Curvature programmed inkjet printing enables adaptive deposition for Gaussian sintering lasers

Domain: physics
Published: 2026-01-24
Editorial outcome: major_revision

Abstract
The inherent Gaussian intensity distribution of laser beams causes critical issues such as ablation, spattering, and porosity during laser sintering and melting. Although modulating the intensity distribution by a beam shaper can alleviate these problems, it suffers from high cost, limited durability, and significant energy loss. To address these challenges, we propose a thickness-matching strategy that aligns film geometry with the laser intensity profile. Mathematical analysis provides the optimal thickness distribution, while inkjet printing with computable parameters enables curved circuits with ideal profiles. The curved profile strategy demonstrates enhanced performance in both semiconducting and metallic circuits. For indium tin oxide (ITO) conductive glass, up to a 3.8-fold improvement in conductance and a 5.1% increase in transmittance are achieved compared with planar circuits, while for copper (Cu) conformal circuits, the electrical conductivity is improved by 160% compared with planar circuits. This work establishes a practical additive manufacturing route for high-performance conformal circuits.

Introduction
Selective laser sintering, as a rapid densification process of micro- and nanoparticles, has emerged as a critical technique for powder bed fusion and flexible electronics fabrication owing to its small radiation area, high power density, and controllable scanning paths1–3. Aiming to approach the high mechanical or electrical performance of bulk materials, investigations have been conducted to minimize the defects and improve the uniformity of the laser sintered materials4–9.

Sintering uniformity is crucial for enhancing component density and minimizing defects such as keyholes10,11, ablation12,13, and spattering14,15. These issues primarily stem from the inherent non-uniformity in the spot energy distribution of single-mode lasers16,17, which account for over 90% of industrial applications. Laser beam shaping is a straightforward solution, which includes techniques such as focusing, beam broadening, masking18, and converting Gaussian beams into locally uniform profiles (e.g., Bessel and rectangular beams19). However, laser beam shaping methods suffer from higher energy loss in the optical system (exceed 35%)20,21, as shown in Fig. S1 in supplementary information, limited stability and lifespan of shaping elements22, higher system complexity and lower compatibility with laser galvanometer systems, which poses challenges for large-scale industrial applications23.

In flexible electronics and powder bed fusion, the influence of laser parameters on sintering has been extensively studied. As laser energy input increases, nanoparticles undergo necking, coarsening, and ablation, which peak during the roughening stage and then decline due to material degradation24,25. To precisely control the sintering degree, most studies have focused on optimizing laser parameters, such as beam diameter and power, to identify suitable conditions for different materials26,27. More recently, to break through the performance limit, attention has shifted to the impact of film properties, particularly thickness, on grain coarsening, leading to preliminary models predicting sintering behavior as a function of thickness2. However, existing research remains largely limited to planar films2,15,28, while the interaction of Gaussian beams with inhomogeneous curved films presents unexplored opportunities for advancing laser sintering strategies (Fig. 1a).

Alternatively, in this work, we propose a method to improve the sintering uniformity induced by the natural, widely-used non-uniform laser. Unlike the complex and costly laser beam shaping, we propose a strategy to adapt the thickness of the deposition layer to the laser beam energy profile, which is simple and applicable, as illustrated in Fig. 1b, c. Therefore, the objective of the current work is to present proof of concept and to demonstrate the potential of this approach in real applications such as conductive glasses and conformal circuits.

Results
Gaussian energy distribution of a normal scanning laser beam
It is well recognized that during propagation, a laser beam contracts to its smallest diameter and highest intensity at the beam waist before expanding again. This behavior arises from the Gaussian nature of the beam, where focusing or diffraction effects cause convergence near the focal point, followed by gradual divergence due to diffraction29. Based on this feature, researchers modulate the beam diameter (D) by controlling the lens-to-object distance (z). Here, the laser beam used in this study had a focal length of Lf = 125 mm and for the convenience of sintering, the lens-to-object distance is always larger than the focal length, Lf. To quantify beam expansion beyond the focal point, we measured the beam diameter D as a function of axial distance z within the range of 125 ≤ z ≤ 155 mm (Fig. 2a). In this beam-expanding region (z > Lf), the beam diameter changes linearly with beam distance with a relation of D = 0.042·z − 5.15 (in mm), as indicated by the red line in Fig. 2a. In this study, the beam diameter D is defined as the average of two orthogonal diameters (Dx and Dy), as shown in Fig. 2b. Within the range of 125 ≤ z ≤ 155 mm, the two diameters exhibit a high degree of overlap, with a spot symmetry index of |Mx2 − My2| ≤ 0.08, which indicates that the laser beam used in this study maintains excellent axial symmetry30.

To adapt the deposition thickness with the laser profile, one needs to obtain the laser profile of the laser used for sintering. Thus, a beam quality analyzer is employed to measure the exact energy profile of a typical single-mode laser. Figure 2c illustrates the measured energy profiles at different laser powers of 2, 4, 6, and 8 W, respectively. The beam distance (z) is fixed at 135 mm, which gives the beam diameter of around 520 ± 10 μm (1/e2 beam diameter). Consistent with previous studies[30-31], the results show that the radial laser intensity profile agrees well with Gaussian curve (Eq. 1) with a determination coefficient (R2) of 0.998. The laser intensity distribution, I(x, y), as shown in the inset of Fig. 2c, can be described as follows31:
I(x,y) = I0 exp (−2 (x2+y2)/w2) = I0 exp (−8 (x2+y2)/D2) (1)
where I0 is the peak intensity at the beam center, x and y are the transverse coordinates, w and D are defined as the 1/e2 radius and diameters, respectively. Additionally, beam intensity profiles were measured at various diameters, and the coefficient of determination (R2) for the Gaussian fits of the energy profiles was at least 0.997 within the beam diameter range of 320 μm ≤ D ≤ 1500 μm (125 mm ≤ z ≤ 155 mm), confirming the beam’s stable Gaussian characteristics at different spot sizes, as shown in Fig. 2d. The corresponding fitting parameters are summarized in Table S1 of the Supplementary Information.

In the laser sintering process, the laser is normally scanning through the materials (Fig. 2e). Assuming that the scanning length is significantly larger than the width of the laser beam, one can calculate the energy profile of the accumulated energy in the following manner.
In the case that the laser moves in the x-direction, the mean projected laser energy on the substrate in the y-direction can be calculated as follows:
Es(y) = ∫−∞+∞ I(x,y)dx = I0 · exp (−8 y2/D2) · πD2 / 8 · 0.5 (2)
As a result, the energy distribution after laser scanning depends only on the y-coordinate (Fig. 2e) and can be well described by a Gaussian function (a comparison between the laser intensity distribution and the resulting energy distribution is illustrated in Fig. S2).

Desired material deposition profiles adapted to Gaussian laser
To adapt the profile of deposition thickness, h(y), with laser energy distribution, E(y), one needs to find out the relation, Es = f(h). A simplistic assumption is that the energy density is proportional to the mass to be sintered. However, our previous study shows that the relation between Es and h is relatively complex due to the complex laser penetration, reflection, and absorption mechanisms2. Therefore, based on a heat transfer analysis, the following equation was developed:
Es = f(h) = ΔHρh / ηα · exp(−μh) + 1 + (1−α)exp(−μh) / 1−exp(−μh) (3)
where h is deposition thickness, η is the ratio of the energy conducted to the deposited nanoparticles to the overall energy absorbed by the substrate, the value of η is dependent on the physical properties of the substrate and is approximately 0.6 for glass substrates (calculated with the theoretical formula for the heat conduction of a semi-infinite body with transient heat conduction under Dirichlet boundary conditions, detailed in supplementary information, pages S12–S13). And μ, ΔH, ρ are the attenuation coefficient, enthalpy, and density of nanoparticles, deposition, α is the absorbance of the substrate. The derivation of Eq. (3) is provided in detail in our previous study2.

Once the laser energy distribution is known, the ideal corresponding thickness of the deposition layer can be obtained by finding the inverse function of Es = f(h)
h = f−1(Es) (4)
However, due to the complexity of the function of Es = f(h), it is difficult to have the explicit analytical expression of f−1(Es). Alternatively, one can get h by means of iterative calculation with the following iteration equation, hn+1 = g(hn), which is derived from Eq. (4).
hn+1 = g(hn) = Es / (ηα · exp(−μhn) + 1 + (1−α)exp(−μhn) / 1−exp(−μhn) · ΔHρ) (5)
Therefore, by discretizing Es(y) at selected values, which are uniformly sampled at discrete intervals within the range of −D to +D, and applying Eq. (2) and Eq. (5), the deposition thickness h(y) at each discrete y position is calculated using the fixed-point iteration based on Eq. (5). Finally, the thickness distribution is obtained by fitting the discrete results with the Gaussian function as follows:
h(y) = c1 exp (−y2 / c2) (6)
where c1 and c2 are coefficients to be determined. For the Gaussian curve, h, a peak value of Acalc, width of Wcalc (1/e2 width), it can be expressed as Eq. (7), and the maximum thickness Acalc and the width Wcalc of the deposition layer can be calculated as
h(y) = Acalc exp (−8y2 / Wcalc2) (7)
Acalc = c1; Wcalc = sqrt(8c2) (8)
As a result, the energy distribution after laser scanning depends only on the y-coordinate (Fig. 2e) and can be well described by a Gaussian function (a comparison between the laser intensity distribution and the resulting energy distribution is illustrated in Fig. S2).

Fabrication of coffee-ring-suppressed unit circuits in inkjet printing
Although Eq. (7) provides the theoretically optimal profile, fabricating and precisely controlling the circuit profile remains a significant challenge. Given that the traditional film deposition techniques, such as physical and chemical vapor deposition, are normally employed for depositing films with uniform thickness, here, we developed a calculable strategy that employs inkjet printing to deposit curved circuit through layer-by-layer stacking, such that their profiles match the laser distribution.

For mathematical tractability and computational feasibility of stacked unit circuits, uniform deposition of the unit circuit is highly desirable. However, spatially non-uniform evaporation during inkjet printing often results in the coffee-ring effect, a widely reported and well-known feature leading to non-uniform cross-sections32,33. To address this issue, we extended our previous strategy of regulating single-drop deposition profiles by employing a binary solvent and an external temperature field34 for the fabrication of unit circuits. Specifically, a binary solvent system composed of ethylene glycol (EG) and isopropyl alcohol (IPA) in a 1:1 volume ratio was adopted, and ink droplets were evaporated on a heated copper block under a controlled external temperature field. As the substrate temperature increased and sequentially reached the boiling points of IPA and EG, the relative strengths of the flows inside the liquid column changed significantly32,34.

Figure 3a illustrates the competing flows during droplet evaporation. Capillary flow (La) and thermal Marangoni flow (MaT) drive the nanoparticles to the contact line, while solutal Marangoni flow (MaC) transports nanoparticles inward, suppressing the effect. Based on flow theory, the strengths of these flows can be expressed as35,36:
La = ρlσ / μ, MaT = ldσ/dT · ΔT / 2μ α, MaC = ldσ/dC · ΔC / 2μ Df (9)
where l is the circuit width, ΔC is the concentration difference between the droplet apex and the contact line, dσ/dC and dσ/dT are the variation of surface tension with concentration and temperature, μ is the viscosity, and Df is the diffusion coefficient of IPA in EG. In addition, ρ is the droplet density, σ is the liquid–vapor surface tension, ΔT is the temperature difference between the droplet apex and the contact line, and α is the thermal diffusivity of the liquid.

According to theoretical analysis, uniform deposition is expected when MaC ≈ La + MaT (commonly taken as 0.5 ≤ MaC / (La + MaT) ≤ 234,37). To examine this condition, we calculated the values of MaC / (La + MaT) over the range 60 °C ≤ T ≤ 220 °C (see Table S2 in supplementary information for details). The results show that within 150 °C ≤ T ≤ 190 °C, the balance index indeed falls in the range 0.5 ≤ MaC / (La + MaT) ≤ 2, indicating effective suppression of the coffee-ring effect (Fig. 3b). To verify this theoretical prediction, we printed ITO unit circuits on single-crystal silicon substrates at different temperatures (see Fig. 3c). The results revealed that when T = 160 °C and T = 180 °C, the circuits exhibited nearly uniform deposition with minimal coffee-ring effect, in agreement with the theoretical expectation. Furthermore, ITO unit circuits were also printed on substrates with different wettabilities (glass, silicon, and superalloy) at T = 160 °C, and their cross-sections were measured, as shown in Fig. 3d. The results showed that regardless of the substrate material, the printed ITO circuit cross-sections could be regarded as quasi-rectangular with a deviation of η ≤ 3.7%, η is calculated by the following equation:
η = 1/Srec ∫ |z1(x) − z2(x)| dx (10)
where, z1(x) and z2(x) denote the measured and ideal rectangular profile heights at position x, respectively, and Srec is the area of the reference rectangle.

Stacking-based inkjet-printing strategy for curved circuits with Gaussian-matched profiles
As mentioned above, by employing the binary solvent and external temperature field strategy, inkjet printing arranges a series of droplets into a straight line, resulting in a quasi-rectangular unit circuit with a width of w0 and a thickness of h0. By stacking unit circuits with a number of n and a displacement of d, which can be easily adjusted by the programs in the printer, we can fabricate deposition layers with different profiles in a shape-matched stacking manner, as illustrated in Fig. 4a. The profile of the stacked circuit can be manipulated by adjusting the printing parameters w0, h0, d, and n (Fig. 4b, c). The displacement d (Fig. 4c) and layer number n can be readily modified by the printer program. Furthermore, the width w0 of the unit circuit decreases linearly with increasing substrate temperature, while the thickness h0 increases inversely with increasing substrate temperature (Fig. 4d). Owing to mass conservation, it is expected that:
w0h0 = C (11)
As shown in Fig. 4e, this relation is in good agreement with experimental data (w0 and h0 were measured from surface optical images and cross-sectional SEM, as shown in Fig. S4).

For the stacked circuit, the width (Wprint), thickness (Aprint), as shown in Fig. 4f, can be estimated as follows (when n < w0/d):
Wprint = w0 + (n−1)d (12)
Aprint = nh0 (13)
For pairing a target Gaussian profile of deposition layer with a printed stacked circuit (Fig. 4f) we matched the cross-sectional thickness, Aprint, and the width, Wprint, of the printed circuit with the Acalc and Wcalc of the target Gaussian circuit (Aprint = Acalc, Wprint = Wcalc). Here, the parameter Wcalc in the Gaussian curve is the featured width, normally called 1/e2 width38,39, which represents the concentration of the curve after filtering out the secondary regions.

By associating the Eqs. (11)–(13), one can calculate the desired inkjet printing parameters for matching the laser with a profile described with Acalc and Wcalc (see Eqs. (6)–(8)) as follows,
w0 = nC / Acalc (14)
d = (Wcalc − w0) / (n−1) (15)
To calculate the printing parameters w0 and d, one needs to know the values of Acalc, Wcalc, C and n. Among these, Acalc and Wcalc are the coefficients of the model-predicted Gaussian profile of the deposition layer, which is the best-match of a given laser. According to Eqs. (5)–(8), as described in Section 2.2, it can be determined that Acalc = 14.5 μm and Wcalc = 235 μm for a laser with P = 4 W and D = 520 μm. Besides, the constant C ≈ 340 μm2 was determined from the scanning electron microscope (SEM) cross-sectional image of the ITO unit circuit (Fig. S4). The parameter n, representing the number of stacked layers, can be estimated from the maximum target height of the deposition profile, Acalc, and the thickness of each printed layer, h0. Measurements indicate that the thickness of a single uniform ITO unit circuit is 2.1–2.8 μm, depending on the substrate temperature (Fig. S4). The target stacked height is Aprint = Acalc = 14.5 μm, thereby allowing the number of layers to be approximated as n = int[Acalc/h0], yielding n = 6 or 7, with n = 6 adopted in this study. Now, we have determined all the required parameters as follows, Acalc = 14.5 μm, Wcalc = 235 μm, a C = 340 μm2 and n = 6. According to Eqs. (14)–(15), the inkjet printing parameters can be calculated as d = 18.9 μm and w0 = 140.7 μm. For the convenience of printing, they are rounded to d ≈ 20 μm and w0 ≈ 140 μm.

To validate the theoretical model, the stacked circuits were printed using the recommended parameters (d = 20 μm, w0 = 140 μm) and the cross-sectional morphology, labeled as the optimal profile (opt.), were examined using scanning electron microscopy (SEM), as shown in the inset of Fig. 4g. It can be seen that the profile of the printed circuit agrees reasonably with the desired function, indicating that the printing model works well.

To quantitatively evaluate the difference of the profiles between the target and the printed one, a parameter E is defined as follows:
E = 1/Scalc ∫ |hprint(y) − hcalc(y)| dy = ∫ |hprint(y) − hcalc(y)| dy / sqrt(π)AcalcWcalc (16)
where hprint(y) and hcalc(y) are the variations of printed and model-calculated heights, respectively. Having noted that the printed curve may be partially higher or lower than the calculated one, as shown in the inset image of Fig. 4g, the absolute difference between two heights is used in Eq. (16). According to Fig. 4h, a shifting of the printing parameters, such as droplet spacing and unit circuit width, from the model-predicted ones would result in a deviation of the printed circuits away from the target profile, which further proves the validity and accuracy of the proposed printing strategies (complete cross-sectional SEM images are available in Fig. S5).

To further proof the entire concept, the traditional uniform deposition and curved deposition were sintered with a laser with a Gaussian energy profile (P = 4 W, D = 520 μm, matching Eq. (7)). As shown in Fig. 5a and Fig. S6, for the planar deposition, the excessive energy concentration at the beam center causes severe ablation and the formation of coarse grains, while the insufficient energy at the periphery results in partially sintered or even unsintered nanograins; only a narrow intermediate zone exhibits moderate grain coarsening, which provides limited improvement in conductivity and transmittance. In contrast, Fig. 5b demonstrates that the curved deposition profile effectively redistributes the laser energy, enabling uniform sintering across the center, mid-span, and edge regions of the circuit; as a result, the grains are well connected throughout the film, leading to markedly enhanced electrical performance. Moreover, the X-ray diffraction (XRD) patterns in Fig. 5c further support these findings: compared with the planar circuit, the curved circuit exhibit sharper and narrower diffraction peaks, indicating an narrower grain size distribution and higher crystallinity40.

Application demonstration: from high-performance ITO conductive glass to Cu conformal circuits
Having noticed that the well-sintered ITO film could exhibit excellent conductivity and transmittance, we employed ITO conformal circuits on glass substrates as an example for demonstrating the application of the proposed strategy. It is well recognized that conductive glass conductance and transmittance are two key performance metrics41,42. However, the simultaneous optimization of these properties is challenging due to their differing dependencies on processing parameters. Specifically, higher laser energy improves the overall sintering degree and electrical conductivity but induces localized ablation at the beam center, adversely affecting optical transmittance. Similarly, increasing film thickness lowers resistivity but may compromise visible-light transparency. In this context, the curved circuit strategy shows significant advantages in controlling film thickness and achieving uniform sintering without ablation, thereby enabling potential synergistic enhancement of both electrical and optical performance.

For electrical performance evaluation, a series of curved circuits (profile-opt. and other curve profiles) as well as uniform planar circuits (same mass of nanoparticles as the curved circuits kept) were printed and sintered. We used the profile deviation, E, from the model-predicted shape to index each circuit. The corresponding conductivity as well as the transmittance of the circuits were measured. As shown in Fig. 6a, the conductivity decreases monotonically with the parameter E, among which the optimum circuit achieves the highest conductivity (3.8-fold higher than that of planar circuits). In addition, the laser-sintered curved circuits exhibited superior stability in the accelerated thermal cycling test, with resistance increasing by less than 10% after 50 cycles, compared to 35% for the planar circuits (see Fig. S7).

For optical performance evaluation, as shown in Fig. 6b, we arranged curved ITO circuits on a glass substrate in a crisscross pattern with a uniform circuit spacing of 300 μm in both horizontal and vertical directions. The transmittance (angle of incidence, θ = 0°) of the conductive glass was subsequently measured. It shows that the monochromatic transmittance is almost identical for the radiation with a wavelength above 390 nm (inset of Fig. 6b). Moreover, the transmittance also decreases with an increase in E.

For the purpose of co-optimization of electrical and optical performance, the data were plotted in a space of transmittance-resistance, as shown in Fig. 6c. Here, the reciprocal of sheet resistance (1/Rs has units of □/Ω) is employed as the horizontal variable43,44, and the transmittance of λ = 550 nm radiation at an incident angle of θ = 0° is employed as the vertical variable. The data in literature were also added in Fig. 6c for comparisons45–47, and it could be seen that the elevation of transmittance was normally achieved by trading-off the electrical conductivity. However, with the strategy proposed in this work, high transmittance and high conductivity can be simultaneously achieved. Say, the curved circuit exhibits the best synergistic performance of ITO conductive glass (1/Rs > 0.05 □/Ω, transmittance > 92.5% at λ = 550 nm) compared to the cases reported in literature to the best of our knowledge. Interestingly, due to the moth-eye-like morphology of the curved circuits, the directional transmittance can be significantly improved, especially for the incidence angle higher than 45°, as shown in Fig. 6d.

In addition, we further extended the theoretical model to different materials. Figure 6e shows the optimal predicted curved profiles for Ag, Cu, ITO, and SrTiO3 under the same Gaussian beam, confirming that materials with higher reflectivity and thermal conductivity (e.g., Ag, Cu) require narrower and taller optimal profiles, while ITO and SrTiO3 exhibit relatively broader and flatter shapes. For Cu circuits, experimental validation demonstrates that the predicted optimal profile indeed corresponds to the best sintering performance, as reflected by the highest conductivity at minimal profile deviation E (Fig. 6f). Furthermore, we also fabricated a large-scale conformal circuit sample (Fig. S8), which exhibited an average conductivity as high as 1.3×105 S·cm−1, representing a 1.6-fold improvement compared with planar circuits and further demonstrating the scalability and robustness of the proposed strategy.

Furthermore, by systematically comparing Gaussian-beam sintering of curved circuits with beam-shaped planar circuits, we identified several clear advantages of the proposed strategy (Fig. 6g). The required energy to achieve optimal sintering is lower, the processing window is wider as indicated by the larger area where conductivity exceeds 104 S·cm−1, and the maximum achievable performance is superior, avoiding the local cracking issues often observed in sharp-edged planar circuits.

Finally, Fig. 6h benchmarks laser sintering against traditional thermal sintering on different substrates. For high-melting substrates such as Al2O3, the short sintering time of laser processing minimizes oxidation and leads to better electrical performance. For low-melting substrates such as polyimide, the localized heating nature of the laser prevents thermal damage to the substrate (as shown in Fig. 6h, PI films can only withstand sintering up to 200 °C), further underscoring the broad applicability and superiority of the laser approach.

In summary, the curved circuit strategy shows high tolerance to both circuit and substrate materials, simultaneously improving the transmittance and sheet conductance of ITO conductive glass, as well as the conductivity of Cu circuits.

Methods
Nano-ink preparation
Conformal circuits were fabricated on glass, Al2O3 ceramic substrates, and polyimide (PI) films using ITO and Cu nanoparticles via inkjet-based additive manufacturing. First, nanoparticles were dispersed in a mixed solvent to formulate the nanoinks for inkjet printing. The ITO nanoparticles (purity = 99.9 wt%, Deke Daojin, China; average particle size = 30 nm) were dispersed in a binary solvent composed of ethylene glycol (purity = 99.9 wt%, Macklin, China) and isopropanol (purity = 99.9 wt%, Macklin, China) at a volume ratio of 1:1, with an nanoparticle concentration of 200 mg/mL. Polyvinyl pyrrolidone (PVP) powder (purity = 99.99 wt%, molecular weight = 58,000 g/mol, Macklin, China) was added at 2.5 mg/mL as a steric stabilizer for the suspension. The mixture was mechanically dispersed using an ultrasonic cell crusher (Scientz-IID, Scientz, China) operated at 150 W for 180 min, while the dispersion temperature was maintained at 10 °C using a water bath. After sonication, the ITO nanoink was passed through a polytetrafluoroethylene (PTFE) filter (pore size = 0.45 μm) to remove large aggregates. The physical properties of the ITO ink were adjusted to typical ranges suitable for stable inkjet printing, with a surface tension of 35–45 mN/m.

The Cu nanoink was prepared following the same formulation, dispersion, and filtration protocol as the ITO nanoink. Specifically, Cu nanoparticles (purity = 99.9 wt%, Deke Daojin, China; average particle size = 30 nm) were dispersed in the identical ethylene glycol/isopropanol (1:1 v/v) solvent mixture at a concentration of 200 mg/mL, with PVP added at 2.5 mg/mL as stabilizer. The suspension was ultrasonically dispersed at 150 W for 180 min at 10 °C and subsequently filtered through a 0.45 μm PTFE membrane prior to printing.

Inkjet printing
The ITO and Cu nanoinks were deposited as droplets (nominal diameter = 20 μm) onto flat SiO2 glass, Al2O3 ceramic, PI film, single-crystal silicon, and superalloy substrates using an inkjet printer with a positioning repeatability of ±5 μm (Jetlab 4xl, MicroFab, USA). Prior to printing, all substrates were cleaned in an ultrasonic bath using isopropyl alcohol, ethanol, and ultrapure water sequentially, each for 3 min, and then dried in a hot-air oven. To promote solvent evaporation and improve deposition uniformity, the substrate temperature was controlled in the range of 140–180 °C during printing using a proportional-integral-derivative (PID) controller. The ambient relative humidity was maintained between 30% and 80%, and the surface energy of the cleaned substrates was controlled in the range of 25–45 mN/m to ensure stable droplet spreading and coalescence.

Laser sintering
The deposited nanoparticle films were sintered using a continuous-wave ytterbium-doped fiber laser (MFSC75, Max Photonics, China). The laser beam was steered by a programmable galvanometer scanner system (RC1001, Jinhaichuang, China), which allowed precise control of the laser power and scanning speed along predefined trajectories. The beam diameter and intensity distribution at the sample plane were characterized using a beam profiler (SP620U, Ophir Optronics, Israel) and used to determine the effective spot size and energy density for the laser sintering process.

Characterizations and testing
The characteristics of the fabricated curved circuits were evaluated using a series of optical, structural, and electrical measurements. An optical super-field microscope (DSX1000, Olympus, Japan) was employed to observe the macroscopic morphology of the films, while field-emission scanning electron microscopy (FE-SEM, SU8020, Hitachi, Japan) was used to examine the microstructure. The circuit resistance was measured using a direct current resistance tester (HPS2661, Helpass, China). The optical transmittance of conductive glass samples was measured using a UV-vis-NIR spectrophotometer (UV-3600, Shimadzu, Japan).

X-ray diffraction (XRD) patterns were recorded on a diffractometer (D8 Advance, Bruker, Germany) equipped with a CuKα source (wavelength = 1.5406 Å), operated at 40 kV and 40 mA. The scans were carried out in step-scan mode with a step size of 0.02° and a scan rate of 4°/min. Thermal cycling tests were conducted by heating the glass substrate with a thin-film heater (LP-24, Dongtai, China), while the temperature was monitored with a K-type thermocouple. As illustrated in Fig. S7, each cycle consisted of rapid heating from room temperature to 150 °C, a short isothermal hold at 150 °C, and subsequent cooling to near room temperature by natural air convection.

The laser beam was shaped using a multi-element optical path, as schematically shown in Fig. S1. The raw Gaussian beam first passed through an iris-diaphragm aperture stop (Iris Diaphragm, Thorlabs, USA), which introduced an energy loss exceeding 15%, and was then focused onto a circularly serrated aperture apodizer (Serrated Aperture, Light Trans, Germany) to further tailor the intensity distribution, with an additional loss of more than 20%. Finally, a collimating lens assembly (Collimating Optics, Thorlabs, USA) was used to form a flat-top beam profile on the substrate.

For comparison, thermal sintering experiments were conducted in a tube furnace (BTF-1400C, BEQ, China) to evaluate the electrical performance of thermally sintered circuits. The samples were heated at a rate of 10 °C/min to the target temperature, held isothermally for 30 min, and then cooled naturally in air to below 75 °C before electrical measurements.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors reported a concept of uniformly laser sintering nanoparticle thin film with curved structure in thickness. The varying thickness of the inkjet-printed nanoparticle thin film to be sintered is used to adapt the Gaussian distribution of laser intensity, thus making the heating and sintering of the nanoparticle thin film more uniform. The center of the deposited nanoparticle thin film is thicker than that on the edges since the laser intensity at the center is higher than that on the sides. The claimed advantage of this proposed method compared to the conventional approaches for reaching uniform laser sintering includes reducing the complexity of the laser optics, as well as the cost of the system. Review comments are as follows:\n1. Although the temperature uniformity of the curved nanoparticle thin film is improved during Gaussian laser scanning, owing to the nature of heat transfer, the real-application feasibility of this approach of forming laser-sintered nano/micro structures for circuity remains unclear. For instance, the curvature, shape, width, and thickness of the inkjet printed thin film, which is optimized accordingly, are restricted by the laser intensity distribution at the same time. This limitation greatly affects the flexibility of circuitry design, which is in contradiction to the common idea that manufacturing technology shall support the design and function of the designated products.\n2. In addition, the trend of circuitry and electronic devices is 3D stacking and packaging. For this purpose, circuitry patterns with uniform and controllable thickness are preferable to curved circuitry. Therefore, curved circuit patterns made by the proposed method in this study may raise significant concerns in this regard.\nThe current manuscript also contains some flaws in writing. For instance:\n3. It is unclear why several axial distances of the laser beam after the focusing lens were used in this study while measuring the laser intensity distributions. Specifically, on page 4, line 50, the range of z is 125~155 mm. On the same page, line 71, the range of z is 130 to 145 mm.\n4. Esy in Equation (2) is apparently different from that shown in Figure 2(e).\n5. In Figure 5(c), those symbols are not shown in the legend correspondingly.\nOverall, this concept, using curved thin film deposited by inkjet printing to adapt a Gaussian laser beam intensity in order to reach a uniform temperature of the thin film to enable uniform sintering quality, is interesting. The mathematics and approaches are quite straightforward. The main concern is the feasibility of applying this proposed manufacturing technology to the real products of circuitry.", "reviewer_2": "This manuscript introduces a method to address the uneven sintering caused by Gaussian laser beams by matching film thickness to the laser’s intensity profile. Traditional beam-shaping techniques are costly and inefficient, while the proposed approach uses inkjet printing to fabricate curved circuits with optimized thickness distribution. A mathematical model calculates the ideal deposition profile, and a Tetris-like printing strategy precisely controls circuit geometry. Experiments confirm uniform sintering without ablation or porosity, significantly improving performance. Demonstrative ITO conductive glass achieved a 3.8-fold increase in conductance and 5.1% higher transmittance compared to planar circuits. This adaptive deposition method offers a simple, cost-effective solution for high-performance conformal electronics and additive manufacturing. After careful reading of this manuscript, I recommend its publication if the following issues are properly addressed.\n1. It is necessary to clarify what materials are being printed and laser-sintered in Figures 3 and 4.\n2. Inkjet printing usually exhibits a severe coffee-ring effect, resulting in a film morphology opposite to that of the manuscript. How did the author overcome the coffee-ring effect?\n3. While ITO demonstrates success, would this approach work equally well for other functional materials (e.g., metals, semiconductors) with different thermal/optical properties? The mathematical model (Eq. 3-5) links deposition thickness to laser energy distribution, but how was its accuracy experimentally validated beyond the single case of ITO? Were alternative materials or laser parameters tested to confirm generalizability?\n4. The Tetris-like stacking method requires precise alignment. What is the measured registration accuracy between layers.\n5. The method appears optimized for small-scale lab demonstrations. What technical barriers exist for scaling to industrial production speeds (e.g., m/s printing rates)?\n6. The SEM images show an improvement in uniformity, but were XRD or TEM analyses conducted to quantify the differences in material crystallization between the planar and curved approaches?\n7. Are there accelerated aging tests showing how conductivity and transmittance evolve over time under operational conditions (mechanical flexing, thermal cycling, etc.)?\n8. What level of environmental control (temperature, humidity, surface tension or surface energy) is required to maintain the demonstrated performance consistency?", "reviewer_3": "The revised manuscript is suggested for conditional acceptance with major revision.\nThe authors put forward an approach to match the film thickness to laser intensity distribution. For the given laser intensity, the optimal thickness distribution was determined. Furthermore, an inkjet printing method was developed to fabricate the optimally determined curved circuits. Nevertheless, there are the following points needing further revision.\n1. Please double check the spelling of “laser been shaping” in line 14 of page 2.\n2. Please elucidate the physical meaning of the coefficient “8” seen in Eq. (1)? Since D is defined as the beam diameter, where the laser intensity drops to 1/e^2 of I0.\n3. What is the relationship between Eq. (2) and the last equation seen in Fig. 2e? Do they refer to the same equation? It looks there are different, but several terms are the same.\n4. The expression “h = g(h)” in line 102 of page 6 is misleading. It would be better to add subscripts “n” and “n+1”.\n5. Please make sure the uniformity of expressions for the figures. Such as, “Fig. 5B” and “Fig. 5c”.\n6. What does “0.05 □/Ω” mean in line 230 of page 14?\n7. Even though the laser been shaping has the shortcoming of higher energy loss in the optical system, how does the electrical-optical performance of the fabricated circuit compare with the optimally determined circuit proposed by the authors? Please add more detailed information on the comparison.\nTo sum up, it is suggested re-read and re-exam the manuscript carefully to avoid the careless typos and inconsistent expressions.", "reviewer_4": "This study presents an approach to addressing the critical issue of Gaussian beam-induced defects in laser sintering/melting by tailoring circuit thickness distribution via inkjet printing. However, several aspects require clarification and strengthening to fully support the claims and ensure robustness:\n1.Droplet Spreading Dynamics Omitted: The model and fabrication strategy assume ideal inkjet droplet deposition and controlled thickness distribution. Crucially, the analysis does not account for the fundamental role of droplet surface tension and substrate wettability (hydrophilicity/hydrophobicity) in determining droplet spread shape, final footprint, and consequently, the actual printed height/thickness profile. This is a significant simplification, as these factors directly govern the achievable resolution and thickness uniformity in inkjet printing. The authors should address how variations in these parameters (e.g., across different substrate materials or ink formulations) might impact the fidelity of their thickness-matching strategy and discuss potential mitigations or calibration requirements.\n2.Non-Rectangular Cross-Section Assumption: The mathematical optimization and performance analysis appear to assume an ideal rectangular cross-section for the printed conductive traces. This assumption is frequently inconsistent with the reality of inkjet-printed lines, which typically exhibit rounded, bulging, or coffee-ring effect profiles. The discrepancy between the model's assumed geometry and the actual printed morphology could substantially affect the accuracy of the predicted conductance, laser absorption/heat distribution, and ultimately, the sintering outcome and final properties. The manuscript should acknowledge this limitation and discuss its potential implications or validate the model against realistic cross-sectional profiles.\n3.High-Frequency Signal Integrity Concern: While the demonstrated DC/low-frequency conductance improvement is impressive, the proposed \"stair-step\" thickness profile (inherent to the layer-by-layer inkjet approach) raises concerns for high-frequency circuit applications. Such non-uniform, stepped cross-sections can introduce significant impedance discontinuities, signal reflections, and increased transmission losses at microwave/RF frequencies. If the technology targets high-performance conformal circuits broadly, the authors should explicitly discuss this limitation for high-frequency operation or provide data/analysis demonstrating acceptable RF performance.\n4.Justification for Laser Sintering vs. Thermal: The manuscript positions the laser intensity modulation approach as a solution to problems inherent in laser sintering. However, it does not adequately justify why laser sintering is essential for this application compared to conventional thermal sintering processes. Thermal sintering (oven, belt furnace, localized heating) often offers superior process efficiency, potentially higher final conductivity, and avoids the specific complexities of laser beam shaping and Gaussian distribution issues altogether. The authors should strengthen the rationale for choosing laser sintering specifically. A direct comparison of the performance (conductivity, transmittance, speed, energy efficiency) and potential limitations (e.g., substrate thermal stability) of circuits fabricated using their laser-sintered, thickness-optimized approach versus thermally sintered circuits (with or without thickness optimization) would be highly valuable."}, "author_response": "Response to Reviewer 1\nThe authors reported a concept of uniformly laser sintering nanoparticle thin film with curved structure in thickness. The varying thickness of the inkjet-printed nanoparticle thin film to be sintered is used to adapt the Gaussian distribution of laser intensity, thus making the heating and sintering of the nanoparticle thin film more uniform. The center of the deposited nanoparticle thin film is thicker than that on the edges since the laser intensity at the center is higher than that on the sides. The claimed advantage of this proposed method compared to the conventional approaches for reaching uniform laser sintering includes reducing the complexity of the laser optics, as well as the cost of the system. Review comments are as follows:\nComment:\n1. Although the temperature uniformity of the curved nanoparticle thin film is improved during\nGaussian laser scanning, owing to the nature of heat transfer, the real-application feasibility of this\napproach of forming laser-sintered nano/micro structures for circuity remains unclear. For instance,\nthe curvature, shape, width, and thickness of the inkjet printed thin film, which is optimized\naccordingly, are restricted by the laser intensity distribution at the same time. This limitation greatly\naffects the flexibility of circuitry design, which is in contradiction to the common idea that\nmanufacturing technology shall support the design and function of the designated products.\nReply: Thank you for your insightful comment.\nIt is true that the underlying logic of our approach is to match the circuit dimensions (including\nwidth and thickness) to the laser beam distribution (diameter and intensity profile). Under the\npresent conditions, once the laser parameters are fixed, the optimal circuit cross-section is\ndetermined.\nTo achieve the higher degree of design freedom envisioned by the reviewer—where circuit\ngeometries could be arbitrarily tailored—the design logic could be reversed: the laser profile itself\nmight be dynamically modulated to match custom curved circuit shapes, which is technically\nfeasible. Specifically, Yu et al. demonstrated a galvanometer-based dynamic focusing system\ncapable of rapid, precise 3-axis laser focus positioning (response time ~600 μs), enabling real-time\nprofile adjustment [1*]. Similarly, Bremer et al. developed a mathematical framework comparing\ngalvanometer scanners and deformable mirrors for dynamic beam shaping of high-power lasers [2*].\nSuch a new direction would still benefit from the performance advantages of curved circuits over\nplanar ones, as demonstrated in this study, and thus represents a scientifically and technologically\nvaluable avenue of research. We sincerely thank the reviewer for inspiring us in this new direction,\nand we will upgrade our experimental setup to initiate research on high-performance, customizable\ncurved circuits enabled by controllable laser sintering.\nThe above discussion has also been added to the revised manuscript (page 19, lines 337-342).\n“Limitations and outlook. Despite these advances, the curved-circuit strategy still faces several\nchallenges for industrial deployment. In terms of profile-design freedom of circuits, it will be\nnecessary to introduce digitally programmable control of laser spot size and intensity so that the\nbeam profile can be adapted to target geometries of curved circuits [48], thereby overcoming the\nconstraints of the laser on the profile of curved circuits.”\nComment:\n2. In addition, the trend of circuitry and electronic devices is 3D stacking and packaging. For this\npurpose, circuitry patterns with uniform and controllable thickness are preferable to curved\ncircuitry. Therefore, curved circuit patterns made by the proposed method in this study may raise\nsignificant concerns in this regard.\nReply: Thank you for your attention to and insights on the trend of 3D stacking and packaging. We\nagree that 3D stacking and packaging is a crucial development direction for electronic devices, and\nthis scenario indeed requires strict control of circuit thickness uniformity [3*].\nHowever, it is important to emphasize that the “curved circuit” proposed in this study is essentially\na performance enhancement method, rather than treating “curvature” as the final geometry. Based\non established techniques, the temporary curvature of the circuits introduced during sintering is\nexpected to be removable in subsequent processing. For instance, in practical 3D packaging, low-\ntemperature calendaring or ultra-thin coating methods could planarize the curved circuits into\nfunctional layers with uniform thickness, with tolerances potentially controllable to within ±1 μm\n[4*, 5*]. Therefore, our current view is to realize planarization through packaging or other\nsubsequent processes, which we consider an important direction for future research. Nevertheless,\nthe present work primarily introduces and demonstrates the curved-circuit strategy, highlighting its\nability to significantly enhance circuit performance as the central innovation.\nThe relevant discussions have been supplemented in the revised manuscript (see page 19, lines 342-\n347).\n“In terms of packaging and 3D stacking, compatibility can be realized through post-sintering\nplanarization, in which the temporary curvature formed during sintering is eliminated and the\ncircuits are transformed into uniform-thickness functional layers with tolerances controllable to\nbelow 1 μm by employing advanced low-temperature calendaring or ultra-thin coating methods\n[49].”\nComment:\n3. The current manuscript also contains some flaws in writing. For instance:\n It is unclear why several axial distances of the laser beam after the focusing lens were used in\nthis study while measuring the laser intensity distributions. Specifically, on page 4, line 50, the\nrange of z is 125~155 mm. On the same page, line 71, the range of z is 130 to 145 mm.\n Esy in Equation (2) is apparently different from that shown in Figure 2(e).\n In Figure 5(c), those symbols are not shown in the legend correspondingly.\nReply: Thank you for carefully pointing out the omissions in the manuscript’s writing and detail\nlabeling; these comments are highly helpful for improving the manuscript’s rigor.\n(1) Missing statement on the axial distance z: In practice, z is adjusted to control the laser spot\nsize for different sintering requirements (page 3, lines 45 and 46).\n“Based on this feature, researchers modulate the beam diameter (D) by controlling the lens-to-\nobject distance (z).”\nDue to our oversight, the pre-revised manuscript contained inconsistent descriptions of the z-\nrange (125–155 mm and 130–145 mm). This has now been unified to “125–155 mm”\nthroughout the revised manuscript (page 4, line 70).\n“…within the beam diameter range of 320 μm≤ D ≤ 1500 μm (125 mm ≤ z ≤ 155 mm)”\n(2) Incorrect symbol “Esy” in Equation (2): The Esy has been corrected to E(y) in the revised\ns\nmanuscript to ensure full consistency (page 5).\n∞ 𝑦(cid:2870) 𝜋𝐷(cid:2870) (cid:2868).(cid:2873)\n𝐸 (cid:4666)𝑦(cid:4667)=(cid:3505) 𝐼(cid:4666)𝑥,𝑦(cid:4667)𝑑𝑥 =𝐼 ⋅exp(cid:4678)−8 (cid:4679)⋅(cid:4678) (cid:4679) (cid:4666)2(cid:4667)\ns 0 𝐷(cid:2870) 8\n(cid:2879)∞\n(3) Incomplete legend in Figure 6c (the Figure 5c in the original version): The legend has been\nsupplemented in the revised manuscript to ensure clarity and self-explanatory presentation\n(page 16).\nFig. 6c, Transmittance–resistance mapping highlights the simultaneous enhancement of\nconductivity and transmittance achieved by the curved circuit strategy, in contrast to\nliterature-reported trade-offs [43-45].\nWe sincerely thank the reviewer again for identifying these issues, which has allowed us to further\nimprove the clarity and quality of the manuscript.\nComment:\n4. Overall, this concept, using curved thin film deposited by inkjet printing to adapt a Gaussian\nlaser beam intensity in order to reach a uniform temperature of the thin film to enable uniform\nsintering quality, is interesting. The mathematics and approaches are quite straightforward. The\nmain concern is the feasibility of applying this proposed manufacturing technology to the real\nproducts of circuitry.\nReply: Thank you for acknowledging the innovativeness of our concept and our methods—this\nrecognition is a strong encouragement for us.\nAbout the concern of its real-world feasibility, we emphasize that the practicality of the proposed\nstrategy is supported on three levels:\n1. Equipment compatibility: This strategy uses standard inkjet and laser tools, requiring no\nstringent environmental control (unlike PVD/CVD), thus enabling low-cost, large-area scalable\nfabrication.\n2. Process adaptability: post-sintering encapsulation can planarize the circuits to a uniform\nthickness with a tolerance within ±1 μm [4*, 5*], thereby eliminating potential drawbacks of\ncurved profiles for 3D stacking.\n3. Performance improvement: for typical application scenarios (conformal circuits and\nconductive glass), curved circuits enhance electrical and optical performance (Fig. 6c, g and h),\nachieving the current state-of-the-art level of laser sintering.\nLooking ahead. To translate this laboratory demonstration toward application-oriented processes,\nwe plan to:\n1. Expand profile-design freedom by introducing digitally programmable control of laser spot size\nand intensity to adapt beam profiles to curved geometries.\n2. Ensure compatibility with packaging and 3D stacking via post-sintering planarization,\ntransforming curved profiles into uniform functional layers with sub-micrometer tolerances.\n3. Scale throughput from laboratory (about 10 mm/s) to industrial levels (m/s) by stabilizing high-\nfrequency droplet ejection, suppressing coffee-ring flows at shortened drying times, and\nintegrating in-situ optical/thermal feedback.\n4. Extend performance validation to GHz-frequency regimes to confirm that conductivity\nuniformity translates into stable RF signal integrity for device applications.\nWe believe these directions will further bridge the gap between proof-of-concept and industrial\napplication. In the revised manuscript, we have also added a “Limitations and Outlook” section in\nthe Discussion (page 19, lines 337-356), where we concisely summarize above four challenges of\nimplementing curved circuits in practical manufacturing, highlighting them as important directions\nfor our future research.\nResponse to Reviewer 2\nThis manuscript introduces a method to address the uneven sintering caused by Gaussian laser\nbeams by matching film thickness to the laser's intensity profile. Traditional beam-shaping\ntechniques are costly and inefficient, while the proposed approach uses inkjet printing to fabricate\ncurved circuits with optimized thickness distribution. A mathematical model calculates the ideal\ndeposition profile, and a Tetris-like printing strategy precisely controls circuit geometry.\nExperiments confirm uniform sintering without ablation or porosity, significantly improving\nperformance. Demonstrative ITO conductive glass achieved a 3.8-fold increase in conductance and\n5.1% higher transmittance compared to planar circuits. This adaptive deposition method offers a\nsimple, cost-effective solution for high-performance conformal electronics and additive\nmanufacturing. After careful reading of this manuscript, I recommend its publication if the following\nissues are properly addressed.\nComment:\n1. It is necessary to clarify what materials are being printed and laser-sintered in Figures 3 and 4.\nReply: Thanks for the reviewer’s suggestion. The materials in Figures 4 and 5 (Figures 3 and 4 in\nthe original version) are indium tin oxide (ITO), and we have clearly specified this in the revised\nmanuscript text (page 12, lines 202 and 205) and the captions for Figures 4 and 5.\n“ … scanning electron microscope (SEM) cross-sectional image of the ITO unit circuit (Fig. S4).”\n“Measurements indicate that the thickness of a single uniform ITO unit circuit is … ”\n“Fig. 4 d, Printing temperature T regulates w and h of the ITO unit circuit.”\n0 0\n“Fig. 5 Comparison of sintering homogeneity between planar and profile-optimized curved ITO\ncircuits.”\nComment:\n2. Inkjet printing usually exhibits a severe coffee-ring effect, resulting in a film morphology opposite\nto that of the manuscript. How did the author overcome the coffee-ring effect?\nReply: Thank you for your comment. It is true that the coffee-ring effect is common in inkjet\nprinting, as you mentioned. To suppress this effect, our research group has proposed a “binary\nsolvent + external temperature field” strategy, in which the concentration-driven Marangoni flow\ncounterbalances the combined effects of the temperature-driven Marangoni flow and capillary flow,\nthereby suppressing the coffee-ring effect and enabling the deposition of uniform films (for details,\nsee the analysis below or Reference [6*]).\nSuppression of the Coffee-Ring Effect via Binary Solvent\n(Ethylene Glycol + Isopropyl Alcohol) and Thermal Field (Heated Substrates)\nIt is well recognized that during the evaporation of nano-inks, nanoparticles are transported\ntoward the three-phase contact line due to capillary flow and thermal Marangoni flow,\ngiving rise to the coffee-ring effect. To suppress this effect, we employed a binary solvent\nink (EG:IPA = 1:1 by volume) and controlled the evaporation temperature. As the\ntemperature increases and sequentially reaches the boiling points of EG and IPA, the\nrelative strengths of different internal flows—capillary flow, solutal Marangoni flow, and\nthermal Marangoni flow—can be significantly regulated, thereby enabling effective\ncontrol of the deposition morphology and suppression of the coffee-ring effect.\nThe added Fig. 3a illustrates the mechanisms of capillary flow, solutal Marangoni flow,\nand thermal Marangoni flow in a partially evaporated circuit. As shown, capillary and\nthermal Marangoni flows drive nanoparticles outward toward the contact line (enhancing\nthe coffee-ring effect), while the solutal Marangoni flow transports nanoparticles inward\n(suppressing the effect). Thus, balancing these competing flows is critical for uniform\ncircuit deposition. According to flow theory [6*], the strengths of solutal Marangoni flow\n(𝑀𝑎 ), thermal Marangoni flow (𝑀𝑎 ), and capillary flow (𝐿𝑎) can be expressed as [7*,\n(cid:3004) (cid:3021)\n8*]:\n𝑙 𝑑𝜎/𝑑𝐶 𝜌 𝑙 𝜎 𝑙 𝑑𝜎/𝑑𝑇\n(cid:3039)(cid:3049)\n𝑀𝑎 = Δ𝐶, 𝐿𝑎 = , 𝑀𝑎 = Δ𝑇\n(cid:3004) 2𝜇𝐷 𝜇(cid:2870) (cid:3021) 2𝜇𝛼\n(cid:3033)\nwhere 𝑙 is the circuit width (see added Fig. 3b), Δ𝐶 is the concentration difference\nbetween the droplet apex and the contact line, 𝑑𝜎/𝑑𝐶 and 𝑑𝜎/𝑑𝑇 is the variation of\nsurface tension with concentration and temperature, 𝜇 is the viscosity, and 𝐷 is the\n(cid:3033)\ndiffusion coefficient of IPA in EG. In addition, 𝜌 is the droplet density, 𝜎 is the liquid–\n(cid:3039)(cid:3049)\nvapor surface tension, Δ𝑇 is the temperature difference between the droplet apex and the\ncontact line, and 𝛼 is the thermal diffusivity of the liquid (definitions shown\nschematically in Fig.3a).\nFig. 3. a, Schematic of the competing flows in an evaporating droplet on a heated substrate:\ncapillary flow (𝐿𝑎), solutal Marangoni flow (𝑀𝑎 ), and thermal Marangoni flow (𝑀𝑎 ).\n(cid:3004) (cid:3021)\nWhen 𝑀𝑎 ≈𝐿𝑎+𝑀𝑎 (𝑀𝑎 /(𝐿𝑎+𝑀𝑎 )≈1) the three flows reach a balance and\n(cid:3004) (cid:3021) (cid:3004) (cid:3021)\nthe coffee-ring effect can be effectively suppressed. Our experiments confirmed this\nprediction: as shown in added Figs. 3b, c, uniform unit circuits can be observed at 𝑇 =\n160℃ and 𝑇 =180℃ (Fig. 3c), which falls within the theoretically predicted uniform-\ndeposition temperature range of 150℃≤𝑇 ≤190℃ , corresponding to 0.5≤𝑀𝑎 /\n(cid:3004)\n(𝐿𝑎+𝑀𝑎 )≤2.\n(cid:3021)\nFig. 3. b, Theoretical prediction of the uniform-deposition window based on flow-strength\nanalysis (see Table S1 for details); uniformity is expected when 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition (scale bar: 100 μm).\nIn the revised manuscript, we have added an entire Section 2.3, “Fabrication of coffee-ring–\nsuppressed unit circuits in inkjet printing” to present the mechanism and experimental results of\nuniform unit circuit deposition (pages 7-10, lines 119-166).\nComment:\n3. While ITO demonstrates success, would this approach work equally well for other functional\nmaterials (e.g., metals, semiconductors) with different thermal/optical properties? The\nmathematical model (Eq. 3-5) links deposition thickness to laser energy distribution, but how was\nits accuracy experimentally validated beyond the single case of ITO? Were alternative materials or\nlaser parameters tested to confirm generalizability?\nReply: Thank you for your valuable suggestion.\nIn addition to the ITO case, we have added experiments on a new material, copper (Cu), where\ncircuits with the model-predicted optimal curved profile were fabricated to confirm the generality\nof the mathematical model (Eqs. 3–5). As shown in the revised Fig. 6f, the Cu optimized curved\ncircuits achieved the best sintering performance when their cross-sectional morphology matched the\nprediction, confirming the model’s accuracy under a metallic system with very different thermal and\noptical properties from ITO. Furthermore, we also fabricated large-area conformal circuit samples\n(Fig. S8 in supplementary information), which exhibited an average conductivity as high as 1.3×\nFig. 6f, Experimental validation for Cu confirms that the predicted optimal profile corresponds\nto the best sintering performance.\nIn addition, the model has been extended to other representative materials (Ag, SrTiO ), and the\n3\ncalculated optimal curved profiles (Fig. 6e) highlight material-dependent variations in peak height\nand width (1/e2), supporting the theoretical applicability of the strategy to a broad range of functional\nmaterials.\nFig. 6e, Theoretically predicted optimal curved profiles for Ag, Cu, ITO, and SrTiO under the\n3\nsame Gaussian beam, showing material-dependent differences in peak height and width (1/e2).\nFig. S8. Large-area conformal circuit validation. Left: Photograph of a fabricated large-size\ncurved circuit sample. Right: Electrical resistance measurement of the sample using a digital\nmultimeter, showing high conductivity (1.3×105 S·cm-1).\nThe relevant discussions have been added to the revised manuscript (pages 17-18, lines 289-305)\nand the revised supplementary information (page S9). The preparation of Cu nano-ink can be found\nin page 20, lines 375-379.\nComment:\n4. The Tetris-like stacking method requires precise alignment. What is the measured registration\naccuracy between layers.\nReply: Thank you for your comment. As you noted, stacking accuracy has a significant impact on\nthe morphology of the curved circuit. The interlayer stacking (registration) accuracy is determined\nby the repeat positioning accuracy of the printer’s X-Y motion stage; for the MicroFab Jet-Lab 4xl\nused in this work, the specified repeatability is ±5 μm (relatively small for the 100 μm-wide unit\ncircuit).\nWe have also added this information in the revised manuscript (page 20, lines 381-384).\n“The ITO and Cu nanoinks were deposited on flat SiO glass, Al O ceramic, PI film, single-crystal\n2 2 3\nsilicon, and superalloy substrates in the form of droplets (diameter = 20 μm) using an inkjet printer\nwith repeatability of ±5 μm (Jetlab 4xl, MicroFab, America).”\nComment:\n5. The method appears optimized for small-scale lab demonstrations. What technical barriers exist\nfor scaling to industrial production speeds (e.g., m/s printing rates)?\nReply: Thank you for your comment. We agree that the present work has been demonstrated only\nin a small-scale laboratory environment, with an inkjet printing speed of approximately 10 mm/s.\nScaling up to industrial production speeds on the order of meters per second would indeed raise\nseveral technical barriers.\n1. Droplet stability: at high firing frequencies, the stability of droplet ejection and placement may\ndeteriorate, compromising line continuity and registration accuracy.\n2. Fluid dynamics: rapid solvent evaporation during high-speed printing can alter the balance of\nMarangoni and capillary flows, thereby reducing the effectiveness of coffee-ring suppression.\n3. System reliability: at such high throughput, nozzle clogging, synchronization of multi-nozzle\narrays, and substrate thermal management become increasingly critical.\nThese challenges underscore important directions for future development, and we have begun\nexploratory efforts toward industrial-scale implementation to address the above issues, and we also\nhave noted this limitation in the revised manuscript (page 19, lines 347-352).\n“Limitations and outlook. In terms of processing speed, our current demonstrations are limited\nto laboratory-scale printing speeds (~10 mm/s), and achieving m/s-level throughputs may require\naddressing droplet stability at high actuation rates, maintaining suppression of coffee-ring flows\nunder shortened drying times, and incorporating in situ thermal/optical feedback for closed-loop\ncontrol of the sintering window.\nComment:\n6. The SEM images show an improvement in uniformity, but were XRD or TEM analyses conducted\nto quantify the differences in material crystallization between the planar and curved approaches?\nReply: Thank you for your valuable suggestion. To further substantiate the SEM observations, we\nhave added XRD characterization of the laser-sintered planar and curved ITO circuits (Fig. 5c).\nThe results reveal that the planar circuit exhibits broader and less symmetric diffraction peaks,\nindicative of a wider grain size distribution and microstructural non-uniformity. In contrast, the\ncurved circuit shows sharper and narrower peaks, which correspond to more homogeneous grain\ngrowth and higher crystallinity. These findings are consistent with the SEM results and confirm that\nthe curved deposition strategy promotes improved microstructural uniformity.\nFig. 5c, XRD patterns of laser-sintered planar and curved ITO circuits. Compared with the\nplanar circuit, the curved circuit exhibits sharper and narrower diffraction peaks, indicating\nmore homogeneous grain growth and higher crystallinity.\nThe relevant content has been added to the revised manuscript (page 14, lines 240-243).\n“Moreover, the X-ray diffraction (XRD) patterns in Fig. 5c further support these findings: compared\nwith the planar circuit, the curved circuit exhibits sharper and narrower diffraction peaks, indicating\na narrower grain size distribution and higher crystallinity [40].”\nThe XRD testing equipment and procedure have also been added to the “Methods” section (page\n21, lines 406-400).\n“The X-ray diffraction (XRD) analysis was performed using a diffractometer (Bruker D8 Advance,\nGermany) equipped with a Cu target (wavelength = 1.5406 Å), operating at a tube current of 40 mA\nand a tube voltage of 40 kV. The measurements were conducted in a step-scan mode with a step\nsize of 0.02° and a scan rate of 4°/min.”\nComment:\n7. Are there accelerated aging tests showing how conductivity and transmittance evolve over time\nunder operational conditions (mechanical flexing, thermal cycling, etc.)?\nReply: Thank you for your comment. We have added accelerated aging tests under thermal cycling\nfor both laser-sintered planar and curved ITO circuits, as shown in the Supplementary Information\n(Fig. S7).\nThe results indicate that the resistance of the planar circuit increases significantly with cycling,\nreaching about 35% higher than its initial value after 50 cycles. In contrast, the curved circuit shows\nonly a minor resistance change (<10%) over the same process, demonstrating much better stability\nagainst thermal fatigue (Fig. S7a). These results confirm that the curved configuration enhances\ndurability and reliability under repeated thermal stress. For completeness, the thermal cycles were\napplied by heating the glass substrate to 150 °C using a thin-film heater and then cooling it back to\nroom temperature by air convection (Fig. S7b).\nFig. S7. Thermal cycling stability of laser-sintered ITO circuits. a, Normalized resistance\n(R/R ) of planar and curved circuits during 50 thermal cycles, showing much higher stability for\n0\nthe curved circuit (<10% increase) compared to the planar circuit (35% increase). b, Temperature\nprofile of a typical thermal cycle, including heating to 150 °C, a short plateau, and cooling to\nroom temperature by natural air convection.\nThe relevant content and test process have been added to the revised manuscript (page 15, lines 265-\n267; page 21, lines 410-415).\n“In addition, the laser-sintered curved circuits exhibited superior stability in the accelerated thermal\ncycling test, with resistance increasing by less than 10% after 50 cycles, compared to 35% for the\nplanar circuits (see Fig. S7).”\n“The thermal cycle was applied by heating the glass substrate with a thin-film heater (LP-24,\nDongtai, China), while the temperature was monitored using a K-type thermocouple. As illustrated\nin Fig. S7, each cycle consisted of a rapid heating stage (room temperature to 150 °C), a short\nisothermal plateau at 150 °C, and a subsequent cooling stage back to near room temperature by air\nconvection.”\nComment:\n8. What level of environmental control (temperature, humidity, surface tension or surface energy)\nis required to maintain the demonstrated performance consistency?\nReply: Thank you for your question. The demonstrated performance was obtained under standard\nlaboratory conditions, without the need for an exceptionally stringent environment. In our\nexperiments, the substrate temperature was controlled at 140–180 °C to promote solvent\nevaporation and uniform deposition, while the ambient relative humidity was maintained at 30–80%,\nwhich is a typical range for inkjet printing. The surface tension of the ITO ink was 35–45 mN/m\nand the surface energy of the cleaned substrate was 25–45 mN/m, both of which fall within common\nranges for stable jetting and wetting. Within these conditions, the deposition was highly reproducible\nand the performance consistency was well maintained. These physical parameters are not extreme\nand can be readily achieved under standard laboratory conditions.\nThe relevant details have been added to the revised manuscript (page 20, lines 373-374; pages 20-\n21, lines 387-392).\n“The physical parameters of the ITO ink were maintained within common ranges for stable printing,\nwith a surface tension of 35-45 mN/m.”\n“To accelerate solvent evaporation and enhance deposition uniformity, the substrate temperature\nwas increased to 140–180 °C during inkjet printing, where a proportional-integral-derivative\ncontroller was employed to maintain the temperature. During printing, the ambient relative humidity\nwas maintained between 30% and 80%, and the surface energy of the cleaned substrates was\ncontrolled at 25–45 mN/m.”\nResponse to Reviewer 3\nThe revised manuscript is suggested for conditional acceptance with major revision.\nThe authors put forward an approach to match the film thickness to laser intensity distribution. For\nthe given laser intensity, the optimal thickness distribution was determined. Furthermore, an inkjet\nprinting method was developed to fabricate the optimally determined curved circuits. Nevertheless,\nthere are the following points needing further revision.\nComment:\n1. Please double check the spelling of “laser been shaping” in line 14 of page 2.\nReply: Thanks for the reviewer. We apologize for the spelling error of \"laser beam\". We have\ncorrected this error (page 2, line 14) and checked the entire manuscript to avoid any spelling issues.\n“However, laser beam shaping methods suffer from higher energy loss …”\nComment:\n2. Please elucidate the physical meaning of the coefficient “8” seen in Eq. (1)? Since D is defined\nas the beam diameter, where the laser intensity drops to 1/e^2 of I0.\nReply: Thank you for the reviewer’s insightful question. The coefficient “8” originates from the\ndefinition of the Gaussian beam diameter 𝐷 as the 1/e² diameter, rather than the more common 1/e²\nradius. In the standard form, the transverse Gaussian intensity profile is expressed as [9*, 10*], and\n𝑤 is the 1/e2 radius.\n𝑟(cid:2870)\n𝐼(𝑟)=𝐼 exp(cid:4678)−2 (cid:4679)\n(cid:2868) 𝑤(cid:2870)\nSince in our work 𝐷 = 2𝑤, substituting 𝑤 =𝐷/2, and 𝑥(cid:2870)+𝑦(cid:2870) =𝑟(cid:2870) leads to,\n𝑟(cid:2870) 𝑥(cid:2870)+𝑦(cid:2870)\n𝐼(𝑟)=𝐼 exp(cid:4678)−8 (cid:4679), 𝐼(𝑥,𝑦)= 𝐼 exp(cid:4678)−8 (cid:4679)\n(cid:2868) 𝐷(cid:2870) (cid:2868) 𝐷(cid:2870)\nThus, the coefficient “8” is introduced based on the definition of the 1/e2 radius and derived through\ncalculation. We have added this clarification, together with a relevant reference, to the revised\nmanuscript (page 4, lines 64-67).\n“The laser intensity distribution, I(x,y), as shown in the inset of Fig. 2c, can be described as follows\n[31]:\n𝑥(cid:2870)+𝑦(cid:2870) 𝑥(cid:2870)+𝑦(cid:2870)\n𝐼(𝑥,𝑦)=𝐼 exp(cid:4678)−2 (cid:4679)= 𝐼 exp(cid:4678)−8 (cid:4679) (1)\n(cid:2868) 𝑤(cid:2870) (cid:2868) 𝐷(cid:2870)\nwhere 𝐼 is the peak intensity at the beam center, 𝑥 and 𝑦 are the transverse coordinates, 𝑤 and\n(cid:2868)\n𝐷 are defined as the 1/e² radius and diameter, respectively.”\nComment:\n3. What is the relationship between Eq. (2) and the last equation seen in Fig. 2e? Do they refer to\nthe same equation? It looks there are different, but several terms are the same.\nReply: Thank you for the reviewer's comment. Eq. (2) is equivalent to the equation shown in Fig.\n2e. To avoid any confusion, we have unified their expressions in the revised manuscript to ensure\nconsistency.\nThe revised Eq. (2) and Fig. 2e are shown below:\n∞ 𝑦(cid:2870) π𝐷(cid:2870) (cid:2868).(cid:2873)\n𝐸 (𝑦)=(cid:3505) 𝐼(𝑥,𝑦)𝑑𝑥 =𝐼 ⋅exp(cid:4678)−8 (cid:4679)⋅(cid:4678) (cid:4679) (2)\ns 0 𝐷(cid:2870) 8\n(cid:2879)∞\nFig. 2 e, The energy distribution is obtained by integrating the beam intensity over the scanning\npath.\nComment:\n4. The expression “h = g(h)” in line 102 of page 6 is misleading. It would be better to add subscripts\n“n” and “n+1”.\nReply: Thanks for the reviewer's comment. We have replaced “h = g(h)” with “h = g(h )” in the\nn+1 n\nrevised manuscript (page 6, line 101).\n“ … with the following iteration equation, h = g(h ), which is derived from Eq. (4).”\nn+1 n\nComment:\n5. Please make sure the uniformity of expressions for the figures. Such as, “Fig. 5B” and “Fig. 5c”.\nReply: Thank you for pointing this out. We have corrected “Fig. 6B” (the Fig. 5B in the original\nversion) to “Fig. 6b” in the revised manuscript (see page 16, line 273), and rechecked all figure\ncitations to ensure consistent expression.\n“ … for the radiation with a wavelength above 390 nm (inset of Fig. 6b).”\nComment:\n6. What does “0.05 □/Ω” mean in line 230 of page 14?\nReply: Thank you for the reviewer’s comment. The symbol “□/Ω” denotes the unit of the reciprocal\nof sheet resistance (1/R). Since R is in Ω/□, its reciprocal (□/Ω) scales positively with conductivity\ns s\nand is sometimes more intuitive for thin‑film performance benchmarking. Here, “□” is a\nconventional symbol indicating that the resistance is normalized to a square geometry, independent\nof the actual size of the square. This unit is widely used to characterize the electrical performance\nof thin films, especially transparent conducting oxides and printed conductors [11*, 12*].\nIn the revised manuscript, a brief explanation of this unit has been added (page 17, lines 276-278),\ntogether with the relevant references.\n“Here, the reciprocal of sheet resistance (1/R has units of □/Ω) is employed as the horizontal\ns\nvariable [46, 47], ”\nComment:\n7. Even though the laser been shaping has the shortcoming of higher energy loss in the optical\nsystem, how does the electrical-optical performance of the fabricated circuit compare with the\noptimally determined circuit proposed by the authors? Please add more detailed information on the\ncomparison.\nReply: Thank you for the insightful comment.\nMotivated by your suggestion, we supplemented direct comparisons between Gaussian-beam\nsintered curve circuits and beam-shaped laser sintered planar circuits, as shown in Fig. 6g of the\nrevised manuscript. The results reveal that the curved circuit strategy provides clear advantages:\n(i) lower laser energy is required to achieve optimal sintering;\n(ii) the processing window is significantly broader, as indicated by the larger region with\nconductivity exceeding 104 S·cm-1;\n(iii) the maximum conductivity is higher, while avoiding the local cracking issues frequently\nobserved in sharp-edged planar circuits.\nThese results demonstrate that, even considering the additional energy loss in the optical shaping\nsystem, the fabricated curved circuits maintain excellent electrical–optical performance and deliver\nsuperior robustness compared with planar designs.\nFig. 6 g, Comparison of Gaussian-beam curved circuits and beam-shaped planar circuits\ndemonstrates the advantages of the curved circuit strategy: lower energy requirement, wider\nprocessing window, and higher achievable conductivity.\nThe experimental comparison between the curved circuits and beam-shaped lasers sintered circuits\nhas been added on pages 17-18, lines 300–305 of the revised manuscript.\n“Furthermore, by systematically comparing Gaussian-beam sintering of curved circuits with beam-\nshaped planar circuits, we identified several clear advantages of the proposed strategy (Fig. 6g). The\nrequired energy to achieve optimal sintering is lower, the processing window is wider as indicated\nby the larger area where conductivity exceeds 10⁴ S·cm⁻¹, and the maximum achievable\nperformance is superior, avoiding the local cracking issues often observed in sharp-edged planar\ncircuits.”\nThe description of the laser beam shaping method has been added on pages 21-22, lines 415–422.\n“The laser beam was shaped using a multi-element optical path, as shown in Fig. S1. The raw\nGaussian beam first passed through an iris-diaphragm aperture stop (Iris Diaphragm, Thorlabs,\nUSA), causing over 15% energy loss, and was then focused onto a circularly serrated aperture\napodizer (Serrated Aperture, LightTrans, Germany), which further modified the intensity\ndistribution but induced an additional loss exceeding 20%. Finally, a collimating lens package\n(Collimating Optics, Thorlabs, USA) was used to form a flat-top shaped profile.”\nComment:\n8. To sum up, it is suggested re-read and re-exam the manuscript carefully to avoid the careless\ntypos and inconsistent expressions.\nReply: Thank you for pointing out the spelling and expression issues in our manuscript. We have\nthoroughly proofread the manuscript and standardized spelling, formatting, and notation to avoid\ncareless typos and inconsistent expressions.\nResponse to Reviewer 4\nThis study presents an approach to addressing the critical issue of Gaussian beam-induced defects\nin laser sintering/melting by tailoring circuit thickness distribution via inkjet printing. However,\nseveral aspects require clarification and strengthening to fully support the claims and ensure\nrobustness:\nComment:\n1. Droplet Spreading Dynamics Omitted: The model and fabrication strategy assume ideal inkjet\ndroplet deposition and controlled thickness distribution. Crucially, the analysis does not account\nfor the fundamental role of droplet surface tension and substrate wettability\n(hydrophilicity/hydrophobicity) in determining droplet spread shape, final footprint, and\nconsequently, the actual printed height/thickness profile. This is a significant simplification, as these\nfactors directly govern the achievable resolution and thickness uniformity in inkjet printing. The\nauthors should address how variations in these parameters (e.g., across different substrate\nmaterials or ink formulations) might impact the fidelity of their thickness-matching strategy and\ndiscuss potential mitigations or calibration requirements.\nReply: Thank you for your insightful comment. We fully agree with the reviewer that droplet\nspreading dynamics, governed by factors such as surface tension and substrate wettability,\nplay a fundamental role in determining the final footprint and thickness uniformity. In fact, all unit-stacked\ncircuits in our experiments exhibited highly uniform line morphology, which was achieved through\nthe combined regulation of a binary solvent system and a controlled thermal field.\nBalancing “Solutal Marangoni Flow” with “Capillary + Thermal Marangoni\nFlows” for Coffee-Ring Suppression\nIt is widely recognized that the coffee-ring effect arises during nano-ink evaporation\nbecause capillary flow and thermal Marangoni flow drive suspended nanoparticles\noutward toward the three-phase contact line. In our strategy, the combined use of a binary\nsolvent (Ethylene Glycol: Isopropyl Alcohol at a 1:1 volume ratio, determined from\npreliminary orthogonal experiments on droplet evaporation [6*]) and a controlled external\ntemperature field enables precise regulation of the internal flow competition. As the\nevaporation temperature increases, IPA and EG evaporate sequentially according to their\nboiling points, creating dynamic variations in both concentration gradients and\ntemperature gradients within the droplet.\nThese gradients give rise to three key flows (see added Fig.3a in revised manuscript): (i)\nCapillary flow, induced by liquid replenishment toward the pinned contact line; (ii)\nThermal Marangoni flow, driven by surface tension gradients from temperature\ndifferences between the droplet apex and the contact line; and (iii) Solutal Marangoni\nflow, generated by local EG enrichment at the contact line due to the preferential\nevaporation of IPA. The relative magnitudes of these flows can be quantified by the\nLaplace number (𝐿𝑎), thermal Marangoni number (𝑀𝑎 ), and solutal Marangoni number\n(cid:3021)\n(𝑀𝑎 ), which can be expressed as [7*, 8*]:\n(cid:3004)\n𝑙 𝑑𝜎/𝑑𝐶 𝜌 𝑙 𝜎 𝑙 𝑑𝜎/𝑑𝑇\n(cid:3039)(cid:3049)\n𝑀𝑎 = Δ𝐶, 𝐿𝑎 = , 𝑀𝑎 = Δ𝑇\n(cid:3004) 2𝜇𝐷 𝜇(cid:2870) (cid:3021) 2𝜇𝛼\n(cid:3033)\nwhere 𝑙 is the circuit width, Δ𝐶 is the concentration difference between the droplet apex\nand the contact line, 𝑑𝜎/𝑑𝐶 and 𝑑𝜎/𝑑𝑇 is the variation of surface tension with\nconcentration and temperature, 𝜇 is the viscosity, and 𝐷 is the diffusion coefficient of\n(cid:3033)\nIPA in EG. In addition, 𝜌 is the droplet density, 𝜎 is the liquid–vapor surface tension,\n(cid:3039)(cid:3049)\nΔ𝑇 is the temperature difference between the droplet apex and the contact line, and 𝛼 is\nthe thermal diffusivity of the liquid (definitions shown schematically in Fig.3a).\nFig. 3. a, Schematic of the competing flows in an evaporating droplet on a heated substrate:\ncapillary flow (𝐿𝑎), solutal Marangoni flow (𝑀𝑎 ), and thermal Marangoni flow (𝑀𝑎 ).\n(cid:3004) (cid:3021)\nWhile capillary flow and thermal Marangoni flow both enhance outward nanoparticle\ntransport and thus amplify the coffee-ring effect, the solutal Marangoni flow provides an\ninward counter-transport that counteracts ring formation. In other words, when 𝑀𝑎 ≈\n(cid:3004)\n𝐿𝑎+𝑀𝑎 (𝑀𝑎 /(𝐿𝑎+𝑀𝑎 )≈1) the three flows reach a balance and the coffee-ring\n(cid:3021) (cid:3004) (cid:3021)\neffect can be effectively suppressed.\nFig. 3. b, Theoretical prediction of the uniform-deposition window based on flow-strength\nanalysis; uniformity is expected when the balance index 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nWe calculated the flow balance index 𝑀𝑎 /(𝐿𝑎+𝑀𝑎 ) in the temperature range 60℃≤𝑇 ≤\n(cid:3004) (cid:3021)\n200℃ , as shown in the added Fig. 3b (see Table S1 in the supplementary information for\ncalculation details). Within the possible uniform-circuit temperature range (120 °C ≤ T ≤ 220 °C),\nwhere 𝑀𝑎 /(𝐿𝑎+𝑀𝑎 ) approaches 1, ITO unit circuits were printed on Si substrates (Fig. 3c).\n(cid:3004) (cid:3021)\nThe results show that uniform unit circuits are observed at T = 160 °C and T = 180 °C, which\nfalls within the theoretically predicted uniform-deposition temperature window of 150 °C ≤ T ≤\n190 °C, corresponding to 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition (scale bar: 100 μm).\nWe have added an entire Section 2.3 “Fabrication of coffee-ring–suppressed unit circuits in\ninkjet printing” in the revised manuscript (pages 7–10, lines 119–166) to elucidate the above\nmechanism, and corresponding figures and discussion have also been included in the supplementary\ninformation (pages S10–S11).\nComment:\n2. Non-Rectangular Cross-Section Assumption: The mathematical optimization and performance\nanalysis appear to assume an ideal rectangular cross-section for the printed conductive traces. This\nassumption is frequently inconsistent with the reality of inkjet-printed lines, which typically exhibit\nrounded, bulging, or coffee-ring effect profiles. The discrepancy between the model's assumed\ngeometry and the actual printed morphology could substantially affect the accuracy of the predicted\nconductance, laser absorption/heat distribution, and ultimately, the sintering outcome and final\nproperties. The manuscript should acknowledge this limitation and discuss its potential implications\nor validate the model against realistic cross-sectional profiles.\nReply: Thank you for pointing out the potential discrepancy between the rectangular cross-section\nassumption in the model and the actual printed line morphology; this is an important clarification\nthat improves the rigor of the manuscript.\nIn the Reply to Comment 1, we elaborated on how the “binary-solvent + external thermal field”\nstrategy balances the combined effects of solutal Marangoni flow, thermal Marangoni flow, and\ncapillary flow, thereby eliminating the coffee-ring effect. Based on this strategy, nearly coffee-ring–\nfree unit circuits were fabricated by inkjet printing at a substrate temperature of T = 160 °C (Fig.\n3c). To verify the validity of the rectangular assumption raised by the reviewer, the printed line\nprofiles were measured using a confocal microscope (DSX-1000, Olympus, Japan), as shown in Fig.\n3d. The results demonstrate that, regardless of whether the substrate is glass, silicon, or superalloy,\nthe cross-section of the printed ITO circuits can be regarded as nearly ideal rectangles, with a\n(cid:2870)(cid:2868)(cid:2868)\ndeviation of η ≤ 3.7%, where 𝜂 =(cid:1516) |𝑧 (𝑥)−𝑧 (𝑥)|𝑑𝑥/𝑆 (𝑧 (𝑥) and 𝑧 (𝑥) denote the\n(cid:2868) (cid:2869) (cid:2870) (cid:3045)(cid:3032)(cid:3030) (cid:2869) (cid:2870)\nmeasured and ideal rectangular profile heights at position x, respectively, and 𝑆 is the area of\n(cid:3045)(cid:3032)(cid:3030)\nthe reference rectangle).\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition.\nFig. 3. d, Uniform unit circuits on different substrates (glass, silicon, superalloy) showing\nquasi-rectangular cross-sections (deviation η≤3.7 %).\nThe corresponding content has also been added to the revised manuscript (pages 9-10, lines 150-\n166).\nComment:\n3. High-Frequency Signal Integrity Concern: While the demonstrated DC/low-frequency\nconductance improvement is impressive, the proposed \"stair-step\" thickness profile (inherent to the\nlayer-by-layer inkjet approach) raises concerns for high-frequency circuit applications. Such non-\nuniform, stepped cross-sections can introduce significant impedance discontinuities, signal\nreflections, and increased transmission losses at microwave/RF frequencies. If the technology\ntargets high-performance conformal circuits broadly, the authors should explicitly discuss this\nlimitation for high-frequency operation or provide data/analysis demonstrating acceptable RF\nperformance.\nReply: Thank you for highlighting the importance of high-frequency signal integrity, which is\nindeed a critical consideration for the broader applicability of conformal circuits.\nWe acknowledge that dedicated RF measurements (e.g., S-parameters and TDR analysis) have not\nyet been performed. These experiments are planned as part of our future work to quantitatively\nvalidate impedance continuity and transmission performance in the GHz range. The current\nlimitations and prospects for GHz-frequency applications have also been explicitly noted in the\nrevised manuscript (page 19, lines 352-356).\n“Limitations and outlook. In terms of high-frequency signal integrity, while this study focused\non direct current and low-frequency performance, future work will extend to GHz-frequency\ncharacterization in order to validate that the improved conductivity uniformity can be translated into\nstable RF signal integrity, which is essential for industrial applications.”\nThat said, we would like to clarify that the circuits formed in this work are not step-like structures.\nAlthough the fabrication process involves layer-by-layer stacking, the combined effects of interlayer\nmaterial flow during deposition and local nanoparticle melting during laser sintering yield a smooth\nand continuous profile (as confirmed by confocal and profilometer measurements in Fig. S5). This\nmorphology avoids the sharp impedance discontinuities typically associated with stepped\ngeometries. Moreover, because high-frequency performance is strongly affected by local\nconductivity variations, the curved strategy helps avoid non-uniform sintering and the resulting local\nresistance fluctuations, which is expected to be beneficial for RF signal integrity [13*]. While\nfurther RF measurements are needed, these features suggest that the curved circuits may minimize\nadditional signal losses at high frequencies.\nFig. S5. Cross-sectional SEM images of profiles I-VIII.\nComment:\n4. Justification for Laser Sintering vs. Thermal: The manuscript positions the laser intensity\nmodulation approach as a solution to problems inherent in laser sintering. However, it does not\nadequately justify why laser sintering is essential for this application compared to conventional\nthermal sintering processes. Thermal sintering (oven, belt furnace, localized heating) often offers\nsuperior process efficiency, potentially higher final conductivity, and avoids the specific\ncomplexities of laser beam shaping and Gaussian distribution issues altogether. The authors should\nstrengthen the rationale for choosing laser sintering specifically. A direct comparison of the\nperformance (conductivity, transmittance, speed, energy efficiency) and potential limitations (e.g.,\nsubstrate thermal stability) of circuits fabricated using their laser-sintered, thickness-optimized\napproach versus thermally sintered circuits (with or without thickness optimization) would be highly\nvaluable.\nReply: Thank you for the insightful comment.\nFollowing your suggestion, we supplemented comparative experiments on different substrates, as\npresented in Fig. 6h, where both curved Cu circuits and planar circuits were fabricated by laser\nsintering and benchmarked against thermal sintering.\nThe results show that on high-melting-point substrates (e.g., Al O ), laser sintering achieved\n2 3\nsuperior electrical performance owing to its short processing time, which effectively reduced\noxidation compared with thermal sintering. On low-melting-point substrates (e.g., PI films),\nconventional thermal sintering is infeasible due to severe substrate damage, whereas laser sintering\nenabled the fabrication of high-conductivity circuits without deformation.\nThese findings highlight the intrinsic advantages of laser sintering: ultrafast localized heating\nminimizes the heat-affected zone, suppresses oxidation, and protects sensitive substrates. Building\non this, our proposed curved circuit strategy further enhances performance by mitigating the non-\nuniform sintering issue inherent to conventional laser processing. As shown in Fig. 6h, curved-\nbased laser sintering retains the low-oxidation and high-performance benefits of laser processing,\nwhile improving conductivity uniformity and broadening the tolerance to both circuit and substrate\nmaterials. Importantly, its performance is slightly superior even to thermal sintering, underscoring\nthe incremental contribution of this work.\nFig. 6 h, Benchmarking against thermal sintering on Al O and polyimide substrates shows that\n2 3\nlaser processing avoids oxidation on high-melting substrates and prevents thermal damage on\nlow-melting substrates, highlighting the broad adaptability of the curved circuit strategy.\nThe relevant content has been added to the revised manuscript (pages 17-18, lines 307-312). And\nthe thermal sintering equipment and procedure have also been added to the “Methods” section (page\n22, lines 422-425).\n“Finally, Fig.6h benchmarks laser sintering against traditional thermal sintering on different\nsubstrates. For high-melting substrates such as Al O , the short sintering time of laser processing\n2 3\nminimizes oxidation and leads to better electrical performance. For low-melting substrates such as\npolyimide, the localized heating nature of the laser prevents thermal damage to the substrate (as\nshown in Fig. 6h, PI films can only withstand sintering up to 200 °C), further underscoring the\nbroad applicability and superiority of the laser approach.”\n“Thermal sintering experiments were conducted using a tube furnace (BTF-1400C, BEQ, China) to\nevaluate the electrical performance of thermal sintered circuits. The sintering process was carried\nout with a heating rate of 10 °C/min, followed by an isothermal hold at the target temperature for\n30 min, and natural cooling to below 75 °C.”\nReferences.\n[1*]. Yu, L. et al. Galvanometer driven optical system for laser dynamic focusing. Optics Express 31,\n673–685 (2023).\n[2*]. Bremer, S. J. L., Aarts, R. G. K. M. & Römer, G.-W. R. Mathematical analysis of dynamic high\npower laser beam shaping using Galvanometer Scanners or Deformable Mirrors. Optics & Laser\nTechnology (2025).\n[3*]. Gupta, S.et al. Ultra-thin chips for high-performance flexible electronics. npj Flexible Electronics\n2, 8 (2018).\n[4*]. Shao, Y. et al. A universal packaging substrate for mechanically stable module integration in\nstretchable bioelectronics. Nat. Commun. 15, 6106 (2024).\n[5*]. Bo, R. et al. Mechanically-guided 3D assembly for architected flexible electronics. ACS Applied\nMaterials & Interfaces 15, 47879–47910 (2023).\n[6*]. Zhang, M., Chen, J., Zhu, J., Tao, Z. & Qiu, L. Hybrid manipulation of inkjet-printing deposition\npattern of high particle concentration droplet by means of thermal and binary solvent effects.\nInternational Journal of Heat and Mass Transfer 223 (2024).\n[7*]. M. Parsa, R. Boubaker, S. Harmand, K. Sefiane, M. Bigerelle, R. Deltombe, Patterns from dried\nwater-butanol binary-based nanofluid drops, Journal of Nanoparticle Research, 19 (8) (2017) 251.\n[8*]. D. Zang, S. Tarafdar, Y.Y. Tarasevich, M. Dutta Choudhury, T. Dutta, Evaporation of a Droplet:\nFrom Physics to Applications, Physics Reports, 804 (2019) 1–56.\n[9*]. Paschotta, R. RP Photonics Encyclopedia: Gaussian beams (RP Photonics Consulting GmbH,\n(2025); https://www.rp-photonics.com/gaussian_beams.html\n[10*]. Pampaloni, F. & Enderlein, J. Gaussian, Hermite–Gaussian, and Laguerre–Gaussian beams: A\nprimer. J. Opt. A: Pure Appl. Opt. 6, S283–S291 (2004).\n[11*]. Lee, J.‐Y., Connor, S. T., Cui, Y. & Peumans, P. Solution‐processed metal nanowire mesh\ntransparent electrodes. Nat. Nanotechnol. 3, 238–242 (2008).\n[12*].Liang, L. et al. Intrinsically stretchable and transparent thin-film transistors based on printable\nsilver nanowires, carbon nanotubes and an elastomeric dielectric. Nat. Commun. 6, 7647 (2015).\n[13*]. Y. Zhou, et al., The Effect of Scratch-Induced Microscale Surface Roughness on Signal\nTransmission in Radio Frequency Coaxial Connectors, Micromachines, 16 (8) (2025) 837."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Authors have addressed those issues raised in the previous review.", "reviewer_2": "The authors have provided a revised version and sufficient data and analysis to address my concerns such as the coffee-ring effect. I have no more questions and recommend it for publishing.", "reviewer_5": "Response to Reviewer 1\nThe authors reported a concept of uniformly laser sintering nanoparticle thin film with curved\nstructure in thickness. The varying thickness of the inkjet-printed nanoparticle thin film to be\nsintered is used to adapt the Gaussian distribution of laser intensity, thus making the heating and\nsintering of the nanoparticle thin film more uniform. The center of the deposited nanoparticle thin\nfilm is thicker than that on the edges since the laser intensity at the center is higher than that on the\nsides. The claimed advantage of this proposed method compared to the conventional approaches\nfor reaching uniform laser sintering includes reducing the complexity of the laser optics, as well as\nthe cost of the system. Review comments are as follows:\nComment:\n1. Although the temperature uniformity of the curved nanoparticle thin film is improved during\nGaussian laser scanning, owing to the nature of heat transfer, the real-application feasibility of this\napproach of forming laser-sintered nano/micro structures for circuity remains unclear. For instance,\nthe curvature, shape, width, and thickness of the inkjet printed thin film, which is optimized\naccordingly, are restricted by the laser intensity distribution at the same time. This limitation greatly\naffects the flexibility of circuitry design, which is in contradiction to the common idea that\nmanufacturing technology shall support the design and function of the designated products.\nReply: Thank you for your insightful comment.\nIt is true that the underlying logic of our approach is to match the circuit dimensions (including\nwidth and thickness) to the laser beam distribution (diameter and intensity profile). Under the\npresent conditions, once the laser parameters are fixed, the optimal circuit cross-section is\ndetermined.\nTo achieve the higher degree of design freedom envisioned by the reviewer—where circuit\ngeometries could be arbitrarily tailored—the design logic could be reversed: the laser profile itself\nmight be dynamically modulated to match custom curved circuit shapes, which is technically\nfeasible. Specifically, Yu et al. demonstrated a galvanometer-based dynamic focusing system\ncapable of rapid, precise 3-axis laser focus positioning (response time ~600 μs), enabling real-time\nprofile adjustment [1*]. Similarly, Bremer et al. developed a mathematical framework comparing\ngalvanometer scanners and deformable mirrors for dynamic beam shaping of high-power lasers [2*].\nSuch a new direction would still benefit from the performance advantages of curved circuits over\nplanar ones, as demonstrated in this study, and thus represents a scientifically and technologically\nvaluable avenue of research. We sincerely thank the reviewer for inspiring us in this new direction,\nand we will upgrade our experimental setup to initiate research on high-performance, customizable\ncurved circuits enabled by controllable laser sintering.\nThe above discussion has also been added to the revised manuscript (page 19, lines 337-342).\n“Limitations and outlook. Despite these advances, the curved-circuit strategy still faces several\nchallenges for industrial deployment. In terms of profile-design freedom of circuits, it will be\nnecessary to introduce digitally programmable control of laser spot size and intensity so that the\nbeam profile can be adapted to target geometries of curved circuits [48], thereby overcoming the\nconstraints of the laser on the profile of curved circuits.”\nComment:\n2. In addition, the trend of circuitry and electronic devices is 3D stacking and packaging. For this\npurpose, circuitry patterns with uniform and controllable thickness are preferable to curved\ncircuitry. Therefore, curved circuit patterns made by the proposed method in this study may raise\nsignificant concerns in this regard.\nReply: Thank you for your attention to and insights on the trend of 3D stacking and packaging. We\nagree that 3D stacking and packaging is a crucial development direction for electronic devices, and\nthis scenario indeed requires strict control of circuit thickness uniformity [3*].\nHowever, it is important to emphasize that the “curved circuit” proposed in this study is essentially\na performance enhancement method, rather than treating “curvature” as the final geometry. Based\non established techniques, the temporary curvature of the circuits introduced during sintering is\nexpected to be removable in subsequent processing. For instance, in practical 3D packaging, low-\ntemperature calendaring or ultra-thin coating methods could planarize the curved circuits into\nfunctional layers with uniform thickness, with tolerances potentially controllable to within ±1 μm\n[4*, 5*]. Therefore, our current view is to realize planarization through packaging or other\nsubsequent processes, which we consider an important direction for future research. Nevertheless,\nthe present work primarily introduces and demonstrates the curved-circuit strategy, highlighting its\nability to significantly enhance circuit performance as the central innovation.\nThe relevant discussions have been supplemented in the revised manuscript (see page 19, lines 342-\n347).\n“In terms of packaging and 3D stacking, compatibility can be realized through post-sintering\nplanarization, in which the temporary curvature formed during sintering is eliminated and the\ncircuits are transformed into uniform-thickness functional layers with tolerances controllable to\nbelow 1 μm by employing advanced low-temperature calendaring or ultra-thin coating methods\n[49].”\nComment:\n3. The current manuscript also contains some flaws in writing. For instance:\n It is unclear why several axial distances of the laser beam after the focusing lens were used in\nthis study while measuring the laser intensity distributions. Specifically, on page 4, line 50, the\nrange of z is 125~155 mm. On the same page, line 71, the range of z is 130 to 145 mm.\n Esy in Equation (2) is apparently different from that shown in Figure 2(e).\n In Figure 5(c), those symbols are not shown in the legend correspondingly.\nReply: Thank you for carefully pointing out the omissions in the manuscript’s writing and detail\nlabeling; these comments are highly helpful for improving the manuscript’s rigor.\n(1) Missing statement on the axial distance z: In practice, z is adjusted to control the laser spot\nsize for different sintering requirements (page 3, lines 45 and 46).\n“Based on this feature, researchers modulate the beam diameter (D) by controlling the lens-to-\nobject distance (z).”\nDue to our oversight, the pre-revised manuscript contained inconsistent descriptions of the z-\nrange (125–155 mm and 130–145 mm). This has now been unified to “125–155 mm”\nthroughout the revised manuscript (page 4, line 70).\n“…within the beam diameter range of 320 μm≤ D ≤ 1500 μm (125 mm ≤ z ≤ 155 mm)”\n(2) Incorrect symbol “Esy” in Equation (2): The Esy has been corrected to E(y) in the revised\nmanuscript to ensure full consistency (page 5).\n∞ 𝑦(cid:2870) 𝜋𝐷(cid:2870) (cid:2868).(cid:2873)\n𝐸 (cid:4666)𝑦(cid:4667)=(cid:3505) 𝐼(cid:4666)𝑥,𝑦(cid:4667)𝑑𝑥 =𝐼 ⋅exp(cid:4678)−8 (cid:4679)⋅(cid:4678) (cid:4679) (cid:4666)2(cid:4667)\ns 0 𝐷(cid:2870) 8\n(cid:2879)∞\n(3) Incomplete legend in Figure 6c (the Figure 5c in the original version): The legend has been\nsupplemented in the revised manuscript to ensure clarity and self-explanatory presentation\n(page 16).\nFig. 6c, Transmittance–resistance mapping highlights the simultaneous enhancement of\nconductivity and transmittance achieved by the curved circuit strategy, in contrast to\nliterature-reported trade-offs [43-45].\nWe sincerely thank the reviewer again for identifying these issues, which has allowed us to further\nimprove the clarity and quality of the manuscript.\nComment:\n4. Overall, this concept, using curved thin film deposited by inkjet printing to adapt a Gaussian\nlaser beam intensity in order to reach a uniform temperature of the thin film to enable uniform\nsintering quality, is interesting. The mathematics and approaches are quite straightforward. The\nmain concern is the feasibility of applying this proposed manufacturing technology to the real\nproducts of circuitry.\nReply: Thank you for acknowledging the innovativeness of our concept and our methods—this\nrecognition is a strong encouragement for us.\nAbout the concern of its real-world feasibility, we emphasize that the practicality of the proposed\nstrategy is supported on three levels:\n1. Equipment compatibility: This strategy uses standard inkjet and laser tools, requiring no\nstringent environmental control (unlike PVD/CVD), thus enabling low-cost, large-area scalable\nfabrication.\n2. Process adaptability: post-sintering encapsulation can planarize the circuits to a uniform\nthickness with a tolerance within ±1 μm [4*, 5*], thereby eliminating potential drawbacks of\ncurved profiles for 3D stacking.\n3. Performance improvement: for typical application scenarios (conformal circuits and\nconductive glass), curved circuits enhance electrical and optical performance (Fig. 6c, g and h),\nachieving the current state-of-the-art level of laser sintering.\nLooking ahead. To translate this laboratory demonstration toward application-oriented processes,\nwe plan to:\n1. Expand profile-design freedom by introducing digitally programmable control of laser spot size\nand intensity to adapt beam profiles to curved geometries.\n2. Ensure compatibility with packaging and 3D stacking via post-sintering planarization,\ntransforming curved profiles into uniform functional layers with sub-micrometer tolerances.\n3. Scale throughput from laboratory (about 10 mm/s) to industrial levels (m/s) by stabilizing high-\nfrequency droplet ejection, suppressing coffee-ring flows at shortened drying times, and\nintegrating in-situ optical/thermal feedback.\n4. Extend performance validation to GHz-frequency regimes to confirm that conductivity\nuniformity translates into stable RF signal integrity for device applications.\nWe believe these directions will further bridge the gap between proof-of-concept and industrial\napplication. In the revised manuscript, we have also added a “Limitations and Outlook” section in\nthe Discussion (page 19, lines 337-356), where we concisely summarize above four challenges of\nimplementing curved circuits in practical manufacturing, highlighting them as important directions\nfor our future research.\nResponse to Reviewer 2\nThis manuscript introduces a method to address the uneven sintering caused by Gaussian laser\nbeams by matching film thickness to the laser's intensity profile. Traditional beam-shaping\ntechniques are costly and inefficient, while the proposed approach uses inkjet printing to fabricate\ncurved circuits with optimized thickness distribution. A mathematical model calculates the ideal\ndeposition profile, and a Tetris-like printing strategy precisely controls circuit geometry.\nExperiments confirm uniform sintering without ablation or porosity, significantly improving\nperformance. Demonstrative ITO conductive glass achieved a 3.8-fold increase in conductance and\n5.1% higher transmittance compared to planar circuits. This adaptive deposition method offers a\nsimple, cost-effective solution for high-performance conformal electronics and additive\nmanufacturing. After careful reading of this manuscript, I recommend its publication if the following\nissues are properly addressed.\nComment:\n1. It is necessary to clarify what materials are being printed and laser-sintered in Figures 3 and 4.\nReply: Thanks for the reviewer’s suggestion. The materials in Figures 4 and 5 (Figures 3 and 4 in\nthe original version) are indium tin oxide (ITO), and we have clearly specified this in the revised\nmanuscript text (page 12, lines 202 and 205) and the captions for Figures 4 and 5.\n“ … scanning electron microscope (SEM) cross-sectional image of the ITO unit circuit (Fig. S4).”\n“Measurements indicate that the thickness of a single uniform ITO unit circuit is … ”\n“Fig. 4 d, Printing temperature T regulates w and h of the ITO unit circuit.”\n0 0\n“Fig. 5 Comparison of sintering homogeneity between planar and profile-optimized curved ITO\ncircuits.”\nComment:\n2. Inkjet printing usually exhibits a severe coffee-ring effect, resulting in a film morphology opposite\nto that of the manuscript. How did the author overcome the coffee-ring effect?\nReply: Thank you for your comment. It is true that the coffee-ring effect is common in inkjet\nprinting, as you mentioned. To suppress this effect, our research group has proposed a “binary\nsolvent + external temperature field” strategy, in which the concentration-driven Marangoni flow\ncounterbalances the combined effects of the temperature-driven Marangoni flow and capillary flow,\nthereby suppressing the coffee-ring effect and enabling the deposition of uniform films (for details,\nsee the analysis below or Reference [6*]).\nSuppression of the Coffee-Ring Effect via Binary Solvent\n(Ethylene Glycol + Isopropyl Alcohol) and Thermal Field (Heated Substrates)\nIt is well recognized that during the evaporation of nano-inks, nanoparticles are transported\ntoward the three-phase contact line due to capillary flow and thermal Marangoni flow,\ngiving rise to the coffee-ring effect. To suppress this effect, we employed a binary solvent\nink (EG:IPA = 1:1 by volume) and controlled the evaporation temperature. As the\ntemperature increases and sequentially reaches the boiling points of EG and IPA, the\nrelative strengths of different internal flows—capillary flow, solutal Marangoni flow, and\nthermal Marangoni flow—can be significantly regulated, thereby enabling effective\ncontrol of the deposition morphology and suppression of the coffee-ring effect.\nThe added Fig. 3a illustrates the mechanisms of capillary flow, solutal Marangoni flow,\nand thermal Marangoni flow in a partially evaporated circuit. As shown, capillary and\nthermal Marangoni flows drive nanoparticles outward toward the contact line (enhancing\nthe coffee-ring effect), while the solutal Marangoni flow transports nanoparticles inward\n(suppressing the effect). Thus, balancing these competing flows is critical for uniform\ncircuit deposition. According to flow theory [6*], the strengths of solutal Marangoni flow\n(𝑀𝑎 ), thermal Marangoni flow (𝑀𝑎 ), and capillary flow (𝐿𝑎) can be expressed as [7*,\n(cid:3004) (cid:3021)\n8*]:\n𝑙 𝑑𝜎/𝑑𝐶 𝜌 𝑙 𝜎 𝑙 𝑑𝜎/𝑑𝑇\n(cid:3039)(cid:3049)\n𝑀𝑎 = Δ𝐶, 𝐿𝑎 = , 𝑀𝑎 = Δ𝑇\n(cid:3004) 2𝜇𝐷 𝜇(cid:2870) (cid:3021) 2𝜇𝛼\n(cid:3033)\nwhere 𝑙 is the circuit width (see added Fig. 3b), Δ𝐶 is the concentration difference\nbetween the droplet apex and the contact line, 𝑑𝜎/𝑑𝐶 and 𝑑𝜎/𝑑𝑇 is the variation of\nsurface tension with concentration and temperature, 𝜇 is the viscosity, and 𝐷 is the\n(cid:3033)\ndiffusion coefficient of IPA in EG. In addition, 𝜌 is the droplet density, 𝜎 is the liquid–\n(cid:3039)(cid:3049)\nvapor surface tension, Δ𝑇 is the temperature difference between the droplet apex and the\ncontact line, and 𝛼 is the thermal diffusivity of the liquid (definitions shown\nschematically in Fig.3a).\nFig. 3. a, Schematic of the competing flows in an evaporating droplet on a heated substrate:\ncapillary flow (𝐿𝑎), solutal Marangoni flow (𝑀𝑎 ), and thermal Marangoni flow (𝑀𝑎 ).\n(cid:3004) (cid:3021)\nWhen 𝑀𝑎 ≈𝐿𝑎+𝑀𝑎 (𝑀𝑎 /(𝐿𝑎+𝑀𝑎 )≈1) the three flows reach a balance and\n(cid:3004) (cid:3021) (cid:3004) (cid:3021)\nthe coffee-ring effect can be effectively suppressed. Our experiments confirmed this\nprediction: as shown in added Figs. 3b, c, uniform unit circuits can be observed at 𝑇 =\n160℃ and 𝑇 =180℃ (Fig. 3c), which falls within the theoretically predicted uniform-\ndeposition temperature range of 150℃≤𝑇 ≤190℃ , corresponding to 0.5≤𝑀𝑎 /\n(cid:3004)\n(𝐿𝑎+𝑀𝑎 )≤2.\n(cid:3021)\nFig. 3. b, Theoretical prediction of the uniform-deposition window based on flow-strength\nanalysis (see Table S1 for details); uniformity is expected when 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition (scale bar: 100 μm).\nIn the revised manuscript, we have added an entire Section 2.3, “Fabrication of coffee-ring–\nsuppressed unit circuits in inkjet printing” to present the mechanism and experimental results of\nuniform unit circuit deposition (pages 7-10, lines 119-166).\nComment:\n3. While ITO demonstrates success, would this approach work equally well for other functional\nmaterials (e.g., metals, semiconductors) with different thermal/optical properties? The\nmathematical model (Eq. 3-5) links deposition thickness to laser energy distribution, but how was\nits accuracy experimentally validated beyond the single case of ITO? Were alternative materials or\nlaser parameters tested to confirm generalizability?\nReply: Thank you for your valuable suggestion.\nIn addition to the ITO case, we have added experiments on a new material, copper (Cu), where\ncircuits with the model-predicted optimal curved profile were fabricated to confirm the generality\nof the mathematical model (Eqs. 3–5). As shown in the revised Fig. 6f, the Cu optimized curved\ncircuits achieved the best sintering performance when their cross-sectional morphology matched the\nprediction, confirming the model’s accuracy under a metallic system with very different thermal and\noptical properties from ITO. Furthermore, we also fabricated large-area conformal circuit samples\n(Fig. S8 in supplementary information), which exhibited an average conductivity as high as 1.3×\n105 S·cm-1, further demonstrating the scalability and robustness of the proposed strategy.\nFig. 6f, Experimental validation for Cu confirms that the predicted optimal profile corresponds\nto the best sintering performance.\nIn addition, the model has been extended to other representative materials (Ag, SrTiO ), and the\n3\ncalculated optimal curved profiles (Fig. 6e) highlight material-dependent variations in peak height\nand width (1/e2), supporting the theoretical applicability of the strategy to a broad range of functional\nmaterials.\nFig. 6e, Theoretically predicted optimal curved profiles for Ag, Cu, ITO, and SrTiO under the\n3\nsame Gaussian beam, showing material-dependent differences in peak height and width (1/e2).\nFig. S8. Large-area conformal circuit validation. Left: Photograph of a fabricated large-size\ncurved circuit sample. Right: Electrical resistance measurement of the sample using a digital\nmultimeter, showing high conductivity (1.3×105 S·cm-1).\nThe relevant discussions have been added to the revised manuscript (pages 17-18, lines 289-305)\nand the revised supplementary information (page S9). The preparation of Cu nano-ink can be found\nin page 20, lines 375-379.\nComment:\n4. The Tetris-like stacking method requires precise alignment. What is the measured registration\naccuracy between layers.\nReply: Thank you for your comment. As you noted, stacking accuracy has a significant impact on\nthe morphology of the curved circuit. The interlayer stacking (registration) accuracy is determined\nby the repeat positioning accuracy of the printer’s X-Y motion stage; for the MicroFab Jet-Lab 4xl\nused in this work, the specified repeatability is ±5 μm (relatively small for the 100 μm-wide unit\ncircuit).\nWe have also added this information in the revised manuscript (page 20, lines 381-384).\n“The ITO and Cu nanoinks were deposited on flat SiO glass, Al O ceramic, PI film, single-crystal\n2 2 3\nsilicon, and superalloy substrates in the form of droplets (diameter = 20 μm) using an inkjet printer\nwith repeatability of ±5 μm (Jetlab 4xl, MicroFab, America).”\nComment:\n5. The method appears optimized for small-scale lab demonstrations. What technical barriers exist\nfor scaling to industrial production speeds (e.g., m/s printing rates)?\nReply: Thank you for your comment. We agree that the present work has been demonstrated only\nin a small-scale laboratory environment, with an inkjet printing speed of approximately 10 mm/s.\nScaling up to industrial production speeds on the order of meters per second would indeed raise\nseveral technical barriers.\n1. Droplet stability: at high firing frequencies, the stability of droplet ejection and placement may\ndeteriorate, compromising line continuity and registration accuracy.\n2. Fluid dynamics: rapid solvent evaporation during high-speed printing can alter the balance of\nMarangoni and capillary flows, thereby reducing the effectiveness of coffee-ring suppression.\n3. System reliability: at such high throughput, nozzle clogging, synchronization of multi-nozzle\narrays, and substrate thermal management become increasingly critical.\nThese challenges underscore important directions for future development, and we have begun\nexploratory efforts toward industrial-scale implementation to address the above issues, and we also\nhave noted this limitation in the revised manuscript (page 19, lines 347-352).\n“Limitations and outlook. In terms of processing speed, our current demonstrations are limited\nto laboratory-scale printing speeds (~10 mm/s), and achieving m/s-level throughputs may require\naddressing droplet stability at high actuation rates, maintaining suppression of coffee-ring flows\nunder shortened drying times, and incorporating in situ thermal/optical feedback for closed-loop\ncontrol of the sintering window.\nComment:\n6. The SEM images show an improvement in uniformity, but were XRD or TEM analyses conducted\nto quantify the differences in material crystallization between the planar and curved approaches?\nReply: Thank you for your valuable suggestion. To further substantiate the SEM observations, we\nhave added XRD characterization of the laser-sintered planar and curved ITO circuits (Fig. 5c).\nThe results reveal that the planar circuit exhibits broader and less symmetric diffraction peaks,\nindicative of a wider grain size distribution and microstructural non-uniformity. In contrast, the\ncurved circuit shows sharper and narrower peaks, which correspond to more homogeneous grain\ngrowth and higher crystallinity. These findings are consistent with the SEM results and confirm that\nthe curved deposition strategy promotes improved microstructural uniformity.\nFig. 5c, XRD patterns of laser-sintered planar and curved ITO circuits. Compared with the\nplanar circuit, the curved circuit exhibits sharper and narrower diffraction peaks, indicating\nmore homogeneous grain growth and higher crystallinity.\nThe relevant content has been added to the revised manuscript (page 14, lines 240-243).\n“Moreover, the X-ray diffraction (XRD) patterns in Fig. 5c further support these findings: compared\nwith the planar circuit, the curved circuit exhibits sharper and narrower diffraction peaks, indicating\na narrower grain size distribution and higher crystallinity [40].”\nThe XRD testing equipment and procedure have also been added to the “Methods” section (page\n21, lines 406-400).\n“The X-ray diffraction (XRD) analysis was performed using a diffractometer (Bruker D8 Advance,\nGermany) equipped with a Cu target (wavelength = 1.5406 Å), operating at a tube current of 40 mA\nand a tube voltage of 40 kV. The measurements were conducted in a step-scan mode with a step\nsize of 0.02° and a scan rate of 4°/min.”\nComment:\n7. Are there accelerated aging tests showing how conductivity and transmittance evolve over time\nunder operational conditions (mechanical flexing, thermal cycling, etc.)?\nReply: Thank you for your comment. We have added accelerated aging tests under thermal cycling\nfor both laser-sintered planar and curved ITO circuits, as shown in the Supplementary Information\n(Fig. S7).\nThe results indicate that the resistance of the planar circuit increases significantly with cycling,\nreaching about 35% higher than its initial value after 50 cycles. In contrast, the curved circuit shows\nonly a minor resistance change (<10%) over the same process, demonstrating much better stability\nagainst thermal fatigue (Fig. S7a). These results confirm that the curved configuration enhances\ndurability and reliability under repeated thermal stress. For completeness, the thermal cycles were\napplied by heating the glass substrate to 150 °C using a thin-film heater and then cooling it back to\nroom temperature by air convection (Fig. S7b).\nFig. S7. Thermal cycling stability of laser-sintered ITO circuits. a, Normalized resistance\n(R/R ) of planar and curved circuits during 50 thermal cycles, showing much higher stability for\n0\nthe curved circuit (<10% increase) compared to the planar circuit (35% increase). b, Temperature\nprofile of a typical thermal cycle, including heating to 150 °C, a short plateau, and cooling to\nroom temperature by natural air convection.\nThe relevant content and test process have been added to the revised manuscript (page 15, lines 265-\n267; page 21, lines 410-415).\n“In addition, the laser-sintered curved circuits exhibited superior stability in the accelerated thermal\ncycling test, with resistance increasing by less than 10% after 50 cycles, compared to 35% for the\nplanar circuits (see Fig. S7).”\n“The thermal cycle was applied by heating the glass substrate with a thin-film heater (LP-24,\nDongtai, China), while the temperature was monitored using a K-type thermocouple. As illustrated\nin Fig. S7, each cycle consisted of a rapid heating stage (room temperature to 150 °C), a short\nisothermal plateau at 150 °C, and a subsequent cooling stage back to near room temperature by air\nconvection.”\nComment:\n8. What level of environmental control (temperature, humidity, surface tension or surface energy)\nis required to maintain the demonstrated performance consistency?\nReply: Thank you for your question. The demonstrated performance was obtained under standard\nlaboratory conditions, without the need for an exceptionally stringent environment. In our\nexperiments, the substrate temperature was controlled at 140–180 °C to promote solvent\nevaporation and uniform deposition, while the ambient relative humidity was maintained at 30–80%,\nwhich is a typical range for inkjet printing. The surface tension of the ITO ink was 35–45 mN/m\nand the surface energy of the cleaned substrate was 25–45 mN/m, both of which fall within common\nranges for stable jetting and wetting. Within these conditions, the deposition was highly reproducible\nand the performance consistency was well maintained. These physical parameters are not extreme\nand can be readily achieved under standard laboratory conditions.\nThe relevant details have been added to the revised manuscript (page 20, lines 373-374; pages 20-\n21, lines 387-392).\n“The physical parameters of the ITO ink were maintained within common ranges for stable printing,\nwith a surface tension of 35-45 mN/m.”\n“To accelerate solvent evaporation and enhance deposition uniformity, the substrate temperature\nwas increased to 140–180 °C during inkjet printing, where a proportional-integral-derivative\ncontroller was employed to maintain the temperature. During printing, the ambient relative humidity\nwas maintained between 30% and 80%, and the surface energy of the cleaned substrates was\ncontrolled at 25–45 mN/m.”\nResponse to Reviewer 3\nThe revised manuscript is suggested for conditional acceptance with major revision.\nThe authors put forward an approach to match the film thickness to laser intensity distribution. For\nthe given laser intensity, the optimal thickness distribution was determined. Furthermore, an inkjet\nprinting method was developed to fabricate the optimally determined curved circuits. Nevertheless,\nthere are the following points needing further revision.\nComment:\n1. Please double check the spelling of “laser been shaping” in line 14 of page 2.\nReply: Thanks for the reviewer. We apologize for the spelling error of \"laser beam\". We have\ncorrected this error (page 2, line 14) and checked the entire manuscript to avoid any spelling issues.\n“However, laser beam shaping methods suffer from higher energy loss …”\nComment:\n2. Please elucidate the physical meaning of the coefficient “8” seen in Eq. (1)? Since D is defined\nas the beam diameter, where the laser intensity drops to 1/e^2 of I0.\nReply: Thank you for the reviewer’s insightful question. The coefficient “8” originates from the\ndefinition of the Gaussian beam diameter 𝐷 as the 1/e² diameter, rather than the more common 1/e²\nradius. In the standard form, the transverse Gaussian intensity profile is expressed as [9*, 10*],\nand\n𝑤 is the 1/e2 radius.\n𝑟(cid:2870)\n𝐼(𝑟)=𝐼 exp(cid:4678)−2 (cid:4679)\n(cid:2868) 𝑤(cid:2870)\nSince in our work 𝐷 = 2𝑤, substituting 𝑤 =𝐷/2, and 𝑥(cid:2870)+𝑦(cid:2870) =𝑟(cid:2870) leads to,\n𝑟(cid:2870) 𝑥(cid:2870)+𝑦(cid:2870)\n𝐼(𝑟)=𝐼 exp(cid:4678)−8 (cid:4679), 𝐼(𝑥,𝑦)= 𝐼 exp(cid:4678)−8 (cid:4679)\n(cid:2868) 𝐷(cid:2870) (cid:2868) 𝐷(cid:2870)\nThus, the coefficient “8” is introduced based on the definition of the 1/e2 radius and derived through\ncalculation. We have added this clarification, together with a relevant reference, to the revised\nmanuscript (page 4, lines 64-67).\n“The laser intensity distribution, I(x,y), as shown in the inset of Fig. 2c, can be described as follows\n[31]:\n𝑥(cid:2870)+𝑦(cid:2870) 𝑥(cid:2870)+𝑦(cid:2870)\n𝐼(𝑥,𝑦)=𝐼 exp(cid:4678)−2 (cid:4679)= 𝐼 exp(cid:4678)−8 (cid:4679) (1)\n(cid:2868) 𝑤(cid:2870) (cid:2868) 𝐷(cid:2870)\nwhere 𝐼 is the peak intensity at the beam center, 𝑥 and 𝑦 are the transverse coordinates, 𝑤 and\n(cid:2868)\n𝐷 are defined as the 1/e² radius and diameter, respectively.”\nComment:\n3. What is the relationship between Eq. (2) and the last equation seen in Fig. 2e? Do they refer to\nthe same equation? It looks there are different, but several terms are the same.\nReply: Thank you for the reviewer's comment. Eq. (2) is equivalent to the equation shown in Fig.\n2e. To avoid any confusion, we have unified their expressions in the revised manuscript to ensure\nconsistency.\nThe revised Eq. (2) and Fig. 2e are shown below:\n∞ 𝑦(cid:2870) π𝐷(cid:2870) (cid:2868).(cid:2873)\n𝐸 (𝑦)=(cid:3505) 𝐼(𝑥,𝑦)𝑑𝑥 =𝐼 ⋅exp(cid:4678)−8 (cid:4679)⋅(cid:4678) (cid:4679) (2)\ns 0 𝐷(cid:2870) 8\n(cid:2879)∞\nFig. 2 e, The energy distribution is obtained by integrating the beam intensity over the scanning\npath.\nComment:\n4. The expression “h = g(h)” in line 102 of page 6 is misleading. It would be better to add subscripts\n“n” and “n+1”.\nReply: Thanks for the reviewer's comment. We have replaced “h = g(h)” with “h = g(h )” in the\nn+1 n\nrevised manuscript (page 6, line 101).\n“ … with the following iteration equation, h = g(h ), which is derived from Eq. (4).”\nn+1 n\nComment:\n5. Please make sure the uniformity of expressions for the figures. Such as, “Fig. 5B” and “Fig. 5c”.\nReply: Thank you for pointing this out. We have corrected “Fig. 6B” (the Fig. 5B in the original\nversion) to “Fig. 6b” in the revised manuscript (see page 16, line 273), and rechecked all figure\ncitations to ensure consistent expression.\n“ … for the radiation with a wavelength above 390 nm (inset of Fig. 6b).”\nComment:\n6. What does “0.05 □/Ω” mean in line 230 of page 14?\nReply: Thank you for the reviewer’s comment. The symbol “□/Ω” denotes the unit of the reciprocal\nof sheet resistance (1/R). Since R is in Ω/□, its reciprocal (□/Ω) scales positively with conductivity\ns s\nand is sometimes more intuitive for thin‑film performance benchmarking. Here, “□” is a\nconventional symbol indicating that the resistance is normalized to a square geometry, independent\nof the actual size of the square. This unit is widely used to characterize the electrical performance\nof thin films, especially transparent conducting oxides and printed conductors [11*, 12*].\nIn the revised manuscript, a brief explanation of this unit has been added (page 17, lines 276-278),\ntogether with the relevant references.\n“Here, the reciprocal of sheet resistance (1/R has units of □/Ω) is employed as the horizontal\ns\nvariable [46, 47], ”\nComment:\n7. Even though the laser been shaping has the shortcoming of higher energy loss in the optical\nsystem, how does the electrical-optical performance of the fabricated circuit compare with the\noptimally determined circuit proposed by the authors? Please add more detailed information on the\ncomparison.\nReply: Thank you for the insightful comment.\nMotivated by your suggestion, we supplemented direct comparisons between Gaussian-beam\nsintered curve circuits and beam-shaped laser sintered planar circuits, as shown in Fig. 6g of the\nrevised manuscript. The results reveal that the curved circuit strategy provides clear advantages:\n(i) lower laser energy is required to achieve optimal sintering;\n(ii) the processing window is significantly broader, as indicated by the larger region with\nconductivity exceeding 104 S·cm-1;\n(iii) the maximum conductivity is higher, while avoiding the local cracking issues frequently\nobserved in sharp-edged planar circuits.\nThese results demonstrate that, even considering the additional energy loss in the optical shaping\nsystem, the fabricated curved circuits maintain excellent electrical–optical performance and deliver\nsuperior robustness compared with planar designs.\nFig. 6 g, Comparison of Gaussian-beam curved circuits and beam-shaped planar circuits\ndemonstrates the advantages of the curved circuit strategy: lower energy requirement, wider\nprocessing window, and higher achievable conductivity.\nThe experimental comparison between the curved circuits and beam-shaped lasers sintered circuits\nhas been added on pages 17-18, lines 300–305 of the revised manuscript.\n“Furthermore, by systematically comparing Gaussian-beam sintering of curved circuits with beam-\nshaped planar circuits, we identified several clear advantages of the proposed strategy (Fig. 6g). The\nrequired energy to achieve optimal sintering is lower, the processing window is wider as indicated\nby the larger area where conductivity exceeds 10⁴ S·cm⁻¹, and the maximum achievable\nperformance is superior, avoiding the local cracking issues often observed in sharp-edged planar\ncircuits.”\nThe description of the laser beam shaping method has been added on pages 21-22, lines 415–422.\n“The laser beam was shaped using a multi-element optical path, as shown in Fig. S1. The raw\nGaussian beam first passed through an iris-diaphragm aperture stop (Iris Diaphragm, Thorlabs,\nUSA), causing over 15% energy loss, and was then focused onto a circularly serrated aperture\napodizer (Serrated Aperture, LightTrans, Germany), which further modified the intensity\ndistribution but induced an additional loss exceeding 20%. Finally, a collimating lens package\n(Collimating Optics, Thorlabs, USA) was used to form a flat-top shaped profile.”\nComment:\n8. To sum up, it is suggested re-read and re-exam the manuscript carefully to avoid the careless\ntypos and inconsistent expressions.\nReply: Thank you for pointing out the spelling and expression issues in our manuscript. We have\nthoroughly proofread the manuscript and standardized spelling, formatting, and notation to avoid\ncareless typos and inconsistent expressions.\nResponse to Reviewer 4\nThis study presents an approach to addressing the critical issue of Gaussian beam-induced defects\nin laser sintering/melting by tailoring circuit thickness distribution via inkjet printing. However,\nseveral aspects require clarification and strengthening to fully support the claims and ensure\nrobustness:\nComment:\n1. Droplet Spreading Dynamics Omitted: The model and fabrication strategy assume ideal inkjet\ndroplet deposition and controlled thickness distribution. Crucially, the analysis does not account\nfor the fundamental role of droplet surface tension and substrate wettability\n(hydrophilicity/hydrophobicity) in determining droplet spread shape, final footprint, and\nconsequently, the actual printed height/thickness profile. This is a significant simplification, as these\nfactors directly govern the achievable resolution and thickness uniformity in inkjet printing. The\nauthors should address how variations in these parameters (e.g., across different substrate\nmaterials or ink formulations) might impact the fidelity of their thickness-matching strategy and\ndiscuss potential mitigations or calibration requirements.\nReply: Thank you for your insightful comment. We fully agree with the reviewer that droplet\nspreading dynamics, governed by factors such as surface tension and substrate wettability,\nplay a fundamental role in determining the final footprint and thickness uniformity. In fact, all unit-stacked\ncircuits in our experiments exhibited highly uniform line morphology, which was achieved through\nthe combined regulation of a binary solvent system and a controlled thermal field.\nBalancing “Solutal Marangoni Flow” with “Capillary + Thermal Marangoni\nFlows” for Coffee-Ring Suppression\nIt is widely recognized that the coffee-ring effect arises during nano-ink evaporation\nbecause capillary flow and thermal Marangoni flow drive suspended nanoparticles\noutward toward the three-phase contact line. In our strategy, the combined use of a binary\nsolvent (Ethylene Glycol: Isopropyl Alcohol at a 1:1 volume ratio, determined from\npreliminary orthogonal experiments on droplet evaporation [6*]) and a controlled external\ntemperature field enables precise regulation of the internal flow competition. As the\nevaporation temperature increases, IPA and EG evaporate sequentially according to their\nboiling points, creating dynamic variations in both concentration gradients and\ntemperature gradients within the droplet.\nThese gradients give rise to three key flows (see added Fig.3a in revised manuscript):\n(i) Capillary flow, induced by liquid replenishment toward the pinned contact line;\n(ii) Thermal Marangoni flow, driven by surface tension gradients from temperature\ndifferences between the droplet apex and the contact line; and (iii) Solutal Marangoni\nflow, generated by local EG enrichment at the contact line due to the preferential\nevaporation of IPA. The relative magnitudes of these flows can be quantified by the\nLaplace number (𝐿𝑎), thermal Marangoni number (𝑀𝑎 ), and solutal Marangoni number\n(cid:3021)\n(𝑀𝑎 ), which can be expressed as [7*, 8*]:\n(cid:3004)\n𝑙 𝑑𝜎/𝑑𝐶 𝜌 𝑙 𝜎 𝑙 𝑑𝜎/𝑑𝑇\n(cid:3039)(cid:3049)\n𝑀𝑎 = Δ𝐶, 𝐿𝑎 = , 𝑀𝑎 = Δ𝑇\n(cid:3004) 2𝜇𝐷 𝜇(cid:2870) (cid:3021) 2𝜇𝛼\n(cid:3033)\nwhere 𝑙 is the circuit width, Δ𝐶 is the concentration difference between the droplet apex\nand the contact line, 𝑑𝜎/𝑑𝐶 and 𝑑𝜎/𝑑𝑇 is the variation of surface tension with\nconcentration and temperature, 𝜇 is the viscosity, and 𝐷 is the diffusion coefficient of\n(cid:3033)\nIPA in EG. In addition, 𝜌 is the droplet density, 𝜎 is the liquid–vapor surface tension,\n(cid:3039)(cid:3049)\nΔ𝑇 is the temperature difference between the droplet apex and the contact line, and 𝛼 is\nthe thermal diffusivity of the liquid (definitions shown schematically in Fig.3a).\nFig. 3. a, Schematic of the competing flows in an evaporating droplet on a heated substrate:\ncapillary flow (𝐿𝑎), solutal Marangoni flow (𝑀𝑎 ), and thermal Marangoni flow (𝑀𝑎 ).\n(cid:3004) (cid:3021)\nWhile capillary flow and thermal Marangoni flow both enhance outward nanoparticle\ntransport and thus amplify the coffee-ring effect, the solutal Marangoni flow provides an\ninward counter-transport that counteracts ring formation. In other words, when 𝑀𝑎 ≈\n(cid:3004)\n𝐿𝑎+𝑀𝑎 (𝑀𝑎 /(𝐿𝑎+𝑀𝑎 )≈1) the three flows reach a balance and the coffee-ring\n(cid:3021) (cid:3004) (cid:3021)\neffect can be effectively suppressed.\nFig. 3. b, Theoretical prediction of the uniform-deposition window based on flow-strength\nanalysis; uniformity is expected when the balance index 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nWe calculated the flow balance index 𝑀𝑎 /(𝐿𝑎+𝑀𝑎 ) in the temperature range 60℃≤𝑇 ≤\n(cid:3004) (cid:3021)\n200℃ , as shown in the added Fig. 3b (see Table S1 in the supplementary information for\ncalculation details). Within the possible uniform-circuit temperature range (120 °C ≤ T ≤ 220 °C),\nwhere 𝑀𝑎 /(𝐿𝑎+𝑀𝑎 ) approaches 1, ITO unit circuits were printed on Si substrates (Fig. 3c).\n(cid:3004) (cid:3021)\nThe results show that uniform unit circuits are observed at T = 160 °C and T = 180 °C, which\nfalls within the theoretically predicted uniform-deposition temperature window of 150 °C ≤ T ≤\n190 °C, corresponding to 0.5≤𝑀𝑎 /(𝑀𝑎 +𝐿𝑎)≤2.\n(cid:3004) (cid:3021)\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition (scale bar: 100 μm).\nWe have added an entire Section 2.3 “Fabrication of coffee-ring–suppressed unit circuits in\ninkjet printing” in the revised manuscript (pages 7–10, lines 119–166) to elucidate the above\nmechanism, and corresponding figures and discussion have also been included in the supplementary\ninformation (pages S10–S11).\nComment:\n2. Non-Rectangular Cross-Section Assumption: The mathematical optimization and performance\nanalysis appear to assume an ideal rectangular cross-section for the printed conductive traces. This\nassumption is frequently inconsistent with the reality of inkjet-printed lines, which typically exhibit\nrounded, bulging, or coffee-ring effect profiles. The discrepancy between the model's assumed\ngeometry and the actual printed morphology could substantially affect the accuracy of the predicted\nconductance, laser absorption/heat distribution, and ultimately, the sintering outcome and final\nproperties. The manuscript should acknowledge this limitation and discuss its potential implications\nor validate the model against realistic cross-sectional profiles.\nReply: Thank you for pointing out the potential discrepancy between the rectangular cross-section\nassumption in the model and the actual printed line morphology; this is an important clarification\nthat improves the rigor of the manuscript.\nIn the Reply to Comment 1, we elaborated on how the “binary-solvent + external thermal field”\nstrategy balances the combined effects of solutal Marangoni flow, thermal Marangoni flow, and\ncapillary flow, thereby eliminating the coffee-ring effect. Based on this strategy, nearly coffee-ring–\nfree unit circuits were fabricated by inkjet printing at a substrate temperature of T = 160 °C (Fig.\n3c). To verify the validity of the rectangular assumption raised by the reviewer, the printed line\nprofiles were measured using a confocal microscope (DSX-1000, Olympus, Japan), as shown in Fig.\n3d. The results demonstrate that, regardless of whether the substrate is glass, silicon, or superalloy,\nthe cross-section of the printed ITO circuits can be regarded as nearly ideal rectangles, with a\n(cid:2870)(cid:2868)(cid:2868)\ndeviation of η ≤ 3.7%, where 𝜂 =(cid:1516) |𝑧 (𝑥)−𝑧 (𝑥)|𝑑𝑥/𝑆 (𝑧 (𝑥) and 𝑧 (𝑥) denote the\n(cid:2868) (cid:2869) (cid:2870) (cid:3045)(cid:3032)(cid:3030) (cid:2869) (cid:2870)\nmeasured and ideal rectangular profile heights at position x, respectively, and 𝑆 is the area of\n(cid:3045)(cid:3032)(cid:3030)\nthe reference rectangle).\nFig. 3. c, ITO unit circuits printed on silicon at different substrate temperatures, confirming the\npredicted transition from ring-dominated to uniform deposition.\nFig. 3. d, Uniform unit circuits on different substrates (glass, silicon, superalloy) showing\nquasi-rectangular cross-sections (deviation η≤3.7 %).\nThe corresponding content has also been added to the revised manuscript (pages 9-10, lines 150-\n166).\nComment:\n3. High-Frequency Signal Integrity Concern: While the demonstrated DC/low-frequency\nconductance improvement is impressive, the proposed \"stair-step\" thickness profile (inherent to the\nlayer-by-layer inkjet approach) raises concerns for high-frequency circuit applications. Such non-\nuniform, stepped cross-sections can introduce significant impedance discontinuities, signal\nreflections, and increased transmission losses at microwave/RF frequencies. If the technology\ntargets high-performance conformal circuits broadly, the authors should explicitly discuss this\nlimitation for high-frequency operation or provide data/analysis demonstrating acceptable RF\nperformance.\nReply: Thank you for highlighting the importance of high-frequency signal integrity, which is\nindeed a critical consideration for the broader applicability of conformal circuits.\nWe acknowledge that dedicated RF measurements (e.g., S-parameters and TDR analysis) have not\nyet been performed. These experiments are planned as part of our future work to quantitatively\nvalidate impedance continuity and transmission performance in the GHz range. The current\nlimitations and prospects for GHz-frequency applications have also been explicitly noted in the\nrevised manuscript (page 19, lines 352-356).\n“Limitations and outlook. In terms of high-frequency signal integrity, while this study focused\non direct current and low-frequency performance, future work will extend to GHz-frequency\ncharacterization in order to validate that the improved conductivity uniformity can be translated into\nstable RF signal integrity, which is essential for industrial applications.”\nThat said, we would like to clarify that the circuits formed in this work are not step-like structures.\nAlthough the fabrication process involves layer-by-layer stacking, the combined effects of interlayer\nmaterial flow during deposition and local nanoparticle melting during laser sintering yield a smooth\nand continuous profile (as confirmed by confocal and profilometer measurements in Fig. S5). This\nmorphology avoids the sharp impedance discontinuities typically associated with stepped\ngeometries. Moreover, because high-frequency performance is strongly affected by local\nconductivity variations, the curved strategy helps avoid non-uniform sintering and the resulting local\nresistance fluctuations, which is expected to be beneficial for RF signal integrity [13*]. While\nfurther RF measurements are needed, these features suggest that the curved circuits may minimize\nadditional signal losses at high frequencies.\nFig. S5. Cross-sectional SEM images of profiles I-VIII.\nComment:\n4. Justification for Laser Sintering vs. Thermal: The manuscript positions the laser intensity\nmodulation approach as a solution to problems inherent in laser sintering. However, it does not\nadequately justify why laser sintering is essential for this application compared to conventional\nthermal sintering processes. Thermal sintering (oven, belt furnace, localized heating) often offers\nsuperior process efficiency, potentially higher final conductivity, and avoids the specific\ncomplexities of laser beam shaping and Gaussian distribution issues altogether. The authors should\nstrengthen the rationale for choosing laser sintering specifically. A direct comparison of the\nperformance (conductivity, transmittance, speed, energy efficiency) and potential limitations (e.g.,\nsubstrate thermal stability) of circuits fabricated using their laser-sintered, thickness-optimized\napproach versus thermally sintered circuits (with or without thickness optimization) would be highly\nvaluable.\nReply: Thank you for the insightful comment.\nFollowing your suggestion, we supplemented comparative experiments on different substrates, as\npresented in Fig. 6h, where both curved Cu circuits and planar circuits were fabricated by laser\nsintering and benchmarked against thermal sintering.\nThe results show that on high-melting-point substrates (e.g., Al O ), laser sintering achieved\n2 3\nsuperior electrical performance owing to its short processing time, which effectively reduced\noxidation compared with thermal sintering. On low-melting-point substrates (e.g., PI films),\nconventional thermal sintering is infeasible due to severe substrate damage, whereas laser sintering\nenabled the fabrication of high-conductivity circuits without deformation.\nThese findings highlight the intrinsic advantages of laser sintering: ultrafast localized heating\nminimizes the heat-affected zone, suppresses oxidation, and protects sensitive substrates. Building\non this, our proposed curved circuit strategy further enhances performance by mitigating the non-\nuniform sintering issue inherent to conventional laser processing. As shown in Fig. 6h, curved-\nbased laser sintering retains the low-oxidation and high-performance benefits of laser processing,\nwhile improving conductivity uniformity and broadening the tolerance to both circuit and substrate\nmaterials. Importantly, its performance is slightly superior even to thermal sintering, underscoring\nthe incremental contribution of this work.\nFig. 6 h, Benchmarking against thermal sintering on Al O and polyimide substrates shows that\n2 3\nlaser processing avoids oxidation on high-melting substrates and prevents thermal damage on\nlow-melting substrates, highlighting the broad adaptability of the curved circuit strategy.\nThe relevant content has been added to the revised manuscript (pages 17-18, lines 307-312). And\nthe thermal sintering equipment and procedure have also been added to the “Methods” section (page\n22, lines 422-425).\n“Finally, Fig.6h benchmarks laser sintering against traditional thermal sintering on different\nsubstrates. For high-melting substrates such as Al O , the short sintering time of laser processing\n2 3\nminimizes oxidation and leads to better electrical performance. For low-melting substrates such as\npolyimide, the localized heating nature of the laser prevents thermal damage to the substrate (as\nshown in Fig. 6h, PI films can only withstand sintering up to 200 °C), further underscoring the\nbroad applicability and superiority of the laser approach.”\n“Thermal sintering experiments were conducted using a tube furnace (BTF-1400C, BEQ, China) to\nevaluate the electrical performance of thermal sintered circuits. The sintering process was carried\nout with a heating rate of 10 °C/min, followed by an isothermal hold at the target temperature for\n30 min, and natural cooling to below 75 °C.”\nReferences.\n[1*]. Yu, L. et al. Galvanometer driven optical system for laser dynamic focusing. Optics Express 31,\n673–685 (2023).\n[2*]. Bremer, S. J. L., Aarts, R. G. K. M. & Römer, G.-W. R. Mathematical analysis of dynamic high\npower laser beam shaping using Galvanometer Scanners or Deformable Mirrors. Optics & Laser\nTechnology (2025).\n[3*]. Gupta, S.et al. Ultra-thin chips for high-performance flexible electronics. npj Flexible Electronics\n2, 8 (2018).\n[4*]. Shao, Y. et al. A universal packaging substrate for mechanically stable module integration in\nstretchable bioelectronics. Nat. Commun. 15, 6106 (2024).\n[5*]. Bo, R. et al. Mechanically-guided 3D assembly for architected flexible electronics. ACS Applied\nMaterials & Interfaces 15, 47879–47910 (2023).\n[6*]. Zhang, M., Chen, J., Zhu, J., Tao, Z. & Qiu, L. Hybrid manipulation of inkjet-printing deposition\npattern of high particle concentration droplet by means of thermal and binary solvent effects.\nInternational Journal of Heat and Mass Transfer 223 (2024).\n[7*]. M. Parsa, R. Boubaker, S. Harmand, K. Sefiane, M. Bigerelle, R. Deltombe, Patterns from dried\nwater-butanol binary-based nanofluid drops, Journal of Nanoparticle Research, 19 (8) (2017) 251.\n[8*]. D. Zang, S. Tarafdar, Y.Y. Tarasevich, M. Dutta Choudhury, T. Dutta, Evaporation of a Droplet:\nFrom Physics to Applications, Physics Reports, 804 (2019) 1–56.\n[9*]. Paschotta, R. RP Photonics Encyclopedia: Gaussian beams (RP Photonics Consulting GmbH,\n(2025); https://www.rp-photonics.com/gaussian_beams.html\n[10*]. Pampaloni, F. & Enderlein, J. Gaussian, Hermite–Gaussian, and Laguerre–Gaussian beams: A\nprimer. J. Opt. A: Pure Appl. Opt. 6, S283–S291 (2004).\n[11*]. Lee, J.‐Y., Connor, S. T., Cui, Y. & Peumans, P. Solution‐processed metal nanowire mesh\ntransparent electrodes. Nat. Nanotechnol. 3, 238–242 (2008).\n[12*].Liang, L. et al. Intrinsically stretchable and transparent thin-film transistors based on printable\nsilver nanowires, carbon nanotubes and an elastomeric dielectric. Nat. Commun. 6, 7647 (2015).\n[13*]. Y. Zhou, et al., The Effect of Scratch-Induced Microscale Surface Roughness on Signal\nTransmission in Radio Frequency Coaxial Connectors, Micromachines, 16 (8) (2025) 837."}, "author_response": ""}]

Decision letter