods.

In view of above, there exists a dire need in the state of art for providing a method for forming electrically conductive Ga film having thickness less than 100 nm on substrate, having applications in soft and stretchable electronics.

OBJECTS OF THE INVENTION:

The principle object of the present invention is to provide a method for forming electrically conductive Ga film having thickness less than 100 nm on SEBS substrate.

Another object of the present invention is to provide a method for forming electrically conductive Ga film on substrate, where Ga nanodroplet nucleation leads to self-assembled conductive films via tunneling and ohmic contacts.

Yet another object of the present invention is to provide a substrate with Ga film, wherein the thickness of Ga film is less than 100 nm.

Another object of the present invention is to provide a substrate with Ga film having applications in soft and stretchable electronics.

SUMMARY OF THE INVENTION:

In an aspect, the present invention provides a method for forming electrically conductive Ga film on SEBS substrate, the method comprising exposing atmospheric plasma to SEBS substrate at a pressure in the range of 0.2 to 0.8 mbar for a time period in a range of 3-7 minute to form plasma exposed SEBS substrate and thermally evaporating liquid Ga on to said plasma exposed SEBS substrate to form a film of electrically conductive Ga on said SEBS substrate.

The present method deposit electrically conductive thin Ga film over large areas by altering the surface energy of the Styrene-Ethylene-Butylene-Styrene (SEBS) block copolymer and forming Ga via thermal evaporation on it. Exposing said SEBS substrate to plasma increases the surface energy of the substrate and there by aiding in wetting of the Ga nanodroplets to result in conducting films through percolation network. The Ga film is also formed on other substrates such as acrylic, polycarbonate and commercially available scotch tape, which has surface energy similar to that of surface energy enhanced SEBS, via thermal evaporation.

In another aspect, the present invention provides a substrate with Ga film as described herein, wherein the thickness of Ga film is less than 100 nm.

The SEBS substrate with Ga film is encapsulated with a polymer to form a stretchable device.

DESCRIPTION OF ACCOMPANYING FIGURES:

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 together with the description.

Figure 1 illustrates (a) Fabrication steps: Schematic illustration of SEBS substrate exposed to atmospheric plasma in the thermal evaporator and forming thermally evaporated Ga from a tungsten boat to the plasma-treated SEBS substrate; (b) Schematic of the Ga film on SEBs encapsulated with Silicone; SEM image of Ga nanoparticles on pristine and plasma exposed SEBS: (c) & (e) top view and (d) & (f) cross-sectional view respectively; (g) Surface energy of different substrates: PC, PMMA, Scotch tape, pristine and plasma exposed SEBS and (h) Stress-Strain curve for pristine SEBS, Ga formed on SEBS and SEBS-Ga encapsulated with Silicone Gel, in accordance with an implementation of the present invention.

Figure 2 illustrates (a) Representation of surface energies at the three-phase contact line of solid, liquid and vapour phases; (b) and (c) Scanning electron microscopic image of the cross-sectional view representing the shape of Ga nanodroplets on pristine SEBS and SEBS after exposed to plasma respectively, in accordance with an implementation of the present invention.

Figure 3 illustrates scanning electron microscopic images of Ga droplets on Scotch tape, PMMA, Glass and plasma-treated SEBS respectively, in accordance with an implementation of the present invention.

Figure 4 illustrates (a) Scanning electron microscopy image of the morphology of the Ga nanodroplets with increase in thickness of Ga formed; Variation of (b) resistance of the Ga film and (c) average area of the Ga droplets with increase in thickness of the Ga, in accordance with an implementation of the present invention.

Figure 5 illustrates (a) Scanning electron microscopy image of the morphology of the Ga droplets with an increase in the rate of Ga formed; Variation of (b) resistance of the Ga film and (c) average area of the Ga droplets with the increase in the rate of the Ga deposition, in accordance with an implementation of the present invention.

Figure 6 illustrates electro-Mechanical Characteristics: Variation of the resistance of the device with strain for 6 continuous cycles at (a) 25%, (b) 50%, (c) 100% and (d) 200% respectively. S and R denote the stretching and relaxation phases marked for the first and fourth cycle, in accordance with an implementation of the present invention.

Figure 7 illustrates scanning electron microscopy image of the Ga film (t=120nm, r=1Aps) at different strains, (a) 25% (b) 50%, (c) 100%, (d) 200%, and (e) the relaxed sample after 200% strain; (f) and (g) Length and width of the cracks with strain respectively. Scale bar represents 5 µm, in accordance with an implementation of the present invention.

Figure 8 illustrates variation of ΔR/R with time for periodic (a) uniaxial strain of 25% and (b) bending, in accordance with an implementation of the present invention.

Figure 9 illustrates (a) A complete resistive network for an entire nanosheet; (b) Resistive connections between four adjacent Ga nanodrops in a nanosheet. The inter-droplet resistances could be of ohmic, tunneling, or open (conductance = 0) type. Here, only tunneling type contacts are shown; (c) The gap distance is g. When a gap voltage V_g is applied, electrons tunnel from both sides, J=J_1-J_2 is the net tunneling current density. Potential barrier Φ(x) in the insulator layer sandwiched between two Ga nanodrops; (d) Resistance as a function of Ga film thickness at 0% strain. The black symbols are measurement data and the blue dashed line is from theoretical calculation; and (e) Total film resistance in stretching cycle for different strains from theoretical model. Strains of 25% and 100% are represented by blue and dotted green curves respectively, in accordance with an implementation of the present invention.

Figure 10 illustrates (a) Demonstration of curvature sensing with a single arm pneumatic actuator and (b) curvature is shown for the steps (1 -7) marked in fig (a); (c) Positive and negative change in resistance with concave and convex curvatures; (d) Demonstration of change in the intensity of resistance while holding a petri dish of 150 mm diameter (left) and a plastic ball of 70 mm diameter (right) with a four-arm pneumatic gripper; and (e) Working of thin Ga film integrated with surface mount LED’s under different bending curvatures, in accordance with an implementation of the present invention.

Figure 11 illustrates plot showing the resistance of the Ga film on different substrates.

Figure 12 illustrates (a) Fabrication of the actuators using a three-part mold system from silicone casting; and (b) Demonstration of a single arm gripper attached to a syringe.

DETAILED DESCRIPTION OF THE INVENTION:

While the invention is susceptible to various modifications and alternative forms, specific embodiment thereof will be described in detail below. It should be understood, however that it is not intended to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternative falling within the scope of the invention as defined by the appended claims.

Although one or more features and/or elements may be described herein in the context of only a single embodiment, or alternatively in the context of more than one embodiment, or further alternatively in the context of all embodiments, the features and/or elements may instead be provided separately or in any appropriate combination or not at all. Conversely, any features and/or elements described in the context of separate embodiments may alternatively be realized as existing together in the context of a single embodiment.

The terminology used herein is for the purpose of describing particular various embodiments only and is not intended to be limiting of various embodiments. As used herein, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

As discussed in the background section of the present invention, the existing processes reported in the literature are for manufacturing stretchable and flexible electronics. However, the conventional material used to prepare said electronics tend to fail under excessive stretching, especially when the difference between applied and pre-strain exceeds 10% or when they are sharply bended. Further, the effectiveness of soft polymer used in place of conventional material is restricted by the filling fraction of conducting materials such as carbon nanotubes, rigid nanoparticles, or nanorods made of silver, gold, and copper. Furthermore, the usage of liquid metal Gallium results in the formation of discrete droplets and non-continuous films or surfaces due to high surface energy of Gallium and the formation of native oxide layer limits the Gallium to wet the surfaces.

Therefore, to overcome the existing problems in the art, the present invention provides a method which overcomes surface tension limitation, is scalable and substrate versatile and demonstrate practical applications, including curvature sensors for grippers and flexible LED-integrated devices, showcasing potential for soft electronics.

In an embodiment, the present invention provides a method for forming electrically conductive Ga film on SEBS substrate, the method comprising:
exposing atmospheric plasma to SEBS substrate at a pressure in the range of 0.2 to 0.8 mbar for a time period in a range of 3-7 minute to form plasma exposed SEBS substrate; and
thermally evaporating liquid Ga on to plasma exposed SEBS substrate of step a) to form a film of electrically conductive Ga on said SEBS substrate.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of Ga on SEBS substrate is less than 100 nm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the pressure and time period during exposing atmospheric plasma to SEBS substrate is 5e-1 mbar and 5 minutes respectively.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the SEBS substrate is prepared by dissolving SEBS beads in toluene to form a mixture, which is stirred to form a solution, followed by casting said solution in a glass container to form a transparent film.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of transparent film is in the range of 200- 300 µm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of transparent film is 250 µm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the Ga film on SEBS substrate is encapsulated with a polymer to form a stretchable device.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the polymer is selected from the group consisting of silicone, PDMS and SEBS.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the contact angle of Ga droplets decreases from 145°C to 35° with increased SEBS surface energy due to plasma exposure.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the Ga film is formed in step b) through tunneling and ohmic contacts.

In another embodiment, there is provided a substrate as described herein, wherein the thickness of Ga film is less than 100 nm.

In another embodiment, there is provided a substrate as described herein, wherein the substrate is selected from SEBS, polycarbonate (PC), scotch tape, acrylic (PMMA), cellulose and thin covering glass.

In another embodiment, there is provided a substrate as described herein, as and when used in soft electronics.

EXAMPLES

The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and the description of how to make and use the present invention, and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all and only experiments performed. The methodology of preparing few of the preferred embodiments shall become clearer with working examples provided below.

A. Fabrication of Ga-based stretchable conducting device:

Preparation of SEBS substrates: SEBS block copolymer is chosen as a substrate owing to its high stretchability characteristics. SEBS substrate is prepared by dissolving SEBS beads (Kraton, G1657) in toluene in the ratio of 1.5 grams for 25 mL. The mixture is magnetically stirred until a homogeneous solution is obtained. Solution is casted on a glass petri dish, covered with an aluminum foil of uniform pores to get a thin transparent film of around 250 μm thickness.

Exposure of SEBS substrates to plasma: The SEBS substrate is exposed to atmospheric plasma (HHV thermal evaporator, 5e-1 mbar) for 5 minutes at 0.3 A current.

Plasma exposure increases the SEBS substrate's surface energy by 40% compared to unexposed SEBS, as shown in parts (a) and (g) of Figure 1. Distinct wetting behavior of Ga droplets on plasma-exposed SEBS is observed, as shown in parts (b), (e) and (f) of Figure 1, thus facilitating tunneling conductivity and resulting in a conductive surface with resistance ~1 KΩ. The wetting behavior of Ga droplets is explained by the surface forces at the three-phase contact line of the droplet. Increase in the substrate surface energy γ_s pulls the three-phase contact line of the droplet and decreases the contact angle θ the droplet makes with the substrate, as shown in part (a) of Figure 2. FIB-SEM cross-sectional images show the contact angle of Ga droplets decreasing from approximately 145° to 35° with increased SEBS surface energy due to plasma exposure, as shown in parts (b) and (c) of Figure 2.

Deposition of liquid Gallium: Liquid gallium (ThermoScientific Chemicals, 99.9% metal basis, packaged in polyethylene bottle) is thermally evaporated on to the plasma exposed SEBS substrate (HHV thermal evaporator) to form a thin film of nanodroplets. Experiments are performed for different thickness (40 to 120 nm) and rate of deposition (1 to 5 Å/s). The thickness of the substrate is monitored via in-built Quart crystal sensor.

Thermal evaporation of Ga onto pristine SEBS results in the formation of spherical Ga droplets which exhibit minimal contact as shown in the top and cross-sectional views, as shown in parts (c) and (d) of Figure 1, thus resulting in non-conducting films. The limited spreading of Ga droplets is attributed to the low surface energy of SEBS (~32 N/mm), as shown in part (g) of Figure 1 and the high surface tension of Ga (~700 N/mm). The higher the substrate's surface energy more pronounced the wetting of films, influencing the formation of conductive pathways.

Final making of the device: Thin copper wires are used as interconnects, which are secured to the substrate by applying carbon grease (MG Chemicals Carbon Conductive Silicone Grease, 846-80g) locally over the wires. Silicone part A and part B of Smooth-On Ecoflex 00-50 is mixed in 1:1 and poured over the connects with grease to make the connects firm and encapsulate the thin film of Ga nanodroplets. Silicone cures in 3 hours at room temperature to give a completely protected stretchable device with stable connects.

Testing with other substrates

The process can be extended to substrates with high surface energies to achieve conductive films without plasma exposure. Substrates demonstrating tunneling conductivity with Ga films include polycarbonate (PC), Scotch tape, acrylic (PMMA), cellulose, and thin Corning glass, all of which are flexible, as shown in Figure 3. Encapsulation of Ga thin films on these substrates enhances durability. Both pristine SEBS and SEBS coated with Ga films exhibited stretchability up to 900% strain. However, encapsulation with silicone reduced stretchability to 350% strain, which is still sufficient for practical applications, as shown in part (h) of Figure 1.

Thin film of Ga was formed on different substrates such as SEBS, Polycarbonate (PC), Acrylic (PMMA) and commercially available scotch tape, as shown in part (g) of Figure 1, which depicts that the surface energy of SEBS is lower compared to other materials. In the experiments, only SEBS substrate was exposed to plasma to increase its surface energy before deposition of Ga. Other substrates were directly used for Ga deposition. The plot showing the resistance of the Ga film on different substrates is shown in Figure 11.

B. Experimental characterization of the device:

In order to gain deeper insights into how the morphology of Ga nanodroplets influences the device's electrical properties, the thickness and deposition rate of Ga are varied while keeping the plasma exposure parameters constant. The area of the droplets is observed to increase with increase in the thickness of the Ga formed, as shown in parts (a) and (c) of Figure 4 and gap between the droplets is observed to decrease with increasing thickness. The combined effect of the reduced gap between the droplets and higher overlap length of the droplets with increasing area leads to exponential decrease in resistance of the device with increase in Ga thickness formed, as shown in part (b) of Figure 4. Similar trend is observed with increasing the rate of Ga formed, as shown in Figure 5.

Understanding the response of nanofilms under various mechanical behaviors such as bending and uni-axial strain is crucial for applications such as flexible electronics, stretchable sensors, and biomedical devices. The synthesized nanofilms are subjected to stretching along the longitudinal direction, followed by a relaxation phase for different strains. As the film undergoes deformation during the stretching cycle, both its mechanical and electrical properties are affected. In order to analyse, a SEBS-Ga device encapsulated with silicone was subjected to 25% strain, followed by relaxation for ten cycles, and then stretched again and relaxed for 50%, 100% and 200% strain sequentially for ten cycles, as shown in Figure 6. Although some of the deformation may be recovered during the relaxation phase, the film does not fully return to its original state. That explains the different starting resistance at the beginning of the stretching cycle for all the applied strain.

The phases of stretching and relaxation are marked by S and R, for the first and fourth cycles, as shown in Figure 6. The measurements reveal that during the stretching cycle, the resistance initially increases before subsequently declining, a consistent trend observed across all stretching cases. As the stretching cycle progresses, the resistance continues to decrease for smaller strains, as shown in part (a) of Figure 6. However, for higher strain (> 25%), the resistance begins to rise again. This unusual behavior results in a dual-peak response for the entire stretching cycle, as depicted in the first cycle of parts (b) and (d) of Figure 6. The subsequent increase in resistance at higher strains is likely due to the development of cracks, resulting in more open connections and increased impedance to current transport across the film, as shown in Figure 7. The second peak in resistance disappears after initial few cycles as the formation of cracks would get stabilized at that strain, which is clear from the stretching phase in the fourth cycle in comparison to the first cycle, as shown in parts (b) and (d) of Figure 6. The periodic cyclic study experiment with stretching confirms that formation of cracks gets stabilized with time, as shown in Figure 8.

A thorough analysis of crack formation at various strain levels is essential in understanding the effect of mechanical strain on electrical properties. For this purpose, an unencapsulated SEBS-Ga film is mounted on a compact stretching setup that can be placed inside an SEM chamber for imaging. Imaging is performed at strains of 25%, 50%, 100% and 200% sequentially and then again at 0% to analyze the cracks, as shown in parts (a) - (e) of Figure 7. As expected, the density of cracks increases with stretching, and the area of the cracked region expands from 8% at 25% strain to 50% at 200% strain, as shown in parts (a) and (d) of Figure 7. The length of the cracks increases at a higher rate with strain than crack width, as shown in parts (f) and (g) of Figure 7, both contributing to the increased resistance at higher strains. Even after relaxing the sample from 200% strain, the cracks remain as a permanent dislocation, as shown in part (e) of Figure 7, which is evident in the increased resistance of the film after few cycles of stretching, as shown in Figure 6.

C. Theoretical Modeling of Liquid Gallium Nanosheet:

Understanding the mechanisms of conducting pathways in Ga thin films, as well as their benefits and limitations, is essential for optimizing device designs for specific applications. The film's total resistance as a function of strain was studied using theoretical approaches. This enabled predictive analysis and help validate the hypothesis drawn from experimental results. The nanosheet thin film can be represented as a large resistive network, as shown in part (a) of Figure 9, where inter-droplet contacts can be ohmic, tunneling, or open (no conductance). Ohmic contacts occur when nanodrops touch perfectly, tunneling contacts form with a thin insulating layer (e.g., Gallium Oxide or air), and open contacts exist when these insulating layers (or gaps) are too large for tunneling. As shown in part (b) of Figure 9 resistive connections between four adjacent nanodrops, primarily shows tunneling contacts, which dominate the system. Kirchhoff's network and Simmons' tunneling model are used to model the system.

For tunneling type contacts, resistance between two contact members r_ij depends on the potential barrier profile Φ, gap voltage V_g, contact gap g, contact length l_c, and thickness of the drops t_d, as shown in part (c) of Figure 9. g is a random variable that follows Gaussian distribution. In the model, first, r_ij are calculated from Simmon’s generalized tunneling current formula for metal-insulator-metal junction. Then, the total resistance of the film is calculated from the Laplacian matrix associated with the network. Tunneling current along x direction between two Ga drops is:

J=(6.2×〖10〗^10)/(Δx^2 [Φ e_I^(1.025Δx√Φ)-(Φ+V_g ) e_I^(1.025Δx√(Φ+V_g )) ] )×(1+3×(〖10〗^(-9) Δx^2 T^2)/Φ) (1)
wherein Φ=ϕ_0-(V_g/2g)(x_1+x_2)-(5.57/(2ϵ_r Δx))ln [(x_2 (g-x_1 ))/(x_1 (g-x_2 ) )], Δx=x_2-x_1, x_1=3/(ϵ_r ϕ_0 ) and x_2=g[1-46/(6ϕ_0 ϵ_r g+20-4V_g ϵ_r g)]+x_1 if V_g<ϕ_0 and x_2=(ϕ_0 ϵ_r g-14)/(ϵ_r V_g ) if V_g>ϕ_0, with eϕ_0=W-χ. V_g is the gap voltage, g is the gap distance, W is the work function of Ga, and χ is the electron affinity of the insulating layer. In eq. 1, J is in A/cm2, x in Å, ϕ in V, and T is in K.

In the network as shown in part (a) of Figure 9, not all contacts are of the tunneling type. The percentages of open and short (ohmic) contacts, N_oc and N_sc, in both the x and y directions, are considered and assigned randomly. The remaining positions are filled with tunneling conductances. Additionally, randomness in contact gap g along the x and y directions, are represented by mean values g_xm and g_ym, with standard deviations σ_x and σ_y. While l_cx and l_cy should also be random variables in practice, the model is simplified by using their average values. Open contacts have zero conductance, whereas ohmic contacts have conductivity of 7×106 S/m. The Kirchhoff’s law states that, ∑_(j=1)^N▒〖c_ij (V_i-V_j )=I_i,〗 excluding terms where j=i. Here, c, V, and I denote the conductance, voltage, and current respectively. This can be written as: LV ⃗=I ⃗ where

L=(█(■(c_1&-c_12@-c_21&c_2 ) ■(⋯&-c_1N@⋯&-c_2N )@■(⋮&⋮@-c_N1&-c_N2 ) ■(⋱&⋮@⋯&c_N ))) (2)

L is the Laplacian matrix (also known as the Kirchhoff matrix or tree matrix) of the resistor network with c_i≡∑_(j=1)^N▒c_ij . Here V ⃗ and I ⃗ are N-vectors whose components are V_i and I_i respectively. The resistance between two arbitrary nodes is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix L. If L has non-zero Eigen values λ_i with orthonormal Eigen vectors Ψ_i=(ψ_i1,ψ_i2,………,ψ_iN ), i=1,2,3,…….,N, then the resistance between nodes α and β is given by:
R_αβ= ∑_(i=2)^N▒〖1/λ_i |ψ_iα-ψ_iβ |^2 〗. (3)

The results from the theoretical calculations are shown in parts (d) and (e) of Figure 9, with parameter values listed in Table. 1. The experimental measurements are based on a substrate size of 3 cm × 1 cm, containing approximately 35,000 × 12,000 droplets in the film. Due to computational limitations, the theoretical calculations are performed using a smaller 100 × 100 resistive network. The goal is not to directly compare the theoretical and experimental values, but to understand the trend of key model parameters and overall resistance under mechanical strain, while validating the hypothesis from experimental observations.

As observed from experimental data, increasing the film's thickness leads to larger droplet areas, and an exponential decrease in the film's resistance, as shown in part (b) of Figure 4. This is expected, as the nanodrops' dimensions—length, width, and thickness—grow with the film's thickness. In the resistive network, this causes fewer open contacts and more short (ohmic) contacts. The gap between tunneling-type contacts also shrinks, which increases the tunneling current exponentially. A similar trend is observed, as shown in part (d) of Figure 9 with the developed theoretical model. As shown in part (e) of Figure 9, key model parameters change during the stretching cycle was analysed when the film is stretched along the x-axis. Specifically, the double-peak behavior observed in the experiment, is shown in Figure 6. The cycle is divided into three domains – i) Domain 1, where resistance increases with time; ii) Domain 2, where resistance decreases; and iii) Domain 3, where resistance continues to decrease at lower strains but rises at higher strains.

When the film is stretched in the x direction, i) the mean gap distance increases along the x-axis (g_xm), but decreases along the y-axis (g_ym) and diagonal (g_dm); ii) the contact length increases along x (l_x) and decreases along y (l_y); iii) the percentage of open contacts along x (N_ocx) and low-resistance ohmic contacts along y (N_scy) both increase, while N_ocy and N_scx decrease. The thickness (t_d) and width (w) of the nanodrops also change according to the volume conservation principle. At first, resistance increases due to the rise in g_xm and N_ocx, as shown in part (e) of Figure 9 (domain 1). Later, the reduction in g_ym and g_dm, combined with the increase in N_scy, enhances tunneling conductivity, reducing the resistance, as shown in part (e) of Figure 9 (domain 2).

Experiments showed that cracks form at higher strains, which impact the film's overall conductivity and must be accounted for in the model. These cracks are represented as clusters of open circuits in the resistive network, with their length, width, and density varying based on the applied strain. As shown in part (e) of Figure 9, domain 3, for 25% strain, resistance continues to decrease, but at 100% strain, the cracks significantly reduce conductivity by restricting current flow and raising the overall resistance. This behavior contributes to the double-peak pattern observed in the plot during the stretching cycle at higher strains. Above modeling effort gives critical insights into how the film's conductivity correlates with key model parameters and strain.

Table 1 - Description of the parameters used in the theoretical model

Parameter Description Value Comment
g_xm Mean gap distance between drops along x direction 6 – 20 Å g_x is a random variable and follows Gaussian distribution
g_ym Mean gap distance between drops along y direction 6 – 20 Å g_y is a random variable and follows Gaussian distribution
g_dm Mean gap distance between drops along diagonal direction 8 – 20 Å g_d is a random variable and follows Gaussian distribution
σ_(g_x ) Standard deviation of gap distance between drops along x direction 1 – 5 Å NA
σ_(g_y ) Standard deviation of gap distance between drops along y direction 1 – 5 Å NA
σ_(g_d ) Standard deviation of gap distance between drops along diagonal direction 1 – 5 Å NA
l_x Mean contact length between drops along x direction 80 – 400 nm In reality l_x and l_y should also be random variables following Gaussian distribution but for simplicity we assumed average contact lengths along both x and y direction.
l_y Mean contact length between drops along y direction 80 – 200 nm
N_ocx Percentage of open contacts along x direction. 3 – 20 % Percentage of tunneling type contacts is calculated from total number of contacts, N_oc, and N_sc.
N_ocy Percentage of open contacts along y direction. 3 – 20 % NA
N_scx Percentage of short (actually ohmic) contacts along x direction. 3 – 20 % NA
N_scy Percentage of short (actually ohmic) contacts along y direction. 3 – 20 %
NA
t Thickness of the drops 50 – 300 nm Same as thickness of the film
w Width of the drops Same as l_(x/y) NA
V_g Gap voltage between drops to calculate the tunneling current density between two nano contacting members 0.1 V For simplicity, we assumed same voltage to calculate the tunneling resistivities for all the tunneling contacts.
W Work function of Gallium 4.02 eV NA
X Number of drops in x direction 100 Due to computational resource constraints, we employed a smaller network.
Y Number of drops in y direction 100

D. Ga-based stretchable conducting device applications:
[71] The Ga-based stretchable conducting device exhibit piezoresistive characteristics, a change in resistance when subjected to strain, making them ideal for applications as strain sensors and for sensing the angle of gripper movement in robotic arms. Accordingly, a single-arm pneumatic gripper is fabricated using silicone, with the developed soft strain sensor made from Ga nanodroplets on polycarbonate or SEBS attached to it.
[72] The Silicone Pneumatic Gripper is composed of four individual silicone pneumatic actuators mounted on a 3D-printed holder that incorporates embedded pneumatic distribution channels.
Fabrication Process of Silicone Pneumatic Gripper:
[73] The actuators are fabricated using a three-part mold system from silicone casting, as shown in part (a) of Figure 12. The first two molds are used to form the top half of the actuator, which inflates upon air pressure. The bottom half is casted using the third mold. Once cured, both halves are demolded, and the top part is bonded to the bottom part using the same silicone material. Functionality of the actuator is verified using a syringe, as shown in part (b) of Figure 12. A gallium-based encapsulated sensor, along with wiring, is then affixed to the exposed surface of the bottom part using the same silicone adhesive.
Working Mechanism of Silicone Pneumatic Gripper:
[74] The four completed actuators, each integrated with a sensor, are mounted onto the 3D-printed holder. To ensure airtight connections, an additional silicone layer is applied at the actuator-holder interface. Air is supplied through a 50 ml syringe, which can be operated manually or via a stepper motor mechanism. When the syringe is compressed, air flows into the actuator chambers, causing them to expand and grip nearby objects. Conversely, retracting the syringe evacuates air from the actuators, returning them to their original shape and releasing the object. Thin films of gallium (Ga) formed on polycarbonate or SEBS substrate, is attached to the grippers. As the actuators expand under pneumatic pressure, these films undergo strain, resulting in a measurable change in electrical resistance, which can be used for sensing and feedback purposes.
Utility of Ga-based stretchable conducting device:
[75] The Pneumatic Gripper device can sense curvature while bending from 12 to 40 〖cm〗^(-1) in multiple steps with high sensitivity, as shown in parts (a) and (b) of Figure 10. The soft sensor can detect both positive and negative curvature during bending, as shown in part (c) of Figure 10. The droplets within the sensor experience tensile or compressive strain under different bending curvatures, resulting in corresponding positive or negative changes in resistance. To further validate the performance of the device with sensing different objects, a four-arm pneumatic gripper is developed. The gripper showcases the device's capability to detect objects through changes in resistance intensity while holding a Petri dish of 150 mm diameter, as shown in left of part (d) of Figure 10 and a plastic ball of 70 mm diameter, as shown in right of part (d) of Figure 10. Additionally, a soft sensor device made from SEBS is integrated with surface mount LEDs to demonstrate its functionality in response to bending-induced strain, as shown in part (e) of Figure 10.


FIELD OF INVENTION:

The present invention is related to a method for forming electrically conductive Ga film on Styrene-Ethylene-Butylene-Styrene (SEBS) substrate. More particularly, the present invention is related to a method in which SEBS substrate is exposed to plasma and liquid Ga is thermally evaporated on said substrate to form electrically conductive Ga film on SEBS substrate. The SEBS substrate with electrically conductive Ga film have applications in stretchable and flexible electronics.

BACKGROUND OF INVENTION:

[2] The stretchable and flexible electronics has attracted considerable attention in recent times, primarily owing to its wide-ranging applications in consumer electronic displays, wearable devices, interfacing of biosensors with humans, and soft robotics. Stretchable electronic devices are mainly prepared by either developing new structural layouts with conventional materials or by employing new materials in conventional layouts.

[3] Conventional materials such as gold and silver are often used as thin films generally relies on wrinkling, in-plane and out-of-plane buckling, and bending-induced deformations in stretchable electronics. However, said conventional materials tend to fail under excessive stretching, especially when the difference between applied and pre-strain exceeds 10% or when they are sharply bended. In view of said limitations, there is an excessive demand for materials with greater stretchability, driving research into inherently soft materials as a promising alternative.

[4] Soft polymers are combined with conducting materials such as carbon nanotubes, rigid nanoparticles, or nanorods made of silver, gold, and copper in order to achieve both stretchability and conductivity. However, the effectiveness of said soft polymer could be restricted by the filling fraction. In contrast, liquid metals have emerged as a highly promising alternative due to their exceptional blend of fluidity and conductivity. However, the use of mercury, a well-known room-temperature liquid metal, is mainly limited due to its toxic nature. Hence, Gallium and its alloys, which are nearly room-temperature liquid metals, offer a promising alternative to enable the development of flexible and stretchable electronic devices.

[5] Liquid metal Gallium offers multiple advantages such as viscosity just twice that of water at room temperature, good conductivity of 3.86×104 S/cm, a low vapour pressure and a melting point of around 28° C. Despite these advantages, high surface energy of Gallium and the formation of native oxide layer limits the Gallium to wet the surfaces, thus resulting in the formation of discrete droplets and non-continuous films or surfaces.

[6] Researchers have extensively explored various techniques to integrate Gallium (Ga)-based liquid metal (LM) into diverse materials and structures for soft electronics applications. These methods include additive processing techniques such as inkjet printing, microcontact printing, and stencil or screen printing, as well as subtractive processing approaches like lift-off and laser ablation. Other approaches involve the wetting and sintering of droplets formed through sonication and the creation of polymer composites. However, all of these methods have largely been constrained to produce Ga films, droplets, or structures at the scale of 10 µm, primarily due to the high surface tension of Ga and the formation of oxide layers. Therefore, achieving the desired functionalities with reduced material consumption remains a critical challenge when moving to thin films with sub-micron range of thickness.

[7] Physical vapor deposition (PVD) is a well-established process for creating thin films in fabrication of integrated circuits with high accuracy. However, PVD process when applied to deposit Ga results in isolated spherical droplets, instead of films due to its high surface tension. Researchers have attempted to overcome the high surface tension of Ga by depositing on top of microstructures covered with thin film of gold or during deposition, oxygen is purged inside the deposition chamber to react with Ga and form bigger size droplets. However, these works are either limited by the size of the substrate due to lithographic process or doesn’t form a mono layer of Ga which could prevent the theoretical analysis of conducting pathways. Nevertheless, developing a monolayer of Ga-based thin-film devices with sub-100 nm thicknesses and scalable to a large area, that demonstrate innovative applications could unlock vast potential in the soft electronics domain, offering new pathways for highly efficient, flexible, and stretchable technologies.

[8] For instance, reference is made to EP1090159B1 which discloses plasma-enhanced, chemical vapor deposition of coatings and, more particularly, to the use of an atmospheric-pressure, plasma discharge jet for deposition of films on substrates. However, it requires application of high deposition temperature.

[9] Reference is further made to A. Hirsch et al. in A Method to Form Smooth Films of Liquid Metal Supported by Elastomeric Substrate, Adv. Sci. 2018, 5, 1800256, which discloses method to produce smooth film of liquid gallium (Ga) on extended surface areas with controlled thickness and electrical properties. The surface chemistry and topography of silicone rubber (poly(dimethylsiloxane)) is engineered with microstructured pillars and gold precoating layer to produce Ga superlyophilic substrates. Physical vapor deposition of Ga on such substrates leads to the formation of smooth and homogeneous films by imbibition of the surface topography rather than coalescence and formation of Ga drops. By capillarity, Ga accumulates in between the pillars up to their top surface, forming a smooth film with a root mean square roughness (Rq) smaller than 100 nm. However, said method suffers from drawback of precoating with gold in order to form a Ga layer. Further, said method requires nanopatterning which is time consuming and not scalable to large area.

Therefore, there is a crucial need for simple and efficient method for forming electrically conductive Ga film on substrate that addresses all of the major challenges associated with the existing methods.

In view of above, there exists a dire need in the state of art for providing a method for forming electrically conductive Ga film having thickness less than 100 nm on substrate, having applications in soft and stretchable electronics.

OBJECTS OF THE INVENTION:

The principle object of the present invention is to provide a method for forming electrically conductive Ga film having thickness less than 100 nm on SEBS substrate.

Another object of the present invention is to provide a method for forming electrically conductive Ga film on substrate, where Ga nanodroplet nucleation leads to self-assembled conductive films via tunneling and ohmic contacts.

Yet another object of the present invention is to provide a substrate with Ga film, wherein the thickness of Ga film is less than 100 nm.

Another object of the present invention is to provide a substrate with Ga film having applications in soft and stretchable electronics.

SUMMARY OF THE INVENTION:

In an aspect, the present invention provides a method for forming electrically conductive Ga film on SEBS substrate, the method comprising exposing atmospheric plasma to SEBS substrate at a pressure in the range of 0.2 to 0.8 mbar for a time period in a range of 3-7 minute to form plasma exposed SEBS substrate and thermally evaporating liquid Ga on to said plasma exposed SEBS substrate to form a film of electrically conductive Ga on said SEBS substrate.

The present method deposit electrically conductive thin Ga film over large areas by altering the surface energy of the Styrene-Ethylene-Butylene-Styrene (SEBS) block copolymer and forming Ga via thermal evaporation on it. Exposing said SEBS substrate to plasma increases the surface energy of the substrate and there by aiding in wetting of the Ga nanodroplets to result in conducting films through percolation network. The Ga film is also formed on other substrates such as acrylic, polycarbonate and commercially available scotch tape, which has surface energy similar to that of surface energy enhanced SEBS, via thermal evaporation.

In another aspect, the present invention provides a substrate with Ga film as described herein, wherein the thickness of Ga film is less than 100 nm.

The SEBS substrate with Ga film is encapsulated with a polymer to form a stretchable device.

DESCRIPTION OF ACCOMPANYING FIGURES:

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 together with the description.

Figure 1 illustrates (a) Fabrication steps: Schematic illustration of SEBS substrate exposed to atmospheric plasma in the thermal evaporator and forming thermally evaporated Ga from a tungsten boat to the plasma-treated SEBS substrate; (b) Schematic of the Ga film on SEBs encapsulated with Silicone; SEM image of Ga nanoparticles on pristine and plasma exposed SEBS: (c) & (e) top view and (d) & (f) cross-sectional view respectively; (g) Surface energy of different substrates: PC, PMMA, Scotch tape, pristine and plasma exposed SEBS and (h) Stress-Strain curve for pristine SEBS, Ga formed on SEBS and SEBS-Ga encapsulated with Silicone Gel, in accordance with an implementation of the present invention.

Figure 2 illustrates (a) Representation of surface energies at the three-phase contact line of solid, liquid and vapour phases; (b) and (c) Scanning electron microscopic image of the cross-sectional view representing the shape of Ga nanodroplets on pristine SEBS and SEBS after exposed to plasma respectively, in accordance with an implementation of the present invention.

Figure 3 illustrates scanning electron microscopic images of Ga droplets on Scotch tape, PMMA, Glass and plasma-treated SEBS respectively, in accordance with an implementation of the present invention.

Figure 4 illustrates (a) Scanning electron microscopy image of the morphology of the Ga nanodroplets with increase in thickness of Ga formed; Variation of (b) resistance of the Ga film and (c) average area of the Ga droplets with increase in thickness of the Ga, in accordance with an implementation of the present invention.

Figure 5 illustrates (a) Scanning electron microscopy image of the morphology of the Ga droplets with an increase in the rate of Ga formed; Variation of (b) resistance of the Ga film and (c) average area of the Ga droplets with the increase in the rate of the Ga deposition, in accordance with an implementation of the present invention.

Figure 6 illustrates electro-Mechanical Characteristics: Variation of the resistance of the device with strain for 6 continuous cycles at (a) 25%, (b) 50%, (c) 100% and (d) 200% respectively. S and R denote the stretching and relaxation phases marked for the first and fourth cycle, in accordance with an implementation of the present invention.

Figure 7 illustrates scanning electron microscopy image of the Ga film (t=120nm, r=1Aps) at different strains, (a) 25% (b) 50%, (c) 100%, (d) 200%, and (e) the relaxed sample after 200% strain; (f) and (g) Length and width of the cracks with strain respectively. Scale bar represents 5 µm, in accordance with an implementation of the present invention.

Figure 8 illustrates variation of ΔR/R with time for periodic (a) uniaxial strain of 25% and (b) bending, in accordance with an implementation of the present invention.

Figure 9 illustrates (a) A complete resistive network for an entire nanosheet; (b) Resistive connections between four adjacent Ga nanodrops in a nanosheet. The inter-droplet resistances could be of ohmic, tunneling, or open (conductance = 0) type. Here, only tunneling type contacts are shown; (c) The gap distance is g. When a gap voltage V_g is applied, electrons tunnel from both sides, J=J_1-J_2 is the net tunneling current density. Potential barrier Φ(x) in the insulator layer sandwiched between two Ga nanodrops; (d) Resistance as a function of Ga film thickness at 0% strain. The black symbols are measurement data and the blue dashed line is from theoretical calculation; and (e) Total film resistance in stretching cycle for different strains from theoretical model. Strains of 25% and 100% are represented by blue and dotted green curves respectively, in accordance with an implementation of the present invention.

Figure 10 illustrates (a) Demonstration of curvature sensing with a single arm pneumatic actuator and (b) curvature is shown for the steps (1 -7) marked in fig (a); (c) Positive and negative change in resistance with concave and convex curvatures; (d) Demonstration of change in the intensity of resistance while holding a petri dish of 150 mm diameter (left) and a plastic ball of 70 mm diameter (right) with a four-arm pneumatic gripper; and (e) Working of thin Ga film integrated with surface mount LED’s under different bending curvatures, in accordance with an implementation of the present invention.

Figure 11 illustrates plot showing the resistance of the Ga film on different substrates.

Figure 12 illustrates (a) Fabrication of the actuators using a three-part mold system from silicone casting; and (b) Demonstration of a single arm gripper attached to a syringe.

DETAILED DESCRIPTION OF THE INVENTION:

While the invention is susceptible to various modifications and alternative forms, specific embodiment thereof will be described in detail below. It should be understood, however that it is not intended to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternative falling within the scope of the invention as defined by the appended claims.

Although one or more features and/or elements may be described herein in the context of only a single embodiment, or alternatively in the context of more than one embodiment, or further alternatively in the context of all embodiments, the features and/or elements may instead be provided separately or in any appropriate combination or not at all. Conversely, any features and/or elements described in the context of separate embodiments may alternatively be realized as existing together in the context of a single embodiment.

The terminology used herein is for the purpose of describing particular various embodiments only and is not intended to be limiting of various embodiments. As used herein, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

As discussed in the background section of the present invention, the existing processes reported in the literature are for manufacturing stretchable and flexible electronics. However, the conventional material used to prepare said electronics tend to fail under excessive stretching, especially when the difference between applied and pre-strain exceeds 10% or when they are sharply bended. Further, the effectiveness of soft polymer used in place of conventional material is restricted by the filling fraction of conducting materials such as carbon nanotubes, rigid nanoparticles, or nanorods made of silver, gold, and copper. Furthermore, the usage of liquid metal Gallium results in the formation of discrete droplets and non-continuous films or surfaces due to high surface energy of Gallium and the formation of native oxide layer limits the Gallium to wet the surfaces.

Therefore, to overcome the existing problems in the art, the present invention provides a method which overcomes surface tension limitation, is scalable and substrate versatile and demonstrate practical applications, including curvature sensors for grippers and flexible LED-integrated devices, showcasing potential for soft electronics.

In an embodiment, the present invention provides a method for forming electrically conductive Ga film on SEBS substrate, the method comprising:
exposing atmospheric plasma to SEBS substrate at a pressure in the range of 0.2 to 0.8 mbar for a time period in a range of 3-7 minute to form plasma exposed SEBS substrate; and
thermally evaporating liquid Ga on to plasma exposed SEBS substrate of step a) to form a film of electrically conductive Ga on said SEBS substrate.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of Ga on SEBS substrate is less than 100 nm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the pressure and time period during exposing atmospheric plasma to SEBS substrate is 5e-1 mbar and 5 minutes respectively.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the SEBS substrate is prepared by dissolving SEBS beads in toluene to form a mixture, which is stirred to form a solution, followed by casting said solution in a glass container to form a transparent film.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of transparent film is in the range of 200- 300 µm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the thickness of transparent film is 250 µm.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the Ga film on SEBS substrate is encapsulated with a polymer to form a stretchable device.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the polymer is selected from the group consisting of silicone, PDMS and SEBS.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the contact angle of Ga droplets decreases from 145°C to 35° with increased SEBS surface energy due to plasma exposure.

In another embodiment, there is provided a method for forming electrically conductive Ga film on SEBS substrate as described herein, wherein the Ga film is formed in step b) through tunneling and ohmic contacts.

In another embodiment, there is provided a substrate as described herein, wherein the thickness of Ga film is less than 100 nm.

In another embodiment, there is provided a substrate as described herein, wherein the substrate is selected from SEBS, polycarbonate (PC), scotch tape, acrylic (PMMA), cellulose and thin covering glass.

In another embodiment, there is provided a substrate as described herein, as and when used in soft electronics.

EXAMPLES

The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and the description of how to make and use the present invention, and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all and only experiments performed. The methodology of preparing few of the preferred embodiments shall become clearer with working examples provided below.

A. Fabrication of Ga-based stretchable conducting device:

Preparation of SEBS substrates: SEBS block copolymer is chosen as a substrate owing to its high stretchability characteristics. SEBS substrate is prepared by dissolving SEBS beads (Kraton, G1657) in toluene in the ratio of 1.5 grams for 25 mL. The mixture is magnetically stirred until a homogeneous solution is obtained. Solution is casted on a glass petri dish, covered with an aluminum foil of uniform pores to get a thin transparent film of around 250 μm thickness.

Exposure of SEBS substrates to plasma: The SEBS substrate is exposed to atmospheric plasma (HHV thermal evaporator, 5e-1 mbar) for 5 minutes at 0.3 A current.

Plasma exposure increases the SEBS substrate's surface energy by 40% compared to unexposed SEBS, as shown in parts (a) and (g) of Figure 1. Distinct wetting behavior of Ga droplets on plasma-exposed SEBS is observed, as shown in parts (b), (e) and (f) of Figure 1, thus facilitating tunneling conductivity and resulting in a conductive surface with resistance ~1 KΩ. The wetting behavior of Ga droplets is explained by the surface forces at the three-phase contact line of the droplet. Increase in the substrate surface energy γ_s pulls the three-phase contact line of the droplet and decreases the contact angle θ the droplet makes with the substrate, as shown in part (a) of Figure 2. FIB-SEM cross-sectional images show the contact angle of Ga droplets decreasing from approximately 145° to 35° with increased SEBS surface energy due to plasma exposure, as shown in parts (b) and (c) of Figure 2.

Deposition of liquid Gallium: Liquid gallium (ThermoScientific Chemicals, 99.9% metal basis, packaged in polyethylene bottle) is thermally evaporated on to the plasma exposed SEBS substrate (HHV thermal evaporator) to form a thin film of nanodroplets. Experiments are performed for different thickness (40 to 120 nm) and rate of deposition (1 to 5 Å/s). The thickness of the substrate is monitored via in-built Quart crystal sensor.

Thermal evaporation of Ga onto pristine SEBS results in the formation of spherical Ga droplets which exhibit minimal contact as shown in the top and cross-sectional views, as shown in parts (c) and (d) of Figure 1, thus resulting in non-conducting films. The limited spreading of Ga droplets is attributed to the low surface energy of SEBS (~32 N/mm), as shown in part (g) of Figure 1 and the high surface tension of Ga (~700 N/mm). The higher the substrate's surface energy more pronounced the wetting of films, influencing the formation of conductive pathways.

Final making of the device: Thin copper wires are used as interconnects, which are secured to the substrate by applying carbon grease (MG Chemicals Carbon Conductive Silicone Grease, 846-80g) locally over the wires. Silicone part A and part B of Smooth-On Ecoflex 00-50 is mixed in 1:1 and poured over the connects with grease to make the connects firm and encapsulate the thin film of Ga nanodroplets. Silicone cures in 3 hours at room temperature to give a completely protected stretchable device with stable connects.

Testing with other substrates

The process can be extended to substrates with high surface energies to achieve conductive films without plasma exposure. Substrates demonstrating tunneling conductivity with Ga films include polycarbonate (PC), Scotch tape, acrylic (PMMA), cellulose, and thin Corning glass, all of which are flexible, as shown in Figure 3. Encapsulation of Ga thin films on these substrates enhances durability. Both pristine SEBS and SEBS coated with Ga films exhibited stretchability up to 900% strain. However, encapsulation with silicone reduced stretchability to 350% strain, which is still sufficient for practical applications, as shown in part (h) of Figure 1.

Thin film of Ga was formed on different substrates such as SEBS, Polycarbonate (PC), Acrylic (PMMA) and commercially available scotch tape, as shown in part (g) of Figure 1, which depicts that the surface energy of SEBS is lower compared to other materials. In the experiments, only SEBS substrate was exposed to plasma to increase its surface energy before deposition of Ga. Other substrates were directly used for Ga deposition. The plot showing the resistance of the Ga film on different substrates is shown in Figure 11.

B. Experimental characterization of the device:

In order to gain deeper insights into how the morphology of Ga nanodroplets influences the device's electrical properties, the thickness and deposition rate of Ga are varied while keeping the plasma exposure parameters constant. The area of the droplets is observed to increase with increase in the thickness of the Ga formed, as shown in parts (a) and (c) of Figure 4 and gap between the droplets is observed to decrease with increasing thickness. The combined effect of the reduced gap between the droplets and higher overlap length of the droplets with increasing area leads to exponential decrease in resistance of the device with increase in Ga thickness formed, as shown in part (b) of Figure 4. Similar trend is observed with increasing the rate of Ga formed, as shown in Figure 5.

Understanding the response of nanofilms under various mechanical behaviors such as bending and uni-axial strain is crucial for applications such as flexible electronics, stretchable sensors, and biomedical devices. The synthesized nanofilms are subjected to stretching along the longitudinal direction, followed by a relaxation phase for different strains. As the film undergoes deformation during the stretching cycle, both its mechanical and electrical properties are affected. In order to analyse, a SEBS-Ga device encapsulated with silicone was subjected to 25% strain, followed by relaxation for ten cycles, and then stretched again and relaxed for 50%, 100% and 200% strain sequentially for ten cycles, as shown in Figure 6. Although some of the deformation may be recovered during the relaxation phase, the film does not fully return to its original state. That explains the different starting resistance at the beginning of the stretching cycle for all the applied strain.

The phases of stretching and relaxation are marked by S and R, for the first and fourth cycles, as shown in Figure 6. The measurements reveal that during the stretching cycle, the resistance initially increases before subsequently declining, a consistent trend observed across all stretching cases. As the stretching cycle progresses, the resistance continues to decrease for smaller strains, as shown in part (a) of Figure 6. However, for higher strain (> 25%), the resistance begins to rise again. This unusual behavior results in a dual-peak response for the entire stretching cycle, as depicted in the first cycle of parts (b) and (d) of Figure 6. The subsequent increase in resistance at higher strains is likely due to the development of cracks, resulting in more open connections and increased impedance to current transport across the film, as shown in Figure 7. The second peak in resistance disappears after initial few cycles as the formation of cracks would get stabilized at that strain, which is clear from the stretching phase in the fourth cycle in comparison to the first cycle, as shown in parts (b) and (d) of Figure 6. The periodic cyclic study experiment with stretching confirms that formation of cracks gets stabilized with time, as shown in Figure 8.

A thorough analysis of crack formation at various strain levels is essential in understanding the effect of mechanical strain on electrical properties. For this purpose, an unencapsulated SEBS-Ga film is mounted on a compact stretching setup that can be placed inside an SEM chamber for imaging. Imaging is performed at strains of 25%, 50%, 100% and 200% sequentially and then again at 0% to analyze the cracks, as shown in parts (a) - (e) of Figure 7. As expected, the density of cracks increases with stretching, and the area of the cracked region expands from 8% at 25% strain to 50% at 200% strain, as shown in parts (a) and (d) of Figure 7. The length of the cracks increases at a higher rate with strain than crack width, as shown in parts (f) and (g) of Figure 7, both contributing to the increased resistance at higher strains. Even after relaxing the sample from 200% strain, the cracks remain as a permanent dislocation, as shown in part (e) of Figure 7, which is evident in the increased resistance of the film after few cycles of stretching, as shown in Figure 6.

C. Theoretical Modeling of Liquid Gallium Nanosheet:

Understanding the mechanisms of conducting pathways in Ga thin films, as well as their benefits and limitations, is essential for optimizing device designs for specific applications. The film's total resistance as a function of strain was studied using theoretical approaches. This enabled predictive analysis and help validate the hypothesis drawn from experimental results. The nanosheet thin film can be represented as a large resistive network, as shown in part (a) of Figure 9, where inter-droplet contacts can be ohmic, tunneling, or open (no conductance). Ohmic contacts occur when nanodrops touch perfectly, tunneling contacts form with a thin insulating layer (e.g., Gallium Oxide or air), and open contacts exist when these insulating layers (or gaps) are too large for tunneling. As shown in part (b) of Figure 9 resistive connections between four adjacent nanodrops, primarily shows tunneling contacts, which dominate the system. Kirchhoff's network and Simmons' tunneling model are used to model the system.

For tunneling type contacts, resistance between two contact members r_ij depends on the potential barrier profile Φ, gap voltage V_g, contact gap g, contact length l_c, and thickness of the drops t_d, as shown in part (c) of Figure 9. g is a random variable that follows Gaussian distribution. In the model, first, r_ij are calculated from Simmon’s generalized tunneling current formula for metal-insulator-metal junction. Then, the total resistance of the film is calculated from the Laplacian matrix associated with the network. Tunneling current along x direction between two Ga drops is:

J=(6.2×〖10〗^10)/(Δx^2 [Φ e_I^(1.025Δx√Φ)-(Φ+V_g ) e_I^(1.025Δx√(Φ+V_g )) ] )×(1+3×(〖10〗^(-9) Δx^2 T^2)/Φ) (1)
wherein Φ=ϕ_0-(V_g/2g)(x_1+x_2)-(5.57/(2ϵ_r Δx))ln [(x_2 (g-x_1 ))/(x_1 (g-x_2 ) )], Δx=x_2-x_1, x_1=3/(ϵ_r ϕ_0 ) and x_2=g[1-46/(6ϕ_0 ϵ_r g+20-4V_g ϵ_r g)]+x_1 if V_g<ϕ_0 and x_2=(ϕ_0 ϵ_r g-14)/(ϵ_r V_g ) if V_g>ϕ_0, with eϕ_0=W-χ. V_g is the gap voltage, g is the gap distance, W is the work function of Ga, and χ is the electron affinity of the insulating layer. In eq. 1, J is in A/cm2, x in Å, ϕ in V, and T is in K.

In the network as shown in part (a) of Figure 9, not all contacts are of the tunneling type. The percentages of open and short (ohmic) contacts, N_oc and N_sc, in both the x and y directions, are considered and assigned randomly. The remaining positions are filled with tunneling conductances. Additionally, randomness in contact gap g along the x and y directions, are represented by mean values g_xm and g_ym, with standard deviations σ_x and σ_y. While l_cx and l_cy should also be random variables in practice, the model is simplified by using their average values. Open contacts have zero conductance, whereas ohmic contacts have conductivity of 7×106 S/m. The Kirchhoff’s law states that, ∑_(j=1)^N▒〖c_ij (V_i-V_j )=I_i,〗 excluding terms where j=i. Here, c, V, and I denote the conductance, voltage, and current respectively. This can be written as: LV ⃗=I ⃗ where

L=(█(■(c_1&-c_12@-c_21&c_2 ) ■(⋯&-c_1N@⋯&-c_2N )@■(⋮&⋮@-c_N1&-c_N2 ) ■(⋱&⋮@⋯&c_N ))) (2)

L is the Laplacian matrix (also known as the Kirchhoff matrix or tree matrix) of the resistor network with c_i≡∑_(j=1)^N▒c_ij . Here V ⃗ and I ⃗ are N-vectors whose components are V_i and I_i respectively. The resistance between two arbitrary nodes is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix L. If L has non-zero Eigen values λ_i with orthonormal Eigen vectors Ψ_i=(ψ_i1,ψ_i2,………,ψ_iN ), i=1,2,3,…….,N, then the resistance between nodes α and β is given by:
R_αβ= ∑_(i=2)^N▒〖1/λ_i |ψ_iα-ψ_iβ |^2 〗. (3)

The results from the theoretical calculations are shown in parts (d) and (e) of Figure 9, with parameter values listed in Table. 1. The experimental measurements are based on a substrate size of 3 cm × 1 cm, containing approximately 35,000 × 12,000 droplets in the film. Due to computational limitations, the theoretical calculations are performed using a smaller 100 × 100 resistive network. The goal is not to directly compare the theoretical and experimental values, but to understand the trend of key model parameters and overall resistance under mechanical strain, while validating the hypothesis from experimental observations.

As observed from experimental data, increasing the film's thickness leads to larger droplet areas, and an exponential decrease in the film's resistance, as shown in part (b) of Figure 4. This is expected, as the nanodrops' dimensions—length, width, and thickness—grow with the film's thickness. In the resistive network, this causes fewer open contacts and more short (ohmic) contacts. The gap between tunneling-type contacts also shrinks, which increases the tunneling current exponentially. A similar trend is observed, as shown in part (d) of Figure 9 with the developed theoretical model. As shown in part (e) of Figure 9, key model parameters change during the stretching cycle was analysed when the film is stretched along the x-axis. Specifically, the double-peak behavior observed in the experiment, is shown in Figure 6. The cycle is divided into three domains – i) Domain 1, where resistance increases with time; ii) Domain 2, where resistance decreases; and iii) Domain 3, where resistance continues to decrease at lower strains but rises at higher strains.

When the film is stretched in the x direction, i) the mean gap distance increases along the x-axis (g_xm), but decreases along the y-axis (g_ym) and diagonal (g_dm); ii) the contact length increases along x (l_x) and decreases along y (l_y); iii) the percentage of open contacts along x (N_ocx) and low-resistance ohmic contacts along y (N_scy) both increase, while N_ocy and N_scx decrease. The thickness (t_d) and width (w) of the nanodrops also change according to the volume conservation principle. At first, resistance increases due to the rise in g_xm and N_ocx, as shown in part (e) of Figure 9 (domain 1). Later, the reduction in g_ym and g_dm, combined with the increase in N_scy, enhances tunneling conductivity, reducing the resistance, as shown in part (e) of Figure 9 (domain 2).

Experiments showed that cracks form at higher strains, which impact the film's overall conductivity and must be accounted for in the model. These cracks are represented as clusters of open circuits in the resistive network, with their length, width, and density varying based on the applied strain. As shown in part (e) of Figure 9, domain 3, for 25% strain, resistance continues to decrease, but at 100% strain, the cracks significantly reduce conductivity by restricting current flow and raising the overall resistance. This behavior contributes to the double-peak pattern observed in the plot during the stretching cycle at higher strains. Above modeling effort gives critical insights into how the film's conductivity correlates with key model parameters and strain.

Table 1 - Description of the parameters used in the theoretical model

Parameter Description Value Comment
g_xm Mean gap distance between drops along x direction 6 – 20 Å g_x is a random variable and follows Gaussian distribution
g_ym Mean gap distance between drops along y direction 6 – 20 Å g_y is a random variable and follows Gaussian distribution
g_dm Mean gap distance between drops along diagonal direction 8 – 20 Å g_d is a random variable and follows Gaussian distribution
σ_(g_x ) Standard deviation of gap distance between drops along x direction 1 – 5 Å NA
σ_(g_y ) Standard deviation of gap distance between drops along y direction 1 – 5 Å NA
σ_(g_d ) Standard deviation of gap distance between drops along diagonal direction 1 – 5 Å NA
l_x Mean contact length between drops along x direction 80 – 400 nm In reality l_x and l_y should also be random variables following Gaussian distribution but for simplicity we assumed average contact lengths along both x and y direction.
l_y Mean contact length between drops along y direction 80 – 200 nm
N_ocx Percentage of open contacts along x direction. 3 – 20 % Percentage of tunneling type contacts is calculated from total number of contacts, N_oc, and N_sc.
N_ocy Percentage of open contacts along y direction. 3 – 20 % NA
N_scx Percentage of short (actually ohmic) contacts along x direction. 3 – 20 % NA
N_scy Percentage of short (actually ohmic) contacts along y direction. 3 – 20 %
NA
t Thickness of the drops 50 – 300 nm Same as thickness of the film
w Width of the drops Same as l_(x/y) NA
V_g Gap voltage between drops to calculate the tunneling current density between two nano contacting members 0.1 V For simplicity, we assumed same voltage to calculate the tunneling resistivities for all the tunneling contacts.
W Work function of Gallium 4.02 eV NA
X Number of drops in x direction 100 Due to computational resource constraints, we employed a smaller network.
Y Number of drops in y direction 100

D. Ga-based stretchable conducting device applications:
[71] The Ga-based stretchable conducting device exhibit piezoresistive characteristics, a change in resistance when subjected to strain, making them ideal for applications as strain sensors and for sensing the angle of gripper movement in robotic arms. Accordingly, a single-arm pneumatic gripper is fabricated using silicone, with the developed soft strain sensor made from Ga nanodroplets on polycarbonate or SEBS attached to it.
[72] The Silicone Pneumatic Gripper is composed of four individual silicone pneumatic actuators mounted on a 3D-printed holder that incorporates embedded pneumatic distribution channels.
Fabrication Process of Silicone Pneumatic Gripper:
[73] The actuators are fabricated using a three-part mold system from silicone casting, as shown in part (a) of Figure 12. The first two molds are used to form the top half of the actuator, which inflates upon air pressure. The bottom half is casted using the third mold. Once cured, both halves are demolded, and the top part is bonded to the bottom part using the same silicone material. Functionality of the actuator is verified using a syringe, as shown in part (b) of Figure 12. A gallium-based encapsulated sensor, along with wiring, is then affixed to the exposed surface of the bottom part using the same silicone adhesive.
Working Mechanism of Silicone Pneumatic Gripper:
[74] The four completed actuators, each integrated with a sensor, are mounted onto the 3D-printed holder. To ensure airtight connections, an additional silicone layer is applied at the actuator-holder interface. Air is supplied through a 50 ml syringe, which can be operated manually or via a stepper motor mechanism. When the syringe is compressed, air flows into the actuator chambers, causing them to expand and grip nearby objects. Conversely, retracting the syringe evacuates air from the actuators, returning them to their original shape and releasing the object. Thin films of gallium (Ga) formed on polycarbonate or SEBS substrate, is attached to the grippers. As the actuators expand under pneumatic pressure, these films undergo strain, resulting in a measurable change in electrical resistance, which can be used for sensing and feedback purposes.
Utility of Ga-based stretchable conducting device:
[75] The Pneumatic Gripper device can sense curvature while bending from 12 to 40 〖cm〗^(-1) in multiple steps with high sensitivity, as shown in parts (a) and (b) of Figure 10. The soft sensor can detect both positive and negative curvature during bending, as shown in part (c) of Figure 10. The droplets within the sensor experience tensile or compressive strain under different bending curvatures, resulting in corresponding positive or negative changes in resistance. To further validate the performance of the device with sensing different objects, a four-arm pneumatic gripper is developed. The gripper showcases the device's capability to detect objects through changes in resistance intensity while holding a Petri dish of 150 mm diameter, as shown in left of part (d) of Figure 10 and a plastic ball of 70 mm diameter, as shown in right of part (d) of Figure 10. Additionally, a soft sensor device made from SEBS is integrated with surface mount LEDs to demonstrate its functionality in response to bending-induced strain, as shown in part (e) of Figure 10.


, Claims:1. A method for forming electrically conductive Ga film on SEBS substrate, the method comprising:

a) exposing atmospheric plasma to SEBS substrate at a pressure in the range of 0.2 to 0.8 mbar for a time period in a range of 3-7 minute to form plasma exposed SEBS substrate; and
b) thermally evaporating liquid Ga on to plasma exposed SEBS substrate of step a) to form a film of electrically conductive Ga on said SEBS substrate.

2. The method as claimed in claim 1, wherein the thickness of Ga on SEBS substrate is less than 100 nm.

3. The method as claimed in claim 1, wherein the pressure and time period in step a) is 5e-1 mbar and 5 minutes respectively.

4. The method as claimed in claim 1, wherein the SEBS substrate is prepared by dissolving SEBS beads in toluene to form a mixture, which is stirred to form a solution, followed by casting said solution in a glass container to form a transparent film.

5. The method as claimed in claim 4, wherein the thickness of transparent film is in the range of 200- 300 µm.

6. The method as claimed in claim 4 and 5, wherein the thickness of transparent film is 250 µm.

7. The method as claimed in claim 1, wherein the Ga film on SEBS substrate is encapsulated with a polymer to form a stretchable device.

8. The method as claimed in claim 1 and 7, wherein the polymer is selected from the group consisting of silicone, PDMS and SEBS.

9. The method as claimed in claim 1, wherein the contact angle of Ga droplets decreases from 145°C to 35° with increased SEBS surface energy due to plasma exposure.

10. The method as claimed in claim 1, wherein the Ga film is formed in step b) through tunneling and ohmic contacts.

11. A substrate with Ga film, wherein the thickness of Ga film is less than 100 nm.

12. The substrate with Ga film as claimed in claim 11, wherein the substrate is selected from SEBS, polycarbonate (PC), scotch tape, acrylic (PMMA), cellulose and thin covering glass.

13. The substrate with Ga film as claimed in claim 11, as and when used in soft electronics.