Enhanced cryogenic thermopower in ${\mathrm{SrTiO}}_3$ by ionic gating

Ion-gated transistors have enabled us to electrically control electronic phase transitions such as superconductivity in a variety of materials. On the other hand, the carrier doping mechanism, particularly in oxide semiconductors, still remains elusive. Here, we report on the low-temperature thermopower of two-dimensional electron systems in ion-gated ${\mathrm{SrTiO}}_3$. We found that the metallic states induced by ionic gating exhibit a large peak in thermoelectric power to over 1 mV/K at around 20 K. This enhancement of cryogenic thermoelectric power is ascribed to a phonon-drag effect, which is in general dramatically suppressed by conventional chemical doping because the phonon mean free path is suppressed by chemical disorder. The large sustained peak, even in the high carrier density regime of $2\times {10}^{14}{\mathrm{cm}}^{-2}$, strongly indicates that a less disordered process, i.e., electrostatic charge accumulation, dominates over electrochemical carrier doping in the ionic gating in ${\mathrm{SrTiO}}_3$.

Figure 1

Schematic structures and transfer characteristics of ${\mathrm{SrTiO}}_3$-based ion-gated transistors. (a) Formation of the gate-induced metallic conduction layer at the electric double-layer interface. When a positive gate bias $V_{\mathrm{G}}$ is applied to the gate electrode, ions in the ion gel redistribute and form the electric double layer with a surface charge accumulated on the surface of ${\mathrm{SrTiO}}_3$. Lower figures show the chemical structures of 1-ethyl-3-methylimidazolium cation, EMI+, and bis(trifluoromethylsulfonyl)imide anion, $\mathrm{TFSI}-$. EMI-TFSI is used as conducting ionic liquid in the gel dielectric. (b) Schematic diagram of device structure with Hall bar geometry. (c) Schematic diagram of a setup used for Seebeck effect measurements. The resistance and the Seebeck coefficient are simultaneously measured in this setup. Here, $V_{\mathrm{D}}, I_{\mathrm{D}}$, and TC stand for the source-drain voltage, current, and thermocouple, respectively. (d) Transfer characteristics for devices A, B, and C obtained with configuration in (b). The values of $I_{\mathrm{D}}$ show a sharp rise at $V_{\mathrm{G}}\sim 2$ V and saturate at $V_{\mathrm{G}}\sim 3.5$ V. (e) $V_{\mathrm{G}}$ dependence of sheet carrier density, $N$ = 1/($R_{\mathrm{H}}e$), for devices A, B, and C. The values of $N$ exceed $1\times {10}^{14}{\mathrm{cm}}^{-2}$ at $V_{\mathrm{G}}\sim 3$ V. (f) Plots of sheet resistance $R_{\mathrm{s}}$ vs $N$ at 200 K. The data for the three devices fall on a universal curve. The solid line is a fitting curve for log $R_{\mathrm{s}}$ with a fourth-order polynomial of log $N$.

Figure 2

Transfer characteristics of ion-gated devices in an ${\mathrm{O}}_2$-gas atmosphere. (a) Transfer characteristics of ion-gated ${\mathrm{SrTiO}}_3$ at room temperature. In a high vacuum ($\sim {10}^{-5}$ Torr) and He gas atmosphere (10 Torr), typical $n$-type transistor operations are observed. In an ${\mathrm{O}}_2$ gas atmosphere, however, the drain-source current $I_{\mathrm{D}}$ was dramatically suppressed. The inset plots $I_{\mathrm{D}}$ against the reference voltage $V_{\mathrm{Ref}}$. The hysteresis in $I_{\mathrm{D}}-V_{\mathrm{Ref}}$ characteristics is very tiny, suggesting that the hysteresis in $I_{\mathrm{D}}-V_{\mathrm{G}}$ (the gate voltage) originates from the slow reformation of ions against $V_{\mathrm{G}}$. (b) Transfer characteristics of ion-gated InP at room temperature. The value of $I_{\mathrm{D}}$ under $V_{\mathrm{G}}$ was suppressed in an ${\mathrm{O}}_2$ gas environment, as in the case of ${\mathrm{SrTiO}}_3$.

Figure 3

Carrier density dependence of the diffusion Seebeck coefficient in ${\mathrm{SrTiO}}_3$. The Seebeck coefficient $S$ for an ion-gated device (device E) was measured at 200 K in a wide range of carrier density. Here, the absolute value $\left|S\right|$ is plotted as a function of sheet carrier density $N$ (lower axis) and volume carrier density $n$ (upper axis). The values of $N$ were estimated from the sheet resistance $R_{\mathrm{s}}$ at 200 K. The values of $n$ are evaluated as $n=N/t$ by assuming that the thickness of the charge accumulation layer $t$ is $\sim 10$ nm, referring to the estimation by Ueno $\mathit{et}\mathit{al}.$ [4, 28]. Also plotted is the $n$ dependence of $\left|S\right|$ for the reduced ${\mathrm{SrTiO}}_3$ (${\mathrm{SrTiO}}_{3-\delta }$) single crystals [14, 16], the La-doped ${\mathrm{SrTiO}}_3$ [(Sr,$\mathrm{La}){\mathrm{TiO}}_3]$ single crystals [15], and thin films [11]. The $n$ dependence of $\left|S\right|$ (at 200 K with a negligible phonon drag effect) in the ion-gated devices shows a fair agreement with that in single crystals and thin films over a wide range of $n$.

Figure 4

Phonon-drag thermopower in ${\mathrm{SrTiO}}_3$-based ion-gated transistors. (a) Comparison of Seebeck coefficient $S$ between ${\mathrm{SrTiO}}_3$-based ion-gated transistor (device E), reduced ${\mathrm{SrTiO}}_3$ (${\mathrm{SrTiO}}_{3-\delta }$) single crystal [16], and La-doped ${\mathrm{SrTiO}}_3$ [(Sr,$\mathrm{La}){\mathrm{TiO}}_3]$ single crystal [15]. Here, the absolute value $\left|S\right|$ is plotted as a function of temperature $T$. The samples presented here have similar values of $n$, which is $1\times {10}^{20}$ to $2\times {10}^{20}{\mathrm{cm}}^{-3}$. The dashed line is the rough estimation of the diffusion part $|S_{\mathrm{d}}|$ in device E, assuming that $|S_{\mathrm{d}}|$ is proportional to $T$ and that the phonon contribution is negligible at 200 K. The large peak in $\left|S\right|$ at low temperatures is attributed to the phonon-drag effect. The inset figure presents the $T$ dependence of the sheet resistance $R_{\mathrm{s}}$ in device E, which shows the metallic conduction behavior. (b) Low-temperature peak values of $\left|S\right|$ as a function of $n$ (lower axis) or $N$ (upper axis) for ion-gated ${\mathrm{SrTiO}}_3$ (devices E, F, G, and H) and chemically doped ${\mathrm{SrTiO}}_3$ [11, 14, 15, 16]. These low-temperature peaks are dramatically enhanced in ion-gated devices.

Figure 5

Enhancement of power factor in ion-gated ${\mathrm{SrTiO}}_3$. (a),(b) Schematic top-view illustration of phonon states at low temperatures under the thermal gradient $-\mathbf{\nabla }T$. Field-effect doping and chemical doping correspond to (a) and (b), respectively. The phonon mean free path becomes very large at low temperatures in (a) but is totally suppressed due to the impurity in (b). (c) Comparison of power factor, $S^2\sigma$, for ion-gated ${\mathrm{SrTiO}}_3$ (this work) and (Sr,$\mathrm{La}){\mathrm{TiO}}_3$ thin film [11] both with $n\sim 2\times {10}^{20}{\mathrm{cm}}^{-3}$. Here, $S$ and $\sigma$ are the Seebeck coefficient and conductivity, respectively. The power factor in ion-gated ${\mathrm{SrTiO}}_3$ is two orders larger than that in the (Sr,$\mathrm{La}){\mathrm{TiO}}_3$ thin film at around the peak temperature ($\sim 20$ K).