Femtosecond infra-red laser carbonization and ablation of polyimide for fabrication of Kirigami inspired strain sensor

Microfabrication of polyimide (PI) with femtosecond laser of wavelength 1030 nm is studied in two process conditions. Firstly, the low power-low scan speed regime is investigated for laser carbonization producing piezoresistive laser induced graphene (LIG). The heat accumulation model is modelled to find the temporal evolution of temperature at the laser focus for a single laser scan. Secondly, the high power-high scan speed regime is studied for laser ablation where clean ablation was observed due to multiphoton absorption. To demonstrate the application of this process, a two-dimensional (2D) LIG based strain sensor is drawn on a Kapton PI sheet using laser carbonization and transformed into a three-dimensional (3D) conformal sensor by cutting into a Kirigami design using laser ablation. The strain in the sensor is calculated from finite element analysis and the gauge factor is 88.58 ± 0.16. This laser process enables the transformation of any 2D PI sheet into a 3D conformal sensor using femtosecond laser, which is useful for wearable sensors and health-monitoring applications. The fabricated sensor is demonstrated used on a knee-joint to monitor real-time tracking of bending and twisting knee movements.

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Introduction
Femtosecond-pulsed laser processing is widely used for laser microfabrication of optically transparent polymers because of its high precision and controllable thermal effects [1]. A femtosecond laser beam interacts differently with polymers when compared with lasers with higher pulse durations, due to non-linear absorption arising from high pulse intensity (∼10 12 W cm −2 ). Since its pulse duration (t p ) is shorter than the electron-lattice relaxation time, the ablation process in the laser-affected zone happens faster than the transfer of energy to its surrounding regions, enabling more precise microfabrication, when compared to picosecond and longer pulse-duration counterpart processes [2]. Femtosecond infrared (IR) laser processing of polyimide (PI) gives rise to many interesting properties because of its optical transparency at 1030 nm and its ability for both surface and sub-surface precise microfabrication [3,4]. PI has a bandgap of 3.1 eV [5] causing it to absorb at 400 nm wavelength, at which singlephoton absorption occurs causing electronic excitation from higher occupied molecular orbital to lower occupied molecular orbital creating photochemical scission of the ring structures in the PI molecule causing the clean ablation [6,7]. Photochemical ablation can also be achieved by a multi-photon absorption process with femtosecond IR lasers at high intensity, in which the ablation threshold (F Th ) decreases with decreasing pulse duration (F Th ∝ t p 1/2 ) [8]. In addition, due to having a pulse duration less than the electron-lattice coupling time of PI (∼34 ps) [9], the energy does not thermalize into the lattice, enabling a clean ablation process. When thermally heated, PI forms graphene by a process called carbonization, which exhibits excellent piezoresistive properties and is often used in strain-sensor applications [10][11][12][13][14][15]. Such a thermal process can be achieved by the heat accumulation process using femtosecond lasers where the residual fraction of heat from each of the laser pulses is accumulated over the laser spot, causing vibrational excitation, which results in photothermal conversion of PI to laser induced graphene (LIG) [16][17][18]. So, if the laser is scanned at a fluence below the ablation threshold and at a low speed and high repetition rate, it will allow heat accumulation to occur due to the number of pulses per spot, generating sufficient heat at the laser focus to thermalize PI creating graphene without any ablation. Both photochemical ablation and photothermal carbonization have a wide range of applications. Ablation is applied to surface modification for very large-scale integration applications [19,20] and carbonization enables creation of conducting circuits for flexible sensor applications (figure 1(a)) [13]. Hence, a study on laser parameters to achieve selective ablation and carbonization is required.
Kirigami is a Japanese art form involving cutting ('Kiri') of papers ('-gami') or any two-dimensional (2D) surface to convert them into three-dimensional (3D) objects, which have various applications in soft-robotics, solar tracking, healthmonitoring and wearable sensors [21][22][23][24][25][26][27][28]. Kirigami design enables functional sensor structures to be printed on a 2D planar surface, with cuts to enable the sensor structures to conform to a 3D topological surface. Such design enables the engineering of increased elasticity into composites while adding stress-concentrating points at which to place strain sensors, enabling targeted and unique sensor applications [27]. Such a designing strategy can be applied to a PI film to overcome its stiffness and allow conformal fitting on human body-joints such as knee, ankle, shoulder, etc for healthmonitoring applications [24]. Ultraviolet lasers are mostly used for ablation [9] and carbonization [29] of PI, while CO 2 lasers are used for carbonization of PI only [30,31], but both types of laser lack precision in micro-structuring because of longer pulse durations. Femtosecond IR laser allows us to apply both the photochemical and photothermal processes from a single laser with higher precision [32] to create a Kirigami design from PI and LIG sensors by laser writing or printing.
In this paper, a rotationally symmetric concentric circular Kirigami cut pattern is designed for PI to leverage the photochemical ablation effect of femtosecond laser exposure to cut the design boundaries. The LIG sensor is printed within the inner boundaries of the design (figure 1(b)) utilizing the photothermal carbonization effect of IR laser. The Kirigami structure allows the 2D printed sensor structure to morph into a 3D conformal sensor structure. Out-of-plane displacement is modelled using finite element analysis (FEA) analysis which accurately predicts the displacement of the Kirigami-designed sensor structure upon loading of various weights at the central point of the sensor structure. This model is used to calculate the average strain of the sensor upon loading of 100-700 mg by calculating the von-Mises stress around the notches and edges of the sensor. The sensor is designed for knee-joint monitoring applications detecting the bending and twisting of knees. A comparative study of ablation and carbonization provides a set of values of threshold fluence and incubation coefficient for both processes. Carbonization of PI using femtosecond laser has been reported in other literatures but the process of carbonization using such a laser needs to be studied [33,34]. Such a process of carbonization of PI was modelled for the first time in this paper using the heat accumulation model in Python, enabling estimation of the process parameters to reach the threshold carbonization temperature of 700 • C [35] to initiate the carbonization process. Such a process enables scalable innovative pathways for femtosecond laser microfabrication applications [2].

Laser system
A femtosecond laser (Amplitude Systems S-PULSE HP) with wavelength centred at 1030 nm and generating pulses of width 550 fs at a repetition rate 200 kHz, was used for this experiment. The laser was linearly polarized in TEM00 (Lowest Order Transverse) mode and had a Gaussian distributed intensity profile. The laser beam was focused on the Kapton HN PI film of thickness 127 µm using a beam scanner (Hurryscan, Scanlabs) with a telecentric lens ( f = 100 mm, NA = 0.014) achieving a maximum scan speed (v) of 2000 mm s −1 . The laser power was controlled by using a combination of halfwave plates and a polarized beam-splitter to attenuate the intensity. The power was measured by an adjustable powermeter placed in the beam-path before the focusing lens. The PI film target was placed on an adjustable motor-controlled stage (Aerotech 3200 XYZ) controlled by ViewMMI software, and the locus of the laser scan on this target, was prepared in dynamic machine control (DMC) interface.

Laser carbonization and ablation of PI
PI film (Dupont Kapton ® HN) sheet of thickness 125 µm was cut into dimension of 60 mm × 60 mm, washed with isopropyl alcohol, rinsed, dried, and fixed on the Aerotech stage assisted with a vacuum pump to keep the PI sheet in place, ensuring the focused laser position remained constant throughout the laser scan. Both carbonization and ablation were carried out at a focal point with spot-radius (ω 0 ) 22.66 µm (figures S1 and S2). A linear pattern of 50 mm was designed in the DMC interface for both experiments and the PI sample was monitored by a charge-coupled device camera. The femtosecond laser was scanned at two process conditions (PC): (PC1) Low Power-Low scan speed to study carbonization, and (PC2) High Power-High scan speed to study ablation. For PC1, power was varied between 0.242-0.281 W and scan speed was varied between 2 and 3 mm s −1 at individual power with an interval of 0.25 mm s −1 at a repetition rate (f ) 200 kHz. For PC2, power was varied from 1.726 to 2.512 W at a scan speed of 200-300 mm s −1 with an interval of 25 mm s −1 for each power at repetition rate 200 kHz. A parameter space was developed to find the desired process parameters for carbonization and ablation alone (figure S13). The Kirigami cut pattern was designed and cut using the laser ablation process and the sensor pattern was designed and printed using the laser carbonization process.

Laser scan feature measurements and characterizations
The widths (D) of the carbonized and ablated features were measured using an Olympus BX60M optical microscope (figures S5 and S8). For carbonized features, the presence of graphene was detected by Raman spectroscopy using a 532 nm excitation laser with a RENISHAW inVia Raman Microscope. The depth of the carbonized and ablated tracks was measured using a cross-sectional Hitachi S-2600 scanning electron microscope (SEM). The diameter of single pulse ablated craters was measured by the SEM and the depths were calculated using an optical surface profilometer (Zygo OMP-0360 C).

Laser printing of Kirigami inspired sensor
The Kirigami sensor with external diameter of 51 mm, with a radial spacing of 3 mm between each concentric circle and angular spacing of 5 • , was designed in Autodesk Fusion 360 (figure 1) and imported into DMC software to create the process recipe. The sensor element was drawn within the inner boundaries of the design which helps the 2D sensor element to stretch conformally in 3D. The sensor element was printed with a single pass of a laser at a power 0.242 ± 0.001 W, scan speed 2 mm s −1 , repetition rate 200 kHz, utilizing the photothermal process to create LIG. Then the sensor was covered by 51 mm × 50 mm 3 M clear scotch tape of thickness 54 µm to prevent delamination of LIG from PI. The boundaries were printed on the scotch tape coating the PI, with 100 passes at power 2.524 W, scan speed 300 mm s −1 , repetition rate 200 kHz, thus utilizing the photochemical process to create pure ablation of the PI along with the scotch-tape. Silver pads were created at both ends of the LIG track with commercial silver conductive paint (RS Pro), and steel wires (D = 1 mm) were pasted on them followed by encapsulation with epoxy resin. Sensor data acquisition (DAQ) was performed by connecting the sensor to one of the arms of a balanced Wheatstone Bridge and connecting the bridge output to the PhidgetBridge Wheatstone Bridge Sensor Interface with a voltage supply of 5 V powered by USB ( figure 1(b)). A gain of 128× was selected for monitoring the changes in the output.

Electromechanical characterization of the sensor
The electromechanical characterization of a single LIG track of length 30 mm drawn at 0.154 W, 3 mm s −1 and repetition rate 200 kHz, printed on ASTM D638 Dog-Bone PI was performed using a motorized force tester system (MARK-10 ESM303) to measure the Elastic modulus (E), elastic to plastic deformation strain point, and the gauge factor (GF) of the single-track sensor element. Tensile stress was applied to the Dog-Bone and resistance was measured along with the strain using a source meter unit (Keysight B2900A) at the same sampling rate.

Laser carbonization of PI
For laser powers ranging from 0.242 to 0.281 W, carbonization occurred only at low scan speeds (2-3 mm s −1 ) as fluence lower than the single pulse ablation threshold (0.29 W, 182.98 mJ cm −2 , figures S3 and S4) does not have sufficient photon flux to cause photochemical ablation [36]. Spallation of LIG was observed above 0.29 W (figure S12) due to ablation. The low scan speed enabled heat accumulation from pulses per spot [37,38] to be sufficient to create the photothermal conversion of PI to LIG. The threshold fluence of carbonization at each scan speed (F N,Th ) was calculated from the x-intercept of the plot D 2 vs ln(F) at individual scan speed and the single pulse threshold fluence (F 1,Th ). The incubation coefficient (S) of carbonization was calculated from the y-intercept and slope of the plot ln(N.F N,Th ) vs ln(N) respectively (figures 2(a) and (b)) from equations (1) and (2) [31,37]: where, equation (2) is derived from F N,Th = (F 1,Th ) .N S−1 , number of laser pulses per spot N = 2ω 0 f/v. S and F 1,Th for carbonization were calculated to be 0.21 ± 0.03 and (5.6 ± 1.5) × 10 4 mJ cm −2 respectively. Such a low value of incubation coefficient indicates that heat accumulation plays an important role at low scan speed [38]. The higher value of F 1,Th indicates that it will never be possible to carbonize the material with a single laser pulse since it exceeds the single pulse threshold fluence for ablation, and ablation will predominate over carbonization at such high fluence. Cross-sectional SEM images (figures 3(a)-(e)) showed that the morphology of LIG is not fibrous, compared with LIG obtained from CO 2 lasers found in other studies. This indicates that the crystallite growth is more planar in the axis vertical to PI substrate [39]. The carbonization depth increased with increasing fluence and decreasing scan speed (figure 3(f)) due to increasing heat accumulation. The Raman spectra showed three distinct peaks D, G and 2D at ∼1344 cm −1 , ∼1576 cm −1 , and ∼2688 cm −1 respectively (figure 2(d)) associated with the breathing mode of phonons having A 1g symmetry, in-plane vibrations of E 1g phonons, and overtone of D band respectively [30]. The average crystallite size (L a ) was measured from the ratio of the intensity of D and G peak (I D /I G ) and increased with scan speed, indicating that the planar growth is favoured at higher scan speed [30] (figures S6 and S7). The electrical conductivity also increased with scan speed, due to increasing crystallite size, L a ( figure S7(b)).

Modelling of heat accumulation
The temporal evolution of temperature using femtosecond laser has been previously modelled in many literatures [18,[40][41][42]. But most of them have been reported for other materials such as steel, polymethylacrylate. Here we have modelled the thermal accumulation for carbonization of PI using a 2D heat accumulation model [18]. Heat accumulation occurs when a certain fraction of fluence of a single laser pulse, called the residual heat coefficient (η Heat (v)) is converted into thermal energy before the heat is dissipated. Thus, energy from the consecutive pulses is incident on the material and accumulates, causing increased temperature. Thermal effects are visible when the temperature accumulated at the laser-spot reaches the threshold temperature which is 973 K for carbonization of PI [35]. To model such effects, it is necessary to calculate the value of η Heat (v) as a function of scan speed (v). The rise in temperature for a given power and scan speed is calculated from equation (3) [16] and the minimum temperature required for thermal effect by heat accumulation caused by subsequent pulses for 1D heat flow is calculated from equation (4) [17]. Hence η Heat (v) is calculated by equating equations (3) and (4): Also, where for one-dimensional heat flow, Using equations (3)-(5):  The accumulated temperature over a spot is given by [18]: where, peak laser energy, d s = 2ɷ 0 , and t = duration of processing. The parameters are explained in table 1.F Th for each scan speed was calculated from figure 2(a), and then used to calculate the temporal evolution of temperature at the laser spot on PI using equation (7). Each of the threshold fluences gave the peak spot temperature around 900 K, which is the  threshold temperature of carbonization of PI, validating the model ( figure 2(c)). Hence such a model can be used to find the peak spot temperature for a set of scan speed and fluence values.

Laser ablation of PI
In the high-power regime, clean ablation occurred due to the photochemical process (figures 5(a)-(e)), caused by the high photon flux leading to multiphoton absorption, but the high scan speed did not allow any heat accumulation. S and F 1,Th for ablation were calculated to be 0.66 ± 0.08 and (1.89 ± 0.56) × 10 3 mJ cm −2 respectively from equations (1) and (2) (figures 4(a) and (b)). The ablation depths were calculated from the cross-sectional SEM which showed clean ablation without any residual debris. The depth decreased with increasing scan speed at individual fluences ( figure 5(f)). The effective absorption coefficient at each scan speed can be calculated using the equation [43]: where α eff = effective absorption coefficient at a fixed scan speed, F Th = Threshold fluence of ablation. The incubation coefficients and single pulse threshold fluences are summarized in table 2. The higher value of S for ablation as compared to carbonization, explains the minimal thermal effect at higher powers. The slope of α eff vs v (figure S9) indicates that the effective absorption coefficient increases with scan speed, which explains the saturable absorber property of PI [44,45].

Kirigami designed sensor characterization
A Kirigami designed sensor was created using the femtosecond laser ( figure 6(a)). From the electromechanical characterization of the LIG printed PI ( figure 6(b)), elastic modulus (E) was found to increase non-linearly with strain, which is acceptable since PI is a hyper-elastic polymer [46,47]. The elastic-plastic transition occurs at around 1% strain (figure 6(c)) as reported previously [48]. The resistance of the LIG track increased with applied tensile strain (ε) due to increased separation between the graphene crystallites and the GF was measured in the elastic region from the equation:    GF was found to be 96.97 ± 3.17 ( figure 6(d)). The resistance of the Kirigami sensor was measured to be 1.04 MΩ (figure S11) using IV characterisation. The change in the output voltage from the sensor connected with the PhidgetBridge DAQ system was measured by loading 0-700 mg at the centre of the sensor at amplification of 128× (figures 7(b) and (c)) and the off-plane displacement was measured by a travelling microscope placed in the plane of the sensor ( figure 7(a)). FEA was performed using the Kirigami design in COM-SOL to model the displacement along the z-axis upon loading of weights at the centre of the innermost concentric circle (figure 7(d)). A parametric scan of load mass was performed over 0-700 mg to find the displacement as a function of load which generated a displacement of 5.41-21.38 mm close to the experimentally calculated displacement (figure 7(e)). Hence, this model was used to calculate the von Mises Stress distribution across the sensor as a function of loading ( figure 7(a)). Further loading above 700 mg caused strain more than 1% which is beyond the elastic limit and was not used for GF calculation (figure S16). The FEA results showed that maximum stress of the order 10 7 N m −2 occurred around the notches of the Kirigami design (figure 7(d)) as compared to 10 5 N m −2 in the planar structure (figure S15) which are mostly responsible for the strain-sensitive response of the sensor. The average strain of the sensor for each loading was calculated using the model, and then used to measure the GF by plotting the relative change in the voltage (∆V/V) vs strain (figure 7(c)). GF was evaluated as 88.58 ± 1.11 which is close to that calculated for a single LIG sensor element (96.97 ± 3.17).
The sensor response to bending (X-Z plane) and twisting (X-Y plane) actions of the knee-joint was monitored by placing the sensor on the right knee under a knee-cap (figure 8(a)) along with a Phidget gyroscope to measure the change in angle upon bending and twisting of the knee. The sensor measured the relative change in voltage for bending and twisting of the knee joint, over 16 repetitions which showed an average change of 10.7 ± 1.4% in relative voltage (dV/V) upon an average knee-bending angle of 68.24 ± 2.21 • (figure 8(b)) and an average change of 2.23 ± 0.74% upon an average knee-twist angle of 10.06 ± 2.37 • (figure 8(c)). The sensor showed good reproducibility with a standard deviation of 0.603 in GF (figure S14). Such motion monitoring is useful for various applications such as Gait analysis, knee-joint health monitoring, and motion tracking [49].

Conclusion
The interaction of PI with femtosecond laser of wavelength 1030 nm, pulse duration 550 fs, and repetition rate 200 kHz was studied for two process conditions: PC1-Low Power-Low Scan Speed (0.242-0.281 W at 2-3 mm s −1 ), and PC2-High Power-High Scan Speed (1.726-2.512 W at 200-300 mm s −1 ). In PC1, carbonization only was observed without any traces of ablation. The single pulse ablation threshold and incubation coefficient for Case 1 were (5.6 ± 1.5) × 10 4 mJ cm −2 and 0.21 ± 0.03, respectively. In PC2, ablation only was observed without any traces of carbonization. High fluence causes high photon flux, enabling photochemical ablation of PI. The single pulse ablation threshold and incubation coefficient for Case 2 were (1.89 ± 0.56) × 10 3 mJ cm −2 and 0.66 ± 0.08, respectively. This result indicates that the single pulse carbonization threshold is higher than the single pulse ablation threshold, and thus carbonization cannot be achieved by a single pulse but by the accumulation of laser pulses per spot with a lower fluence for each pulse, which can only be achieved by scanning at low speed at a higher repetition rate. The heat accumulation model was modelled in Python, to determine the temporal evolution of temperature per spot upon scanning the femtosecond laser at various scan speeds over a range of individual powers. The model satisfied the carbonization thresholds at various scan speeds. These parameters provide insight into the selection of laser parameters for a range of microfabrication applications using femtosecond laser processing.
The Kirigami inspired strain sensor was fabricated using the parameters for such defined process conditions. PC1 was utilized to print piezoresistive LIG and PC2 was utilized to transform the 2D oriented sensor into a 3D conformal sensor, by ablating the boundaries of the Kirigami design. FEA analysis was performed using the sensor design, to obtain the von Mises stress distribution across the sensor, and the average strain was calculated for different loadings. Stress concentration points were located at the notches of the Kirigami design, which optimised the sensitivity of the strain-sensor. The change in output voltage from the PhidgetBridge DAQ was measured for individual loading, and thus the GF was calculated to be 88.58 ± 0.16. The sensor fitted conformally on the knee-joint and provided distinct responses for individual bending and twisting of the knee-joint, which are useful for human health monitoring, Gait analysis and motion tracking applications. Hence, the work presented here, demonstrates an application of high precision carbonization and ablation using femtosecond IR laser in Kirigami-inspired sensor fabrication and opens scalable pathways for other microfabrication applications.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.