van der Waals Schottky barriers as interface probes of the correlation between chemical potential shifts and charge density wave formation in $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$

Layered transition-metal dichalcogenide (TMD) materials, i.e., $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$, harbor a second-order charge density wave (CDW) transition where phonons play a key role for the periodic modulations of conduction electron densities and associated lattice distortions. We systematically study the transport and capacitance characteristics over a wide temperature range of Schottky barriers formed by intimately contacting freshly exfoliated flakes of $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$ to $n$-type GaAs semiconductor substrates. The extracted temperature-dependent parameters (zero-bias barrier height, ideality, and built-in potential) reflect changes at the TMD/GaAs interface induced by CDW formation for both TMD materials. The measured built-in potential reveals chemical-potential shifts relating to CDW formation. With decreasing temperature a peak in the chemical-potential shifts during CDW evolution indicates a competition between electron energy redistributions and a combination of lattice strain energies and Coulomb interactions. These modulations of chemical potential in CDW systems, such as $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$ harboring second-order phase transitions, reflect a corresponding conversion from short-range to long-range order.

Figure 1

(a) Schematic of sample structure with top and back contact. (b) AFM images of the cleaved surfaces for thin flakes of $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$. (c), (d) In-plane resistance and temperature derivative of the resistance of thin flakes of $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$ plotted as a function of temperature. Black dashed vertical lines indicate the $T_{\mathrm{CDW}}$ for $1T\text{−}{\mathrm{TiSe}}_2$ and $2H\text{−}{\mathrm{NbSe}}_2$, respectively.

Figure 2

Band diagram of a Schottky junction formed by a metallic layered material [with CDW phase $({\rho }_0\ne 0$, magenta) or without CDW phase $({\rho }_0\sim 0$, black-dashed)] in intimate contact with a Si-doped GaAs semiconductor where the donor impurity band (red dashed line) is close to the conduction band (solid black line). At high $T$ (low $T$), thermionic emission (quantum tunneling) dominates. Barrier height: ${\mathrm{\Phi }}_B$; built-in potential: $V_{bi}$; work function of layered materials: ${\varphi }_m$; electron affinity of GaAs: $\chi$; work function of GaAs: ${\varphi }_s$; Fermi level pinning: FLP; CDW present (absent): ${\rho }_0\ne 0(=0).$

Figure 3

(a), (b) The $I\text{−}V$ characteristics of $1T\text{−}{\mathrm{TiSe}}_2$/$n$-GaAs and $2H\text{−}{\mathrm{NbSe}}_2$/$n$-GaAs junctions at selected temperatures. Insets: Semilogarithmic scaled $I\text{−}V$ characteristics. Red solid lines indicate the theoretical fitting range. (c), (d) Schottky barrier model fitted parameters ${\mathrm{\Phi }}_{SB}^0$ and ${\eta }^{-1}$ as a function of temperature for $1T\text{−}{\mathrm{TiSe}}_2$/$n$-GaAs and $2H\text{−}{\mathrm{NbSe}}_2$/$n$-GaAs junctions. Green dashed lines delineate the temperature span of the kink signature of ${\mathrm{\Phi }}_{SB}^0\left(T\right)$ and ${\eta }^{-1}\left(T\right)$. Inset of (d) Zoomed-in plot in the temperature range of 30–40 K.

Figure 4

Upper panel: temperature-dependent zero-bias capacitance; lower panel: temperature-dependent relative built-in potential $\mathrm{\Delta }{V}_{bi}$ for (a) $1T\text{−}{\mathrm{TiSe}}_2$/$n$-GaAs and (b) $2H\text{−}{\mathrm{NbSe}}_2$/$n$-GaAs junctions. The red dashed lines indicate the scaled $\mathrm{\Delta }{V}_{bi}$ of a graphite/$n$-GaAs junction. The reference temperatures are 250 and 90 K for (a) $1T\text{−}{\mathrm{TiSe}}_2$/$n$-GaAs and (b) $2\mathrm{H}\text{−}{\mathrm{NbSe}}_2$/$n$-GaAs junctions, respectively. Insets of (a) and (b): $C\text{−}V$ characteristics at 10 kHz for both junctions at selected temperatures. Purple dashed lines are guidelines for the eyes. Note: Error bars are not shown.

Figure 5

Extracted temperature-dependent effective chemical potential shift $\mathrm{\Delta }{\mu }_{\mathrm{eff}}$ of (a) $1T\text{−}{\mathrm{TiSe}}_2$ and (b) $2H\text{−}{\mathrm{NbSe}}_2$ from the measured built-in potential $V_{bi}$ of $1T\text{−}{\mathrm{TiSe}}_2$/$n$-GaAs and $2H\text{−}{\mathrm{NbSe}}_2$/$n$-GaAs junctions shown in Fig. 4. The red dashed lines are guides to the eye for the temperature-dependent $\mathrm{\Delta }{\mu }_{\mathrm{eff}}$ proposed to be associated with the short- (high-temperature) to long- (low-temperature) range phase coherence of CDW formation.