Enhanced thermoelectric power in two-dimensional transition metal dichalcogenide monolayers

The carrier-density-dependent conductance and thermoelectric properties of large-area $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$ monolayers are simultaneously investigated using the electrolyte gating method. The sign of the thermoelectric power changes across the transistor off-state in the ambipolar $\mathrm{WS}{\mathrm{e}}_2$ transistor as the majority carrier density switches from electron to hole. The thermopower and thermoelectric power factor of monolayer samples are one order of magnitude larger than that of bulk materials, and their carrier-density dependences exhibit a quantitative agreement with the semiclassical Mott relation based on the two-dimensional energy band structure, concluding the thermoelectric properties are enhanced by the low-dimensional effect.

Figure 1

Thermopower measurement in $\mathrm{Mo}{\mathrm{S}}_2$ monolayer EDLTs. (a) A schematic depiction and an optical image of the thermopower measurement system. The ion-gel-gated EDLTs are placed on two Peltier devices, and the temperature difference $\left(\mathrm{\Delta }T\right)$ is monitored by two thermocouples. The conceptual diagram illustrates the ionic liquid, polymer, and electrostatic doping by the EDLTs. A reference electrode is employed to estimate the voltage drop on the $\mathrm{Mo}{\mathrm{S}}_2$ interface. (b) Transfer and capacitance-voltage characteristics of the $\mathrm{Mo}{\mathrm{S}}_2$ EDLTs. (c) The thermoelectromotive force $\left(\mathrm{\Delta }V\right)$ and $\mathrm{\Delta }T$ profile is presented with a reference voltage $\left(V_{\mathrm{R}}\right)$ application. The gray blanks indicate the measured data, and the solid lines exhibit their linear fitting. (d) The measured thermopower $S$ vs $V_{\mathrm{R}}-V_{\mathrm{th}}$ is shown, indicating the modulation of $S$ against CB filling. Two different $\mathrm{Mo}{\mathrm{S}}_2$ devices are shown for evaluating the $S$. (e) The carrier-density-dependent power factor $(S^2·\sigma$, where $\sigma$ is electrical conductivity) is displayed in two devices.

Figure 2

Electric-filed-modulated thermopower in $\mathrm{WS}{\mathrm{e}}_2$ monolayer EDLTs. (a) Transfer and capacitance-voltage characteristics of the $\mathrm{WS}{\mathrm{e}}_2$ EDLTs. The step-function-like capacitance behavior reflects the continuous VB and CB filling, and the voltage gap between two thresholds corresponds to the bandgap of $\mathrm{WS}{\mathrm{e}}_2$. (b) The $\mathrm{\Delta }V-\mathrm{\Delta }T$ characteristic for tuning $V_{\mathrm{R}}$. The sign inversion of $\mathrm{\Delta }V$ is due to the change in the predominant carrier type from holes to electrons. (c) The measured $S$ is represented as a function of $V_{\mathrm{R}}-V_{\mathrm{th}}$ for both $p$- and $n$-type $\mathrm{WS}{\mathrm{e}}_2$, which is attributed to VB and CB fillings, respectively. The results of three $\mathrm{WS}{\mathrm{e}}_2$ devices with different filling levels are shown. (d) The carrier-density-dependent power factor is exhibited for three devices.

Figure 3

Evaluation of thermoelectric properties. (a) The comparison of $\left|S\right|$ between various semiconducting TMDC bulks (gray area) and large-area monolayers (green area) is plotted against $\sigma$. The obtained data in this paper are represented by red circles for $\mathrm{WS}{\mathrm{e}}_2$ and by blue squares for $\mathrm{Mo}{\mathrm{S}}_2$. The literature results for bulk materials are summarized in the black symbols [36, 37, 38, 39, 40, 41]. (b) The power factor vs $\sigma$ is exhibited for reported bulks (gray area) and large-area monolayers (green area) [36, 37, 38, 39, 40, 41]. A significant enhancement in the 2D monolayer forms results in a power factor that is one order of magnitude larger than that in the 3D bulk forms.

Figure 4

Experimental and theoretical evidence showing 2D thermopower. (a) The schematics of the atomic geometry of the monolayer TMDCs and ESM model based on the DFT for the DOS and quantum capacitance $C_{\mathrm{q}}$ calculations. The relaxed energy band of charged system is calculated for the hole $\left(+Q\right)$ and the electron $\left(-Q\right)$ accumulations. (b) and (c) The calculated DOS (top) and $C_{\mathrm{q}}$ (bottom) for $\mathrm{WS}{\mathrm{e}}_2$ and $\mathrm{Mo}{\mathrm{S}}_2$, respectively. Note that the $V_{\mathrm{q}}(=\pm Q/C_{\mathrm{q}})$ describes the potential at each Fermi level $\left(E_{\mathrm{F}}\right)$, i.e., the required potential for shifting $E_{\mathrm{F}}$. The $C_{\mathrm{q}}$ is displayed with the results of rigid band (gray) and ESM model (red). (d) The calculated $S$ by the Mott equation for $p$-type $\mathrm{WS}{\mathrm{e}}_2$ is shown as a function of $V_{\mathrm{q}}-V_{\mathrm{VB}}$, where $V_{\mathrm{q}}$ is plotted from the VB edge $\left(V_{\mathrm{VB}}\right)$. The $S$ (gray diamonds) is calculated by the direct derivative of $C_{\mathrm{q}}$ derived from the ESM-DFT scheme. The experimental results for the three $\mathrm{WS}{\mathrm{e}}_2$ EDLTs are represented by red symbols, which reasonably agreed with the theoretical data (shadow area). (e) The calculated $\left|S\right|$ for $n$-type $\mathrm{Mo}{\mathrm{S}}_2$ is plotted from the CB edge of $V_{\mathrm{q}}-V_{\mathrm{CB}}$. The measured $\left|S\right|$ for two devices, shown in blue symbols, agree with the theoretical behavior (shadow area).