Roll-to-roll (R2R) nanofabrication processes are recognized as key enabling-technologies for many next-generation applications in flexible electronics, displays, energy generation, storage, as well as healthcare. However, R2R processing techniques reported in the literature currently lack a scalable method of performing high-throughput nanoscale pattern transfer of geometry requiring a high degree of fidelity in terms of critical dimension resolution, etch uniformity, and aspect ratio. Reactive ion etching (RIE) addresses the need for sub-10 nm pattern transfer with large-area uniformity in wafer-scale semiconductor manufacturing, but adapting plasma etch systems for use in R2R nanopatterning has proven to be nontrivial. Moreover, robust models for simulating R2R RIE do not exist, which is an obstacle to the creation of computational approaches to design, control, and scale-up of nanoscale R2R equipment and processes. To address these challenges, we demonstrate a process flow for fabricating Si nanopillar arrays utilizing a combination of nanoimprint lithography and RIE with all pattern transfer steps performed using a R2R plasma reactor system. Specifically discussed are process development details for etching imprint resist and Si including etch rates, cross-web etch uniformity, etch directionality, and etch selectivity at varying gas chemistries, powers, and pressures. 2k full-factorial Design of Experiments (DoEs) and ordinary least-squares regression analysis are also employed to study influence of process parameters on multiple outgoing etch quality characteristics and generate stochastic models of the R2R RIE pattern transfer process into Si. Utilizing these DOE-based models and desired targets for etch quality characteristics, we describe a bounded multivariate inverse-optimization scheme for automated etch process parameter tuning. The culmination of these efforts, to the best of the authors' knowledge, is the first reported RIE-based pattern transfer of 100 nm-scale features performed in continuous R2R fashion with control of feature geometry over large area. The methodology employed herein may be applied similarly to additional materials and geometries for future applications.

High-throughput roll-to-roll (R2R) nanoscale fabrication is recognized as a key enabling-technology for many classes of next-generation devices and flexible electronics.1–5 A prime reason for this is because R2R manufacturing is particularly well-suited to address concerns related to the large economies of scale needed for these products to achieve market competitiveness.6–10 For instance, nanopatterned Si anodes for lithium-ion batteries (LIBs) are a promising solution to meet the needs of the burgeoning electric vehicle market, but the high fabrication cost associated with nanopatterning Si anodes limits their practicality to small-scale niche applications.11–13 R2R fabrication of nanopatterned Si anodes offers a direct way to reduce cost and increases throughput in the near-term. Additional candidate applications for R2R fabrication include displays/optoelectronics,14–21 sensing,22–25 energy conversion and storage,26–30 integrated circuits,31–35 and healthcare.36 

However, these target technologies require precise geometric control of nano- and microscale features patterned over large-areas and into various dielectrics and metals. Continuous R2R nanoimprint lithography (NIL) is a promising technique that offers a scalable and high-resolution method of defining feature geometry in a sacrificial polymeric resist layer.37–39 Nevertheless, NIL requires a subsequent processing step to transfer these patterns into underlying functional material layers.40 The pattern transfer step is, therefore, a critical consideration for the manufacturability of many devices. Existing R2R pattern transfer processing techniques are generally incapable of realizing tight tolerance, high aspect ratio, nanoscale structures in thin films with acceptable yield. These incumbent R2R methods, namely, solution-based wet etching, suffer from poor etch anisotropy, undesirable material selectivity, and unreliable process controllability41–43 

In contrast, reactive ion etching (RIE) is a dry plasma process that permits a high level of directionality, repeatability, and etch selectively.41,42 These advantages make RIE frequently more desirable than wet etching for high-precision applications such as in the semiconductor industry where high-fidelity fabrication of large-area nanostructures on wafers is essential.43 The body of knowledge around wafer-scale plasma etching is rich and has matured to incorporate processing of a large assortment of materials at the nanoscale since its widespread adoption in the 1970s. Furthermore, continued process and equipment refinements have allowed RIE pattern transfer to keep pace with improvements in wafer-scale lithographic resolution.41,43

Despite these advantages, R2R RIE-capable machinery has only recently become commercially available due to numerous technical challenges compared to wafer-scale etchers. These challenges arise from the fact that R2R RIE is significantly different from wafer-scale etch in terms of underlying physics, process parameters, and equipment design. These differences make it nontrivial to replicate wafer-scale etching in R2R fashion. The requirement to convey a web through the process zone necessitates a plasma reactor design that is dissimilar to reactors in wafer-scale etchers. The unique configuration of plasma reactors in R2R equipment results in substantial differences in the characteristics of the glow discharge they generate, for example, the DC bias, Debye sheath, density of reactive ionic species in the plasma, and the residence time of the reactive species compared to wafer-scale etch equipment.44 Furthermore, since the substrate in R2R etching is not stationary as it is in wafer-scale etch processes, R2R etch processes contain additional dynamics that drive spatial transients along the web direction and nonuniformities in the cross-web direction, both of which depend on the reactor design. Conveyance of the substrate web also introduces process variables, such as web speed, web tension, web material, and web thickness, which do not exist in the case of wafer-scale etching. These factors dictate aspects such as the time of etch, the relative position of the target material in the plasma, and thermal behavior of the substrate web during processing. Other important considerations in R2R RIE include ensuring proper conductance of process gases to confine the plasma in the reactor and electrostatic charging of the web during winding/unwinding.45 These parameters do not exist in the case of wafer-scale equipment and processes, but exert influence on the glow discharge in R2R reactors, and, thus, affect the performance of the etch process.

Literature on performing or simulating dynamic RIE pattern transfer in R2R fashion is, similarly, scarce. Initial efforts to study R2R RIE have been confined to conduct model validation on unrepresentative wafer-scale equipment.46 As a result, there exists a knowledge gap in understanding the physical and processing differences between wafer-scale and R2R RIE. This represents an obstacle to the creation of computational approaches to design, control, and scale-up of nanoscale R2R equipment and processes.

This paper addresses the aforementioned gaps by demonstrating an exemplary nanostructure fabrication process scheme for realizing nanopillar arrays in Si utilizing a combination of NIL and RIE with all pattern transfer steps performed in a R2R vacuum machine equipped with a capacitively coupled plasma (CCP) reactor. The reasoning for this choice of large-area nanostructure array is twofold: (1) it serves as a convenient basis for studying the baseline performance of a R2R plasma reactor design and (2) it permits exploring methods to address general challenges associated with nanoscale R2R RIE process development. The following sections detail our experimental setup and methods, etch performance benchmark trials, process characterization technique, and a proposed optimization approach for automated process parameter tuning based on target etch characteristics. The culmination of these efforts applied to the fabrication of Si nanopillar arrays, to the best of the authors' knowledge, is the first reported RIE-based pattern transfer of 100 nm-scale features performed in continuous R2R fashion with control of large-area feature geometry.

The Si nanopillar array fabrication scheme consists of three main unit processes, which are illustrated in Fig. 1. The first step in the process flow entails NIL of nanopillar geometry in polymeric imprint resist onto a Si substrate wafer via Step-and-Flash Imprint Lithography (S-FIL), also known as Jet-and-Flash Imprint Lithography (J-FIL).38,47 The subwavelength critical dimensions (CDs) of nanostructures common in nanophotonic and microelectronic devices48 motivated the following choice of nanopillar geometry: 230 nm in diameter, 100 nm in height, and a pitch of 1 μm between adjacent nanopillars. These nanopillars reside on a uniform 30 nm residual layer thickness (RLT) of imprint resist, which is typical for the J-FIL method. After NIL, a RLT etch or descum step is performed using an Ar and O2 plasma etch chemistry to remove the RLT layer and expose the underlying Si surface. The final step in the process flow is pattern transfer of the nanopillars into the Si substrate using a fluorine-based plasma etch. Note, etch performance tests discussed in the process development section also utilized wafers coated with a roughly 100 nm thick uniform layer of imprint resist deposited similarly via the J-FIL technique.

FIG. 1.

Illustration of exemplary Si nanopillar array fabrication flow and dimensions of imprinted nanopillars.

FIG. 1.

Illustration of exemplary Si nanopillar array fabrication flow and dimensions of imprinted nanopillars.

Close modal

Figure 2 provides a schematic of the general configuration of the R2R RIE machine (E&R Genesis Platform) used in this study and a picture of a view into the lower vacuum chamber where the R2R CCP reactors or etch heads are located. Sample preparation involved first performing wafer-scale J-FIL on 4 in. diameter Si wafers (Molecular Imprints I1100). The NIL patterned wafers were subsequently spliced into roughly 20–30 mm wide coupons and attached with polyimide tape to a free span of a 320 mm wide stainless-steel (SS) web in the R2R RIE machine for processing [see Fig. 3(c)]. Once the vacuum vessel reached the desired process pressure and a stable glow discharge was present in the R2R CCP reactor(s), the machine's web drive system was used to convey the samples through the plasma reactor process zone(s) at controlled speeds. All reported findings are results of processing with a single etch head in the machine and the central drum at ambient temperature. Etch depth measurements utilized a combination of SEM imaging (JEOL JSM IT100 and Zeiss Neon 40), optical reflectometry (Filmetrics F10), and step height stylus profilometry (KLA Tencor Alpha-Step).

FIG. 2.

(a) Schematic of R2R RIE machine main vacuum chambers, configuration of major components, and web path (note reference coordinate system). (b) Picture showing lower vacuum chamber of machine containing the etch heads and temperature-controlled central drum.

FIG. 2.

(a) Schematic of R2R RIE machine main vacuum chambers, configuration of major components, and web path (note reference coordinate system). (b) Picture showing lower vacuum chamber of machine containing the etch heads and temperature-controlled central drum.

Close modal
FIG. 3.

(a) Etch rate vs web speed data for samples positioned in different cross-web locations in terms of both kinetic and temporal etch rate. (b) Schematic showing sample positioning for cross-web etch uniformity trials. (c) Photograph of stainless-steel web with samples attached in the lower vacuum chamber. Schematic of R2R vacuum chambers included to provide context on the location of the samples within the machine.

FIG. 3.

(a) Etch rate vs web speed data for samples positioned in different cross-web locations in terms of both kinetic and temporal etch rate. (b) Schematic showing sample positioning for cross-web etch uniformity trials. (c) Photograph of stainless-steel web with samples attached in the lower vacuum chamber. Schematic of R2R vacuum chambers included to provide context on the location of the samples within the machine.

Close modal

This study employs the use of both temporal (Rt) and kinetic (Rk) etch rates for data analysis of process results. Equations (1) and (2) define temporal and kinetic etch rates, respectively, in terms of etch depth (d), web speed (v), and process zone length (L),

Rt=d(Lv)1,
(1)
Rk=dv.
(2)

Temporal etch rate represents etch depth per unit of time in the process zone of an etch head and has units of nanometers per second (nm/s). Kinetic etch rate relates achievable etch depth by an individual pass through the process zone of a single etch head to web speed and has units of nanometers–meters per minute (nm*m/min). While temporal etch rate allows for comparison to wafer-based systems, kinetic etch rate is more intuitive for R2R operation because dividing kinetic etch rate by web speed directly gives etch depth. For example, a Rk of 30 nm*m/min signifies 30 nm of material will be etched when processed at 1 m/min or 15 nm when processed at 2 m/min.

Prior to process integration, preliminary process trials were conducted with the R2R CCP reactor in order to establish general performance benchmarks for etch rates, cross-web etch uniformity, and etch directionality. These measured performance metrics serve as references that informed later process integration experiments.

Benchmark tests for imprint resist etch rate and cross-web uniformity employed Si wafer coupons with uniform thickness imprint resist layers. These Si coupons were positioned along the cross-web direction at three roughly equally spaced locations: 80, 160, and 240 mm from the left edge of the web [see Fig. 3(b)]. Prior experience performing descum on wafer-scale RIE equipment informed the choice to use a 35:1 Ar to O2 gas chemistry at a pressure of 3.5e–3 mbar and RF power of 250 W as processing conditions for these trials. Figure 3(a) shows etch rate verses web speed data for different positions in the cross-web direction. Average etch rate was 1.7 nm/s or 29.8 nm*m/min with a standard deviation of 0.3 nm/s or 4.5 nm*m/min in terms of Rt and Rk, respectively. Etch rate appears to decrease with increasing web speed, though additional data points across a wider range of speeds are needed to properly elucidate this relationship. Cross-web etch rate uniformity was 5.8% according to the uniformity calculation procedure described here.41 

Etch directionality tests compared the diameters of nanopillars patterned in imprint resist prior to verses after the descum process step. The change in nanopillar diameters post descum provided a measure of the amount of material etched in the horizontal or in-plane direction. The ratio of material etched in the vertical or normal-to-plane direction to that etched in the horizontal direction defined etch directionality. Etch directionality trials employed identical process conditions as the etch rate and uniformity tests described prior. Test results show the R2R CCP plasma reactor exhibits a vertical-to-horizontal etch directionality of roughly 6:1 for imprint resist at these process conditions. Specifically, a 30 nm vertical etch component had an associated 10 nm reduction in the diameter of resist nanopillars or a lateral etch component on average of 5 nm (see Fig. 4).

FIG. 4.

(a) Top-down SEM image of the sample surface with nanoimprinted pillars prior to descum step. Scale bar is 500 nm. (b) Top-down SEM image of sample surface with nanoimprinted pillars after descum step. Scale bar is 500 nm. (c) Photograph of a patterned Si wafer coupon post descum. The bottom area of this sample was covered with polyamide tape during the descum process causing a visual contrast to develop along the interface of the area of the sample directly exposed to plasma.

FIG. 4.

(a) Top-down SEM image of the sample surface with nanoimprinted pillars prior to descum step. Scale bar is 500 nm. (b) Top-down SEM image of sample surface with nanoimprinted pillars after descum step. Scale bar is 500 nm. (c) Photograph of a patterned Si wafer coupon post descum. The bottom area of this sample was covered with polyamide tape during the descum process causing a visual contrast to develop along the interface of the area of the sample directly exposed to plasma.

Close modal

Benchmark trials for Si etching consisted of measuring etch rates at different gas flow proportions of SF6, CF4, and O2 at constant process pressure, web speed, and RF energy of approximately 0.05 mbar, 1 m/min, and 500 W, respectively. These static process parameter values were selected because they produce a reliable, repeatable, and well-confined glow discharge in the R2R RIE machine and are also representative of typical operating conditions for R2R RIE. Figure 5 shows measured Si etch rates at distinct volumetric flow percentages of the constitute gases at the aforementioned process conditions. In general, Si etch rate increased with increasing percentage of SF6 comprising total gas flow in place of CF4, which is in agreement with the literature.41 O2 appears to have a negligible effect on Si etch rates relative to CF4 and SF6, and no clear trend was observed between O2 concentration and Si etch rate.

FIG. 5.

Preliminary process map of Si etch rate vs gas flow composition during operation. The dotted lines are second-order polynomial fits to percent of gas flow that is SF6 and CF4.

FIG. 5.

Preliminary process map of Si etch rate vs gas flow composition during operation. The dotted lines are second-order polynomial fits to percent of gas flow that is SF6 and CF4.

Close modal

Figure 5 provides a rudimentary process parameter map at applicable processing conditions and allows for approximating an appropriate gas chemistry ratio to achieve a desired etch rate target based on concise visual inspection of past empirical data. This is accomplished by first scanning the x axis of Fig. 5 to a desired etch rate and then tracing a line parallel to the y axis from that point. The gas percentage values where this vertical trace intersects the best fit lines of the constitute gases signifies the appropriate gas ratio to use. While not objectively rigorous, this a posteriori graphical method of process parameter selection, nonetheless, serves as a tool that can aid in selecting origin points for more sophisticated empirical process characterization techniques that follow such as full-factorial Design of Experiments (DoEs).

Process integration required combing a successful descum step with a subsequent fluorine-based etch in order to transfer the pattern of 100 nm tall nanopillars into the Si substrate without breaking vacuum. The challenge here is to select the most appropriate process parameters in order to yield desired results while minimizing development time and cost. Without a priori knowledge on these processes, only experimental data from benchmark trials could be used for choosing machine parameters.

Imprint resist etch rates achieved in benchmark testing showed process conditions of a 35:1 Ar to O2 gas chemistry and RF power of 250 W were adequate to remove a 30 nm thick RLT layer at a web speed of 1 m/min, which corresponds to an etch rate of 30 nm*m/min. Similarly, following the procedure described in Sec. III A, Fig. 5 suggests a 9:1 CF4 to SF6 gas chemistry at the corresponding applicable process conditions should result in a Si etch rate of 100 nm*m/min. The selection of 100 nm*m/min as the desired Si etch rate for initial integration trails permitted performing both the descum and pattern transfer steps at the same web speed of 1 m/min. Performing both process steps at the same web speed was both convenient of the operator and representative of real-world production R2R processing.

Figure 6 shows the appearance of sample coupons after each subsequent step in the nanopillar fabrication flow and an SEM micrograph of the resulting nanostructures on the Si substrate. The Si etch is nearly isotropic, resulting in highly undercut sharp needlelike structures capped with remnants of unetched imprint resist. Average height of Si nanopillars after this fluorine-based etch was 143 nm, which exceeds the expected etch depth based on Fig. 5 by roughly 43%. Additionally, the average height of the remaining imprint resist was 63 nm, which suggests a Si-to-resist etch selectivity of 3.9:1.

FIG. 6.

(a) Photograph of sample wafer coupons after each step of the nanopillar fabrication flow during initial process integration. (b) Off-angle SEM micrograph of the initial successful R2R RIE pattern transfer into Si. Scale bar is 500 nm.

FIG. 6.

(a) Photograph of sample wafer coupons after each step of the nanopillar fabrication flow during initial process integration. (b) Off-angle SEM micrograph of the initial successful R2R RIE pattern transfer into Si. Scale bar is 500 nm.

Close modal

Section III underscores the importance of robust process modeling for scale-up of R2R RIE manufacturing. While the results of initial process integration showcase the capability to perform R2R RIE pattern transfer with submicrometer resolution, operating without etch control and relying solely on rudimentary process maps, such as Fig. 5, is prone to rendering undesirable feature geometry. This ultimately leads to poor etch profiles that will likely have yield issues in industrial scale applications of R2R RIE. Solving for the appropriate equipment-specific process parameter values that result in the desired etch geometry is the primary goal of RIE recipe development and typically requires simulating the process with a high degree of fidelity. However, deterministic models for R2R RIE that account for the multitude of additional complexities due to the dynamic nature of this process are not readily available. Instead, we opt for a stochastic approach to characterize the Si etch pattern transfer step using a 2k full-factorial DoE and multinomial regression analysis.49 A multivariate optimization scheme that utilizes these regression models is then employed to simultaneously solve for the most-likely equipment-specific process parameters to achieve desired etch targets.

Process characterization employed a 2-level 4-factor (24) full-factorial DoE to study the influence of SF6 concentration in gas flow (x1), O2 concentration in gas flow (x2), delivered RF power to the etch head (x3), and process pressure (x4) on Si nanopillar geometry in a CF4 dominant plasma chemistry. All samples underwent an identical descum step using the 35:1 Ar to O2 recipe described in Sec. III. Figure 7 contains SEM images of Si pattern transfer results at different test levels of this DoE and a schematic of nanopillar geometry with key features labeled. The images in Fig. 7(a) are provided to illustrate the differences in etch performance and pillar geometries that can result from relatively minor adjustments to process conditions in R2R RIE. SEM imaging was used to measure all pillar geometry features identified in Fig. 7(b).

FIG. 7.

(a) SEM micrographs of Si nanopillars at various DoE test levels. Scale bars in all images are 200 nm. (b) Schematic of Si nanopillar geometry with feature definitions.

FIG. 7.

(a) SEM micrographs of Si nanopillars at various DoE test levels. Scale bars in all images are 200 nm. (b) Schematic of Si nanopillar geometry with feature definitions.

Close modal

Outgoing etch characteristics of interest modeled via the DoE included depth of imprint resist etched (yR), Si etched (ySi), Si nanopillar diameter (yDia), etch selectivity (ySelect), Si undercutting (yUndercut), and Si nanopillar sidewall angle (yAngle). Table I tabulates the definition of each of these metrics in terms of parameters illustrated in Fig. 7(b). Note, Ro here is the height of imprint resist nanopillars after descum and prior to Si etching.

TABLE I.

Definitions of etch characteristics measured during DoE.

Etch characteristicSymbolDefinition/equation
Imprint resist etched (nm) yR =Ro − RH 
Si etched (nm) ySi =SiH 
Etch selectivity (Si:R) ySelect =SiHRoRH 
Si undercut yUndercut =RBSiMin2 
Si sidewall angle (φ) yAngle =tan1(SiHSiBSiMin2) 
Si diameter yDia =SiB 
Etch characteristicSymbolDefinition/equation
Imprint resist etched (nm) yR =Ro − RH 
Si etched (nm) ySi =SiH 
Etch selectivity (Si:R) ySelect =SiHRoRH 
Si undercut yUndercut =RBSiMin2 
Si sidewall angle (φ) yAngle =tan1(SiHSiBSiMin2) 
Si diameter yDia =SiB 

Next, ordinary least-squares regression was used to fit a multinomial model (y^i) for each outgoing etch characteristic of the form,49 

y^i=βo+β1x1+β2x2+β3x3+β4x4+β12x1x2+β13x1x3++β1234x1x2x3x4+e,
(3)

where attributes xis represent the value of each process parameter. Here, process parameters, xis, are normalized to ensure orthogonality according to

xi=xiactual0.5(xihighactual+xilowactual)0.5(xihighactualxilowactual),
(4)

where xilowactual and xihighactual are the real-world low and high process parameter values used in the DoE, respectively. Table II lists the real-world high and low process parameter values used in this DoE. There are a 16 unknown effects or weights, βi's, per model: one for β0, which is simply the average response of the etch statistic, and 15 ranging from β1 to β1234, each of which quantify the influence of the corresponding xi or corresponding possible combinations of xis on the etch statistic.

TABLE II.

24 full-factorial DoE real-world process parameter high and low values.

Process parameter or attributeHigh value (+1)Low value (−1)
SF6 concentration (x115% 5% 
O2 concentration (x220% 10% 
RF power (x3500 W 250 W 
Process pressure (x4∼10–2 mbar ∼10–3 mbar 
Process parameter or attributeHigh value (+1)Low value (−1)
SF6 concentration (x115% 5% 
O2 concentration (x220% 10% 
RF power (x3500 W 250 W 
Process pressure (x4∼10–2 mbar ∼10–3 mbar 

Cost and time constraints prohibited repetition of individual test levels preventing estimates of the statistical distribution of effects and analysis of variance (ANOVA). As an alternative, assessment of effect significance utilized normal probability plots and estimating standard error using higher-order interaction effects, as suggested in.50Figure 8 contains normal probability plots for all fitted models which show higher-order interaction effect estimates of each model tend to appear normally distributed about a line that passes near the (0, 0) point in each plot (indicated by dashed green lines).

FIG. 8.

Normal probability plots of all fitted model effect estimates. The green dashed line indicates the linear trend of higher-order interaction effects for each model and is only a visual aid.

FIG. 8.

Normal probability plots of all fitted model effect estimates. The green dashed line indicates the linear trend of higher-order interaction effects for each model and is only a visual aid.

Close modal

Based on observation of Fig. 8, higher-order interaction effects were assumed to be negligible, and variance of fitted effects was estimated by

seffect2=higherorderinteractions(βiμβi)2N,
(5)

where the true mean value of an effect, μβi, is assigned a value of 0 and N is the number of third- and higher-order interaction effect terms from Eq. (3). The 95% confidence intervals (CI) for effect estimates per each model can then be calculated by

95%CI=βi±t5,0.975Seffect.
(6)

Figure 9 presents the zero-mean normalized values of all effect estimates along with their 95% confidence intervals for each model created from DoE results.52 The following list tabulates the statistically significant effects for each model based on their corresponding 95% confidence intervals.

  • Imprint resist etch model: only the main effect of process power is significant.

  • Si etch model: only the main effects of SF6 concentration and process power are significant.

  • Si pillar diameter model: the main effect of process power and the interaction effect of O2 and process pressure are significant.

  • Si-to-resist selectivity model: only the main effect of SF6 concentration is significant.

  • Si pillar undercut model: the main effects of SF6 and O2 concentration are significant as is the interaction effect of these two parameters.

  • Si pillar sidewall angle model: the main effect of SF6 concentration and the interaction effect of SF6 and O2 concentration are significant.

FIG. 9.

All DoE fitted model effects estimate with 95% confidence intervals in terms of zero-mean normalized values. Horizonal lines represent 95% CI higher and lower values.

FIG. 9.

All DoE fitted model effects estimate with 95% confidence intervals in terms of zero-mean normalized values. Horizonal lines represent 95% CI higher and lower values.

Close modal

In general, first-order parameters were found to be dominant for all Si nanopillar etch characteristics, whereas higher-order interaction parameters only seem to be significant for determining Si pillar diameter, undercutting, and sidewall angle during fluorine etching.

Process optimization consisted of solving the bounded nonlinear programming problem specified by

minxf(x)=i=14(y^iyitarget)2suchthatibxub,
(7)

where

x=[x1,x2,x3,x4],ib=[2.5,2.5,2.5,2.5],ub=[2.5,2.5,2.5,2.5].

The objective function is the root sum square error (RSSE) between the desired etch targets for a particular etch characteristic (yitarget) and the mean predicted value of said statistics (y^i) based on the corresponding DoE fitted regression model. Note, only the four etch characteristic ySi, ySelect, yUndercut, and yAngle are considered during this optimization and each is given equal weighting for simplicity. Note, the objective function here employs the original full-order regression model for each etch statistic of interest, rather than their parsimonious versions, in order to directly utilize the machine-specific findings of the DoE analysis. Variable bounds lb and ub were selected to allow for a larger search area than DoE test levels while remaining within the realm of practical machine operation.

Optimum process parameters were found by implementing the sequential quadratic programming algorithm in MATLAB's fmincon solver. The fmincon solver was called from the GlobalSearch function to maximize likelihood of returning a global minimum within the feasibility region.51 A key advantage of this statistics-based approach to process optimization is that the analytical form of the regression models significantly reduces computational expense compared to deterministic finite-element methods. This low-cost modeling allows for readily mapping out the entire response surface over the design space if needed (see Fig. 10).

FIG. 10.

Response surface contour plot at arbitrary constant process pressure and power as a function of varying percent SF6 and CF4 in total gas flow. RSSE is defined by Eq. (5).

FIG. 10.

Response surface contour plot at arbitrary constant process pressure and power as a function of varying percent SF6 and CF4 in total gas flow. RSSE is defined by Eq. (5).

Close modal

To test the performance of this process characterization and optimization approach, arbitrary but plausible desired etch targets were fed to the solver and its output was experimentally verified by conducting R2R RIE pattern transfer of Si nanopillars at the optimum process parameters determined through that process. Descum was, again, performed using identical process conditions as described in Sec. III. Table III tabulates the desired etch targets and the process parameters identified via DoE-based optimization. Table IV lists the mean predicted etch characteristic values and 95% CI at the identified optimum process parameter values as well as the measured empirical values from validation tests. Experimental etch characteristic of selectivity, undercut, and sidewall angle were all within the 95% CI bounds of predicted values. However, Si etch depth was 6 nm below the lower predicted limit of 129 nm. It should be noted that measurement uncertainty could potentially account for this difference. Imaging features of interest required operating the SEM at magnifications of 150 k which approached the resolution limits of the equipment, and aberrations such as edge blur and sample charging were evident. Figure 11 provides SEM images of test samples used in experimental validation of optimization results post Si etching at the identified optimum process parameters

FIG. 11.

SEM micrographs of Si nanopillars fabricated at optimum process parameters. (a) and (b) Image of nanopillars at 125 k magnification. (c) Image of nanopillars at 150 k magnification. Each image is taken at a different location along the sample edge. Scale bars in all images are 200 nm.

FIG. 11.

SEM micrographs of Si nanopillars fabricated at optimum process parameters. (a) and (b) Image of nanopillars at 125 k magnification. (c) Image of nanopillars at 150 k magnification. Each image is taken at a different location along the sample edge. Scale bars in all images are 200 nm.

Close modal
TABLE III.

Tabulated values of optimization inputs and solved for optimum process parameter values.

Desired target inputsProcess parameters identified via DOE-based optimization
Si etch depth 150 nm % SF6 22% 
Selectivity 2.5 % O2 24% 
Undercut 5 nm Power 321 W 
Sidewall angle 90° Pressure ∼0.01 mbar 
Desired target inputsProcess parameters identified via DOE-based optimization
Si etch depth 150 nm % SF6 22% 
Selectivity 2.5 % O2 24% 
Undercut 5 nm Power 321 W 
Sidewall angle 90° Pressure ∼0.01 mbar 
TABLE IV.

Predicted and measured values of target etch characteristics at solved for optimum process parameters.

Output etch characteristicMean predicted valueLower 95% CI predicted valueUpper 95% CI predicted valueMeasured experimental results
Si etch depth 150 nm 129.3 nm 170.7 nm ∼123 nm 
Selectivity 1.86 0.88 2.84 ∼2.5 
Undercut 5 nm 0 nm 16.1 nm ∼5 nm 
Sidewall angle 90° 81.2° 98.8° >85° 
Output etch characteristicMean predicted valueLower 95% CI predicted valueUpper 95% CI predicted valueMeasured experimental results
Si etch depth 150 nm 129.3 nm 170.7 nm ∼123 nm 
Selectivity 1.86 0.88 2.84 ∼2.5 
Undercut 5 nm 0 nm 16.1 nm ∼5 nm 
Sidewall angle 90° 81.2° 98.8° >85° 

The discrepancy between etch targets and empirical results could, additionally, be attributed to the optimization yielding values for percent SF6 and O2 of total gas flow that were outside the range of DoE test levels on which the models were trained. Similar to the Taylor series approximation method, regression modeling is generally only appropriate in the neighborhood around the points in which the 2k full-factorial DoE is conducted. This is especially true for highly nonlinear phenomena such as RIE processes. Recall, optimization variable bounds allowed for a larger search area. However, as the optimum moves further away from either −1 or 1 for any xi, the prediction accuracy of the model diminishes to an unknown degree. Hence, this process optimization scheme is only justifiable after thorough machine-specific process characterization to determine the best choice of DoE levels and appropriate outer limits.

This paper introduces a complete implementation of nanoscale R2R RIE pattern transfer by demonstrating Si nanopillar arrays fabricated utilizing R2R etch equipment. The etch performance of the R2R CCP plasma reactor in this R2R etch equipment is benchmarked, and pattern transfer of nanopillars into Si is characterized using stochastic, data-driven, and experimental methods. This approach avoids complexity and long development cycles of deterministic models while still providing valuable insight into the nature of nanoscale R2R RIE pattern transfer. Finally, regression analysis and nonlinear optimization are combined to realize the capability to produce feature geometries with desired target parameters. This work represents an initial foray into a new paradigm of nanoscale resolution and high-throughput manufacturing enabled by R2R RIE processing. The methodology employed herein may be applied similarly to additional materials and geometries. Future areas of research should include scaling this etch study to much smaller (sub-50 nm) features, understanding etch loading issues in the presence of diverse types of patterns with sizes ranging from micro- down to nanoscales, and the likely need for an inductively coupled plasma (ICP) equipment configuration for R2R etching. Ultimately, this research has the potential to impact the emerging flexible smart devices markets and make well-established precision manufacturing industries ranging from optics and energy to mobile computing and healthcare more cost-effective.

This work was in part funded by the Cockrell School of Engineering and by the Cockrell Endowed Chair funds. The experimental research was performed at the Texas Nanofabrication Facility supported by NSF Grant No. NNCI-1542159 and by the NASCENT Center supported by the NSF Grant No. EEC-1160494.

The authors have no conflicts to disclose.

Ziam Ghaznavi: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (equal); Validation (lead); Visualization (lead); Writing – original draft (lead). Nicholas Butcher: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal). Dragan Djurdjanovic: Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). S. V. Sreenivasan: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available on request from the corresponding author upon reasonable request. The data are not publicly available due privacy restrictions.

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See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002261 for Table S1 which explicitly lists normalized model effect estimates and corresponding confidence intervals.

Supplementary Material