High-throughput additive manufacturing (AM) techniques with nanoscale resolution are highly desirable for a variety of applications. Two-photon lithography (TPL) is a promising AM technique that is capable of generating features on the scale of 100 nm [1] . TPL uses nonlinear photo-absorption from a focused light spot to generate sub-diffraction features through localized photopolymerization [2] . This fine resolution of TPL is widely exploited in fabrication of a variety of functional micro and nanoscale structures such as mechanical and optical metamaterials [3, 4] , micro-optics [5] , micromachines [6] , bio-scaffolds [7] , and electrochemical interfaces [8] . The most common implementation of TPL involves serially scanning a tightly focused laser spot in a photopolymer resist to fabricate 3D structures by overlapping the individual submicron volumetric pixels (i.e., voxels) [9] . In the past, the low throughput of the serial point-by-point writing mechanism of TPL has been a major impediment to its industrial-scale adoption. For example, printing of foam structures with 300 nm features and a volume of 200 µm 3 takes several hours using commercially-available TPL 3D printer [10] . Thus, there is a need for high-throughput TPL techniques.
Light intensity (TW/cm 2 ) texp Duration of exposure during projection of images (ms) D Exposure dosage (TW 2 -ms/cm 4 
Dosage threshold for onset of polymerization (TW 2ms/cm 4 ) Several approaches have been used in the past to scale up TPL. These approaches include, increasing the linear writing speed of the serial scanning process [11] , parallelizing the process using holographic techniques [12] , and parallelization through projection of 2D images [13] . With increasing writing speed, the duration of exposure at the focal spot keeps decreasing, thereby requiring progressively more sensitive
High-throughput additive manufacturing (AM) techniques with nanoscale resolution are highly desirable for a variety of applications. Two-photon lithography (TPL) is a promising AM technique that is capable of generating features on the scale of 100 nm [1] . TPL uses nonlinear photo-absorption from a focused light spot to generate sub-diffraction features through localized photopolymerization [2] . This fine resolution of TPL is widely exploited in fabrication of a variety of functional micro and nanoscale structures such as mechanical and optical metamaterials [3, 4] , micro-optics [5] , micromachines [6] , bio-scaffolds [7] , and electrochemical interfaces [8] . The most common implementation of TPL involves serially scanning a tightly focused laser spot in a photopolymer resist to fabricate 3D structures by overlapping the individual submicron volumetric pixels (i.e., voxels) [9] . In the past, the low throughput of the serial point-by-point writing mechanism of TPL has been a major impediment to its industrial-scale adoption. For example, printing of foam structures with 300 nm features and a volume of 200 µm 3 takes several hours using commercially-available TPL 3D printer [10] . Thus, there is a need for high-throughput TPL techniques.
Light intensity (TW/cm 2 ) texp Duration of exposure during projection of images (ms) D Exposure dosage (TW 2 -ms/cm 4 ) Dth
Dosage threshold for onset of polymerization (TW 2ms/cm 4 )
Several approaches have been used in the past to scale up TPL. These approaches include, increasing the linear writing speed of the serial scanning process [11] , parallelizing the process using holographic techniques [12] , and parallelization through projection of 2D images [13] . With increasing writing speed, the duration of exposure at the focal spot keeps decreasing, thereby requiring progressively more sensitive
High-throughput additive manufacturing (AM) techniques with nanoscale resolution are highly desirable for a variety of applications. Two-photon lithography (TPL) is a promising AM technique that is capable of generating features on the scale of 100 nm [1] . TPL uses nonlinear photo-absorption from a focused light spot to generate sub-diffraction features through localized photopolymerization [2] . This fine resolution of TPL is widely exploited in fabrication of a variety of functional micro and nanoscale structures such as mechanical and optical metamaterials [3, 4] , micro-optics [5] , micromachines [6] , bio-scaffolds [7] , and electrochemical interfaces [8] . The most common implementation of TPL involves serially scanning a tightly focused laser spot in a photopolymer resist to fabricate 3D structures by overlapping the individual submicron volumetric pixels (i.e., voxels) [9] . In the past, the low throughput of the serial point-by-point writing mechanism of TPL has been a major impediment to its industrial-scale adoption. For example, printing of foam structures with 300 nm features and a volume of 200 µm 3 takes several hours using commercially-available TPL 3D printer [10] . Thus, there is a need for high-throughput TPL techniques.
Light intensity (TW/cm 2 ) texp Duration of exposure during projection of images (ms) D Exposure dosage (TW 2 -ms/cm 4 ) Dth
Dosage threshold for onset of polymerization (TW 2ms/cm 4 )
Several approaches have been used in the past to scale up TPL. These approaches include, increasing the linear writing speed of the serial scanning process [11] , parallelizing the process using holographic techniques [12] , and parallelization through projection of 2D images [13] . With increasing writing speed, the duration of exposure at the focal spot keeps decreasing, thereby requiring progressively more sensitive 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to photopolymer resists. Improving the fabrication throughput via parallelization has been challenging without compromising the resolution and/or the pattern complexity. For example, some past attempts at parallelizing TPL via projection of images from tunable digital masks have failed to achieve the submicron depth-resolution that is routinely achievable in serial writing [13] . Holographic methods developed to generate and scan multiple focal spots simultaneously [12] cannot fabricate arbitrary structures, so they are mostly suitable for printing periodic structures.
We have recently developed a parallel TPL technique in which a million focused light spots are projected at once to generate 3D structures layer-by-layer [14] . This femtosecond projection TPL (FP-TPL) technique increases the throughput up to three orders of magnitude without compromising the submicron resolution. Although FP-TPL significantly scales up the process, it requires tuning of the process parameters to minimize defects due to over-polymerization. These process parameters include the relevant material properties of the photopolymer resist. Tuning of the photopolymer composition to achieve the desired printing quality is an approach that has been used extensively in the past for TPL [15] [16] [17] . In our past work on FP-TPL, we applied this technique to minimize overpolymerization [14] . However, the design freedom to select a photopolymer resist of choice may not be universally available. Therefore, it is important to identify whether control of defects is possible through control of the projection technique alone without resorting to tuning of the photopolymer. Here, we present a modified projection technique that enables suppression of over-polymerization. 
The FP-TPL process is schematically illustrated in Fig. 1 . In this process, an image of the digital mask is projected into the interior of the photopolymer resist using a femtosecond laser as the light source. The digital mask is a commerciallyavailable array of micromirrors called the digital micromirror device (DMD). Femtosecond laser is used in this process because high light intensities on the order of ~ 1 TW/cm 2 are required to ensure that significant light absorption in the photoresist occurs through the nonlinear two-photon absorption mode. The FP-TPL technique enables projecting an entire 2D layer at once by temporally focusing the light into a thin focused light sheet. Specifically, during temporal focusing, the femtosecond pulse is stretched and compressed along the optical path to obtain intensity gradients in the photoresist. Polymerization occurs in those regions of the photoresist where the dosage exceeds a threshold value. Thus, strong intensity gradients along the depth direction enable one to print thin submicron 2D layers. 3D structures are generated by moving the focused light sheet and the photoresist relative to each other. Arbitrary 2D images can be loaded onto the digital mask by switching the individual pixels (i.e., micromirrors) 'on' or 'off'. The focused light sheet comprises a 2D point cloud of focused spots wherein each focused spot corresponds to an 'on' point in the digital mask. Arbitrary structures can be printed by loading a sequence of 2D images onto the DMD. Here, we investigate the effect of the density of 'on' pixels in the digital mask on the defects due to over-polymerization observed during printing. These defects are shown in Fig. 2 .
Upon comparing the over-polymerized defective structures in Fig. 2 with the defect-free structure of Fig. 1(a) , we observe that the defects manifest as over-polymerization in the central region of the projected planes. In both cases (i.e., Fig. 2 and Fig. 1(a) ), the same set of 2D images were projected on the DMD. These images are shown on the left side of Fig. 1(a) . When over-polymerization is absent, the top surface of the 3D structures is observed to be flat and uniform. However, the top surface of the over-polymerized structures is domed and extends beyond the plane of projection. In the past, we have tuned the composition of the photopolymer resist material to tune its thresholding behavior and suppress the overpolymerization. The uniform printing shown in Fig. 1(a) was achieved through such material optimization [14] . Here, we investigate whether a modification of the optical projection technique alone can suppress this over-polymerization without requiring one to tune the photopolymer material.
The temporally-focused light intensity distribution was obtained by simulating the propagation of a broadband femtosecond pulse through the optical system. The optical system consists of the DMD and the print plane inside the photopolymer resist being arranged in a 4f-like arrangement. This arrangement is illustrated in Fig. 3 . The 4f-like arrangement refers to the orientation in which the DMD plane and the print plane are conjugate image planes of each other, i.e., the two lenses generate a demagnified image of the DMD plane on the print plane inside the resist. In addition, this 4flike arrangement also enables temporal focusing, i.e., focusing of the pulses in the time domain. Fig. 3 . Schematic of the optical system for femtosecond projection that implements temporal focusing. The DMD surface and the focal plane of the objective lens are conjugate planes in a 4f-like arrangement between the collimating lens and the objective lens [14] .
To simulate the intensity of light in the focal volume of the resist, we first separately evaluated the electric field for each wavelength using monochromatic coherent optical models and then summed up the contribution of each wavelength to compute the light intensity in the focal volume. Light propagation through the optical system was modeled through the following steps: (i) the DMD surface is illuminated by a uniform beam, (ii) the DMD pattern acts as an amplitude mask that modifies the field amplitude, (iii) the periodic DMD structure acts as a diffraction grating that introduces a linear wavelength-dependent phase shift, (iv) the collimating lens generates an image of the DMD plane on the back focal plane of the objective lens, and (v) the objective lens focuses this image into the resist material to generate the temporally focused light sheet. These propagation steps were mathematically represented using Fourier optics and computationally modeled using the MATLAB software package. A grid of 256 × 256 pixels was used to simulate the DMD structure. In this grid representation, each pixel represents a single micromirror. The pixel spacing in this grid was set equal to the physical micro-mirror spacing of the DMD (i.e., equal to 7.6 µm). The details of the intensity modeling technique are available elsewhere [14] .
A representative intensity profile for projection of line features is shown in Fig. 4 . Upon projection of linear features on the x-y plane of the DMD, a demagnified image of the lines is generated on the focal plane of the photoresist. This image is focused in the depth direction, i.e., intensity is highest at the z = 0 plane but falls off away from that plane. Such an intensity distribution would generate a 3D linear feature of a finite width and a finite height. In these simulations, the refractive index of the photoresist material has been set to 1.52 which is same as that of the immersion oil medium of the objective lens (60× 1.25 NA). Simulation was performed for a Ti-sapphire femtosecond laser with a center wavelength of 800 nm and a spectral bandwidth of 40 nm. The focal length of the collimating lens was set at 200 mm and the focal length of the objective lens was 3 mm. These optical parameters were selected to match the experimental conditions of our past work [14] . 
To identify the source of the over-polymerization-based defects, one must first relate the process parameters to the size of the polymerized features. Prediction of the feature sizes during FP-TPL requires modeling both the intensity distribution in the resist and the subsequent polymerization reactions. Here, we have developed a dosage thresholding model to capture the relevant physics of the polymerization process and used the results of the optical model as an input to this thresholding model. The results from this combined model have then been used to study the effect of pixel density on the over-polymerization defects.
Our thresholding model is based on the approximation that the resist undergoes a localized liquid-to-solid phase transformation when the local dosage exceeds a threshold value for polymerization. Early work in the field of serial TPL [19] suggests that the thresholding approach may accurately predict feature sizes; however, more recent work suggests that more elaborate time-dependent models are necessary to fully capture the reaction-diffusion behavior of TPL [20] . Nevertheless, as a starting point, here we have adopted this simplistic model to study the defects in FP-TPL. The dosage (D) in FP-TPL increases with an increase in both the intensity of light (I) and the duration of exposure (texp). Therefore, we quantify the dosage as:
Here, the quadratic dependence of dosage on I is consistent with the two-photon absorption process that underlies the FP-TPL process. Although the dosage may appear to be a physically arbitrary parameter, it represents the total number of reactive species (i.e., radicals) generated during illumination. Thus, it is a measure of light-based "input" to the printing process. Due to the two-photon absorption process, the amount of light absorbed by the material is proportional to the square of the intensity whereas the total light absorbed is proportional to the duration of illumination [21] . Therefore, the number of reactive species can be obtained by multiplying I 2 texp with an appropriate absorption coefficient of the photoresist material [19] . We have dropped this multiplier from the definition of dosage in Eq. 1 as the thresholding model is insensitive to this parameter.
Based on the dosage thresholding model, printing would be observed in only those regions of the resist where the following relationship holds:
Here, Dth is the dosage threshold for writing and has been approximated as a material property of the photopolymer resist that does not depend on the light projection technique.
We have modeled the light intensity distribution for a set of projected images to study the effect of the density of pixels on the defects observed during FP-TPL. Each projected image comprises a set of 5 lines of the same width (in pixels) and a fixed period. The line width was varied across the different images from 3 to 10 pixels and the period was held at 30 pixels for all images. The magnification of the optical system is such that each pixel on the DMD maps to an area of 113 nm × 113 nm on the focal plane in the resist. The effect of line width on intensity is illustrated in Fig. 5 . We observe that the highest intensity is achieved at the focal plane (i.e., at z = 0 plane) but a finite non-zero background intensity also exists on the planes above and below the focal plane. This background intensity increases with an increase in the projected line width, i.e., with an increase in the density of 'on' pixels in the image. Overpolymerization may occur if the dosage corresponding to this background intensity exceeds the threshold dosage. This overpolymerization effect would be less dominant for images with thinner projected features. We have tested this hypothesis by simulating the printing of features using the dosage thresholding model represented by Eqs. 1 and 2.
We have simulated the size of the printed features for two different line widths: 4-pixel and 8-pixel wide lines. The exposure time for each image was 10 ms and the dosage threshold (Dth) was set equal to 0.025 TW 2 -ms/cm 4 . This value of the dosage threshold was obtained by calibrating the model so that a 4-pixel wide line would generate a 450 nm wide printed feature. The dosage distribution and the printed features for the two cases are shown in Figs. 6 and 7.
The width of the printed feature at the focal plane (z = 0 plane) for the 8-pixel wide line is observed to be 900 nm. Although this width scales with the projected pixel linewidth (i.e., it is twice that obtained for 4-pixel wide line), overpolymerization on the planes away from the focal plane is observed for the 8-pixel case.
As the amount of over-polymerization defect scales with the width of the projected line, it is reasonable to expect that these defects can be minimized by printing wider features through a series of thin lines. Here, we have tested this hypothesis by projecting a sequence of two images wherein each image has 4-pixel wide lines but the two sets of lines are offset from each other by 4 pixels along the x axis. Upon projection, the illuminated region spans a width of 8 pixels wherein the 4 pixels on the left-half are illuminated during the first exposure step and the 4 pixels on the right-half are illuminated during the second exposure step. The net dosage distribution was evaluated by summing up the dosage values for the two exposure steps. Each exposure step lasted 10 ms and the same Dth was used. The net dosage and the simulated features for this projection scheme are shown in Fig. 8 . The widths and heights of the linear features generated under the different projection schemes are summarized in Table 1 . With the modified projection scheme, which uses thinner projected lines to generate thicker features, the width of the linear feature is still the same as that obtained for the 8 px projection However, the feature height reduces by 40%. In addition, the modified scheme minimizes the overpolymerization defects away from the focal plane and reduces the aspect ratio of the features (height/width) from more than 2 to 1.2. Thus, it is an optimal projection technique when high-quality and fine features are desired. One criticism of this technique could be that it reduces throughput due to the higher exposure time (here 20 ms) required to project two images instead of a single image. It is important to note here that this limitation can be overcome by increasing the power of the beam so that the total exposure remains unchanged.
Our model approximates the polymerization process through a simplistic thresholding mechanism. For more realistic predictions, one must also include the dynamics of the polymerization mechanism. Specifically, the spatiotemporal evolution of the diffusion of chemical species and the reaction of the chemical species must be accounted for to improve the predictions. Including these effects would enable one to answer questions such as 'how long can one wait to project the next set of images and still achieve efficient dosage accumulation?'. Nevertheless, the model presented here is sufficiently accurate to demonstrate that the defects due to over-polymerization are dependent on the density of the 'on' pixels in the projected image and can be minimized by projecting thinner features.
High-throughput nanoscale additive manufacturing techniques are highly desirable for a variety of applications. The recently developed FP-TPL technique presents this capability for polymerization-based processing. However, defect-free writing requires one to iteratively tune the material properties of the photopolymer resist. Here, we have utilized a dosage thresholding model to demonstrate that overpolymerization-based defects are dependent on the density of the 'on' pixels in the projected image and can be minimized by projecting a sequence of thinner features. Thus, this modified projection technique can be used to control the defects in FP-TPL purely through optical techniques without requiring one to modify the photopolymer resist. Through simulations, we demonstrate reduction in the amount of polymerization on planes away from the focal plane, a decrease in the height of the features by 40% and a reduction in the aspect ratio from more than 2 to 1.2. Thus, this optimal projection strategy transforms FP-TPL into a more robust process suitable for high-throughput high-quality 3D printing of micro and nanoscale structures.