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## Creator

[Kuan-Cheng Lu](https://orcid.org/0009-0003-5351-9949), [Chetan Awasthi](https://orcid.org/0000-0002-6027-5095), Ta-Wei Chiu, [S. S. Islam](https://orcid.org/0000-0001-7696-5499), [Kimitoshi Kono](https://orcid.org/0000-0002-4446-4419), [Kazuhito Tsukagoshi](https://orcid.org/0000-0001-9710-2692), [Wen-Bin Jian](https://orcid.org/0000-0002-1898-9641)

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Kuan-Cheng Lu, Chetan Awasthi, Ta-Wei Chiu, S. S. Islam, Kimitoshi Kono, Kazuhito Tsukagoshi, Wen-Bin Jian; Optimizing thermal energy harvesting in few-layer MoS2 with measurements of electron's effective mass in two-dimensional semiconductors. Appl. Phys. Rev. 1 March 2026; 13 (1): 011408 and may be found at https://doi.org/10.1063/5.0291091.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Optimizing thermal energy harvesting in few-layer MoS2 with measurements of electron's effective mass in two-dimensional semiconductors](https://mdr.nims.go.jp/datasets/5e6b3715-c4d2-487e-ab8e-1d8abfe19373)

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Template for Electronic Submission to ACS Journals 1  Optimizing Thermal Energy Harvesting in Few-1 Layer MoS2 with Measurements of Electron’s 2 Effective Mass in Two-Dimensional 3 Semiconductors 4 Kuan-Cheng Lu,1,‡ Chetan Awasthi,1,2,‡ Ta-Wei Chiu,1 S. S. Islam,2,* Kimitoshi Kono,1,3 Wen-Bin 5 Jian,1,* Kazuhito Tsukagoshi 1,4 6 1 Department of Electrophysics, National Yang Ming Chiao Tung University, 1001 University 7 Road, Hsinchu 300093, Taiwan 8 2 Centre for Nanoscience and Nanotechnology, Jamia Millia Islamia (A Central University), 9 Jamia Nagar, New Delhi-110025, India 10 3 International College of Semiconductor Technology, National Yang Ming Chiao Tung 11 University, 1001 University Road, Hsinchu 300093, Taiwan 12 4 International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for 13 Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan 14 ‡ These authors contributed equally to this work. 15 * Corresponding Authors: S. S. Islam and Wen-Bin Jian. 16 KEYWORDS: Two-Dimensional Semiconductors, Seebeck Coefficient, Power Factor, Memory 17 Step, MoS2, Mott’s Hopping Transport, Electron Transport 18  2 ABSTRACT. The ultrathin two-dimensional semiconductor of MoS2 demonstrates prominent 19 field-effect performances and is the best candidate for down-sizing transistors. Its electron 20 transport and thermoelectric properties have been explored only in a few layers of MoS2 or at low 21 temperatures, and the interrelation between the electrical and thermoelectric properties has not 22 been studied yet. We fabricate thermoelectric and field-effect transistor devices with MoS2 23 thicknesses ranging from 1 to 39 layers and carry out electrical and thermoelectric property 24 measurements in a wide temperature range from 80 to 600 K. Mott’s hopping transport, thermal 25 activation, and phonon scattering theories in electrical and thermoelectric properties are 26 simultaneously and systematically investigated. Temperature behaviors and carrier concentration 27 dependences are drawn and described in detail. Moreover, Seebeck coefficients, conductivities, 28 and thermoelectric power factors are sketched as a function of MoS2 flake thickness (number of 29 layers). We point to the high Seebeck coefficient and the power factors for MoS2 flakes with 30 thicknesses of less than 20 layers, revealing the best candidate for thermopower applications 31 among all two-dimensional semiconductors. In addition, we probe the extrinsic effect of memory 32 steps due to trapped charges at temperatures above 450 K in the modulation of electron transports 33 and thermoelectric properties. The extrinsic effect of trapped charges in the substrate presents 34 promising applications as high-temperature thermal sensors. 35 INTRODUCTION 36 The history and developments of the thermoelectric (TE) field have been detail illustrated in 37 the review article authored by Mildred Dresselhaus et al. [1]. The TE field drew much attention 38 in the 1950s for the discovery of three-dimensional TE bulk materials and niche applications 39 [1,2]. It was followed by the definition of a dimensionless figure of merit [3] and the exploration 40 of materials of a high TE figure of merit, such as bismuth telluride with related materials and 41  3 SiGe alloys. It triggered, as well, the seeking of phonon-glass electron-crystal materials [1,4] 42 such as TE clathrates [4]. The essential parameter of TE materials is the Seebeck coefficient (𝑆), 43 which offers the output voltage of harvested energy. The Seebeck coefficient (𝑆) is enhanced 44 with excessive density of states near the Fermi level [5,6] that exists in low-dimensional and 45 nanostructured materials. As a result, low-dimensional TE materials, including quantum wells, 46 nanowires, quantum dots, and agglomerated low-dimensional materials, like nanocomposite and 47 nanostructured TE materials, have drawn much attention in the past two decades [1,2,7,8]. In 48 addition to the Seebeck coefficient (𝑆), another essential parameter, the power factor (𝑃𝐹 =49 𝑆2𝜎), where 𝜎 is conductivity, offers the output power as well as the current of harvested energy. 50 In recent studies, it was addressed that increasing the 𝑃𝐹 is a better strategy to boost power 51 generation for a given figure of merit [9]. 52 The unearthing of graphene [10] initiated the exploration of the highest potential low-53 dimensional materials, the two-dimensional (2D) semiconductors [11,12], for mass production and 54 feasible employment, especially for semiconductor technologies. Among most 2D semiconductors, 55 MoS2 exhibited relatively high device manufacturing stability and was more thoroughly studied 56 [11,13,14]. It has been demonstrated to exhibit high on-current, on/off ratio, and mobility with a 57 low subthreshold swing for single-layer MoS2 field-effect transistors (FETs) [11,15]. To achieve 58 complementary FET operations, natively n-type and multilayer MoS2 flakes were chemically 59 doped and converted to p-type devices [16]. It was demonstrated to reduce the MoS2 channel length 60 to sub-100 nm and to push an on-current approaching 1 mA/𝜇m [17]. Crested FETs fabricated 61 with rippled MoS2 sheets placed on crested and corrugated SiNx substrates presented boosting of 62 carrier mobility up to two orders of magnitude under ambient conditions [18,19]. In addition to 63 device performance, monolayer MoS2 flakes exhibited a metal-insulator transition due to strong 64  4 Coulomb interactions in the two-dimensional electron system [20] and, with an increasing carrier 65 density, multilayer MoS2 flakes presented a superconducting phase at temperatures lower than 10 66 K [21]. 67 In addition to intrinsic MoS2 properties for the FET applications, other demonstrations used 68 heterostructures with extrinsic features, such as the nonvolatile memory device with a floating gate 69 device structure [22]. Moreover, the extrinsic effect of trapping charges between the MoS2 and the 70 metal gate led to memory steps in transfer curves at temperatures above 450 K [23] and to 71 hysteresis loops and thermally assisted memory effects [24,25]. On the other hand, MoS2 exhibited 72 promising TE properties such as a high photothermoelectric Seebeck coefficient (𝑆) of 20 mV/K 73 in a single-layer flake [26] and a remarkably large TE power (𝑆) of 30 mV/K in a chemical-vapor-74 deposition grown single-layer film at 280 K [27]. It was theoretically predicted to have a large TE 75 power factor of 28 mW/m K2 in a suspended single-layer MoS2 [28]. In previous experimental 76 results, the TE power factor of few-layer MoS2 was estimated to be as large as 5 mW/m K2 in the 77 on state in the bilayer flake [29] and approaching 8.5 mW/m K2 in the metallic region in the bilayer 78 flake [30]. Most interestingly, an anomalous carrier sign change at low temperatures, a Kondo-like 79 behavior and band hybridization of MoS2/h-BN heterostructure were recently studied. A positive 80 TE power (𝑆) of ~2 mV/K and a TE power factor of ~50 mW/m K2 were obtained at temperatures 81 below 50 K [31]. 82 Although the emergence of hopping transport in TE power and conductance of single-layer 83 MoS2 was experimentally studied, the relation between the disorder parameter of the hopping 84 transport and the TE power has not been investigated yet. Nor did the conduction mechanism at 85 high temperatures be studied regarding to the TE power. In addition, the TE power factor was 86 essential for the TE applications, but its temperature, layer thickness, and carrier concentration 87  5 dependences were not completely explored. On the other hand, the extrinsic effect of the memory 88 step was observed at temperatures above 450 K, but the effect on the TE power has not yet been 89 inspected. In this work, we explored MoS2 with a thickness from a single layer up to 40 layers on 90 the TE power and TE power factor in a wide temperature range from 80 to 600 K. We discovered 91 enhanced TE power and temperature sensing capabilities due to memory steps at very high 92 temperatures. 93 RESULTS AND DISCUSSIONS 94 MoS2 flakes are isolated from the bulk counterpart and placed on Si wafers capped with a 300-95 nm thick SiO2 layer. For MoS2 flakes with a thickness of less than 6 layers, the differences in 96 optical contrast between the substrate and the flakes are adopted to determine the flake thicknesses, 97 as shown and discussed in Fig. S1 in the Supporting Information. The thicknesses of those thick 98 flakes are determined using an atomic force microscope (AFM). MoS2 flakes are patterned with 99 Au metal electrodes to form a simultaneous TE and field-effect transistor (FET) device. Figure 1a 100 presents a top view of a TE-FET device with Au electrodes marked by numbers. Electrodes 1 and 101 2 are source and drain electrodes for measuring field-effect properties. Device parameters, 102 including field-effect performances of several typical MoS2 TE-FET devices, are listed in Table 103 S1 in the Supporting Information. The thicknesses of those TE-FET devices range from 1 to 39 104 layers, and the mobilities and on-currents of all devices are high enough that the issue of contact 105 resistance can be ignored. In addition, Electrodes 1 and 2 are also used as temperature sensors and 106 for detecting spatial TE voltage variations. Electrode 3 is a micro heater driven by an alternating 107 current (AC) voltage at the frequency of 6.85 Hz. The measurements of temperature differences 108 between Electrodes 1 and 2 are described in detail in the discussion of Fig. S2 in the Supporting 109 Information. The TE voltage is obtained using the standard 2𝜔  method (see Experimental 110  6 Section). The electrical connection and measurement of the TE properties of TE-FET devices are 111 provided in Fig. 1b, where the heavily doped Si substrate is used as a back-gating electrode to 112 adjust the carrier concentration as well as the Fermi level of the MoS2 channel. 113 Figure 1c shows transfer curves of Devices M1 and M5 with thicknesses of 1 and 2 layers, 114 revealing typical electron-contributed, n-type FET behaviors, on-currents of 8.49 and 2.80 μA/μm 115 at the back gating voltage (𝑉𝐵𝐺) of 60 V, and on/off ratios of 3.6× 107 and 1.2× 107. The inset to 116 Fig. 1c gives a linear source-drain current-voltage (𝐽𝐷𝑆-𝑉𝐷𝑆) behavior, indicating an Ohmic contact 117 between the MoS2 channel and the Au metal electrodes. Our previous work has investigated the 118 FET performance of few-layer MoS2 flakes in detail [13]. It is discovered that, due to different 119 degrees of intrinsic disorders, the MoS2 FETs present an insulating state that can be analyzed using 120 the 2D Mott’s variable range hopping (VRH) conduction [32, 13] at low temperatures. Here, we 121 focus on disorder effects on the TE-FET devices and investigate devices of MoS2 flakes with either 122 intrinsic or extrinsic disorders. On the other hand, Fig. 1c shows the steepest ascending dotted line 123 and the horizontal dashed line with the intersection at 𝑉𝐵𝐺 of about -34.7 V, which gives the turn-124 on 𝑉𝐵𝐺 (denoted as 𝑉𝑥) of electron doping in the MoS2 channel [14]. The native electron doping 125 concentration (𝑛𝑒) of Device M1 is estimated to be 2.34× 1012 cm-2 according to the form of 𝑛𝑒 =126 𝐶𝑜𝑥(0 − 𝑉𝑥)/𝑞 [14], where 𝐶𝑜𝑥 of about 1.15× 10−8 F cm-2 is the areal capacitance of the SiO2 127 dielectric layer. Such a high native doping concentration points to a degenerated semiconductor in 128 2D MoS2 flakes. Figure 1d presents corresponding Seebeck coefficients as a function of 𝑉𝐵𝐺 for 129 Devices M1 and M5. The Seebeck coefficient is negative, confirming again the electron doping at 130 high, positive 𝑉𝐵𝐺  with the n-type TE-FET switched on. The negative Seebeck coefficient of 131 Device M1, following the trend of transfer curves in Fig. 1c, goes up to the maximum of 281 𝜇𝑉/𝐾 132  7 at 𝑉𝐵𝐺  of -12 V (denoted as 𝑉𝑝𝑒𝑎𝑘 ). According to the Cutler-Mott theory [6], the Seebeck 133 coefficient (𝑆) of degenerated semiconductors is described as: 134 𝑆 = −(𝜋2𝑘𝐵2𝑇/3𝑞)(𝑑 ln 𝐺 /𝑑𝐸)𝐸=𝐸𝐹,   (1) 135 where 𝑘𝐵 is the Boltzmann constant, 𝑇 is temperature, 𝐺 is conductance, 𝑞 is charge, and 𝐸 is the 136 energy of charge carriers [6]. The term of the derivative of ln 𝐺 with respect to 𝐸 in Eq. (1) can be 137 rewritten as (𝑑 ln 𝐺/𝑑𝑉𝐵𝐺)(𝑑𝑉𝐵𝐺/𝑑𝐸)𝐸=𝐸𝐹 [33]. The data of (𝑑 ln 𝐺/𝑑𝑉𝐵𝐺) of Device M1 are 138 presented as black open circles in Fig. 1d. A large shift between the (𝑑 ln 𝐺/𝑑𝑉𝐵𝐺) and the 139 Seebeck coefficient is identified, implying an extrinsic effect such as additional charges of 140 interface trap states in the interface between the MoS2 flakes and the SiO2 dielectric layer.  141  142 Figure 1. (a) Scanning electron microscope (SEM) image of a typical monolayer MoS2 TE-FET 143 device (Device M1). Electrodes 1 and 2 are used as source and drain electrodes and are 144 employed as thermometers. Electrodes 1 and 2 are given to measure the thermovoltage across 145  8 themselves. Electrode 3 is a heater that offers sinusoidal heat flux. (b) Scheme of the MoS2 TE-146 FET device with an electrical circuit for TE measurements. The substrate is offered as a back-147 gating electrode, and a lock-in amplifier is implemented to conduct thermovoltage 148 measurements. (c) Transfer curves of Devices M1 and M5 with thicknesses of 1 and 2 layers at 149 room temperature. The inset offers a current-voltage (I-V) curve of Device M1. (d) Seebeck 150 coefficients as a function of back gating voltage (𝑉𝐵𝐺) for Devices M1 and M5. The extreme 151 Seebeck coefficient of 281 𝜇𝑉/𝐾 (207 𝜇𝑉/𝐾) exists at 𝑉𝑝𝑒𝑎𝑘 of -12 V (+4 V) for Device M1 152 (M5). The open circles delineate data of 𝑑(ln 𝐺)/𝑑𝑉𝐵𝐺 of Device M1. 153  154 Figure 2 presents complete information on Seebeck coefficients as a function of 𝑉𝐵𝐺  at 155 temperatures ranging from 120 to 600 K. Like mono- and bi-layer MoS2 flakes, Device M6 of 156 three layers in thickness shows a nonzero thermopower started from 𝑉𝐵𝐺 of -33 V (see Fig. 2a) at 157 300 K. The thermopower increases with increasing 𝑉𝐵𝐺 up to the maximum value of ~281 𝜇𝑉/𝐾 158 at 𝑉𝐵𝐺 of 6 V. The magnitude of the thermopower then decreases with a further increase of 𝑉𝐵𝐺 159 due to an increase of electron carrier concentration that will be discussed in the following 160 paragraphs as well as in the Supporting Information. When the temperature is raised up to 600 161 K, the extreme thermopower boosts up to ~698 𝜇𝑉/𝐾. In contrast, the maximum thermopower 162 decreases to be about 69.8 𝜇𝑉/𝐾 at 120 K. The temperature behavior, correlating to 2D Mott’s 163 VRH and metallic conduction, will be separably discussed later for Figs. 3 and 4. Particularly, a 164 small downward step (marked as a step in Fig. 2a) on the Seebeck coefficient is commonly 165 perceived in few-layer MoS2 devices at temperatures higher than 450 K, whereas it is hardly 166 observed for TE-FETs of very thick MoS2 flakes. We will also provide comprehensive discussions 167 about the marked step later. 168  9 In Fig. 2b, another example of the MoS2 TE-FET (Device M1) exposes the same feature as that 169 displayed in Fig. 2a. The thermopower is turned on, consistent with the field-effect behavior of 170 the n-type FET. Additionally, we point out that the 𝑉𝑝𝑒𝑎𝑘 at the extremum of the thermopower 171 varies with temperature. The 𝑉𝑝𝑒𝑎𝑘  moves to further negative voltages with an increase in 172 temperature. The temperature-dependent 𝑉𝑝𝑒𝑎𝑘 is accordingly displayed in Fig. 2c. To explore the 173 mechanism further, the 𝑉𝑥′𝑠 of the turn-on of the field-induced electron doping are offered in Fig. 174 2c, as well, for comparison. It is noted that the 𝑉𝑝𝑒𝑎𝑘 adequately follows the temperature behavior 175 of the 𝑉𝑥. The 𝑉𝑥 moves to lower voltages at higher temperatures, indicating de-trapping of the 176 interface trapped states in the interface between the MoS2 flakes and the SiO2 dielectric layer [24, 177 34]. The result corroborates our previous conjecture about the extrinsic disorder and scattering 178 effect from the supporting substrate. On the other hand, the temperature behavior of the 179 thermopower at 𝑉𝐵𝐺  of 60 V is drawn in Fig. 2d. At temperatures lower than 180 K, the 180 temperature-dependent thermopower is proportional to 𝑇1/3 while it linearly follows 𝑇 above 300 181 K. In particular, the thermopower of the 2D MoS2 TE-FETs always increases with the increasing 182 temperature at all 𝑉𝐵𝐺′𝑠 (see Fig. 2a). 183  184  10  185 Figure 2. (a) Seebeck coefficients of the trilayer MoS2 TE-FET device (Device M6) as a 186 function of 𝑉𝐵𝐺 at temperatures ranging from 120 to 600 K. (b) Seebeck coefficients of the 187 monolayer MoS2 TE-FET device (Device M1) at temperatures of 100, 140, 180, 220, 260, and 188 300 K. (c) 𝑉𝑝𝑒𝑎𝑘 and 𝑉𝑥 of Device M1 as a function of temperature. (d) The Seebeck coefficient 189 as a function of temperature (𝑇) at 𝑉𝐵𝐺 of 60 V. The red line shows the best linear least-square 190 fitting in the temperature range from 300 to 600 K, and the blue line presents the best least-191 square fitting to 𝑇1/3 in the temperature range from 120 to 200 K. 192  11 To explore the mechanism of thermopower in 2D MoS2, we investigate thermoelectric properties 193 in correlation with electron transport, and we study as a first step in the temperature range at which 194 the 2D Mott’s VRH conduction dominates. The 2D Mott’s VRH conduction describes that the 195 resistivity of the 2D channel (𝜌2𝐷 ) varies with temperature 𝑇 according to the form of 𝜌2𝐷 ∝196 exp((𝑇0/𝑇)1/3), where 𝑇0 is the disorder parameter [32]. Figure 3a presents the hopping behavior 197 and the best least-square fitting lines at temperatures ranging from 80 to 180 K. The resistivity 198 suitably follows the 2D hopping conduction when the channel is turned on at 𝑉𝐵𝐺  above 0 V. 199 Moreover, the disorder parameters 𝑇0′𝑠 are estimated from the linear least-square fittings in Fig. 200 3a. In the same temperature range, the thermopower 𝑆 depends on 𝑇 in line with the equation of 201 𝑆(𝑇) ∝ 𝑇𝑑−1𝑑+1, where 𝑑 = 2 is the dimension of the electron system [35,32]. Figure 3b presents the 202 linear behavior between the negative Seebeck coefficient −𝑆 and 𝑇1/3. The range of temperatures 203 within which the fitting obeys well follows the same temperature range in Fig. 3a, indicating the 204 contribution from the disorder effect. Figure 3c presents the 𝑇01/3 and −𝑆 as a function of the 205 logarithm of the carrier concentration (ln(𝑛2𝐷)), showing a linear dependent feature at carrier 206 concentrations ranging from 2.27× 1012  to 6.58× 1012  cm-2. The resistivity 𝜌2𝐷  is inversely 207 proportional to the carrier concentration 𝑛2𝐷 and, it is also proportional to exp((𝑇0/𝑇)1/3) due to 208 the disorder effect. Thus, the 𝑇01/3 is proportional to ln(𝑛2𝐷) in the same temperature range. On 209 the other hand, the Seebeck coefficient 𝑆 at the constant temperature of 180 K is also proportional 210 to 𝐶 + ln(𝑛2𝐷) [36], where 𝐶 is a constant. The result corroborates the same mechanism of the 211 disorder effect, and it indicates the same relationship to the 2D carrier concentration 𝑛2𝐷. 212  12  213 Figure 3. (a) ln(𝑅) as a function of 𝑇−1/3 of Device M4 at various 𝑉𝐵𝐺’s in the temperature 214 range from 80 to 300 K. The solid lines provide the best linear least-square fitting results over 215 the temperature range from 80 to 180 K. (b) Seebeck coefficients versus 𝑇1/3 at 𝑉𝐵𝐺’s of 0, 20, 216 40, and 60 V over the temperature range from 90 to 200 K. The solid lines give the best linear 217 least-square fittings to the data over the temperature from 90 to 180 K. (c) Disorder parameter 218 (𝑇01/3) and Seebeck coefficients as a function of 𝑛2𝐷 in a logarithmic scale. The 𝑇0’s are obtained 219 from linear fittings in Fig. 3b, and the Seebeck coefficients are taken at 180 K. 220 As expected, the disorder effect may disappear under the circumstances of a high thermal energy. 221 When the temperature increases above 300 K, and the channel is turned on at 𝑉𝐵𝐺 above 0 V, the 222  13 electron transport exhibits thermally activated transport, which is always observed in connection 223 with the 2D hopping conduction at low temperatures. Figure 4a reveals the thermally activated 224 behavior described by the form of  𝜌2𝐷 ∝ exp(𝐸𝐴/𝑘𝐵𝑇), where 𝐸𝐴 is the activation energy. The 225 fitting lines indicate that the temperature dependence of resistance exactly follows the thermally 226 activated transport in the temperature range from 330 to 460 K. Through the linear least-square 227 fitting, the activation energy 𝐸𝐴 is estimated. At temperatures above 460 K, the resistance behavior 228 changes remarkably. We present the same data in a linear scale in Fig. S3 of the Supporting 229 Information. The temperature dependence of resistance is linearly dependent on temperature, 230 which signifies the phonon scattering and the metallic state above 460 K. The electron transport 231 changes from 2D Mott’s hopping with thermally activated transport to the metallic state, 232 presenting an interesting metal-to-insulator transition [20]. 233 The corresponding Seebect coefficients as a function of temperature are unveiled in Fig. 4b. The 234 Seebeck coefficient is just linearly dependent on temperature without any perceivable transition in 235 the whole temperatures ranging from 300 to 600 K. Usually, the Seebeck coefficient will decrease 236 with an increase of temperature if the thermopower follows the electron transport of thermal 237 activation [36]. In all the devices of MoS2 TE-FET, the decrease of the Seebeck coefficient with 238 an increase in temperature has never been noticed yet (see, for example, Fig. 2d). The 239 disappearance of the decreasing thermopower could be attributed to the enhanced phonon 240 scattering at high temperatures that dominates the electron diffusion in the generation of 241 thermopower. To explore about the electron transport and the thermopower, we present the 242 activation energy 𝐸𝑎 and the logarithm of the Seebeck coefficient ln(|𝑆|) varied with the carrier 243 concentration 𝑛2𝐷  in Fig. 4c. The resistivity 𝜌2𝐷  is inversely proportional to the carrier 244 concentration 𝑛2𝐷 and it is proportional to exp(𝐸𝐴/𝑘𝐵𝑇), thus the 𝐸𝑎 is proportional to ln(𝑛2𝐷) at 245  14 the same temperature. In addition, the Seebeck coefficient at a constant temperature is proportional 246 to 𝑛2𝐷−2/3 according to the theory for nearly free electrons [37]. Consequently, we investigate the 247 reliance between the ln(|𝑆|)  and the ln(𝑛2𝐷) , and it reveals the linear manner at carrier 248 concentrations ranging from 2.41× 1012 to 6.72× 1012 cm-2. The 𝑛2𝐷−2/3 behavior at high carrier 249 concentrations (𝑉𝐵𝐺 > 𝑉𝑝𝑒𝑎𝑘) infers the depression of thermopower and thermally induced carrier 250 diffusion due to more charge carriers compacted in the channel. On the other hand, we shall 251 consider both effects presented in Figs. 3c and 4c to investigate the dependence of the Seebeck 252 coefficient on the back gate voltage (𝑉𝐵𝐺) such as those shown in Fig. 1d. The 𝑉𝐵𝐺 behavior of the 253 thermopower is displayed in Fig. S4 in the Supporting Information. The thermopower is 254 separately fitted at either a lower carrier concentration ( 𝑉𝐵𝐺 < 𝑉𝑝𝑒𝑎𝑘 ) or a higher carrier 255 concentration (𝑉𝐵𝐺 > 𝑉𝑝𝑒𝑎𝑘) according to the carrier concentration behaviors revealed in Figs. 3c 256 and 4c. The details are expressed in the discussion of Fig. S4, and, particularly, the fitting results 257 lead to evaluating the universal constant of 𝑘𝐵/𝑞 and the carrier effective mass of 0.1 𝑚0, where 258 𝑘𝐵 is the Boltzmann constant, 𝑞 is the charge, and 𝑚0 is the mass of the electron.  The results of 259 the extracted values in line with theories and other group’s experiments that corroborate the 260 robustness of our accurate and precise thermopower measurements in the TE-FETs. 261  15  262 Figure 4. (a) ln 𝑅 versus 1000/𝑇 at temperatures ranging from 300 to 460 K. The solid lines 263 display the best linear least-square fittings. (b) Seebeck coefficients versus 𝑇 of Device M7 at 264 various 𝑉𝐵𝐺’s over the temperature range from 300 to 600 K. The solid lines represent the best 265 linear least-square fittings at temperatures ranging from 330 to 460 K. (c) Activation energy (𝐸𝑎) 266 and Seebeck coefficients as a function of 𝑉𝐵𝐺. The 𝐸𝑎’s are obtained from fittings in Fig. b and 267 the Seebeck coefficients are measured at 450 K. 268  269 In previous paragraphs, we point out an extrinsic effect due to interface trapped charges between 270 the MoS2 flake and the SiO2 substrate according to the shift between the field-effect and the 271 thermopower behaviors in Fig. 1d and the step designated in Fig. 2a. We will then investigate 272 deeply into the extrinsic effect. The inset to Fig. 5a reveals the back-gating behavior of the Seebeck 273  16 coefficients for Device M7 at temperatures above 300 K. A clear step is probed in the 𝑉𝐵𝐺 274 dependent thermopower at 600 K, like that marked in Fig. 2a for Device M6. To multiply the 275 effect, we expose the 𝑑𝑆/𝑑𝑉𝐵𝐺 as a function the 𝑉𝐵𝐺 in Fig. 5a. The differential of the Seebeck 276 coefficient exhibits a peak close to the 𝑉𝐵𝐺 of 0 V. The peak at zero back-gating voltage indicates 277 the trapping and detrapping due to the extrinsic effect of trapped charges in the SiO2 substrate. In 278 particular, the differential of the Seebeck coefficient is extremely sensitive to the ambient 279 temperature. In addition to the thermopower, the 𝑉𝐵𝐺 dependent currents at temperatures above 280 300 K reveal a similar behavior that a step feature is observed in the curve at 600 K in the inset to 281 Fig. 5b. The results are consistent with those reported in the literature [24] in which a mode of 282 trapped states in the dielectric is proposed to explain the trapping (injection) of electrons at 283 negative 𝑉𝐵𝐺 as well as the detrapping of electrons at positive 𝑉𝐵𝐺. We plot the transconductance 284 as a function of the 𝑉𝐵𝐺 in Fig. 5b to expose its sensitive temperature dependency. At temperatures 285 above 480 K, the transconductance exposes the peak near the 𝑉𝐵𝐺 of 0 V, indicating the trapping 286 and detrapping of charges in the SiO2 substrate with a very low positive or negative 𝑉𝐵𝐺. 287 We further dig into the current's dependence on the back-gating voltage, 𝑉𝐵𝐺. In Fig. S5 in the 288 Supporting Information, the analysis of the trapped carrier concentration for Device M7 at 600 289 K is sketched and described in detail. Through the shifted behavior of the linear current-𝑉𝐵𝐺 290 manner above and below the 𝑉𝐵𝐺  of 0 V, the trapped carrier concentration is evaluated to be 291 ~6.84 × 1011 cm-2, which is very close to that estimated in the previous report [24]. The release 292 of the trapped electrons causes an increase in conductivity and current by up to ~45%. In contrast, 293 it generates a decrease of the Seebeck coefficient from 522 to 509 𝜇V/K, about a 2.5% reduction. 294 The power factor is calculated using 𝑃𝐹 = 𝑆2𝜎, where 𝜎 is the conductivity, and the release of the 295 trapped electrons causes a rise of power factor of ~38%. To integrate information from insets to 296  17 Figs. 5a and 5b, the carriers released from the additional gating of extrinsic trapping charges in 297 the SiO2 contribute to an increase of channel current and a decrease of thermopower 298 simultaneously when the gating voltage 𝑉𝐵𝐺 is slightly biased to a low positive voltage. On the 299 other hand, the sensitive temperature dependences of the differential of the thermopower (Fig. 5a) 300 and transconductance (Fig. 5b) are quantitatively portrayed in Fig. 5c. It is crystal clear to 301 distinguish the strong temperature dependency at temperatures above 450 K. The extrinsic effect 302 due to the trapping charges in the SiO2 plays an important role in applying to high-temperature 303 thermal sensors. 304  305  18 Figure 5. (a) Differential Seebeck coefficients as a function of 𝑉𝐵𝐺 of trilayer MoS2 TE device 306 (Device M7) at various temperatures. The inset displays corresponding Seebeck coefficients 307 versus 𝑉𝐵𝐺 with an arrow pointing out a steep variation near 𝑉𝐵𝐺 of 0 V at temperatures above 308 450 K. (b) Transconductances as a function of 𝑉𝐵𝐺. The inset provides current as a function of 309 𝑉𝐵𝐺 with an arrow indicating a sharp change near 𝑉𝐵𝐺 of 0 V. (c) Transconductances and 310 differential Seebeck coefficients at 𝑉𝐵𝐺 of 0 V at temperatures from 450 to 600 K. 311 As emphasized in the introduction section, we point to the importance of the TE power factor in 312 addition to the Seebeck coefficient. Figure 6a presents the temperature behavior of the power 313 factor for Devices M1 and M9. The power factor always increases with increasing temperature. In 314 particular, the thinner MoS2 device (Device M1) exhibits a much higher power factor. For the 315 thicker MoS2 device, the power factor is lower while it increases exponentially with the 316 temperature. The result also indicates a decreasing manner of the power factor with an increase in 317 MoS2 flake thickness, which will be disclosed in the bottom panel of Fig. 6b. In Fig. 6b, we 318 provide summarized results of the Seebeck coefficient, the conductivity, and the power factor as a 319 function of the MoS2 flake thickness with dashed line as guides to eyes, drawn by the least-square 320 fitting. On the upper panel, the Seebeck coefficient increases from ~0.15 mV/K, and it reaches a 321 maximum above 0.3 mV/K for the MoS2 TE-FET device with a flake thickness of ~20 layers. The 322 Seebeck coefficient turns down afterward, dropping to be less than 0.05 mV/K for the device with 323 a flake thickness of ~40 layers. On the other hand, the middle panel of Fig. 6b presents a 324 monotonical decrease in room-temperature conductivity with an increase of the MoS2 flake 325 thickness. The decreasing trend decelerates for thicker MoS2 flakes. However, as shown in the 326 lower panel of Fig. 6b, the power factor reveals a monotonic decreasing feature with increasing 327 flake thickness for MoS2 TE-FET devices. The decreasing manner is aggravated for MoS2 TE-328  19 FET devices with a thickness higher than 30 layers. The Seebeck coefficient and the power factor 329 are all important in energy export. Thus, choosing the MoS2 with a thickness of less than 20 layers 330 gives the optimum performance for the TE application. Figure 6c presents the benchmarking 331 performance of the power factors obtained in the 2D semiconductors. The red star points to the 332 current result of the monolayer MoS2 TE-FET device, and it points to the power factor of 1.05 333 mW/m K2 at room temperature. According to the literature survey, only bilayer WSe2 and MoS2 334 flakes demonstrate power factors higher than the current result. This indicates that the surrounding 335 conditions and passivating materials are important, and few-layer MoS2 films with a thickness of 336 less than 20 layers could be the best candidate for TE applications among all 2D semiconductors. 337  338  339 Figure 6. (a) Power factor (𝑃𝐹) in logarithm scale as a function of temperature (in linear scale) 340 of Devices M1 and M9 with thicknesses of 1 and 7 layers at 𝑉𝐵𝐺 of 60 V. (b) Seebeck 341 coefficient, conductance, and 𝑃𝐹 as a function of MoS2 thickness at 300 K. The dashed curves 342  20 drawn according to the least-square fitting are guides to eyes. (c) 𝑃𝐹 of several different 2D 343 materials at room temperature: (i) bilayer PtSe2[38] (ii) 40 nm thick BP flake[39], (iii) 5 nm 344 thick PdSe2 flake[40], (iv) bilayer WSe2 single crystal flake [41], and (v) bilayer MoS2 flake[30]. 345 The red star points to the result of this work (Device M1).  346 Conclusions 347 Thermopower and electron transport are simultaneously explored in MoS2 TE-FET devices with 348 thicknesses ranging from monolayer up to 39 layers in a wide temperature range from 80 to 600 349 K. The electron transport reveals Mott’s 2D variable range hopping at temperatures lower than 350 300 K, thermally activated transport at temperatures ranging from 300 to ~450 K, and phonon 351 scattering at temperatures higher than 460 K. The corresponding Seebeck coefficient, however, 352 presents only Mott’s 2D variable range hopping and phonon scattering behaviors as a 353 monotonically increasing feature with increasing temperature. The maximum of the Seebeck 354 coefficient is ~698 𝜇V/K for the tri-layer MoS2 TE-FET device at 600 K. Particularly, the feature 355 of decreasing manner with an increase in temperature as a symbol of the thermally activated 356 transport has not been discovered yet in all TE-FET devices with different thicknesses. In addition 357 to temperature dependences, the carrier concentration behaviors of the thermally activated energy, 358 the disorder parameter 𝑇0, and the Seebeck coefficients are examined simultaneously to confirm 359 the theories implemented in the wide temperature range. In particular, the Seebeck coefficients as 360 a function of carrier concentration are analyzed separately in either low or high carrier 361 concentrations. In those fittings, the universal constant of 𝑘𝐵/𝑞 and the carrier’s effective mass 362 have been estimated. The effective mass of electrons in the monolayer MoS2 is evaluated to be 363 ~0.1 𝑚0. Moreover, the power factors of the MoS2 TE-FET devices are measured, and the layer 364 number dependences of the Seebeck coefficient, the conductivity, and the power factor are studied 365  21 and sketched in diagrams. The power factor of the current work is benchmarked with others’ results. 366 It is confirmed that the few-layer MoS2 films with thicknesses of less than 20 layers could be the 367 best candidates for TE applications. On the other hand, we have explored the extrinsic effect due 368 to trapped electrons in the SiO2 substrates. The extrinsic effect exists in both electron transport and 369 thermopower for the TE-FET devices at temperatures higher than ~450 K. Very sensitive 370 temperature dependences of the differential of the Seebeck coefficient and the transconductance 371 are discovered. The trapped carrier concentration is evaluated to be ~6.84 × 1011 cm-2 for the tri-372 layer MoS2 TE-FET device at 600 K. The release of the trapped electrons causes an increase in 373 conductivity and current by up to ~45%. It causes a rise in the power factor of ~38% while it 374 decreases the Seebeck coefficient by ~2.5%. The extrinsic effect of trapping charges in the 375 substrate can be applied to thermal sensors at high temperatures. 376 Experimental Sections 377 Fabrication of Few-layer MoS2 TE-FETs. Few-layer MoS2 flakes were obtained by 378 mechanically exfoliation from a MoS2 bulk, purchased from Structure Probe, Inc., USA. The few-379 layer MoS2 flakes were transferred to a heavily p-doped Si wafer, with a resistivity of 380 approximately 0.001 ohm ∙ cm , and capped with 300-nm thick SiO2 using a high-precision 381 alignment stacking system (HPAS Mono, Nanovie Co. Ltd., Taiwan) and polydimethylsiloxane 382 (PDMS, PF-40-X4, Gel-Pak, USA). A standard electron beam lithography system, including a 383 scanning electron microscope (JSM-IT300, JEOL, Japan) and an electron-beam controller 384 (ELPHY Quantum, Raith GmbH, Germany), was used to pattern contact electrodes. Subsequently, 385 Ti/Au (10 nm/100 nm) metals were deposited by thermal evaporation in a high vacuum of 386 ~3 × 10−6 torr. After the lift-off process by acetone, the source, drain and heater electrodes were 387 formed, and the MoS2 TE-FET devices were manufactured. 388  22 Determination of The Thickness of MoS2 Flake. The thickness of MoS₂ flakes of less than 5 389 layers was determined using an optical microscope, based on contrast differences in green- and 390 red-color channels. The optical contrast variations with thickness were calibrated by Raman 391 spectroscopy (Shamrock SR500, Andor Technology, Northern Ireland) with laser light of 532 nm 392 in wavelength and spot size of ~1 𝜇m. The details of the calibration are discussed in Fig. S1 in the 393 Supporting Information. The thicknesses of those thicker MoS₂ flakes were measured using an 394 atomic force microscope (AFM, SPA-300HV, Seiko Instruments Inc., Japan) which was operating 395 in a tapping mode. AFM tips (PPP-SEIHR, Nanosensors, Switzerland) with a radius of ~10 nm, a 396 force constant of 15 N/m, and a resonance frequency of 130 kHz were employed for the 397 measurements. 398 Electrical Characterization. The as-fabricated MoS2 TE-FET devices are placed in the probe 399 station (TTPX, Lake Shore Cryotronics, Inc., USA) in a high vacuum of ~10−6 torr. The electrical 400 transport characterizations wer carried out by electrometers of Keithley 6430 and Keithley 2400 401 (Tektronix, Inc., USA). The Keithley 6430 was used to supply source-drain voltages and acquire 402 currents with preamplifier, and the Keithley 2400 was used to offer the back-gating voltages on 403 the back side of the substrate. 404 Thermal electrical characterization. The Seebeck coefficients (𝑆) were calculated according to 405 the form 𝑆 = −𝑉𝑇𝐸/∆𝑇, where ∆𝑇 is a temperature difference and 𝑉𝑇𝐸 is a thermoelectric voltage. 406 To generate a temperature gradient of ∆𝑇, an AC voltage at the specified frequency of 6.85 Hz 407 was applied on the heater electrode using a function generator (Agilent 33522A, Agilent, USA). 408 Detailed measurements of ∆𝑇  are provided in the discussion of Fig. S2 in the Supporting 409 Information. The 𝑉𝑇𝐸  was determined using the standard 2ω method, recorded by a lock-in 410  23 amplifier (SR830, Stanford Research Systems, USA) at a frequency of 13.7 Hz. During the 411 measurement, the back-gating voltage was supplied by Keithley 2400 (Tektronix, Inc., USA). 412  413 ASSOCIATED CONTENT 414 Supporting Information. The information of the identification of layer numbers of MoS2 flakes, 415 device parameters, estimation of temperature gradient for the evaluation of the Seebeck 416 coefficients, temperature dependent resistance at high temperatures, estimation of the 𝑘𝐵/𝑞 and 417 the electron effective mass, estimation of trapped charges in the SiO2, thickness dependences of 418 the differential of the Seebeck coefficient, and thermoelectric parameters of all devices are 419 described in detail in the Supporting Information. This material is available free of charge via the 420 Internet at http://pubs.acs.org. 421 AUTHOR INFORMATION 422 Corresponding Authors 423 *S. S. Islam, Email: sislam@jmi.ac.in 424 *Wen-Bin Jian, Email: wbjian@nycu.edu.tw 425 ORCID 426 Wen-Bin Jian: 0000-0002-1898-9641 427 Author Contributions 428 The manuscript was written through contributions of all authors. All authors have given approval 429 to the final version of the manuscript. 430 mailto:sislam@jmi.ac.inmailto:wbjian@nycu.edu.tw 24 ACKNOWLEDGMENT 431 This work was supported by the National Science and Technology Council, Taiwan, under Grant 432 Nos. NSTC-111-2124-M-A49-008 and NSTC-111-2112-M-A49-038. This work was also 433 financially supported by the “Center for the Semiconductor Technology Research” from The 434 Featured Areas Research Center Program within the framework of the Higher Education Sprout 435 Project by the Ministry of Education, Taiwan, and supported in part by the National Science and 436 Technology Council, Taiwan, under Grant No. NSTC 111-2634-F-A49-008. 437 REFERENCES 438 (1) Dresselhaus, N. S.; Chen, G.; Tang, M. 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