Electrical conductivity (σ) indicates the efficiency of current flow through electronic materials, and varies with both carrier density (n2D) and mobility (µ). Studying the temperature-dependent σ of a material allows for the elucidation of various carrier transport mechanisms such as metal-insulator phase transition, Coulomb impurity scattering, metal-semiconductor barrier, and quantum tunneling features. Herein, we report a considerable interlayer resistance (RIT) effects on the carrier scattering mechanism occurring in a multilayer rhenium disulfide (ReS2) transistor, particularly at high temperatures. At room temperature (T = 300 K), a channel centroid gradually migrates from the bottom to the top surface of ReS2 multilayers by contributing to the suppressed RIT with increasing electrostatic drain (VD) and gate (VG) bias conditions. Meanwhile, for temperatures above 380 K, the effective interlayer resistance quickly decreases with increasing VG, and the ReS2 multilayer consequently demonstrates an anomalous carrier mobility enhancement. For a better insight into the charge scattering mechanism, the obtained temperature-dependent carrier mobility was further analyzed by employing Matthiessen’s rule for Coulomb impurity scattering, phonon scattering, and interlayer resistance scattering, respectively. Our study would shed light on deep understanding for the high temperature carrier scattering mechanism and further improvements in diverse optoelectronic applications of ReS2 multilayers.
Electrical conductivity (σ), which relies on carrier density (n2D) and mobility (µ), represents the efficiency of current flow through electronic materials . Both the carrier density and mobility at a given electrostatic bias condition are sensitive to temperature (T). Therefore, an investigation of T-dependent carrier mobility not only elucidates various transport mechanisms such as metal-insulator phase transition, Coulomb impurity scattering, metal-semiconductor barrier, and quantum tunneling, but also provides a clear picture of charge scattering mechanisms that originate from lattice vibration, Coulomb impurities inside dielectrics, atomic defects, and surface roughness [2,3]. In addition, as device size is reduced, determining the origins of undesired numerous scatterers becomes crucial, particularly in the case of two-dimensional (2D) layered materials, because they are easily able to mask intrinsic channel properties. In this regard, a 2D multilayer platform could provide improved insusceptibility against the aforementioned surrounding Coulomb scatterers, and a higher carrier mobility than its monolayer counterpart.
Thus far, among 2D layered materials such as molybdenum disulfide (MoS2), black phosphorus (BP), and tungsten diselenide (WSe2), rhenium disulfide (ReS2) multilayer systems have garnered interest because of various distinctive features; i) extremely weak interlayer coupling, ii) an absence of the crossover from direct bandgap to indirect band gap with increasing thickness, iii) anisotropic carrier transport, iv) thermodynamic stability, and v) a distorted 1T′ structure [4–8]. In particular, the decoupled van der Waals interaction with neighboring layers and thickness-independent band structure of ReS2 leads to a high interlayer resistance (RIT) compared to other 2D materials, indicating the increased importance of RIT effects on carrier transport inside a multilayer ReS2.
In this study, we report significant interlayer resistance effects on the carrier scattering of a multilayer ReS2 field-effect transistor. In particular, interlayer resistance effects at high temperatures are evaluated by demonstrating i) T-dependent output/transfer characteristic curves, ii) transconductance normalized by drain voltage, and iii) field-effect mobility. At room temperature (T = 300 K), the conducting channel migration along the c-axis of 2D multilayers is clearly exhibited with increasing gate and drain bias. Moreover, an anomalous transconductance enhancement is exhibited for T ≥ 380 K. We ascribe this observed behavior to a rapid reduction of the effective interlayer resistivity of ReS2 in the high-temperature regime. Furthermore, the obtained T-dependent carrier mobility is further analyzed by employing Matthiessen’s rule for Coulomb impurity scattering, phonon scattering, and interlayer resistance scattering, to provide a better insight into charge scattering mechanisms.
A conventional scotch-tape method was used to fabricate 2D multilayer ReS2 transistors (purchased from 2D Semiconductors), as illustrated in Figs. 1(a) and 1(b). After finding a proper ReS2 flake whose thickness ranges from 8 to 15 nm on a 90 nm SiO2/p+-Si substrate, selective electron-beam lithography (MIRA3, TESCAN) was conducted to define the active channel area. Au (100 nm) metal was then deposited using an electron-beam evaporator (INFOVION). Figure 1(b) displays a device image obtained using an atomic force microscope (AFM, Park Systems, NX10). Geometrical channel information, such as channel length (L ≈ 1 µm), width (W ≈ 0.614 µm), and the thickness of the multilayer ReS2 (≈ 11 nm), was confirmed by AFM, in addition to values obtained using an optical microscope (BX53M, Olympus). The fabricated device was thermally annealed for 10 h at 200 °C under a high vacuum of less than 10−6 Torr. The detailed fabrication method employed in this study is described in the literature [9–11]. The optical Raman spectrum of 11 nm-thick ReS2 was obtained using a laser excitation wavelength (λEX) with a laser power (P) of 5 mW. The observed dominant Eg (≈ 150−160 cm−1), A1g-like (≈ 215 cm−1) and Eg-like (≈ 312 cm−1) peaks are consistent with those obtained in previous reports, and clearly indicate the presence of a ReS2 multilayer, as shown in Fig. 1(c) [7,9,11,12]. All electrical measurements were conducted using a commercial semiconductor analyzer (B1500A Keysight).
Figure 1. (a) Device schematic of the proposed multilayer ReS2 structure. (b) Atomic force microscope (AFM) image (left panel) and thickness profile of the ReS2 along the red line (right panel). (c) Raman spectrum of the 11 nm-thick ReS2 flake.
To demonstrate good metal-to-semiconductor contact formation, the drain current and voltage (ID–VD) output characteristics curves for back-gate bias (VG) values ranging from −50 to 50 V at T = 300 and 420 K are shown in Figs. 2(a) and 2(b). A clear linearity regardless of VG is presented in these figures at small VD regimes (< 0.5 V), which indicate negligible Au-ReS2 Schottky barrier (SB) effects [9,11,13]. However, a non-monotonic behavior gradually appears after VD exceeds 1 V. This distinct behavior has been mainly ascribed to the suppressed RIT and/or enhanced carrier mobility effects on conducting channel migration in the ReS2 multilayers [10,14]. Moreover, typical n-type behavior is clearly exhibited, in which electron population increases with increasing VG.
Figure 2.ID–VD output characteristic curves at (a) T = 300 K and (b) T = 420 K for different VG conditions. Inset: Extended view of (a) and (b). (c) VD-dependent Y function method (YFM) (lines) at T = 300 K and the corresponding fitting curves (dotted lines). (d) Width-normalized VD-dependent contact and channel resistance, and (e) their effective contribution ratio to total resistance at T = 300 K. (f) VD-dependent EA as a function of VG, determined by fitting G(T) to a thermal activation transport model.
To provide a clear picture of the contributions of the effective channel (RCH) and contact resistance (RCT) to total resistance (RTot = RCH + RCT), we employed the Y-function method (YFM) as described by the following expression:
where gm, COX, µ0, and VFB denote the transconductance (= ∂ID/∂VG), oxide capacitance per unit area, low-field mobility, and flat-band voltage, respectively [Figs. 2(c)–(e)] . From the slope and x-axis intercept for YFM shown in Fig. 2(c), both µ0 and VFB were simply determined without RCT effects at a given VD value. In addition, RCT as a function of VD was also evaluated on the basis of the mobility attenuation factor, using the expression:
where θ0 and θ1 are mobility degradation parameters relating to intrinsic carrier scattering and RCT, respectively . As θ0 is generally significantly lower than θ1, the expression for θ may be approximated by
The obtained contact resistivity (RCT·W) ranges from 75 to 150 kΩ·µm, while the channel resistivity varies from 120 to 300 kΩ·µm, indicating that RCH dominates RCT in the observed VD range at room temperature, as shown in Fig. 2(d). For a better understanding of this phenomenon, the relative resistance ratios, i.e., RCH/RTot and RCT/RTot, are also displayed in Fig. 2(e), implying a negligible SB and RCT effects.
The T-dependent conductance (G(T)) was given by the following expression:
where G0(T) is the T-dependent pre-factor, EA is the activation energy, and kB is the Boltzmann constant. The VG-dependent EA as a function of VD at high temperatures is obtained, as shown in Fig. 2(f) . The observed linear trend of EA deviates with increasing VG, in particular, at VG ≈ 0 V. This represents a change in the carrier transport mechanism from that of direct tunneling to drift-diffusion regime. The small reliance of VD on EA at VD < 0.5 V and the observed linear output characteristic features suggest a negligible effect of SB in our ReS2 multilayer device. However, EA decreases sharply as VD increases further (VD > 0.5 V), signaling the presence of suppressed interlayer resistance in addition to conducting channel migration.
The VG-dependent ID transfer curves (ID–VG) for several VD values ranging from 100 mV to 5 V at T = 300 and 420 K are displayed in Figs. 3(a) and 3(b), respectively. Drain current increases with VG at a given VD, indicating the conventional n-type semiconductor characteristic of our multilayer ReS2. The on- and off-current ratio is approximately ~103 at T = 300 K, whereas the ratio decreases (~ 30) at T = 420 K. This suppression of current switching performance in the high-T regime could be attributed to the enhanced leakage current caused by the negative shift in the VFB and reduced interlayer resistance effects. In addition, the humping point appears at VG ≈ 5 V exclusively at T = 420 K, indicating rapid conductance (or mobility) enhancement. This distinct feature may be related to a change in the charge scattering mechanism that is present in a 2D multilayer system.
Figure 3.ID–VD transfer curve at (a) T = 300 K and (b) T = 420 K as a function of VD. VD-normalized gm curves at (c) T = 300 K and (d) T = 420 K, respectively.
To further determine a clear transport mechanism for the fabricated 2D multilayer ReS2 device, the VD-normalized gm (= gm/VD) curves at T = 300 and 420 K are shown in Figs. 3(c) and 3(d), respectively. At T = 300 K [Fig. 3(c)], two gm/VD plateaus are evident under relatively small VD regimes (VD < 200 mV), demonstrating the emergence of conducting channel migration from the bottom surface to the top surface, which is triggered by the reduced interlayer resistance via increasing VG . This anomalous carrier transport feature of 2D multilayers can be further supported by the larger amplitude of the 2nd gm peak compared to that of the 1st gm peak, which indicates enhanced field-effect mobility µFE (= gm·L/(W·COX·VD)) via reduced RIT and/or RCT with increasing VG. But, as VD increases further (VD > 200 mV), the plateaus merge together and broaden, and consequently this carrier transport behavior leads to superior immunity to undesired various scatterers such as oxide traps, structural defects of ReS2, and chemical residues on the channel surface [2,17,18]. It is of note that the VG-dependent gm/VD curves should be identical regardless of VD, unless the system is subject to significant contributions from other carrier transport mechanisms.
At high temperatures, for example, at T = 420 K [Fig. 3(d)], the effective RIT is quickly reduced within such a narrow VG region (0 V < VG < 10 V), enabling the substantial gm (or carrier mobility) enhancement of the fabricated ReS2 multilayer. More specifically, while the high interlayer resistivity of ReS2 (~105 Ω·µm)  compared to other 2D multilayers such as MoS2 (~103 Ω·µm) and graphite (~102 Ω·µm)  is gradually suppressed at room temperature, at high temperatures it triggers a reduction in ReS2 interlayer resistivity under electrostatic VG and VD bias conditions. Device operating temperature is therefore an important factor for optoelectronic applications based on ReS2 multilayers.
For a better insight into the charge scattering mechanism occurring in ReS2 multilayers, the obtained T-dependent µFE is further analyzed according to the conventional Matthiessen’s rule:
where µPh, µC, α, and β denote the optical phonon-limited mobility, Coulomb impurity scattering-limited mobility, and their power exponents, respectively (Fig. 4) . To exclude channel migration effects in the fabricated ReS2 device, we considered the µFE exclusively at VD ≥ 1.0 V, in which range a single gm peak is present. As shown in Fig. 4, the employed Matthiessen’s rule appropriately describes the VDdependent µFE for T ≤ 380 K. In this temperature regime, the dominant scattering mechanism varies from µC to µPh, mainly because of conducting channel migration with increasing VD. Since the SiO2 used in this study consists of numerous positive fixed trap sites near the bottom surface of the proposed ReS2 structure, µC should dominate µFE when the channel centroid is located near dielectrics [1,11,21]. However, as the channel centroid shifts upward to minimize the RIT contribution to carrier transport with increasing VD, the effect on µFE of µC (or µPh) becomes weaker (or stronger), resulting in a sign reversal of the temperature exponent of µFE, ranging from −0.4 to 1.2.
Figure 4. T-dependent µFE (symbols) and corresponding fitting curves to Matthiessen’s rule (dotted lines) at different VD values.
At T ≥ 380 K, the general trend of Matthiessen’s rule fails to explain the T-dependent µFE, mainly because of the largely enhanced µFE at high temperatures, as shown in Fig. 3(d). Thus, as the contributions of the previous µPh and µC to µFE are not valid for high-T regimes, we consider interlayer resistance limited mobility (µInt(T)) for the Tdependent µFE, according to the following expression:
To elucidate the origin of this anomalous behavior, a systematic study should be further considered, in which T-dependent Hall-effect measurement or split capacitance-voltage measurement is employed to directly define carrier density-dependent carrier mobility (or conductivity) as a function of T .
This study demonstrates the significant effect of RIT on the carrier scattering mechanism in a proposed multilayer ReS2. The Tdependent output/transfer characteristic curves, gm/VD, and µFE are presented and discussed. At relatively low temperatures (T ≤ 380 K), the conventional Matthiessen’s rule appropriately describes the T-dependent µFE. However, for T ≥ 380 K, the general trend of Matthiessen’s rule fails to describe the T-dependent µFE of the system. We attribute this anomalous behavior to the rapid suppression of RIT at such a narrow VG region (0 V < VG < 10 V), enabling our ReS2 multilayer to exhibit substantial carrier mobility enhancement. Our results pave the way for diverse viable optoelectronic applications of ReS2 multilayers at high temperatures.