Ion implantation is a robust and established method to customize the electronic properties of Si. However, fabricating doped, ultrafine semiconductor nanostructures can be challenging. Ion implantation has well-established effects on the dry etch rates of Si, which becomes increasingly consequential as the target dimension shrinks below a few tens of nanometers. While dry etching arrays of block copolymer-templated nanoscale holes (pitch = 37.5 nm, diameter ∼25 nm) into p-type, n-type, and undoped Si, we observed that the lateral etch rate was notably larger for the n-type regions than p-type or undoped regions. By doing image analyses on high resolution electron micrographs of the nanostructured hole arrays, we were able to extract the porosity and average radii of the holes with subnanometer sensitivity and compare the relative etch rates between different doping conditions. We found that degenerately doped n-type silicon consistently etches between approximately 17% and 27% faster in the lateral direction than p-type Si, resulting in significantly larger porosity and, consequently, less mechanical stability. Here, we demonstrate that top-down dimensional analysis of a densely packed porous nanostructure is a robust method for assessing extremely small differences in the lateral, chemical etch rate of doped Si to a degree of sensitivity that was previously unachievable. The minute, dense-packed nature of block copolymer self-assembled nanostructures is shown to be ideal for this application. This proposed method could be useful for designing fabrication processes for heterogeneous nanostructures, as slight dry etch rate variations that may be within process tolerance at the micrometer-scale appear to have nontrivial consequences at the nanometer scale.

Ion implantation is a well-established method for tailoring the electrical properties of silicon (Si). Area-selective doping of silicon is a promising avenue for fabricating high-efficiency monolithic Si devices such as thermoelectric devices and bolometric IR sensors, which require low electronic noise, heat capacity, and thermal conductivity (in the case of bolometers) for good performance.1 

The device performance of both thermoelectrics and IR sensors is inversely proportional to the material thermal properties; thus, minimizing thermal conductivity is desirable for optimizing performance. For context, consider the relevant figures of merit, ZT factor2 and responsivity Rv,3 for thermoelectrics and IR sensors, respectively. The ZT factor can be written as ZT=S2σ/κ, where S is the Seebeck coefficient, T is the temperature, κ is the thermal conductivity, and σ is the electrical conductivity.2 The Rv of a single IR pixel can be written as Rv=IbαRηP0/G(1+ω2τ2)0.5, where Ib is the bias current through the pixel, α is the temperature coefficient of resistance, P0 is the amplitude of modulated IR radiation power falling on the pixel, τ is the thermal response time, ω is the angular frequency of modulation of the radiation, η is the absorbance of IR sensitive films, and G is the thermal conductance of the support structure.3 

As α, η, σ, and κ are typically intrinsic material properties, designing and fabricating high-efficiency room-temperature thermoelectric and bolometric devices without utilizing expensive, rare-earth materials remains a challenge. Silicon is one material with the potential to overcome some of these technological challenges due to its compatibility with an enormous range of nanolithographic processes, its relatively low cost and high availability, and most importantly its electronic customizability through doping.1,4,5 However, Si is disadvantaged by its large native thermal conductivity. An emerging avenue for overcoming this disadvantage is to introduce a phononic crystal nanostructure into Si, which has been shown to reduce the thermal conductivity of Si by as much as 80%–90% relative to bulk without significantly degrading the electronic properties.6–10 By leveraging selectively doped Si nanostructures, it becomes possible to independently engineer the thermal and electronic material properties of Si. An additional benefit to using doped, nanostructured, monolithic Si for these types of devices is the elimination of thermal boundary resistance between the sensor and the substrate caused by layering different materials.1 

However, fabricating doped Si nanostructures is challenging. Ion implantation has well-established effects on the dry etch rates of silicon materials, which is increasingly consequential as the critical dimension shrinks below a few tens of nanometers. In this work, we present an investigation into the nanoscale lateral variation in dry etch rates of Si as a function of doping, as well as a quantitative method for measuring and calibrating etches to take these etch rate variations into account. Doped (p- and n-type) and undoped Si nanostructured thin films were fabricated using a self-assembled (SA) cylinder-forming block copolymer (BCP) nanolithography process to form arrays of hexagonally close-packed nanopores with pitch (center-center distance) p = 37.5 nm. We demonstrate that implant condition strongly affects the nanoscale, lateral etch rate of doped Si in an otherwise anisotropic Cl plasma etch, with the n-type Si having the fastest etch rate and p-type having the slowest.

While vertical variation in Si etch rates caused by doping has been documented previously, very little has been reported about lateral variations in the etch rate, especially under highly anisotropic etching conditions. This is likely due to the minute scale of these variations (<5 nm), which are typically well below the error of measurement for most etching processes, geometries, and image analysis procedures. While studying the precise physical mechanisms behind these rate variations was beyond the scope of this work, we are able to demonstrate that SEM image-based metrology of a densely packed array of (predominantly) isoporous holes is a robust method for quantifying extremely small differences in the lateral etch rate of Si nanostructures, which we believe to be dominated by chemical etching processes. These small etch rate variations are significant when dry etching nanoscale holes spaced at 37.5 nm and resulted in large differences in the overall porosity, average hole radius, and mechanical stability of the Si nanostructures we fabricated. More broadly, we believe our proposed metrology method could be a valuable tool in evaluating and calibrating nanofabrication processes for etching heterogeneous semiconductor nanostructures.

Silicon-on-insulator (SOI) 200 mm wafers were purchased from Silicon Valley Microelectronics (USA) with the following specifications: 〈100〉 monocrystalline Si, 100 nm; buried oxide (BOX), 3 μm; handle wafer, 725 μm; wafer diameter, 200 mm. Wafers were used without further cleaning. Toluene (≥99.5%) was purchased from Sigma Aldrich and used as received. Trimethylaluminum (TMA) was provided by the Pritzker Nanofabrication Facility.

The BCP used in the study was a cylinder-forming polystyrene-block-poly(methyl methacrylate) (Mn 20k-b-50k, denoted as C2050, bulk period p = 37.5 nm) that was purchased from Polymer Source and used as received. For perpendicular BCP assembly, wafers were first coated with a random poly(styrene-r-(methyl methacrylate)) copolymer mat that was designed to be energetically neutral to both blocks of the PS-b-PMMA. Solutions of all polymers used in this work were filtered prior to spin-coating using a 1 ml polypropylene syringe and an mdi Membrane Technologies PTFE syringe filter with 0.2 μm pore size. All polymer solutions were prepared in toluene.

A schematic illustration of the process used to fabricate BCP-templated Si nanostructures is shown in Fig. 1. First, three SOI chips with different doping conditions (p-type, n-type, and undoped Si) were prepared. Dopant condition refers only to the device layer of the SOI stack. To prepare the doped Si, each 200mm SOI wafer was first cut into 45 mm2 chips. Then, two of the 45 mm2 chips were sent for ion implantation at Cutting Edge Ions, LLC. For p-type Si, boron was implanted at an energy of 10 keV and a dose of 1.70 × 1015 ions/cm2. For n-type Si, phosphorous was implanted at an energy of 30 keV and a dose of 2.30 × 1015 ions/cm2. After ion implantation, the samples were activated by dry annealing in a Tystar Mini-Tytan 4600 furnace at 900 °C for 30 min. After activation, each 45 mm2 chip was cut into four 22.5 mm2 chips. Etch tests were conducted on 22.5 mm2 chips for the n-doped, p-doped, and undoped Si.

FIG. 1.

Schematic illustration of fabrication process used to form Si nanostructures templated by a self-assembled BCP. (a) A substrate (one each of p-type, n-type, and undoped Si) based on an SOI stack is prepared. (b) C2050 BCP film is spin-coated and annealed to form perpendicular cylinders in randomly nucleated grains. (c) Films are subjected to SIS to selectively nucleate AlOx within the PMMA domain. (d) O2 plasma is used to selectively remove the PS cylinders, resulting in a nanoporous SIS AlOx structure. (e) Samples are subjected to an anisotropic Cl2 etch in order to etch holes from the AlOx nanoporous etch mask into the underlying Si. (f) Samples are subjected to a VHF etch to remove the underlying BOX layer.

FIG. 1.

Schematic illustration of fabrication process used to form Si nanostructures templated by a self-assembled BCP. (a) A substrate (one each of p-type, n-type, and undoped Si) based on an SOI stack is prepared. (b) C2050 BCP film is spin-coated and annealed to form perpendicular cylinders in randomly nucleated grains. (c) Films are subjected to SIS to selectively nucleate AlOx within the PMMA domain. (d) O2 plasma is used to selectively remove the PS cylinders, resulting in a nanoporous SIS AlOx structure. (e) Samples are subjected to an anisotropic Cl2 etch in order to etch holes from the AlOx nanoporous etch mask into the underlying Si. (f) Samples are subjected to a VHF etch to remove the underlying BOX layer.

Close modal

Next, the p-type, n-type, and undoped Si SOI samples were coated with the C2050 BCP thin film. First, each sample was coated with the 57S mat, which was designed to be energetically neutral to both blocks of C2050. To prepare the mat, a 0.3 wt. % solution of 57S in toluene was spin-coated to a thickness of ∼9.5 nm. The mat was cross-linked by annealing on a hot plate in an N2 glovebox for 15 min at 220 °C. Then, excess unreacted mat was removed by ultrasonication in toluene for 3–5 min. After annealing and rinsing, the neutral mat thickness decreased slightly to ∼8 nm. Film thicknesses were measured by ellipsometry on witness samples using a Cauchy model.

To fabricate SA BCP nanostructures, a 2 wt. % solution of C2050 in toluene was then spin-coated directly onto the prepared 57S mat to a target film thickness of 85 nm. Next, the samples were annealed at 270 °C for 2.5 h on a hot plate in an N2 glovebox. After 2.5 h, the samples were thermally quenched on a metal block. All samples were coated and annealed at the same time to facilitate comparison.

In order to transfer the BCP nanostructure into the underlying Si layer, the BCP film was subjected to sequential infiltration synthesis (SIS), during which the PMMA block is selectively infiltrated with alternating vapor-phase precursors (TMA and DI H2O) in order to nucleate a significant amount of AlOx within the PMMA domain. This resulted in a hybrid organic/inorganic PMMA/AlOx film containing PS cylinders. The SIS process was performed in an Ultratech/Cambridge Savannah ALD system and has been previously reported for C2050.7,8

After SIS, the 22.5 mm2 samples were mounted via thermal release tape on an Si carrier wafer and lightly O2 plasma etched for 10 min in a PlasmaTherm RIE to selectively remove the PS cylinders. Next, a Cl2−O2 anisotropic plasma etch was used to etch holes into the underlying Si using the SIS nanostructure as an etch mask. All substrates were etched simultaneously to enable comparison. Next, the SIS structure was stripped with an 80C piranha (conc. H2SO4: 30% H2O2 7:3) etch for 45 min, then rinsed copiously with DI H2O, and dried with an N2 gun. Finally, all samples were subjected to an 1800 s vapor HF (VHF) etch to selectively remove the underlying BOX layer. Post-VHF, samples were inspected in top-down SEM using a Carl Zeiss Merlin FE-SEM, and 2 μm wide images of each were collected for subsequent metrology and image analysis. Images of the completed Si nanostructures are shown in Fig. 2.

FIG. 2.

Top-down SEM inspection of self-assembled BCP Si nanostructures fabricated from (a) p-type, (b) undoped, and (c) n-type Si. While higher magnification views of the nanostructures are shown here for clarity, only 2 μm wide (lower magnification) images were used for image analysis. The self-assembled nanostructure forms randomly oriented grains with isoporous, hexagonal packing within each grain, separated by defects along the grain boundaries.

FIG. 2.

Top-down SEM inspection of self-assembled BCP Si nanostructures fabricated from (a) p-type, (b) undoped, and (c) n-type Si. While higher magnification views of the nanostructures are shown here for clarity, only 2 μm wide (lower magnification) images were used for image analysis. The self-assembled nanostructure forms randomly oriented grains with isoporous, hexagonal packing within each grain, separated by defects along the grain boundaries.

Close modal

After inspection, the SEM micrographs of the p-type, n-type, and undoped Si nanostructures were analyzed to extract the porosity and average hole radius. Image analysis and metrology was conducted in fiji (fiji is Just image-j). First, a 2 μm wide image of the nanostructure was imported into fiji. Next, the image scale was set in the software, and the image was cropped slightly to remove the SEM information bar. See Fig. S1 in the supplementary material15 for an example of the cropped SEM micrographs. Next, the images were thresholded to form a binary (black and white) image. There was sufficiently high contrast between the Si nanostructure and vacuum that no bandpass filtering or image smoothing was required in order to form a high quality binary image.

In order to determine whether thresholding condition was introducing artificial trends into the extracted dimensional data, a set of three different threshold conditions in fiji were applied to each analyzed image. See Fig. S2 in the supplementary material15 for images of the thresholded n-type Si images compared to the original. As there were three sample types (p-, n-, and undoped Si) and three threshold conditions, a total of nine different doping/threshold conditions were analyzed. In fiji, the lower threshold limit was set to 0 for all samples, while the upper threshold limit was varied from 50 to 65 to 75. The three thresholding conditions are denoted as 0/50, 0/65, and 0/75.

Once a binary image was obtained, the Analyze Particles function in fiji was used to extract the areas of every hole in the image. From here, the porosity P of the nanostructures could be calculated by dividing the sum of all the hole areas by the area of the image, as described by the following:

P=1jAhole,1Ahole,jAimage.
(1)

This calculation necessarily included the irregularly sized defect holes located on the grain boundaries of the self-assembled nanostructures, as they contribute to the overall porosity of the nanostructure.

Next, the hole areas extracted with fiji Analyze Particles were used to calculate the average radius of the “normal” holes; that is, holes that are not a part of the defect structures at the grain boundaries. Due to the well-ordered nature of BCP microphases, holes located within the grains are roughly isoporous and have a well-defined constant pitch over the size of the grains, which is the same for each grain. While defect structures contribute to the overall porosity, the stochastic hole shapes and sizes at the grain boundaries are not needed to analyze the average hole radius and were excluded from this calculation.

To exclude outliers, the standard deviation σ of the extracted hole areas was calculated using the std function in matlab. Next, all areas falling outside of ±3σ from the median area value were considered outliers and excluded from the calculation. See Fig. S3 in the supplementary material15 for an example plot of all hole areas for a given image distribution and the ±3σ cutoffs. From here, the radius of each hole within the ±3σ area range was calculated using the following:

rhole=Aholeπ.
(2)

Next, the average radius for the entire ±3σ area range was calculated as follows:

ravg=1jrhole,1rhole,j#holes.
(3)

The error in the value of ravg stemming from the distribution of areas δr,avg was calculated using the following:11 

δr,avg=12(δAavg,±3σAavg,±3σ).
(4)

For each of the nine thresholded images, the porosity P and average radius ravg ± δr,avg were calculated, the results of which are summarized in Table I.

TABLE I.

Porosity P and radius ravg as a function of dopant and thresholding condition.

Porosityravg
(nm)
Si typep-typeundopedn-typep-typeUndopedn-type
0/50 0.138 0.177 0.26 7.39 ± 1.08 8.45 ± 1.03 10.2 ± 1.15 
0/65 0.229 0.272 0.352 9.61 ± 1.05 10.7 ± 1.01 12.0 ± 1.10 
0/75 0.278 0.346 0.412 10.7 ± 1.02 12.1 ± 0.956 13.1 ± 1.09 
Porosityravg
(nm)
Si typep-typeundopedn-typep-typeUndopedn-type
0/50 0.138 0.177 0.26 7.39 ± 1.08 8.45 ± 1.03 10.2 ± 1.15 
0/65 0.229 0.272 0.352 9.61 ± 1.05 10.7 ± 1.01 12.0 ± 1.10 
0/75 0.278 0.346 0.412 10.7 ± 1.02 12.1 ± 0.956 13.1 ± 1.09 

We would like to note that for each 2 μm image, approximately 2500 holes were analyzed per image to calculate P and ravg. While 2 μm may seem small compared to the size of the sample (22.5 mm), the minute scale and ultrahigh feature density of the BCP-templated holes allow the averaging of thousands of holes even from a small image. Coupled with the thermodynamically well-defined size and pitch of BCP features, we believe the metrology results from these 2 μm images to be representative of hole dimensions across the entire sample.

The measured porosities and radii for n-type, p-type, and undoped Si for all thresholding conditions are shown in Fig. 3. From this plot, it can easily be seen that p-type Si has the lowest porosity while n-type has the largest porosity, with undoped Si having a porosity value in between p- and n-type. This trend appears for each thresholding condition, indicating that the thresholding parameters did not introduce trends in the measured data. We can conclude from these initial results that ion implantation affects the size of the holes and, by implication, the dry etch rate.

FIG. 3.

Porosity (a) and radius (b) as a function of implant condition and thresholding parameters. Lines are only plotted as guides for the eye. In (b), error bars were calculated according to the method described under Sec. III B.

FIG. 3.

Porosity (a) and radius (b) as a function of implant condition and thresholding parameters. Lines are only plotted as guides for the eye. In (b), error bars were calculated according to the method described under Sec. III B.

Close modal

Having eliminated the thresholding condition as a source of noise, we chose to focus our discussion of radius and porosity exclusively on the thresholding condition designated as 0/75. This condition was the closest to the automatically determined threshold applied chosen by fiji, and we believe the dimensions calculated using this setting to be most representative of the actual feature sizes. The values of porosity and radii for n-type, p-type, and undoped Si are summarized in Table I. From these results, we conclude that the final porosity of our p-type, undoped, and n-type Si nanostructures were 27.8%, 34.6%, and 41.2%, respectively. These porosities, in order, corresponded to radii of 10.7 ± 1.02, 12.1 ± 0.956, and 13.1 ± 1.09 nm. As expected, p-type Si was found to have the smallest porosity and radius of the three samples, while n-type was found to have the largest. Since the samples were etched at the same time for the same amount of time, but differences in radius were measured, we concluded that the relative lateral etch rate order is as follows: n-type Si > undoped Si > p-type Si.

It is relatively well-reported that the etch rates of p- and n-type Si in F- and Cl-chemistry plasma differ significantly for heavily doped (∼1019–20 ions/cm3) Si.12 Generally, heavily n-doped Si and polysilicon have been documented to etch as many as 15–25 times faster than undoped Si and more rapidly than lightly doped n-type Si.13 Lightly doped (∼1015 ions/cm3) p- and n- type Si have been shown to have similar etch rates, while heavily doped p-type Si and polysilicon etches more slowly than heavily n-doped, undoped, and lightly doped p- and n- type Si and polysilicon,2 

Mechanistically, Winters and Haarer reported that surface charge during etching could be the cause of etch rate variation in Si as a function of implantation condition.12 For F-chemistry plasmas, it is thought that exposure of Si to fluorinated plasma species results in the formation of surface-based fluorosilyl groups containing negative ions. The number of negative ions N on the surface is also thought to be affected by doping and is larger for n-doped Si. Winters and Haarer suggest that the electronic field E around the sample during etching is proportional to N, and when N is large, E is large, and vice versa. The etch rate of doped Si is thought to be affected by the combination of the electric field E during etching and the position of the material's Fermi level. For heavily p-doped Si, the Fermi level is shifted within the valence band, and the author suggests there is consequently little band bending upon dry etching. A similar effect is thought to occur for lightly p- or n- doped Si (and undoped Si), in which the position of the Fermi level is not significantly shifted (or not shifted at all), little to no band bending is thought occur upon etching.

However, for heavily n-doped Si in which the Fermi level is shifted within the conduction band, significant band bending is thought to occur upon etching. Due to the creation of this large potential difference, heavily n-doped Si etches more quickly than undoped and p-doped Si. While this study focused primarily on F-chemistry plasmas, the authors suggested that similar etching trends would apply for Si etched in Cl-chemistry plasmas provided that negative ions at the surface were the driving force for etch rate.12 

The porosity—and by implication, lateral etch rate—trends visible in our etching test results are directly in agreement with this predicted trend. While confirming the theoretical foundation behind the observed phenomena was beyond the scope of our work, it was helpful to note that the trend we observed was in agreement with previously reported experimental and theoretical results.

There are two basic regimes of plasma dry etching: anisotropic etching and isotropic etching. Anisotropic etches tend to proceed by a combination of chemical and physical etching processes and etch primarily in the vertical direction to produce high aspect ratio features. Isotropic etches tend to be dominated by chemical etching processes only and etch uniformly in both the vertical and lateral directions and can cause features such as undercuts. In analyzing the porosity of our nanostructured hole arrays from top-down, we can only assess variations in lateral etch rate, as illustrated in Fig. 4. Given that our etch was highly anisotropic and that all our samples were etched simultaneously for the same amount of time, the expansion in radius we observed from the p-type to undoped to n-type Si could only have resulted from differences in the rate at which each material etched laterally. Given the anisotropy of the etch, we conclude that the variations in lateral etch rate between the differently doped Si must be primarily chemical in origin. Thus, by analyzing top-down porosity of simultaneously prepped Si nanostructures, we have developed a means of measuring nanoscopic variation in the lateral, chemical etch rate with single-to-subnanometer precision.

FIG. 4.

Illustration of lateral vs vertical etching modalities. Only etching in lateral directions can be observed from top-down inspection.

FIG. 4.

Illustration of lateral vs vertical etching modalities. Only etching in lateral directions can be observed from top-down inspection.

Close modal

From here, it is possible to estimate the relative etch rate differences between the p-type, undoped, and n-type Si using the average radii ravg, with the p-type ravg as a baseline. To obtain the etch rates of n-type and undoped Si relative to p-type, we divided the ravg of each by that of p-type Si across all thresholding conditions. The results of this calculation are summarized in Table II.

TABLE II.

Comparative etch rates of undoped and n-type Si relative to p-type Si across all thresholding conditions.

Thresholdp-typeUndopedn-type
0/50 Baseline ∼12.3% faster ∼27.5% faster 
0/65 Baseline ∼9.90% faster ∼20.0% faster 
0/75 Baseline ∼10.7% faster ∼17.3% faster 
Thresholdp-typeUndopedn-type
0/50 Baseline ∼12.3% faster ∼27.5% faster 
0/65 Baseline ∼9.90% faster ∼20.0% faster 
0/75 Baseline ∼10.7% faster ∼17.3% faster 

Across all thresholding conditions, we find that undoped Si etches approximately 10%–12% faster than p-type Si, while n-type Si etches approximately 17%–27% faster than n-type Si. While the scale of these etch rate differences are small—on the order of a couple nanometers or less—the overall impact on porosity and the mechanical integrity of the nanostructure is significant. Hole area (and porosity) is a function of radius squared, so small changes in radius have an amplified effect on the porosity. This is significant when fabricating ultrafine nanoporous structures such as those presented in this work, where the pitch of the holes is comparable to the hole diameter, and the width of the neck in between adjacent holes approaches 10 nm. However, we can take advantage of this relationship and use it to sensitively extract the average hole radius over thousands of identical holes with subnanometer precision. This, in turn, allows us to calculate relative etch rates with unprecedented sensitivity. The combination of feature uniformity over large areas, nananoscale dimensions, and ultrahigh feature density enabled by BCP lithography makes BCP-templated porous nanostructures ideal for innovative, ultrasensitive metrology. However, we believe that any nanofabrication methodology capable of generating uniform arrays of densely packed nanoscale holes, such as e-beam lithography, would be appropriate for this application.

By applying this technique to our process, we were able to calibrate the etch rates of p- and n-type Si and etch each region separately to achieve the same final porosity regardless of ion implantation condition. By doing so, we resolved the issues of mechanical collapse and poor yield on the n-type structures. We believe that dimensional analysis on densely packed nanopores to sensitively characterize nanometer-scale variations in dry etching rate could be broadly applied as a part of any etch development process for heterogeneous nanostructures, especially as a comparative tool between similar materials.

As a preliminary demonstration of how this method could be applied to other materials, we conducted the same pattern transfer and image analysis process on amorphous and polycrystalline Si films and compared to the crystalline undoped Si sample. The amorphous and polycrystalline films were etched at the same time as the doped and undoped Si, so they can be directly compared to the undoped, crystalline Si sample. Images of these samples are shown in Fig. 5.

FIG. 5.

SEM micrographs of porous nanostructures etched into amorphous (a), polycrystalline (b), and crystalline (c) silicon.

FIG. 5.

SEM micrographs of porous nanostructures etched into amorphous (a), polycrystalline (b), and crystalline (c) silicon.

Close modal

While undoped amorphous, polycrystalline, and crystalline dry etch rates have not been reported to differ significantly, nanometer-scale variation in dry etch rates have not been explored in depth.14 The results of our porosity and radius analysis for Si as a function of crystallinity are summarized in Table III.

TABLE III.

Porosity P and radius ravg as a function of dopant for the 0/75 thresholding condition only for amorphous, polycrystalline (poly), and crystalline silicon.

Porosityravg
(nm)
Si typeAmorphousPolyCrystallineAmorphousPolyCrystalline
0/75 0.249 0.244 0.346 9.77 ± 1.02 9.98 ± 1.11 12.1 ± 0.956 
Porosityravg
(nm)
Si typeAmorphousPolyCrystallineAmorphousPolyCrystalline
0/75 0.249 0.244 0.346 9.77 ± 1.02 9.98 ± 1.11 12.1 ± 0.956 

These preliminary data show that there appear to be small differences in the nanoscale etch rate between amorphous, polycrystalline, and crystalline Si. The measured porosity for amorphous and polycrystalline Si were approximately 24%–25%, while that of crystalline Si was 34.6%. The average radii showed a stronger trend, with the amorphous Si having the smallest ravg at 9.77± 1.02nm, the crystalline Si having the largest ravg at 12.1 ± 0.956, and the polycrystalline Si being in the middle with a ravg 9.98 ± 1.11nm. It makes sense to see a trend in the average hole radius while not seeing one in porosity, since the porosity calculation is simply the ratio of holes to the total image area including defects (which includes both large holes and large contiguous regions of material), while the ravg calculation purely considers the average dimensions of normal” holes. Our preliminary tests suggest that the crystallinity of Si may have nanoscale effects on its dry etch rate. While thoroughly investigating the etch rate variations between amorphous, polycrystalline, and monocrystalline Si was beyond the scope of this work, we believe that analyzing at the nanoscale is a valuable approach for understanding material properties at the ultrafine nanoscale. Our image analysis method could conceivably be expanded to include analysis of the hole eccentricity with increasing etch time to assess whether the crystal structure emerges with increasing etch time. We believe that further investigation into phenomena such as crystallinity is warranted and that our proposed metrology method is uniquely suitable for such work.

In summary, we documented the lateral (and predominantly chemical) dry etch rates for a variety of doped and undoped Si substrates. We developed a method for using top-down porosity measurements of a hexagonal nanopore array to quantify small differences in the etch rate between differently doped Si substrates. Our results agree with previous reports on vertical dry etch rate differences in p-doped, n-doped, and undoped Si. Our findings also reinforce the literature understanding that the chemical etch rate, and not the ion etch rate, is most sensitive to the substrate type.

These observations provided valuable information that helped us improve our process design. Primarily, we learned that it is necessary to etch the p- and n-implanted membrane components separately to fabricate devices with uniform porosity post-ion implantation, with a shorter etching time for the n-implanted side. Next, we learned that analyzing the dimensions of etched nanopores is a robust method for assessing nanoscopic differences in the chemical etch rate across different types of doped Si. The change in porosity is a function of the radius of the hole squared, meaning that small differences in etching rate are amplified when analyzing the porosity of a sample and are, therefore, more easily inferred from top-down image analysis. We believe this method is potentially suitable for measuring small differences in the dry etch rate between any combination of other substrates and could potentially provide a means of studying and quantifying etch rate differences that were previously unmeasurable in any way.

This work was supported as part of the Advanced Materials for Energy-Water Systems (AMEWS) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This work made use of the Pritzker Nanofabrication Facility (PNF) of the Pritzker School of Molecular Engineering at the University of Chicago, which receives support from Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (No. NSF ECCS-1542205), a node of the National Science Foundation’s National Nanotechnology Coordinated Infrastructure. This work also made use of the shared facilities at the University of Chicago Materials Research Science and Engineering Center, supported by National Science Foundation under Award No. DMR-2011854. The authors thank the PNF staff for their support and insightful discussions.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001287 for details regarding image analysis.

Supplementary Material