Supporting information. Gate-optimized thermoelectric power factor in ultrathin WSe2 single crystals
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1 Supporting information Gate-optimized thermoelectric power factor in ultrathin WSe2 single crystals Masaro Yoshida 1, Takahiko Iizuka 1, Yu Saito 1, Masaru Onga 1, Ryuji Suzuki 1, Yijin Zhang 1, Yoshihiro Iwasa 1,2*, & Sunao Shimizu 2 1 Quantum-Phase Electronics Center (QPEC) and Department of Applied Physics, the University of Tokyo, Tokyo , Japan. 2 RIKEN Center for Emergent Matter Science (CEMS), Wako , Japan. 1. Optical contrast for ultrathin WSe2 flakes We established a systematic relation between the thickness and the optical contrast for mono-, bi-, and trilayer WSe2 flakes. First we exfoliated a WSe2 single crystal and obtained ultrathin flakes on a doped silicon substrate covered with a 300-nm-thick SiO2 layer. We then put the sample into a chamber and flew Ar/H2 gas at 573 K for 3 hours. After this process, we measured the thickness of each flake by AFM. The thickness obtained by AFM was almost a multiple of the thickness of a monolayer, 0.65 nm. We could obtain the value close to 0.65 nm in some ultrathin flakes, indicating that the dirt between the flakes and substrates was significantly removed by the heat cleaning. We concluded that the thickness measured by AFM was accurate after Ar/H2 heat cleaning. We determined the number of layer for each flake based on the thickness obtained by AFM. After the AFM measurement, we took optical images of the samples and obtained the intensity in the three R, G, B channels. We then calculated the optical contrast (C) determined as C = (Iw/o Iw)/Iw/o, where Iw/o is the intensity measured at a bared substrate and Iw is the intensity obtained at a flake. Among the three R, G, B channels, we focused on the R channel because the optical contrast in the R channel was the most sensitive to the difference of thickness. We show the newly obtained optical contrast table in Fig. S1, where the optical contrast in the R channel systematically changes as a function of the number of layer. The absolute values of the contrast are similar to those in WS2 (ref. 18). 1
2 In Fig. S1, we also show the optical contrast of the ultrathin WSe2 flake used as the channel of the thermoelectric EDLT, whose thickness was measured to be 2 nm by AFM. From this, we concluded that the flake was a trilayer. Figure S1. Optical contrast in the R channel for ultrathin WSe 2 flakes. Red circles represent the optical contrast in the R channel for mono-, bi-, and trilayer WSe 2 flakes. Each point corresponds to the average of the contrast measured on seven monolayers, three bilayers, and two trilayers. The error bars are determined by the standard deviation of the measurements. The blue circle represents the optical contrast of the flake that we used as the channel for the thermoelectric EDLT. 2. Details of the thermoelectric measurement All the measurements were performed under high-vacuum condition. Prior to the thermopower measurement, we first performed the calibration of the on-chip thermometers: We measured the resistances of the thermometer electrodes (Th1 and Th2) at cryostat temperatures between T = 300 K and 303 K in steps of 1 K. The resistance of the thermometer was measured by using an AC resistance bridge (Lake Shore Model 370) with the excitation voltage of 2 mv. At a constant cryostat temperature, we kept measuring the resistance of the thermometer Th2 (R_Th2) for more than 600 seconds, sequentially the resistance of the thermometer Th1 (R_Th1), and increased the temperature by 1 K. After the measurement of R_Th1 and R_Th2 at T = 303 K, we decreased the temperature in steps of 1 K, and re-measured the resistances at each temperature in order to confirm the reproducibility of the measurement. All the results 2
3 are shown in Figs S2a and S2b. Because of the characteristics of the AC resistance bridge, it took approximately 200 seconds to stabilize the values of resistance. In Figs S2c and S2d, we show the stabilized values of R_Th1 and R_Th2 as a function of cryostat temperature (T). The green lines are the line fits to the data. Second, we measured the thermometer resistances with applying various voltages to the heater electrode in order to obtain the relation between the heater voltage (VHeat) and the temperature gradient ( T) across the WSe2 single crystal. We first set the cryostat temperature to 300 K, applied the heater voltage VHeat = 0.5 V, and kept measuring R_Th2 for more than 300 seconds. We sequentially measured R_Th1, and increased VHeat to 1.0 V. We obtained the series of the thermometer resistances at VHeat = 0.0 V, 0.5 V, 1.0 V, 1.5 V, and 2.0 V, which is summarized in Figs S2e and S2f. Based on the linear relation between resistance and temperature shown in Figs S2c and S2d, we calculated the local temperatures at the thermometer electrodes under applying voltage to the heater. In Fig. S2g, we show the increase of temperature at each thermometer ( T_Th1 and T_Th2) as a function of square of voltage applied to the heater (VHeat 2 ). The difference of T_Th1 and T_Th2 corresponds to the temperature gradient ( T) across the ultrathin WSe2 single crystal, whose dependence on VHeat 2 is also shown in Fig. S2g. Because T is proportional to the Joule heat or VHeat 2, the obtained linear relation between T and VHeat 2 is reasonable. After finishing the temperature calibration, we carried out the thermopower measurement, whose schematic procedure is shown in Figs 2b-2e. In the thermopower measurement, we assume that the linear relation between VHeat 2 and T shown in Fig. S2g was maintained though we scanned VHeat relatively quickly. We used a semiconductor parametric analyzer (Agilent Technology E5270B) to apply voltage to the heater electrode, and we employed a nanovoltmeter (Agilent Technology 34420A) to measure the consequent thermoelectric voltage ( V). The trigger signal is sent from E5270B to 34420A just after the application of voltage on the heater electrode. Sequentially, 34420A receives the trigger signal, followed by the measurement of V. 3
4 Figure S2. Temperature calibration. (a, b) Time dependences of resistances of thermometers Th1 (R_Th1) and Th2 (R_Th2) measured at temperature T = 300 K, 301 K, 302 K, and 303K. (c, d) The linear relation between thermometer resistance (R_Th1, R_Th2) and temperature (T). Green lines are the fits to the measured data. (e, f) Time evolution of thermometer resistance (R_Th1, R_Th2) measured under applying different voltages (V Heat) to the heater electrode. (g) The increase of temperature at each thermometer ( T_Th1 and T_Th2) and the consequent temperature gradient ( T) across the single crystal as a function of the square of V Heat. 3. Carrier concentration dependence of Seebeck coefficient in other devices In Fig. S3, we show the electronic and thermoelectric properties of a 10-nm-thick WSe2 flake EDLT. Figures S3a and S3b are the transfer curve and the gate voltage (VG) dependence of Seebeck coefficient (S) at 300 K, respectively. We display in Fig. S3c the carrier concentration (n3d) dependence of S, where we assume that the capacitance is 5.8 F/cm 2 and 7.1 F/cm 2 for electrons and holes, respectively, and that the carriers are accumulated in the top bilayer. Figure S3c shows that S(n3D) is larger in electron side 4
5 than in hole side. This asymmetric feature is qualitatively similar to that observed in the device in the manuscript, which is shown in Fig. 4b. Figure S3 (a) The gate voltage (V G) dependence of source-drain current (I DS) measured at source-drain voltage V DS = 0.01 V. The thickness of the flake was 10 nm. (b) V G dependence of Seebeck coefficient (S). (c) The evolution of the absolute value of Seebeck coefficient S as a function of carrier concentration (n 3D). The red and blue circles represent the data obtained during electron and hole doping, respectively. 4. Possible interpretation of the observed S -n3d relation based on a band calculation The electron-doped WSe2 showed the lower mobility (see Fig. 4a) and the larger thermopower S (see Fig. 4b) at a given carrier concentration than hole-doped WSe2. This hole-electron asymmetric character probably has its origin in the electronic structure. We refer to the first-principle calculations on the field effect transistor of a trilayer WSe2 28. In Figs. S4a and 4b, we show the schematic band diagrams and the predicted Fermi surfaces (FSs) of a trilayer WSe2 under the gate bias. Here, in sharp contrast to monolayers, the predicted FS for the gated trilayer WSe2 is very similar to that for the bulk. Brumme et al. showed that valley is initially filled for the low density hole-doping with the charge concentration of 0.01 e/unit cell, which corresponds to cm -3. Also were shown that for the low density electron-doping, K and Q (between and K) valleys are almost simultaneously occupied. Because only K valleys consist of FSs in lightly-doped monolayers, the calculation suggests that the gated trilayer WSe2 is not regarded as a simple 5
6 doped monolayer. The difference in mobility and S between p- and n-type WSe2 can be interpreted by the predicted number of occupied valleys of the gated WSe2 trilayer. First, the lower mobility in the electron side may be attributed to the intervalley scattering: The hole and electron conductions are dominated by the carriers in the single valley, and by the multi-valleys at K and Q points, respectively. Also the multi-valley nature of the conduction band explains the enhancement of S by electron doping: The larger S in n-type WSe2 indicates the larger density of states (DOS) in the conduction band than in the valence band, and the DOS in the conduction band consisting of K valleys and Q valleys is larger than that in the valence band mainly composed of valley. Figure S4. The schematic band diagrams and the predicted Fermi surfaces of a trilayer WSe 2 under the application of (a) negative and (b) positive gate voltages (ref. 28). 5. Thermoelectric properties in gated 2D materials The thermoelectric performances of various 2D materials are being rapidly explored by field effect doping. In Table S5, we summarized the recent achievements in this field. Material Dielectric Polarity Max S Power factor Ref. Graphene Bi2Se3 MoS2 MoS2 MoS2 WSe2 liquid Ambipolar Ambipolar n-type n-type n-type Ambipolar 100 V/K 170 V/K 30 mv/k 500 V/K 400 V/K 300 V/K Optimized (3 W/K 2 cm) Not optimized Not optimized Not optimized Optimized (37 W/K 2 cm) This letter Table S5. A summary of recent reports on the thermoelectric properties in 2D materials controlled by field effect doping. 6
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