Strain Engineering for Enhancing Carrier Mobility in MoTe2 Field‐Effect Transistors

Abstract Molybdenum ditelluride (MoTe2) exhibits immense potential in post‐silicon electronics due to its bandgap comparable to silicon. Unlike other 2D materials, MoTe2 allows easy phase modulation and efficient carrier type control in electrical transport. However, its unstable nature and low‐carrier mobility limit practical implementation in devices. Here, a deterministic method is proposed to improve the performance of MoTe2 devices by inducing local tensile strain through substrate engineering and encapsulation processes. The approach involves creating hole arrays in the substrate and using atomic layer deposition grown Al2O3 as an additional back‐gate dielectric layer on SiO2. The MoTe2 channel is passivated with a thick layer of Al2O3 post‐fabrication. This structure significantly improves hole and electron mobilities in MoTe2 field‐effect transistors (FETs), approaching theoretical limits. Hole mobility up to 130 cm−2 V−1 s−1 and electron mobility up to 160 cm−2 V−1 s−1 are achieved. Introducing local tensile strain through the hole array enhances electron mobility by up to 6 times compared to the unstrained devices. Remarkably, the devices exhibit metal–insulator transition in MoTe2 FETs, with a well‐defined critical point. This study presents a novel technique to enhance carrier mobility in MoTe2 FETs, offering promising prospects for improving 2D material performance in electronic applications.


Introduction
MoTe 2 has emerged as a promising 2D transition metal dichalcogenide (TMDC) in recent years, owing to its unique properties tial aspect of this ALD layer is its ability to introduce tensile strain to the 2D material when the substrate is engineered in such a way that the weight of the passivated ALD layer and the thermal expansion difference between Al 2 O 3 and MoTe 2 exert tensile strain on the material, thereby enhancing device performance.
In this work, we first demonstrate a simple technique to improve the performance of MoTe 2 FETs.Our approach involves creating a hole array in the substrate, using ALD-grown Al 2 O 3 as an additional dielectric layer on SiO 2 , and employing Al 2 O 3 as a passivation layer for the MoTe 2 FET.Our proposed structure induces tensile strain on MoTe 2 , leading to significant enhancement of the carrier mobility and on-off ratio.The improved performance of the MoTe 2 devices can be attributed to the significant damping of the Coulomb and electron-phonon scattering as a result of the change in the band structure of MoTe 2 .Additionally, the stable and good device quality leads to the metalinsulator transition (MIT) in the strained MoTe 2 devices during temperature-dependent electrical measurements, characterized by a sharp MIT critical point.This observation highlights the potential of MoTe 2 for the development of fast-switching devices and memory elements, with applications in efficient sensors, photodetectors, and energy storage devices.

Results and Discussion
Figure 1a illustrates the crystal structure of 2H phase MoTe 2 , where a 2D hexagonal lattice structure is formed by sandwiching one layer of Mo atoms between two layers of S atoms.Relatively, 2H-MoTe 2 is thermodynamically more stable compared to other phases.Figure 1b presents a schematic of a FET on a typical Si/SiO 2 substrate using a few-layer MoTe 2 as the channel material.The room-temperature Raman spectrum of pristine MoTe 2 obtained using a 532 nm (≈2.33 eV) laser excitation is depicted in Figure 1c.The distinctive Raman modes of MoTe 2 appear at 173, 233, and 288 cm −1 corresponding to out-of-plane A 1g , in-plane E 1 2g , and bulk in-active B 1 2g modes, respectively. [21]he transfer characteristics curve of a ≈2 nm thick MoTe 2 FET at room temperature is shown in Figure 1d, revealing a p-dominant ambipolar behavior.The calculated mobility (μ) of the device is 17 cm 2 V −1 s −1 .It is worth noting that, we observe a very thin layer (≈2 nm) of MoTe 2 behaving as p-type or p-dominant ambipolar with Ti/Au electrodes.However, as the thickness of MoTe 2 increases, the n-branch of the transfer curve becomes stronger, leading to n-type MoTe 2 FET.
Usually, Al 2 O 3 grown by ALD induces n-doping in 2D materials when the metal oxide is used as a dielectric material and also as a passivation layer for 2D transistors.The effect of ALD doping is particularly noticeable in the electrical response of 2D FETs when compared with bare 2D FETs on Si/SiO 2 substrate.Al 2 O 3 dopes the material by injecting electrons in the channel, leading to a transition in carrier type from p-type to p-dominant, n-dominant ambipolar, or even n-type behavior.The μ e in the devices also increases with an elevated electron current level.Meanwhile, Al 2 O 3 contributes to a reduction in device hysteresis by minimizing carrier trapping and promoting a high-quality interface.The high-quality interface facilitated by Al 2 O 3 may also enhance μ h in the devices.Detailed discussion on the mechanism of doping by ALD-grown Al 2 O 3 is provided in the last section of this study.
In this experiment, we investigate the role of local strain on MoTe 2 induced by hole-array pattern on the Si/SiO 2 substrate, while considering the ALD influences on the material.To achieve this, we fabricate hole arrays with various diameters on Si/SiO 2 , followed by deposition of 5 nm Al 2 O 3 on the substrate.Subsequently, we transfer MoTe 2 flakes onto the hole-array substrate using the hot pick-up technique. [22]The adhesion between MoTe 2  and ALD-grown Al 2 O 3 substrate relies on van der Waals bonding.The high-quality and uniformity of layer-by-layer growth of Al 2 O 3 in the ALD process enhances the adhesion.MoTe 2 FETs with Ti/Au contacts are fabricated on the substrate, and an additional 50 nm layer of Al 2 O 3 is deposited on the devices using a seeding layer to ensure uniform coverage on the MoTe 2 because of the absence of dangling bonds on the surface of 2D materials (see the Experimental Section for more details).Figure 2a shows a schematic of the device structure.The holes on the substrate are 200 nm in diameter and ≈50 nm in depth after the deposition of 5 nm Al 2 O 3 .Two different thicknesses of MoTe 2 flakes are selected to analyze the strain effects: a ≈2.7 nm flake thickness exhibits p-dominant ambipolar behavior, as shown in Figure 2b, while a thicker flake (≈5.8 nm) exhibits n-type behavior.The transfer characteristics of the devices are presented in Figure 2c, with both devices exhibiting an on-off ratio of 10 5 .The AFM measurement results of these samples are shown in Figure S2 (Supporting Information).
The 2-probe field effect mobilities of these devices are calculated using the following equation where L and W denote the length and width of the channel, respectively, C Al In order to get a deeper understanding, we create hole arrays in the substrate with different diameters, such as 100, 200, 300, and 400 nm.The target depth of the holes is 70 nm; however, the actual depth ranges from 40 to 55 nm after 5 nm Al 2 O 3 deposition (for details see the Experimental Section).The as-transferred flakes of MoTe 2 having a thickness of ≈5 nm, are suspended on the hole arrays experience relatively small strain.To enhance the localized tensile strain on the MoTe 2 flakes, we grow a 50 nm layer of Al 2 O 3 using the ALD process.As we know that Raman spectroscopy is a well-established tool to investigate the stain in 2D materials, we use a 532 nm laser to characterize the nature and magnitude of strain in both strained and unstrained MoTe 2 .The distinct Raman peaks observed in both samples confirm the intact and high-quality of the flakes.We notice that the Raman modes of strained MoTe 2 are redshifted compared to the unstrained regions of the flake, as shown in Figure 3a.Additionally, the intensities of the Raman peaks are decreased in the strained samples.[25] Especially, in our samples, most strained samples exhibit a redshift of ≈2.98 and ≈2.22 cm −1 for prominent E 1 2g and A 1g modes, respectively.Notably, in the previous reports, [23][24][25] the shift in the A 1g mode under tensile strain was almost negligible.We notice a significant shift in the A 1g mode of strained MoTe 2 .We assume that the shift is the result of using a few-layer and unsupported MoTe 2 or the effect of change in the dielectric environment [26] in the hole-array regions of our samples.Another major reason behind this larger shift in A 1g could be the result of the high level of doping in MoTe 2 induced by Al 2 O 3 . [25,27,28]igure 3b illustrates the effect of hole diameter variation on the shift of each Raman mode in strained MoTe 2 samples compared to the unstrained samples.It is evident that the shift of all Raman peaks is increasing with the increase in the hole diameter, with the highest shift observed when the diameter is 300 nm.This indicates that the 300 nm hole diameter exerts the strongest tensile strain on the MoTe 2 flake around the peripheral region of the hole.The amount of strain approximated from the shift of E 1 2g mode is ≈0.67%. [23]The strain in the material decreases at 400 nm, which could be attributed to the increased flat or less strained region at the center of the hole.
Next, we analyze the influence of the hole-array pattern and top Al 2 O 3 -induced strain in the MoTe 2 device performance.Local tensile strain resulting from our proposed structure enhances the electron current and mobility of MoTe 2 FETs by up to ≈6 times compared to the unstrained flat sample.Figure 3c shows the comparison of the current and μ e of the strained and unstrained samples.The optical image and height profile of the MoTe 2 flake are presented in Figure S3 (Supporting Information).The performance enhancement in our devices could be attributed to the reduced electron-phonon scattering due to the band structure changes upon application of the tensile strain to MoTe 2 . [15,29]A schematic of a simplified band structure of MoTe 2 before and after strain is presented in the inset of Figure 3c.The red and black colored energy bands in the figure correspond to unstrained and strained few-layer MoTe 2 .The bandgap E GT of MoTe 2 decreases as the valley of the conduction band at the K point is lowered when tensile strain is applied to the few-layer MoTe 2 flake. [29]s a result, the energy difference between K point and Q point (denoted as ΔE QK ) increases, resulting in very low electron intervalley scattering by reducing the electron effective mass. [15]his could be the major reason for the enhancement of μ e in MoTe 2 devices.In addition, the contact resistance of the devices decreases by reducing the Schottky barrier height in the devices when tensile strain is applied to 2D materials, also leading to the high μ e . [30,31]Among the 2D TMDCs, MoTe 2 is more susceptible to defect formation and charge trapping. [7]The application of tensile strain to MoTe 2 could potentially enhance the carrier lifetime by mitigating the trapping of the charge carriers. [32,33]This could also lead to high current and mobility in the devices.
Figure 3d illustrates the hole diameter-dependent mobility EF.The mobility increases with increasing hole diameter up to 300 nm, which also corresponds to the highest mobility EF.A close value of the EF is also noticed at 200 nm diameter.The EF decreases when the hole diameter increases to 400 nm.This trend in the mobility EF is analogous to the hole diameterdependent strain observed in the samples presented in Figure 3b.From these results, it is apparent that the tensile strain induced by the hole-array pattern in the substrate and top Al 2 O 3 layer enhances the MoTe 2 device performance significantly.
High- dielectric materials improve the device performance by strongly reducing Coulomb scattering [16,17] and enhancing gate capacitance. [19]An additional layer of Al 2 O 3 on SiO 2 has a similar influence on the device performance.Al 2 O 3 provides strong gate controllability and reduces the Schottky barrier height (SBH) between metal and semiconductor, resulting in increased carrier mobility through the thermionic emission process. [20]or further analysis of the Schottky barrier, we investigate the transfer characteristics of the devices at different temperatures.Figure 4a shows the transfer curves of a n-type MoTe 2 transistor made with Ti/Au contacts at various temperatures.Remarkably, we observe MIT in MoTe 2 devices.The drain current, measured as a function of gate voltage, shows a crossover at a specific gate voltage.This crossover point, also known as critical or MIT point is at ≈V g = 62 V. Below the point, the MoTe 2 device behaves as an insulator, as device conductivity increases with temperature increase.Meanwhile, above the MIT point, the conductivity decreases with increasing temperature, behaving as a metal.At the MIT point, the carrier density is estimated to be n D ≈ 3.74 × 10 −12 cm −2 , calculated using , where C ox is the overall capacitance of the dielectrics, V th is the threshold voltage, and q is the charge of an electron.The dependency of the conductivity on the temperature is shown in the inset of Figure 4a.[36] In the insulating regime, the Fermi energy E F moves away from the mobility edge which results in strong localization of the charge carriers.Therefore, the conductivity increases with the increase in the temperature due to thermal activation.Conversely, E F moves toward E c in the metallic regimes, and charge carriers are weakly localized.As the temperature increases, phonon scattering becomes more dominant, leading to a decrease in the conductivity in this regime. [37,38]he variation of mobility of the device with temperature is shown in Figure 4b.The mobility is ≈250 cm 2 V −1 s −1 at 80 K, indicating strong screening of Coulomb scattering due to the low temperature and thin Al 2 O 3 dielectric layer.The mobility of the transistor decreases with the temperature increase as the phonon scattering becomes dominant over Coulomb scattering.The hysteresis in the device increases with the temperature increase as well; however, the value of hysteresis is very small, even at room temperature compared to the FET made solely on flat Si/SiO 2 substrate, as shown in Figure S5 (Supporting Information).This indicates the higher quality of the layers of Al 2 O 3 than SiO 2 in terms of low surface defects resulting from the layer-by-layer deposition of Al 2 O 3 in the ALD process.This results in less carrier trapping during the conduction.
From the temperature-dependent transport measurements of MoTe 2 devices, we can also analyze the quality of the contacts (Ti/Au) on the MoTe 2 channel while considering the influence of top-bottom Al 2 O 3 .The Arrhenius plot in Figure 5a is obtained from the thermionic emission model, where ϕ B represents the Schottky barrier height (SBH) and k B is the Boltzmann constant.The extracted SBH as a function of V g is presented in Figure 5b with a schematic of the thermionic emission of the electrons over the SBH in the inset.The low value and nearly linear dependence on V g of the SBH indicate thermionic emission of the carriers contributing to the current and leading to high mobility in the devices.This could be the result of the combined effect of the top Al 2 O 3 used for inducing strain and the bottom Al 2 O 3 used as an additional dielectric layer for MoTe 2 FETs.Understanding the mechanism of doping in MoTe 2 by ALD-grown Al 2 O 3 can provide further insight into the enhancement of device performance.
The n-type doping in 2D materials by ALD-grown Al 2 O 3 is mainly attributed to the presence of oxygen vacancies in Al 2 O 3 . [39,40]These oxygen vacancies create defect states within the bandgap of Al 2 O 3 as shown in Figure 5c. [41]Depending on the

Conclusion
In summary, we demonstrate a simple and effective method to modulate the carrier type and enhance the performance of fewlayer MoTe 2 FETs.The combination of the hole-array pattern in the substrate and ALD-grown Al 2 O 3 layers as an additional dielectric and passivation layer enables us to achieve significant enhancements in both the hole and electron mobility of MoTe 2 devices.The current and the electron mobility of our MoTe 2 devices are increased by up to 6 times due to the application of tensile strain on MoTe 2 by the proposed structure.The strain applied to MoTe 2 changes the band structure of the material and reduces the electron-phonon scattering in the samples, leading to high electron mobility in the devices.Additionally, we observe MIT in MoTe 2 during analyzing the temperature-dependent behavior of the devices.Overall, our proposed structure represents a promising approach for advancing the performance of MoTe 2 devices for future electronics.

Experimental Section
Hole-Array Substrate: For making hole arrays, a p-doped silicon substrate (0.001-0.005Ω cm) covered with a 285 nm thick thermally grown SiO 2 was cleaned with acetone and IPA.Patterns with different diameters of circles were created by electron beam lithography (EBL Vistec, EPBG 5000) after coating the substrate with PMMA A4.Then the substrate was subjected to a reactive ion etching (RIE) tool (Plasmalab 80 Plus, Oxford Instruments) for SiO 2 etching.CHF 3 and O 2 were used as process gases and the rate was optimized to get 40 ± 5 nm min −1 etch rate.The etching was carried out for 2 min to get 70 nm of SiO 2 etching from the PMMA opening.After etching the PMMA was dissolved in acetone.

Al 2 O 3 Growth in ALD:
The substrates with hole arrays were inserted in the ALD tool (Beneq TFS-500).A 5 nm Al 2 O 3 was grown on the hole-array substrate using trimethylaluminium (TMA) and water at 200 °C, while the process parameters were optimized to deposit Al 2 O 3 with 0.1 nm per cycle rate.Another deposition of Al 2 O 3 was carried out after device fabrication.However, this time before growing the oxide, a 2 nm Al was deposited as a seed layer using e-beam evaporation on the samples because MoTe 2 has no dangling bond on the surface, therefore uniform growth of Al 2 O 3 on 2D materials requires this seeding layer.After that, a 50 nm Al 2 O 3 was grown using the same growth method mentioned before.
Device Fabrication: The few-layer MoTe 2 flakes were mechanically exfoliated from the commercially available MoTe 2 crystal (2D Semiconductors) on a p-doped silicon substrate (0.001-0.005Ω cm) covered with a 285 nm thick thermally grown SiO 2 .A custom-built 2D transfer setup was used to prepare the samples.After exfoliation, electron beam lithography (EBL Vistec, EPBG 5000) and metallization were carried out by using electron beam evaporator (MASA, IM-9912) under ≈10 −7 torr chamber pressure to deposit a 5 nm Ti adhesion layer followed by 50 nm thick Au.The height of the flakes were determined using an atomic force microscope (Bruker, Dimension Icon).
Raman Spectroscopy: The room-temperature Raman spectra were collected in back-scattering geometry with a confocal micro-Raman system (WITec alpha300 RA+).Samples were excited using a 532 nm laser with a spot size of less than 1 μm (×100 objective, 0.9 NA).Low laser power (<500 μW) was used to avoid laser-induced damage in the samples.
Electrical and Temperature-Dependent Measurements: All the electrical measurements were carried out with a custom-built setup based on a Linkam LN600-P probe station with environmental and temperature controller (T96-S) using a source-measure unit (Keithley 2400) and a Keithley 2700 multiplexing/voltage measurement unit.The temperature measurement system could achieve a 150 °C min −1 heating rate and 100 °C min −1 cooling rate with < 0.1 °C temperature stability.All the measurements were repeated twice at each point to get confident data.

Figure 1 .
Figure 1.FET of 2H-MoTe 2 channel material.a) Illustration of the crystal structure of 2H-MoTe 2 .b) Schematic of a back-gated MoTe 2 FET with Ti/Au electrodes on Si/SiO 2 substrate.c) Room-temperature Raman spectrum of a few-layer MoTe 2 and d) Transfer characteristics of the device with Ti/Au electrodes.The inset shows the device image with an atomic force microscopy (AFM) height profile of the flake with a scale bar of 5 μm.

Figure 2 .
Figure 2. Electrical responses of strained MoTe 2 FETs.a) A schematic of the device structure with a hole array in the substrate and Al 2 O 3 passivation layer.b) The transfer curve of a strained ≈2.7 nm thick MoTe 2 exhibiting p-dominant ambipolar device.The hole mobility (μ h ) is presented in the figure.The inset shows an optical image of the device where the red dashed line defines the boundary of the flake.c) Transfer curve of the n-type device with ≈5.8 nm thick MoTe 2 .The calculated electron mobility (μ e ) is also shown in the image.The image of the device is shown in the inset of the figure.A drain voltage of V d = 1 V is used for both of the transfer characteristic measurements.The scale bars in the inset of b) and c) are 3 μm.
2 O 3 and C SiO 2 are the capacitances of Al 2 O 3 and SiO 2 , respectively, V d represents the drain voltage, and dI d dV g is the extrinsic transconductance of the devices.The thicknesses of the SiO 2 and Al 2 O 3 layers are 285 and 5 nm, respectively.The calculated μ h of the device in Figure2bis ≈127 cm 2 V −1 s −1 , while μ e of the device in Figure2cis ≈158 cm 2 V −1 s −1 .Note that the mentioned mobility values are underestimated due to the 2-probe measurements, which include the effect of contact resistance.Accurate mobility numbers can be extracted from 4-probe measurements.

Figure 3 .
Figure 3.The hole-array and top Al 2 O 3 induced strain effects on MoTe 2 FETs.a) Comparison of the Raman shifts of strained and unstrained samples.b) Variation in the Raman peak shifts with different hole diameters.c) Change in the current and μ e of the devices with and without strain.Inset illustrates the simplified band diagram where E GT and ΔE QK refer to the bandgap and the gap between the Q and K point of the conduction band after application of tensile strain, respectively.Note that the energy bands with red colors correspond to unstrained MoTe 2 and the black lines correspond to bands of strained MoTe 2 .d) Mobility enhancement factor (EF) of the devices as a function of hole diameters.

Figure 4 .
Figure 4. Temperature-dependent transport and carrier mobility of strained MoTe 2 FET.a) Variation in conductance () for different values of V g .Inset shows the temperature-dependent  of the device.b) Change of carrier mobility μ as a function of temperature.

Figure 5 .
Figure 5.Effect of ALD Al 2 O 3 on strained MoTe 2 FET performance.a) Arrhenius plot as per thermionic emission model at different gate voltages.b) The extracted Schottky barrier heights (SBHs) at various V g .c) ALD Al 2 O 3 induced doping mechanism.