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Thermally Strained Band Gap Engineering of Transition Metal Dichalcogenide Bilayers with Enhanced LightMatter Interaction toward Excellent Photodetectors Sheng-Wen Wang, Henry Medina, Kuo-Bin Hong, Chun-Chia Wu, Yindong Qu, Arumugam Manikandan, Teng-Yu Su, Po-Tsung Lee, Zhi-Quan Huang, Zhiming Wang, Feng-Chuan Chuang, Hao-Chung Kuo, and Yu-Lun Chueh ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b02444 • Publication Date (Web): 28 Jul 2017 Downloaded from http://pubs.acs.org on July 28, 2017

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Thermally Strained Band Gap Engineering of Transition Metal Dichalcogenide Bilayers with Enhanced Light-Matter Interaction toward Excellent Photodetectors Sheng-Wen Wang†, Henry Medina ∥ ∇, Kuo-Bin Hong†, Chun-Chia Wu†, Yindong Qu‡, Arumugam Manikandan∥, Teng-Yu Su∥, Po-Tsung Lee†, Zhi-Quan Huang§, Zhiming Wang‡, Feng-Chuan Chuang§, HaoChung Kuo†,* and Yu-Lun Chueh∥,#,‡,§,* †Department of Photonics & Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan ∥ Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan #School of Material Science and Engineering, State Key Laboratory of Advanced Processing and Recycling of Non-Ferrous Metals in Gansu Province, Lanzhou University of Technology, Lanzhou City 730050, Gansu Province, P. R. China ‡Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, P. R. China §Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan ∇Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), Innovis, Singapore 138634 *Corresponding author: [email protected] and [email protected]. Abstract- Integration of strain engineering of two-dimensional (2D) materials in order to enhance device performance is still a challenge. Here, we successfully demonstrated the thermally strained band gap engineering of transition metal dichalcogenide bilayers by different thermal expansion coefficients between two-dimensional (2D) materials and patterned sapphire structures where MoS2 bilayers were chosen as the demonstrated materials. In particular, a blue shift in the band gap of the MoS2 bilayers can be tunable, displaying an extraordinary capability to drive electrons toward electrode under the smaller driven bias and the results were confirmed by the simulation. A model to explain the thermal strain in the MoS2 bilayers during the synthesis was proposed, which enables us to precisely predict the band gap-shifted behaviors on patterned sapphire structures with different angles. Furthermore, photodetectors with enhancement of 286 % and 897 % based on the strained MoS2 on a cone- and pyramid-patterned sapphire substrates were demonstrated, respectively.

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Keywords: chemical vapor deposition (CVD), transition metal dichalcogenide, molybdenum disulfide (MoS2), thermal strain, patterned sapphire substrate (PSS), photodetector.


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Continuously tuning band gap in optoelectronic materials is a highly desirable for enhancing the performance of electro-optical applications,1 such as light-emitting diodes,2 solar cells3 and photodetectors.4 By combing with two single two-dimensional materials into a junction, a tunable band gap behavior with a great advantage of electro-optical devices can be achieved. For example, the ultrafast charge migration within interfaces between the stacking of PN junctions by two twodimensional semiconductor layers with different band gaps provides extraordinary abilities of optoelectronics and light harvesting in devices.5 Alloyed mixture phases of two transition metal dichalcogenides (TMDCs) such as MoS2 and MoSe2 result in a wide range of band gap modulation while this manner is subject to significant challenges of uniformity and industrial production.6 Although the MoS2 and MoSe2 powders can accomplish growth of larger scale MoS2(1−x)Se2x alloyed layers on substrates, a high barrier of the transferred process into other substrates for the practical applications in large scale is still a major drawback.7 In addition to the chemical synthesis of TMDCs, a strain-induced process is able to precisely tune not only the electronic band structure but also the electronic transport properties of TMDCs from semiconductor to metal to further achieve the TMDCsbased electronic devices without material mismatch because TMDCs have an outstanding capacity of deformation. For example, the experimental results indicate that the MoS2 would not be fractured until the magnitude of strain over 10 % and the breaking strength of MoS2 is indeed better than general semi-conducted materials.8 The extremely high limitation of strain sufferance create a possibility for developing a device in a single material.

Several straightforward strain-induced methods have been recently proposed, including directly stretching the flexible substrate with a few layers of two-dimensional materials,9, 10 utilization of thermal expansion difference by the substrate11 and transfer of two-dimensional layered materials on the non-flat substrate.12-16 Although these ideas are effective methods to trigger strain into twodimensional materials, most of them still rely on the transfer process, limiting practical applications. Bending of two-dimensional materials on flexible substrates can directly introduce the uniaxial strain in the two-dimensional materials while the strain cannot be maintained for further device preparation.


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Wrinkling can be an alternative to achieve the strained two-dimensional materials while the nonhomogeneous and uncontrollable strength of the strain will be a key issue.9, 17 Non-flat substrates provide the localized strains on the transferred two-dimensional materials while unavoidable issues associated with the transfer process, such as the wrinkles, crumples and air bubbles, which deteriorate back-end processes and device performance, have to be considered.13, 15, 16 Although the soaking of MoS2 in an ethylene glycol solution to remove air bubbles between the interface of the non-flat substrate and two-dimensional materials has been proposed and developed, wrinkles and crumples still existed due to the mismatch issue between two-dimensional materials and the non-flat substrate.18 Therefore, it is much better to introduce the strain during the in situ epitaxial growth of twodimensional materials on patterned substrates directly. By using differently patterned substrates, the energy band gap of TMDCs can be effectively changed, which is attributed to the substratedependently thermal expansion coefficient (TEC) because of ultrasensitive nature to thermal strain due to the high surface-to-volume-ratio characteristic.19 In addition, it is well-known that bilayers of transition metal dichalcogenide materials have been theoretically predicted where the tensile strain can drastically reduce the band gap toward the metallic type while the compressive strain can increase the energy band gap.20

In this regard, we directly demonstrate the band gap tuning utilizing the thermal strain concept on transition metal dichalcogenide bilayers epitaxially grown on the different periodic sapphire structures, including cone and pyramid microstructures. Here, MoS2 bilayers were chosen as a material model for the demonstration. Compared with the MoS2 monolayer, we chose the growth of MoS2 bilayers because of distinct physical properties and potential application for the photodetector, including broad absorption in visible spectra,21 tunable absorption spectra by different stacking orientations22 and a lower work function.23 Besides, from first-principles calculations, the MoS2 bilayers have a higher potential to realize the complete electronic transport property modulation under the same applied strain.20 The MoS2 bilayers are perfectly formed on patterned substrates, achieving a conformal coating by sulfurizing molybdenum trioxide (MoO3) in a two-step process. Raman and photoluminescence spectra and mapping images were used to investigate the strain evolution in the


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MoS2 bilayers. A specific equation made of the simple thermal expansion model on each patterned structure was built for precisely predicting the different thermal strain in the MoS2 bilayers, leading to the band gap shifts of MoS2 bilayers. Furthermore, based on the simulation of the electron migration behavior on the strained MoS2 bilayers, large numbers of electrons migrated from the conical-shaped 1

pattern to the bottom side occur because of an energy funnel effect, which is capable of collecting a masses of electrons under a low drive voltage for photodetection application. The photodetector results based on the patterned MoS2 bilayers in contrast to the smooth MoS2 bilayers show a higher output photocurrent and photosensitivity. Tunable band gap engineering in transition metal dichalcogenide bilayers through a controllable thermal strain on patterned structures opens the next generation in the electro-optical application.

Results and discussion

Although chemical vapor deposition (CVD) and vapor-solid process have been proven to be able to synthesize wafer-scale TMDCs on growing substrates, the variation of TMDCs in morphologies at different locations of the substrate is still a specific challenge because of spatially-dependent growth parameters.24, 25 Lin et al. have demonstrated the two-step method to grow continuous and smooth a few MoS2 layers on a c-plane sapphire substrate in a larger scale. Note that thermally evaporated molybdenum trioxide (MoO3) was reduced to MoO2 in hydrogen environment at 500 °C, followed by sulfurization of MoO2 into MoS2 at 1000 oC.26 Therefore, to achieve a uniform growth of MoS2 bilayers without the surface roughness effect in a large area, we, here, apply the two-step process to proceed with our study. Figures 1a to 1c show schematics of the growth of MoS2 bilayers on the periodically patterned sapphire substrates by two-step sulfurization processes. MoO3 was first deposited as a starting material on the top of the periodically patterned sapphire substrate (Fig. 1a). Subsequently, sulfur powders were placed in the upstream of the gas source in a heating zone (Fig. 1b), resulting in the formation of MoS2 bilayers on the surfaces of patterned substrates (Fig. 1c). During the sulfurization process, the furnace tube will keep a pressure of approximately ~550 torrs with a 25 vol% H2/75 vol % N2 mixed gas of 50 sccm. Figure 1d illustrates a low magnification


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transmission electron microscope (TEM) image of a cone-shaped patterned sapphire substrate with MoS2 bilayers. Figures 1e to 1d show high-resolution TEM (HRTEM) images of three locations in Figure 1a from the top to bottom areas of the cone-patterned structure. Clearly, the growth MoS2 bilayers with the uniform coverage along the different surfaces of the cone-patterned sapphire substrate, including the non-flat areas can be confirmed. Besides, the number of MoS2 layers can be precisely achieved by controlling the accurately 1 nm-thick pre-deposited MoO3 to achieve MoS2 monolayer through the two-step sulfurization processes on the c-plane sapphire substrate. However, once the thickness of the MoO3 is smaller than 1 nm, the island-like and non-uniform MoO3 film was formed on the cone-patterned structure, resulting in the broken MoS2 layers on the surface of the conepatterned structure after the sulfurization process (Supplementary Fig. S1).

According to previous strain engineering calculation on MoS2, the growth of MoS2 bilayers are preferred because of its technological importance, which has a variety of band gap modification from semiconducting toward metallic behaviors compared with the MoS2 monolayer under the same strain condition.20 With an increase in numbers of MoS2 layers, the transition from direct to indirect band gap happens, leading to the shift of the band gap being less sensitive to strain.27 Therefore, the thickness of MoO3 is set to achieve approximately 2 nm-thick, corresponding to MoS2 bilayers after the two-step sulfurization process. To shed light on the band gap engineering induced by the strain from the patterned sapphire structures in the MoS2 bilayers, two kinds of periodic patterned-structure, including cone- and pyramid- patterns were fabricated through a chemical etching process (Supplementary Figs. S2 and S3) on the c-plane sapphire substrates as shown in Figures 1h and i with angles of cone and pyramid corresponding to 0.27π and 0.34π (More SEM images in Figs. S4 and S5).23,24 A particularity of the sapphire substrate is that the thermal expansion coefficient of the c-plane is smaller than that of the plane perpendicular to the c-axis. To simplify the analysis, we refer to the different angles of each pattern related to the flat surface of the sapphire substrate.

Raman spectra were used to understand the strain evolution on the band gap engineering of MoS2 bilayers on cone- and pyramid-patterned sapphire substrates. In addition, Raman mapping images are


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used to shed light on the uniformity of the strain field on MoS2 bilayers in a large area. The corresponding Raman and PL mapping images taken from two kinds of regions, namely top and flat regions of the cone- and pyramid- patterned sapphire substrates are shown in Figures 2a to 2i, respectively. Note that Raman spectra and mapping images of the MoS2 bilayers on the flat sapphire substrate were also measured as a standard reference (Figs. 2a-2c). It is obvious that the in-plane Raman mode (E12g) allocated at 384.6 cm-1 and the out-of-plane Raman mode (A1g) allocated at 406.5 cm-1 were measured on the flat sapphire substrate, indicating of characteristic peaks of MoS2 bilayers.28, 29

In addition, the center peak of PL spectra was located at 676.26 nm.25,26 Uniform contrast in Raman

mapping images taken from two modes of A1g shown in Figure 2e provides a distinct evidence of the uniform growth of the MoS2 bilayers on the cone-patterned sapphire substrate. Blue shifts from 406.5 cm-1 to 407.2 cm-1 in Raman spectra at the A1g mode on the core-patterned sapphire substrates can be distinctly obtained. In addition, blue shift behaviors in the A1g and E12g modes from 406.3 cm-1 to 407.0 cm-1 and from 384.2 cm-1 to 385.2 cm-1on the pyramid-patterned sapphire substrates were found, respectively as shown in Figures 2g and 2h, respectively. Raman mapping images confirm the uniform distribution of the blue shift behaviors in the top region of the MoS2 bilayers grown on both conesand pyramid-patterned sapphire substrates, respectively.

According to previous observation in addition to the thickness effect on TMDCs, the Raman shift can be corroborated to the strain induced into the TMDCs due to different changes in the lattice constant.30, 31 Normally, the tensile strain in TMDCs leads to a red-shifted tendency in Raman spectra32, 33

while the compressive strain in TMDCs leads to a blue-shifted tendency in the Raman spectrum.34

As a result, the Raman blue-shift found in MoS2 bilayers grown on both core- and pyramid-patterned sapphire substrates can be attributed to a larger compressive strain compared to that grown on the flat region due to the different thermal expansion coefficients along the c-axis.19, 11 Besides, theoretical studies are also consistent with our assumption. Lu et al. have predicted the strain induced a band gapshifted behavior of MoS2 mono- and bilayers through the ﬁrst-principle calculation.20 Their simulation results also confirm that tensile and compressive strain on the MoS2 bilayers would lead to a band gap red- and blue-shift, respectively. Band gap changes from the compressive strain in the MoS2 bilayers


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from both cone- and pyramid-patterned sapphire substrates can be confirmed by photoluminescence (PL) mapping images as shown in Figures 2f and 2i. PL mapping images again reveal the uniform growth of MoS2 bilayers on the flat sapphire substrate. Different contrast due to the blue shift of the band gap on top regions with respect to the flat region of the patterned sapphire substrate was found, confirming the blue shift of the band gap caused by the compressive stain on the top regions of both patterned sapphire substrates. The blue shifts of 10.0 and 13.5 nm for the MoS2 bilayers grown on the cone- and pyramid- patterned sapphire substrates can be found in PL spectra as shown in Figure 2l.

A simple mathematical model based on a linear thermal expansion theory can be used to further explain the band gap-shifted behavior induced by the thermal compressive strain on MoS2 bilayers grown on the patterned sapphire substrates as shown in Figure 3a. It can be expected that the substrate temperature was basically maintained at 1000 °C during the sulfurization process. Therefore, the temperature of 1000 °C is assumed to be the natural and released state of the MoS2 bilayers on the sapphire substrates with free of strain. To build a simple mathematical model, a triangle profile of a cone was constructed as shown in Figure 3a where we defined x and θ as a length of a hypotenuse and an inclination angle at the room temperature (25 °C) and the length of the hypotenuse at a synthesized temperature (1000 °C in this case). The lengths of the opposite and adjacent sides increase with the increased temperature. The volume of the corn-patterned sapphire substrate shrinks to the original volume at the room temperature during the cooling process. Based on the Pythagorean Theorem, the length of hypotenuse at room temperature can be expressed by x = y sin 2 θ (1 + A) 2 + cos 2 θ (1 + B )2

(1)

where A and B are the variation of opposite and adjacent sides, respectively (Supplementary information Note 2). Then, the strain along the hypotenuse side in the MoS2 bilayers can be exactly predicted by ε (θ ) = sin 2 θ (1 + A) 2 + cos 2 θ (1 + B )2 − 1

(2)

where ε (θ ) is the relative thermal strain and the amount of thermal strain is related to the inclination angle of a patterned substrate (Supplementary information Note 2). The thermal strain is


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just decided by a specific angle between the flat and hypotenuse sides of the pattern surface.

According to previous observations, the thermal strain on TMDCs would be decided by the value of the thermal expansion coefficient (TEC). After the sulfurization process, the larger TEC of the sapphire substrate will lead to the thermal shrinkage during the cooling process, which can introduce the compressive strain into the MoS2 bilayers.35-37, 19 As a result, the thermal strain of MoS2/sapphire can be plotted in dash line by inputting the physical properties of the sapphire substrate (Supplementary information Figure S7). Interestingly, if we normalize the angle of the flat sapphire substrate at a zero angle, experimental results of the band gap shift in MoS2 bilayers grown on different patterned sapphire substrates can completely match up with the theoretical calculation of our current case as shown in Figure 3b. This result further confirms our assumption of the strain induced by the thermal expansion during the sulfurization process and can be applied to any TMDCs on any patterned substrates. The resolution of our confocal Raman mapping system is approximately 1 µm (laser beam size). However, the dimeter of the flat area on the top pyramid is approximately 630 nm, a half of laser beam size. Therefore, even the pyramid structure has a flat area on the top, the system is still difficult to distinguish the signal.

By taking advantage of this particular band gap shift in the MoS2 bilayers caused by either tensile or compressive strain at the patterned sapphire substrates, it can provide an important aspect to enhance electron transportation behaviors to boost the device performance in electro-optical applications. To understand the influence of the electron migration behaviors by the localized straininduced band gap, two different band gap regions on the same two-dimensional material are simulated and proposed. As our description above, the thermal strain might introduce tensile and compressive strain into two-dimensional materials, which depend on TEC values. Therefore, two different systems, namely Type A and Type B, were taken into account where the band gap at the top region is smaller or larger than that of the surrounding matrix (flat region). Carrier distributions of two-dimensional a cone with MoS2 bilayers calculated by using the finite element method. At the beginning, carriers are generated during the irradiation of light as shown in Figure 3c. By increasing the driven bias to 0.1 V


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(high potential energy (+) and low potential energy (–) display the electric potential energy), the simulation results indicate that the Type A with the smaller band gap on the cone will lead to a “quantum well” region to confine electrons as shown in Figure 3d, resulting in most of the electrons confined inside the cone regions. Therefore, this characteristic is much suitable for light emitting device application, such as light-emitting diodes38-40 and Lasers.41, 42 Additionally, the Type B with the larger band gap on the cone forms a “barrier height” region where electrons have a tendency migrating toward the flat area from cone region since a funneling effect dominates the electron transport as shown in Figure 3e.1 This naturally happened characteristic is undoubtedly able to drive electrons to the metal electrode easier, which is beneficial for absorbing photon devices, such as a photodetector, phototransistor and solar cells. The nature tendency of the electron flow caused by the strain engineering can largely reduce the photoelectrically driven bias with low power consumption. As a result, it is no doubt that the particular band gap opening in the MoS2 bilayers under the compressive strain caused by patterned sapphire substrates can be suitable for applications of light absorption in optoelectronics. The microstructures from the patterned substructures also enhance light interaction with the MoS2.

According to simulation results, the growth of MoS2 bilayers on patterned sapphire substrates are suitable for applications of light absorption in optoelectronics, the MoS2 bilayers-based with periodically patterned sapphire substrates, including cone- and pyramid-patterned structures were fabricated as the photodetector and measured as shown in Figure 4. Three kinds of patterned sapphire substrates were used as the channel materials for photodetector application where finger-type electrodes were prepared using the metal mask (Figures 4a to 4c). Besides, the corresponding optical images were shown in Figures S8a to S8c, respectively. The absorption spectra of each patterned structure are shown in Figure 4d. The growth of MoS2 bilayers on the periodically patterned structures has a larger absorption in contrast to the flat wafer due to the light-scattering effect and both absorption spectrum of patterned sapphire structures has blue shift behavior since the strain affects the band gap shift behavior as the discussion above. Figure 4e shows the photocurrent of MoS2 bilayers on the patterned sapphire substrates, respectively (Figures S8d-S8f). Clearly, the significantly larger


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photocurrent can be indeed found for the MoS2 bilayers on the patterned sapphire substrate compared to those on the flat substrate and the highest enhancement of the photocurrent can be achieved for the MoS2 bilayers grown on a pyramid-patterned sapphire substrate with the enhancement of 897 %. For photodetector measurements, the responsivity is the major index of performance. Larger responsivity indicates a larger electrical output signal (Supplementary Note 3). Therefore, the responsivity of MoS2 bilyaers grown on different sapphire substrates was calculated as plotted in Supplementary information Figure S9. The responsivity of the MoS2 bilayers grown on the flat sapphire substrate can be calculated to be 2.3 (µA/W) while MoS2 bilayers grown on the patterned sapphire substrate exhibits the enhanced responsivity. Especially, the highest responsivity of 24.3 (µA/W) can be achieved for MoS2 bilayers grown on the pyramid-patterned sapphire substrate. To understand the electric field distribution of incident illumination source, the three-dimensional models have been built by the COMSOL software to investigate the photon (wavelength is 638 nm) propagation in different patterned sapphire substrates. Supplementary information Figure S10 presents the three-dimensional electric field distribution and the color represent the intensity of light. Additionally, we have taken the cross-section (x-z plane) profiles of single pattern to further investigate the electric field intensity distribution on different substrates (flat, cone and pyramid) as shown in Figures 4f to 4h. When the light illuminates the substrate, most of the photon pass through the flat sapphire substrate, resulting in the lowest absorption behavior, which is similar to the other experimental results of monolayer or bilayers two-demission materials.43-45 However, the specific periodic pattern structure is capable of confining the photon on the certain region through resonance behaviors. As can be seen in Figures 4g and 4h, the cone can confine the photon inside the structure while most of the photons surround the pyramid, on which the MoS2 bilayers grown and the electrical power flows white arrows also display the resonance behaviors (Figure S9). The three-dimensional current-migrating behavior also demonstrates both of patterned substrate with the MoS2 bilayers have an ability to drive photongenerated electrons toward bottom in bottom insets of Figures 4f to 4h. This is why the strongest light interaction between MoS2 bilayers grown on the pyramid-patterned sapphire substrate exhibits the highest performance. We eventually compare area enhancement ratio with absorption and


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photocurrent enhancement ratios in Supplementary information Table 3 while assuming the flat sample as a baseline. Theoretically, the absorption and the photocurrent will be enhanced as the absorbed material (MoS2 bilayer) area increases, and the amount of their enhancement ratio will follow the same ratio with respect to total area. However, the absorption enhancement ratio at 638 nm is different from the area enhancement ratio. We think that the structure array may influence the absorption ability, resulting in both patterned structures with the higher absorption. In addition, we also observe a larger photocurrent output on both patterned substrates where the photocurrent enhancement ratio still not match the absorption or area enhancement ratios. The amount of photocurrents is dominated by the localized strain and the pyramid structure has a larger localized strain in our explanation and experiment. Therefore, it can be easier to collect the electron on the same driven bias. Conclusion

In summary, we demonstrated an approach using the different thermal expansion properties of the patterned sapphire substrates to induce strain in two-dimensional materials. An epitaxial growth of MoS2 bilayers on the periodic sapphire substrates through a two-step sulfurization process method was chosen as the model for the demonstration of band gap engineering by the thermal strain. After the sulfurization process, the band gap changes of MoS2 bilayers were also measured by Raman and PL spectra and images. Interestingly, by using a simple mathematical model, how the thermal strain affect the band gap-shift behavior of the MoS2 bilayers on different patterned sapphire substrates can be precisely predicted. From the electron migrating simulation, the strained MoS2 bilayers on the patterned sapphire structure was indexed as the Type B interface, which has an excellent capability to drive electrons toward the flat region, allowing the electrode collects electrons easily and saving energy. The simulation results of the FEM simulation indicate the both periodic patterned substrates have the strongest resonant regions within each single structure while localizing on the different positions. For the pyramid-patterned substrate, the strongest resonant region appears on the surrounding pyramid region of MoS2 bilayers. Compared with a flat substrate, the photocurrent enhancement of the cone- and pyramid-patterned substrates are 286 % and 897 %, respectively. We


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profoundly believe that this approach is of great importance for understanding strain effects induced by the substrate and how to control them in order to optimize the device performance as an important step to pursuing for the future development of TMDC technology.

Methods MoS2 synthesis from Two-step process: Molybdenum oxide (MoO3) films as a precursor layer with a thickness of 2 nm were deposited on sapphire substrates by E-gun system with a deposition rate of 0.01 nm/sec. The sulfur powder was placed in the upstream of the gas source and MoO3-deposited sapphire substrates were put inside the furnace tube of the heating zone. Then, the heating tape was wrapped outside the quartz tube and totally covered the region of sulfur powder. During the sulfurization process, the pressure of approximately 550 torrs with an H2/N mixture gas of 50 sccm (ration is 25 % in H2) was kept in the furnace tube. Heating up the heating tape and furnace tube reach to 180 °C at a rate of 5 °C/min and 1000 °C at a rate of 18 °C/min, respectively. After both of heater arrive at targeted temperature, heating tape, and furnace maintains the temperature at 180 °C and 1000 °C for 30 mins. At the same time, MoO3, hydrogen, and sulfur vapor would react each other26, 46, 47

and MoS2 is eventually synthesized on the sapphire surface. Raman and photoluminescence measurements: For Raman and photoluminescence (PL)

mapping, we use a 532 nm laser with the beam spot size of ~1 µm in diameter in a confocal microscope spectrometer to focus the laser beam on the sample in order to collect all reflected signals in reﬂection geometry (NTMDT). Raman and PL spectra were obtained using a 100X objective, 50 µm aperture of the confocal module to obtain high-quality Raman and PL spectrum mapping figures. Simulation of Electric field distribution at different patterned sapphire substrates: Using a finite element package (COMSOL) to build three-dimensional cone- and pyramid-shaped unit cell structure with a MoS2 bilayers. Electric field distributions of three-dimensional hexagonal unit cell structures with cone- and pyramid-shaped islands covered with a 2 nm MoS2 layer calculated by using the finite element method. The unit cell of flat sapphire with 2 nm MoS2 layer used as the reference case. The geometries of the cone- and pyramid-shaped islands including the top width, base width and


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height are taken from corresponding SEM images (Supplementary Figures S4 and S5). For simplifying calculations, the periodic boundary conditions are specified in three principal directions of the hexagonal unit cell. Top and bottom surfaces of those unit cells were set to be wave excitation and detection ports, respectively. The light with a wavelength of 638 nm is normally incident on the patterned islands and MoS2 layer. The refractive indices of sapphire and MoS2 refer to Ref. 1 and Ref. 42, respectively. The absorption of the hexagonal unit cell was defined as 1-T-R where T and R are the reflection and transmission, respectively, detected by port conditions. MoS2-based photodetector fabrication: Electrode metal was deposited by e-gun evaporation using the hard mask to define the electrode area and location. Titanium (Ti) is one of better choice to form the smallest tunneling barrier height between the metal and MoS2 bilayer due to its lower work function, meaning that electrons would be easier collected and from the ohmic contact.48 Though the gold (Au) layer, these photocurrents can be transported to the system with lowest loss since the Au is a better conductive materials for electron device.

Supporting Information Cross-sectional TEM of discontinuous MoS2 monolayer on patterned sapphire substrates; Fabrication process of patterned sapphire substrates Both cone and pyramid pattern SEM images on different view angles; Deriving the variation equation of a pattern substrate and the electric field distribution simulation; Responsivity of photodetector; Modeling of electric field distribution simulation; Area, absorption and photocurrent enhancement ratio of each devices. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements The research is supported by Ministry of Science and Technology through Grant through grants no, 105-3113-E-007-003-CC2, 105-2119-M-009-009, 104-2628-M-007-004-MY3, 104-2221-E-007048-MY3, 105-2633-M-007-003 and the National Tsing Hua University through Grant no. 105A0088J4. Y.L. Chueh greatly appreciates the use of the facility at CNMM. F.C. Chuang acknowledges support from the National Center for Theoretical Sciences and the Ministry of Science


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and Technology of Taiwan under Grants No. MOST-104-2112-M-110-002-MY3. He is also grateful to the National Center for High-performance Computing for computer time and facilities.

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Figure Captions


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Figure 1. Growth processes of MoS2 bilayers on different patterned sapphire substrates. a, Deposition of the MoO3 layer with a thickness of approximately 2 nm on different patterned sapphire substrates. b, Sulfuring these substrates with MoO3 layers through a furnace tube. c, After sulfurization process, MoS2 bilayers can be synthesized on different patterned sapphire substrates. d, A low magnification TEM image of MoS2 bilayers grown on a patterned sapphire substrate. e, f, g, The corresponding high-resolution TEM (HRTEM) images taken from d at different regions, including tip, side and flat regions, respectively. Obviously, it conforms uniform and consistent MoS2 bilayers on the patterned-sapphire substrate. h, i, The growth MoS2 bilayers with angles of 0.27 ߨ and 0.34 ߨ on cone- and pyramidpatterned sapphire substrates, respectively. Figure 2. Raman and photoluminescence (PL) spectra of MoS2 bilayers on different sapphire substrates. The Raman mapping images of the MoS2-synthesized c-plane sapphire substrate are shown in a and b, which represent in-plane E12g and out-of-plane A1g modes, respectively. c, The PL mapping image of MoS2 bilayers grown on the c-plane sapphire substrate. All of above results exhibit the uniform MoS2 bilayers grown on the flat sapphire substrate. d, (in-plane E12g mode) and e, (out-of-plane A1g mode) display the Raman mapping images of MoS2 bilayers grown on the cone-patterned sapphire substrate, which has a circle-like distribution. f, The PL mapping image of MoS2 bilayers grown on the cone-patterned sapphire substrate. g, (in-plane E12g mode) and h (out-of-plane A1g mode) are the Raman mapping images of MoS2 bilayers grown on the pyramid-patterned sapphire substrate. i, The PL mapping image of MoS2 bilayers grown on the pyramid-patterned sapphire substrate. j and k show detail comparison of Raman spectra, which represent cone- and pyramid-patterned sapphire substrates, respectively. l, the PL spectra of each MoS2 bilayers grown on different patterned-sapphire substrates. Figure 3. Tunable band gap engineering in the MoS2 bilayers on different patterned sapphire substrates by thermal expansion effect from simulation and band gap modeling of the electron migration under the bias. a, A simple model to explain thermal strain formed on


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the different environmental temperatures. The green arrow is the direction of biaxial compressive strain during the cooling process. b, A plot of relative thermal strain as the function of angles from the theoretical part (blue-dash cure). Green points indicate the experimental results of the band gap-shifted on different substrates, matching the theoretical plots. c, Simulation of the exciton migrated behavior on the different types of interfaces. Type A and type B show the quantum well-type and barrier height-type conditions, respectively. d, & e, Driving an identical bias (0.1 V), most of the electrons still confine in the cone region in Type A while a few electrons migrate outside from the cone region in Type B. Figure 4. Photodetector characteristics of MoS2 bilayers on different patterned sapphire substrates. a, The MoS2 bilayers grown on the sapphire substrates. b, Placing the hard mask on the samples followed by deposition of the Ti/Au as the electrode. c, The MoS2 bilayers-based photodetector was fabricated. d, Absorption spectra of MoS2 bilayers grown on the flat(black curve), cone- (red curve) and pyramid- (blue curve) sapphire substrates. e, Photocurrent of MoS2 bilayers grown on different sapphire substrates at an applied bias of Vds at 3V illuminated by a laser with a wavelength of 638 nm with a power of 20 mW. Note that the beam diameter of 5 mm and the On/Off time of 20 sec were used, respectively. Simulation of the electric field at the illuminated light wavelength at 638 nm. The excitongenerated densities for the MoS2 bilayers grown on f, flat g, cone and h, pyramid patterned substrates were calculated. The top and bottom images are aligned electron migration of three-dimension model in each substrate.


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Figure 2.


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Figure 4.


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