Electric-Field-Assisted Directed Assembly of Transition Metal

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Electric-Field-Assisted Directed Assembly of Transition Metal Dichalcogenide Monolayer Sheets Donna D Deng, Zhong Lin, Ana Laura Elías, Nestor Perea-Lopez, Jie Li, Chanjing Zhou, Kehao Zhang, Simin Feng, Humberto Terrones, Jeffrey S. Mayer, Joshua A. Robinson, Mauricio Terrones, and Theresa S. Mayer ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b03114 • Publication Date (Web): 15 Apr 2016 Downloaded from http://pubs.acs.org on April 15, 2016

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Electric-Field-Assisted Directed Assembly of Transition Metal Dichalcogenide Monolayer Sheets Donna D. Deng1, 2, †, Zhong Lin2, 3, † , Ana Laura Elías2, 3, Nestor Perea-Lopez2, 3, Jie Li2, 4, Chanjing Zhou1, 2, Kehao Zhang1,2, Simin Feng2, 3, Humberto Terrones5, Jeffrey S. Mayer4, Joshua A. Robinson2,4, Mauricio Terrones 1,2, 3, 6, *, Theresa S. Mayer 2,4,7 * 1. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, United States 2. Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, PA 16802, United States 3. Department of Physics, The Pennsylvania State University, University Park, PA 16802, United States 4. Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802, United States 5. Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180, United States 6. Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, United States 7. Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, United States

†

D. Deng and Z. Lin contributed equally to this work.

* Corresponding authors: [email protected] (M. T.) and [email protected] (T. M.)

ABSTRACT Directed assembly of two-dimensional (2D) layered materials, such as transition metal dichalcogenides (TMDs), holds great promise for large-scale electronic and optoelectronic applications. Here, we demonstrate controlled placement of solution-suspended monolayer tungsten disulfide (WS2) sheets on a substrate using electric-field-assisted assembly. Micrometer-sized triangular WS2 monolayers are selectively positioned on a lithographically defined interdigitated guiding electrode structure using the dielectrophoretic force induced on the sheets in a non-uniform field. Triangular sheets with sizes comparable to the inter-electrode gap assemble with an observed 1 ACS Paragon Plus Environment

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preferential orientation where one side of the triangle spans across the electrode gap. This orientation of the sheets relative to the guiding electrode is confirmed to be the lowest energy configuration using semi-analytical calculations. Nearly all sheets assemble without observable physical deformation, and post-assembly photoluminescence and Raman spectroscopy characterization of the monolayers reveal that they retain their as-grown crystalline quality. These results show that the field-assisted assembly process may be used for large-area bottom-up integration of 2D monolayer materials for nanodevice applications.

KEYWORDS Transition metal dichalcogenide; tungsten disulfide; chemical vapor deposition; dielectrophoretic assembly.

Atomically thin semiconducting transition metal dichalcogenides (TMDs) offer many unique properties that are absent in their bulk counterparts, such as the emergence of a direct band gap, large surface to volume ratio, flexibility, transparency, and valley degree of freedom.15

The versatile chemistry and broad electronic properties of ultra-thin TMD layers have trig-

gered novel applications in a wide range of fields including catalysis, energy storage, electronic and optoelectronic devices.6-11 Driven by the interest in exploiting these unique properties for device applications, a variety of methods have been explored to integrate monolayer TMD’s onto large-area substrates. Chemical vapor deposition (CVD) processes have been successfully used to grow polycrystalline semiconducting TMDs layers on various substrates.12 Sulfurization of transition metal oxides or vaporization of TMD powders also allow monocrystalline triangular TMD sheets to be grown.132 ACS Paragon Plus Environment

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Use of these TMDs often requires post-growth transfer of sheets onto a second substrate.

Thus far, post-growth integration has been accomplished by either wet or dry transfer techniques, corresponding to the transfer process occurring in or out of the releasing solution.19 Using the wet transfer method, thousands of deposited TMD sheets can be transferred simultaneously from the growth substrate to a target substrate with the aid of a handle layer such as poly(methyl methacrylate) (PMMA).20-22 Although highly scalable, this approach does not provide control of the location or orientation of the sheets, which limits its use for many applications. In contrast, dry (or deterministic) transfer offers better control over positioning and orientation.19 In this process, after the material is removed from the growth substrate in similar ways as the wet transfer approach, the TMD sheet of interest can be monitored under an optical microscope and released at a desired position on the target substrate with a preferred orientation by employing a manipulator.23, 24 This transfer process is not scalable because only one particular sheet is deterministically positioned in each transfer. For device integration, techniques that allow parallel assembly of two-dimensional (2D) sheets with control over their position and orientation are highly desirable.11, 25, 26 One such technique uses the dielectrophoretic (DEP) force and torque induced on solution-suspended particles in a non-uniform field to direct their assembly.27, 28 A variety of lithographic guiding electrode structures have been used to tailor the spatially varying field gradient that extends into the supsending solution,29 thereby permitting registry of individual or groups of particles to predefined features on a target substrate. Additionally, heterogeneous integration of multiple types of materials on the same target substrate has been achieved by coordinating material delivery with location-specific biasing of the guiding electrode structure.30 This provides the ability to integrate diverse materials on alternative platforms, including silicon (Si)-based integrated circuits 3 ACS Paragon Plus Environment

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(IC’s) and flexible substrates, by allowing optimization of the material synthesis process to be independent of device fabrication.31, 32 High-yield array assembly has been demonstrated for zero- and one-dimensional (0D and 1D) metallic and semiconducting materials, including nanowires,33 nanotubes,34 nanospheres,35 and nanoribbons36 for use in nanoelectromechanical system (NEMS),37 chem/biosensing,30,

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and nanoelectronic devices.31, 33, 39, 40 More recently, randomly shaped exfoliated 2D graphene and graphene oxide (GO) flakes that are hundreds of nanometers in size have been assembled between pairs of electrode fingers.36, 41-46 Unlike the previously assembled 2D materials, CVDgrown monolayer WS2 crystals have a well-defined triangular shape that is driven by the 2H crystal structure. This provides an opportunity to control both the position and the orientation of 2D sheets simultaneously during assembly, which provides advantages for subsequent device integration. Notably, these triangles are several micrometers in lateral size, which makes them susceptible to folding, wrinkling, or aggregation during the assembly process. Thus, the optimization of assembly parameters to yield systematic and parallel placement of individual TMD sheets with clearly observable control over orientation is challenge that must be overcome. This paper reports on the electric-field assisted directed assembly of CVD grown, atomically thin TMD crystals. Several micrometer-sized WS2 triangular monolayer sheets are released from the growth substrate into a carrier solution for assembly. An electrically biased interdigitated guiding electrode structure creates a non-uniform field that directs monolayer placement on the assembly structure. The assembly parameters are optimized to produce high-yield positioning of the WS2 monolayers along the guiding electrodes with little to no wrinkling, folding, or physical damage. Furthermore, the assembled triangles display a clear orientation preference, which is confirmed to be the minimum energy configuration using a semi-analytical equivalent circuit

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model calculation. Single point and mapped Raman and photoluminescence (PL) characterization of the large and topographically flat monolayers verify that the high material quality of the as-grown 2D WS2 monolayer crystals is maintained post-assembly. RESULTS AND DISCUSSION A pair of electrically isolated interdigitated guiding electrodes that is separated by a uniform width gap was used to assemble WS2 triangular sheets (see Figure 1a). 28, 48 The structure induces an electric field gradient in the suspending medium that is invariant with position along the electrode gap (y-direction) , as discussed later in the paper.27 This enables parallel assembly of the solution-suspended WS2 sheets with control over both their position and orientation across the predefined electrode gap, while also minimizing their assembly outside of the gap region. A pair of electrically isolated interdigitated guiding electrodes was fabricated by depositing 40 nm of Ti/Au on a flat SiO2/Si substrate, resulting in an electrode gap is more accurately described as a shallow trench 3 µm across and 40 nm deep. Single-crystal monolayer WS2 triangles were synthesized by sulfurization of thermally deposited WO3 films on SiO2/Si.47 The majority of the WS2 triangles were 3 to 5 µm on a side, with a small number of larger triangles up to 15 µm on a side. After synthesis, a 300 nm thick PMMA coating was applied to the monolayers as a holding layer for the release process. Once the SiO2 sacrificial layer was removed with a brief soak in NaOH, the holding layer was recovered and dissolved in acetone (see supplementary Figure S1).17, 19 The acetone-WS2 suspension was dispersed onto the assembly structure, as illustrated in Figure 1a. When a bias is applied across the electrodes, a non-uniform electric field radiates into the carrier medium, inducing electric forces on the monolayer sheets. For electricfield assisted assembly, an AC bias is applied to minimize local voltage screening by surface


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charge on the monolayer sheets.48 In this work, the bias was maintained on the guiding electrodes until the acetone evaporated. Organic residue remaining after assembly was removed using an acetone soak. To better understand the assembly process and project the expected results for this process, the force on the assembling WS2 monolayers was estimated. The DEP force on a solutionsuspended particle in a non-uniform electric field can be approximated by: ∗

∗

< > = Re ∗ ∗ ∇

(1)

∗ where ∗ is the complex permittivity of the monolayer sheets, is the complex permittivity of

the suspending medium, is a constant that depends on the shape and size of the particle, and the factor within the braces is the complex Clausius-Mosotti (CM) factor.48 Equation 1 shows

that the DEP force on the particle scales with the gradient of the electric field squared (∇ ) and that particles will be attracted to or repelled from regions of concentrated field strength depending on the sign of the CM factor. Using the material parameters listed in Table S1,49-51 the frequency-dependent CM factor is determined for WS2 assembling out of an acetone solution (see Figure 1b). The CM factor is positive at low frequencies and begins to decrease at 108 Hz until the value becomes negative above approximately 1010 Hz. Figure 1c shows the electric field gradient map of the interdigitated electrodes under AC bias as modeled analytically using finite element analysis. The parameters used for this simulation are identical to those used in the models discussed later in the paper. The field is concentrated along the electrode edges. Based on this information, the WS2 sheets will be directed to the high-field region in the electrode gap below the cross-over frequency of 1010 Hz, and repelled 6 ACS Paragon Plus Environment

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from the gap above this frequency. In contrast to sharp-tipped electrodes, the uniform width gap structure is ideally suited to control the orientation of the triangular particles during assembly because it provides a uniform field concentration and particle-to-electrode overlap along the electrode edge. Equation 1 illustrates the relationship between the DEP force and the system parameters; however, it is only valid in the limit that the change in electric field over the length scale of the assembling monolayer is negligible.52 This assumption is not accurate for the assembly system in this report where the WS2 triangle size (3~5 µm) is comparable to or larger than the electrode gap width (3 µm). To account for such deviations and calculate the DEP force on the 2D sheets more accurately, the Maxwell stress tensor (MST) is used to model the system. This method is a more rigorous approach to studying mechanical forces on an object as a result of electric forces without the assumptions made in Equation 1.52 The DEP force on an assembling sheet is estimated using a 2D cross-sectional approximation of the complete 3D experimental system used in this work (See SI section Computational details). The system is modeled for a WS2 sheet that is that is 3 µm on a side with an applied AC bias of 15 V peak-to-peak at 100 kHz, corresponding to a positive CM factor. Figure 2 shows a mapping of the DEP force of a WS2 sheet as a function of its centroid location above the guiding electrodes. The colors in the map in Figure 2 illustrate the magnitude of the DEP force on the sheet, while the overlaid arrows depict the direction. The map shows a trend of increasing DEP as the sheet approaches the gap region between the biased electrodes. This local region sees up to 10-4 N/m of DEP force, which is more than three orders of magnitude higher than the low DEP regions several micrometers away from the electrode gap. This indicates that as a sheet comes into the vicinity of the electrode edges, it is attracted towards the gap with increasing force. First7 ACS Paragon Plus Environment

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order calculations show that other forces exerted on the sheet, such as gravity and buoyancy, are several orders of magnitude smaller than the lowest DEP forces calculated in the vicinity of the electrode gap (on the order of 10-10 and 10-11 N/m for gravitational and buoyant forces respectively, see SI section Computational details). Although this mapping is a 2D cross-section of the actual experimental structure, it supports experimental results reported for nanowire assembly over similar planar structures,53 and can be expected to serve as a reasonable estimate of the relative forces on the WS2 monolayers in this assembly system. WS2 triangles were assembled out of the acetone dispersion using the same bias parameters studied with the MST model (AC bias 15 V peak-to-peak at 100 kHz). Field emission scanning electron microscope (FESEM) images of the assembled WS2 sheets are shown in Figure 3. The narrow horizontal stripes in Figure 3a and wide horizontal stripes through the center of the images in Figure 3b and 3c correspond to the 3 µm wide gap between the interdigitated guiding electrodes. These images show that individual, atomically thin WS2 triangular sheets were assembled in parallel with one another along the electrode gaps with little stacking, folding, breaking, and corrugating of the sheets. Very few sheets could be found on top of the biased electrodes or outside of the patterned region. These results show that directed assembly continues until nearly all of the sheets are assembled out of solution, which occurs before the acetone evaporates in under 30 sec. The high resistance of an assembled sheet (approximately 56 MΩ for a 3.5 µm sheet, see SI section Details regarding assembly results for details) prevents shorting of the electrode structure after the sheet is assembled, thereby maintaining the high field concentration in the regions of the gap adjacent to the assembled sheets. The high-field preferentially attracts subsequent solution-suspended sheets to these regions of the gap. The assembly process


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was also repeated using bias frequencies ranging from 10 kHz to 1 MHz with no significant differences in the assembly results. The FESEM images show that WS2 triangles with size comparable to the gap width (3 µm) preferentially assemble with one of the triangle sides perpendicular to the electrode edge. In contrast, smaller triangles assemble at the edge of one electrode where the field is concentrated, without a preference in their orientation. To quantify the assembly process, an orientation angle θ is introduced, with the orientation shown in the left panel of Figure 3d, corresponding to θ = 0˚. Due to the three-fold radial symmetry of the triangular shape and the symmetry of the electrode structures, we consider θ to be equivalent to the - θ and 60˚- θ positions. The varying orientations are symmetrical around θ = 0˚ and 30˚, where one triangle side is perpendicular to and parallel to the electrode edges, respectively. The relative orientation of assembled triangles with size comparable to the electrode gap width was quantified for nearly 100 triangles and compiled in the plot shown in Figure 3e. The blue curve in this figure is a Gaussian distribution fitted to the experimental data (See SI section Details regarding assembly results for fitting parameters). The results show a preference for the triangles to assemble in the θ = 0˚ orientation, with one of the triangle sides spanning the electrode gap. The orientation preference of WS2 triangles was studied by considering the torque on the sheet as it assembles out of the acetone solution. The alternating electric field induces dipoles along the sheet edges that not only lead to the DEP force but also a restoring torque; while the DEP force dictates the final position of the 2D triangular sheets, the torque determines the orientation. The torque acting on a triangle slightly larger than the electrode gap was calculated by considering the energy of the single sheet system. A single triangular sheet in solution 1 µm above an electrode gap was modeled using an equivalent circuit model with two series-connected 9 ACS Paragon Plus Environment

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capacitors having capacitances related to the two orientation-dependent areas where the triangle overlaps the electrodes (see Figure 4a and 4b). The torque on the triangle is related to the complementary energy of the system given by Equation 2:54, 55 ( , ") =

$ $ ( %& ( , ") = ' )(") $" $"

*

(2)

where %& is the complementary energy of the system, determined from the total capacitance C and applied voltage V. The assembly system is stabilized when the torque is zero and its partial derivative with respect to orientation " is negative. The curves in Figure 4c represent the torque on triangular sheets of various sizes as a function of orientation "; S refers to the ratio of the triangle side length to the electrode gap. A stability point, where = 0 and

/01 /2

< 0, occurs at

both θ = 0˚ and at θ = 30˚. However, the θ range around θ = 30˚ from which that stability point is accessible is small; at most orientations, the torque leads to the θ = 0˚ configuration instead. As the triangle size decreases, the magnitude of the torque increases while the range of orientations attracted to θ = 30˚ decreases significantly. These calculations provide an analytical interpretation of our experimental results (see Figure 3e) and a further understanding of the forces associated with the assembly of 2D sheets. Experimentally observed deviations from the preferred θ = 0˚ orientation may result from the sheets coming into physical contact with the assembly electrode before the orientation is optimized. In this case, the sheets may adhere to the assembly electrode due to their large surface area, thus preventing further sheet motion. To investigate the viability of the assembly process for device applications, the optical properties of assembled WS2 sheets as compared to as-grown materials was characterized by Raman spectroscopy, photoluminescence spectroscopy (PL), and fluorescence microscopy. These optical characterization techniques provide a very sensitive, non-destructive assessment of the 10 ACS Paragon Plus Environment

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material quality,56-58 which can be used to quantify degradation in the properties of the monolayer WS2 crystals due to the sheet release and assembly processes. PL spectra (see Figure 5a) were acquired from different regions of the assembled triangle, namely the regions over the metal electrode and over the electrode gap. A third spectrum is also shown for comparison purposes, corresponding to the pristine as-grown WS2 sheets on the native Si/SiO2 substrate. For all three cases, fitting the PL data with Lorentzian curves reveals that each PL spectrum has two components: a neutral exciton peak (X0) and a charged trion peak (X-) (see Table 1).59-61 The X0 and Xpeaks do not broaden after assembly, indicating WS2 monolayers maintain their as-grown optical qualities. The intensity ratio of X0/X- increases after WS2 monolayers are transferred from SiO2 to Ti/Au electrodes, because WS2 monolayers are more n-doped by an insulating substrate than by a metallic substrate.60 After assembly, the X0 and X- peaks both red shift slightly because the transfer process releases strain in WS2 lattice introduced during high temperature CVD synthesis.62 Figure 5b plots Raman spectra acquired with a 514.5 nm excitation wavelength. All Raman spectra exhibit similar features characteristic of WS2 monolayers.14, 63, 64 The second order mode 2LA(M) appears with an intensity more than two times larger than that of the A’1 mode. At this particular excitation wavelength, this peak and intensity constitutes an unequivocal sign that the WS2 triangle is indeed a monolayer.63 The LA(M) Raman mode is activated by structural defects since it involves phonons at the edge of the Brillouin zone.65 The intensity of the LA(M) mode is therefore an indicator of defect density.58 Figure 5b shows that the intensity of the LA(M) mode does not increase after assembly, indicating that the assembly process neither damages the monolayers nor introduces additional structural defects to the WS2 lattice. To further examine the optical quality of the assembled triangular WS2 monolayers, an optical image, a fluorescence image, a Raman intensity map, and a PL intensity map from the 11 ACS Paragon Plus Environment

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same WS2 triangle are compared in Figure 6. In all four images, the darker region in the center corresponds to the gap between the metal electrodes. This is mainly due to a higher optical reflectivity from metal electrodes. The fluorescence microscopy image shown in Figure 6c reveals an edge enhanced signal of the assembled WS2 triangular sheets, similar to what was observed in the as-grown samples and has been described in the past.47 A PL intensity map is shown in Figure 6d, exhibiting a large intensity enhancement in the vicinity of edges, consistent with the fluorescence image. According to these maps, there is no clear evidence of material degradation after assembly. In order to demonstrate that this technique can be extended to other 2D materials with different morphologies, similar experiments were performed on MoS2 hexagonal monolayers synthesized by CVD (illustrated in SI section Release and assembly of MoS2 monolayers). Figure S6 shows the assembly of a hexagonal monolayer crystals on the interdigitated electrodes. CONCLUSION Electric-field-assisted assembly was used to controllably position several-micrometer sized monolayer TMD crystals on an interdigitated guiding electrode structure with little stacking, wrinkling, or folding of the sheets. A preferred WS2 triangle orientation was identified and confirmed using a semi-analytical calculation; the minimum energy configuration occurred when the triangles were aligned with one side perpendicular to the electrode edges. Optical characterization of assembled WS2 shows that the properties of the sheets are well preserved after the assembly process, indicating that the solvent processing and exposure to an electrical field do not degrade the intrinsic characteristics of these monolayer sheets. The release and assembly processes detailed here can be extended to other 2D materials, such as MoS2.


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METHODS Materials synthesis. WS2 single crystalline monolayer sheets were synthesized in a two-step process.47 Si wafers with a thermally deposited 285 nm thick SiO2 layer were treated with piranha solution at 80 ºC for 40 minutes and then with oxygen plasma to remove organic residue. The wafers were loaded into a physical vapor deposition chamber (PVD 75, Kurt J. Lesker) for thermal evaporation of a 2 nm layer of WO3. The SiO2/Si substrates were cleaved into approximately 1 cm by 1 cm samples and loaded into a quartz reaction tube (35 mm I.D.) for thermal treatment under a sulfur environment. 300 mg of sulfur powder (99.5%, Alfa Aesar, CAS 770434-9) were placed upstream and wrapped with a heating tape. The sulfurization reaction was performed at atmospheric pressure and at 800 ºC, while the sulfur was independently heated to 250 ºC. These parameters resulted in the sample having 10~30 % substrate coverage of WS2. TMD release process. Figure S1 shows the chemical method used to release the as-grown WS2 monolayers from the growth substrate.21 Substrates with as-grown WS2 triangles were covered with poly(methyl methacrylate) (PMMA, MW 495 000, A6) by spin coating at 4000 rpm for 60 s, resulting in a film that is approximately 300 nm thick. After curing the PMMA overnight at room temperature, the samples were immersed in 1 M NaOH (ACS, 48-51%, Alfa Aesar, CAS 766439-3) at 80 ºC for less than 1 minute to release the PMMA-WS2 film from the SiO2/Si substrate. The film was thoroughly washed with deionized water and removed from the bath with a Si substrate covered with a sacrificial layer of PMMA (Additional details can be found in the Details on experimental methods section in the SI). The PMMA/WS2/PMMA/Si was immersed in approximately 200 µL of acetone, which dissolved both PMMA layers and suspended the WS2 sheets in the solvent. The resulting acetone solution has approximately 0.01 vol% PMMA with ~10-3 cm2/µL area concentration of WS2 sheets. 13 ACS Paragon Plus Environment

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Electric-field assisted assembly process. The assembly of the WS2 was conducted immediately after the sheets are suspended because the sheets settle within 2-3 hours and are very difficult to re-suspend. The suspension was not subjected to ultra-sonication, as it greatly degrades the WS2 triangles even for very short exposure times (5 s). The guiding electrode structure is illustrated in Figure 1a. A 300 nm SiO2 layer was formed on an n+ Si substrate (resistivity 5×10-3 Ωcm) by wet oxidation. Bottom electrodes were subsequently patterned by i-line projection lithography on a double-layer resist stack consisting of PMGI and SPR 3012 (Microchem PMGI SF6 and Microchem Shipley Microposit SPR 3012). The electrode system is 5 mm by 5 mm and consists of 24 fingers total, with 12 fingers inter-connected to each probe contact (full structure shown in Figure S2, additional details can be found in the Details on experimental methods section in the SI). After development by immersion in CD-26 (Microchem, 0.26 N TMAH), 40 nm of Ti/Au metal was deposited onto the patterned substrate. Sheet assembly was performed by applying an alternating peak-to-peak voltage of 15 V at 100 kHz to the pair of electrodes and injecting 3 µL of the acetone/WS2 prepared suspension, corresponding to about 10-3 cm2 total area of WS2. The signal is applied across the electrodes until the drop of acetone entirely dries (approximately 10~20 seconds) to prevent the re-dispersion of sheets into the acetone after removing the electric field. After the process, the assembly die was immersed in acetone to remove the residual PMMA. Further cleaning steps can be introduced to remove other organic contamination, including thermal treatment, and the recently adopted organic strippers (NMP based or chloroform). The assembled triangular sheets were exposed to a heated NMP 1165 solvent at 80 ºC, and no morphological degradation was observed.


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Materials characterization. Optical and fluorescence images were acquired using a Carl Zeiss Axio Imager microscope. Raman and PL measurements were performed with an inVia confocal Renishaw Raman spectrometer. SEM images were obtained on a LEO 1530 field emission SEM. Theoretical modeling. The DEP force map for WS2 sheets in a solution (see Figure 2) was obtained using COMSOL Multiphysics finite element analysis software Version 4.4 and MATLAB. The structure of the model and material parameters used are detailed in the Computational details section in the SI. The electric field throughout the assembly system, but without any sheets present, was calculated using COMSOL and transferred to MATLAB. For numerous points in the assembly volume, the anticipated orientation of a triangular sheet at a point was calculated by evaluating the Maxwell stress tensor from the electric field in the neighborhood of the point; each sheet position and anticipated orientation were then transferred from MATLAB to COMSOL. The force on a sheet at each position and orientation was calculated in COMSOL and transferred to MATLAB where the final map was plotted. To decrease calculation times in COMSOL, the near-zero thickness of the 2D sheets was modeled by approximating it using a thicker sheet with smaller permittivity with equivalent average dipole moment 〈4〉. Comparing two materials based on the polarization equation Eq. 3 leads to Eq. 4: 〈4〉

= 6 ( 7 − 1)

′7 =

(3)

; ( − 1) + 1 ;< 7

(4)

where ; < is the approximated model’s sheet thickness and 7 ′ is the approximated model’s sheet permittivity.66 A simple test model was used to compare approximated results against results ob-


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tained without the above approximation; no significant differences were seen between the two calculations. The torque on triangular sheets (see Figure 4c) was calculated using the methodology detailed in the text, and assembly and material parameters as discussed in the methods section for assembly and SI section Computation details respectively. A MATLAB code was used to calculate the sheet-electrode overlap areas as functions of sheet size and orientation. The resulting areas were then used to calculate equivalent capacitance, complementary energy, and torque. Conflict of interest. The authors declare no competing financial interest. Acknowledgements. D. D. D., J. L., K. Z., J. M., J. A. R., and T. M. were supported by the Center for Low Energy Systems Technology (LEAST), one of six centers supported by the STARnet phase of the Focus Center Research Program (FCRP), a Semiconductor Research Corporation (SRC) program sponsored by MARCO and DARPA. M. T., A. L. E., N. P. L., Z. L., C. Z. and S. F. acknowledge the support from the U.S. Army Research Office MURI grant W911NF-11-10362. All authors acknowledge partial support from the Penn State Center for Nanoscale Science (DMR-0820404 and DMR-1420620). We also thank the National Science Foundation for the following grants: 2DARE-EFRI-1433311 and 2DARE-EFRI-1542707. The authors would like to thank Eva Y. Andrei, Jinhai Mao, Ivan Skachko and Ruitao Lv for helpful discussions. Supporting information available. The supporting Information is available free of charge via the internet at http://pubs.acs.org. Additional details on the experimental and computational methods; estimates of the additional forces acting on assembling WS2 and the approximate resistance of an assembled sheet; additional SEM images of assembled WS2 sheets; and preliminary assembly results of monolayer MoS2. 16 ACS Paragon Plus Environment

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Figure 1. (a) A schematic of the assembly system. (b) A plot of the real part of the calculated Clausius-Mossotti factor as a function of applied bias frequency for WS2 assembling out of acetone. The dotted line corresponds to the crossover point. The material parameters used to calculate the factor are listed in Table S1. (c) Top-view simulation of the field gradient around an electrode gap with AC bias. The field is concentrated at edges of the electrode. The variation in the field gradient in the y-axis in an artifact of the simulation.


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Figure 2. A cross-sectional map of DEP force as a function of sheet centroid location around the electrode gap. The parameters used in the system are equivalent to experimental structure where possible. The attractive force is highest around the electrode gap region and is three orders of magnitude higher than the forces in the surrounding area.


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Figure 3. (a) Low magnification FESEM images of the interdigitated electrodes post-assembly. The WS2 sheets appear dark in contrast to the electrode and gap regions. There is little assembly away from this region. (b) A higher magnification SEM of WS2 sheets assembled along the electrode edges. The gap region across the center is 3 µm wide in (b) and (c). (c) High-magnification images of assembled WS2 triangles (See Figure S3 for additional images). (d) Schematic of definitions of orientation θ. (e) Statistical plot of relative orientation of assembled triangles. There is a clear preference of assembly with θ = 0˚ orientation.


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Figure 4. (a) FESEM image of an assembled WS2 sheet, illustrating the overlap regions that contribute to the capacitance of the system. (b) Cross section illustration and equivalent circuit of a WS2 triangular sheet at a given distance above the electrode surface. (c) Analytical result of the


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in-plane torques on triangular sheets 1.9, 2.0, and 2.1 times the size of the gap as a function of orientation. Equivalent orientation configurations are shaded.


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Figure 5. (a) PL spectra of WS2 monolayers on the as-grown SiO2 substrate, assembled on an electrode, and over a gap between electrode pairs. Black curves are normalized PL data, blue (exciton X0) and red (trion X-) curves are fits to a Lorentzion distribution. The fitting reports are listed in Table 1. (b) Raman spectra for the same set of WS2 monolayers. 514.5 nm and 488 nm lasers are used to excite the samples for Raman and PL measurements, respectively.


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Figure 6. (a) Optical image, (b) Raman intensity map for the A’1 mode, (c) fluorescence image, and (d) PL intensity map of a WS2 monolayer sheet assembled spanning over two electrodes. 514.5 nm and 488 nm lasers are used for Raman and PL measurements, respectively.


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TOC graphic


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Table 1. PL curve fitting for WS2 monolayers. Exciton X0

WS2 PL Energy (eV)

Trion X-

Relative intensity

FWHM

Energy

(meV)

(eV)

Relative intensity

FWHM (meV)

On SiO2

2.02

0.42

42

1.99

0.58

67

Over gap

2.01

0.69

39

1.97

0.31

67

On electrode

2.01

0.68

38

1.97

0.32

69


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