High Temperature Carrier Scattering Mechanisms in Multilayer ReS₂ Field-Effect Transistors

Abstract

1. Introduction

Electrical conductivity (σ), which relies on carrier density (n_2D) and mobility (µ), represents the efficiency of current flow through electronic materials [1]. 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 [48]. In particular, the decoupled van der Waals interaction with neighboring layers and thickness-independent band structure of ReS₂ leads to a high interlayer resistance (R_IT) compared to other 2D materials, indicating the increased importance of R_IT 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.

2. Experimental details

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 [911]. The optical Raman spectrum of 11 nm-thick ReS₂ was obtained using a laser excitation wavelength (λ_EX) with a laser power (P) of 5 mW. The observed dominant E_g (≈ 150−160 cm⁻¹), A_1g-like (≈ 215 cm⁻¹) and E_g-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).

3. Results and discussion

To demonstrate good metal-to-semiconductor contact formation, the drain current and voltage (I_D–V_D) output characteristics curves for back-gate bias (V_G) 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 V_G is presented in these figures at small V_D regimes (< 0.5 V), which indicate negligible Au-ReS₂ Schottky barrier (SB) effects [9,11,13]. However, a non-monotonic behavior gradually appears after V_D exceeds 1 V. This distinct behavior has been mainly ascribed to the suppressed R_IT 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 V_G.

To provide a clear picture of the contributions of the effective channel (R_CH) and contact resistance (R_CT) to total resistance (R_Tot = R_CH + R_CT), we employed the Y-function method (YFM) as described by the following expression:

(1) Y E F = I D / g m 0.5 = ( W / L ) ⋅ C O X ⋅ μ 0 ⋅ V D 1 / 2 ⋅ ( V G − V F B ) ,

where g_m, C_OX, µ₀, and V_FB denote the transconductance (= ∂I_D/∂V_G), oxide capacitance per unit area, low-field mobility, and flat-band voltage, respectively [Figs. 2(c)–(e)] [15]. From the slope and x-axis intercept for YFM shown in Fig. 2(c), both µ₀ and V_FB were simply determined without R_CT effects at a given V_D value. In addition, R_CT as a function of V_D was also evaluated on the basis of the mobility attenuation factor, using the expression:

(2) θ = θ 0 + θ 1 = θ 0 +   W / L ⋅ C O X ⋅ μ 0 ⋅ R C T ,

where θ₀ and θ₁ are mobility degradation parameters relating to intrinsic carrier scattering and R_CT, respectively [15]. As θ₀ is generally significantly lower than θ₁, the expression for θ may be approximated by

(3) θ ≈ θ 1 = ( W / L ) ⋅ C O X ⋅ μ 0 ⋅ R C T ,

and consequently

(4) R C H ≈ R T o t − R C T = I D / V D − θ / W / L ⋅ C O X ⋅ μ .0 .

The obtained contact resistivity (R_CT·W) ranges from 75 to 150 kΩ·µm, while the channel resistivity varies from 120 to 300 kΩ·µm, indicating that R_CH dominates R_CT in the observed V_D range at room temperature, as shown in Fig. 2(d). For a better understanding of this phenomenon, the relative resistance ratios, i.e., R_CH/R_Tot and R_CT/R_Tot, are also displayed in Fig. 2(e), implying a negligible SB and R_CT effects.

The T-dependent conductance (G(T)) was given by the following expression:

(5) G ( T ) = G 0 ( T ) ⋅ exp ( − E A / ( k B ⋅ T ) ) ,

where G₀(T) is the T-dependent pre-factor, E_A is the activation energy, and kB is the Boltzmann constant. The V_G-dependent E_A as a function of V_D at high temperatures is obtained, as shown in Fig. 2(f) [16]. The observed linear trend of E_A deviates with increasing V_G, in particular, at V_G ≈ 0 V. This represents a change in the carrier transport mechanism from that of direct tunneling to drift-diffusion regime. The small reliance of V_D on E_A at V_D < 0.5 V and the observed linear output characteristic features suggest a negligible effect of SB in our ReS₂ multilayer device. However, E_A decreases sharply as V_D increases further (V_D > 0.5 V), signaling the presence of suppressed interlayer resistance in addition to conducting channel migration.

The V_G-dependent I_D transfer curves (I_D–V_G) for several V_D 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 V_G at a given V_D, 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 V_FB and reduced interlayer resistance effects. In addition, the humping point appears at V_G ≈ 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.

To further determine a clear transport mechanism for the fabricated 2D multilayer ReS₂ device, the V_D-normalized g_m (= g_m/V_D) 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 g_m/V_D plateaus are evident under relatively small V_D regimes (V_D < 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 V_G [10]. This anomalous carrier transport feature of 2D multilayers can be further supported by the larger amplitude of the 2^nd g_m peak compared to that of the 1^st g_m peak, which indicates enhanced field-effect mobility µ_FE (= g_m·L/(W·C_OX·V_D)) via reduced R_IT and/or R_CT with increasing V_G. But, as V_D increases further (V_D > 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 V_G-dependent g_m/V_D curves should be identical regardless of V_D, 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 R_IT is quickly reduced within such a narrow V_G region (0 V < V_G < 10 V), enabling the substantial g_m (or carrier mobility) enhancement of the fabricated ReS₂ multilayer. More specifically, while the high interlayer resistivity of ReS₂ (~105 Ω·µm) [19] compared to other 2D multilayers such as MoS₂ (~10³ Ω·µm) and graphite (~10² Ω·µm) [1] is gradually suppressed at room temperature, at high temperatures it triggers a reduction in ReS₂ interlayer resistivity under electrostatic V_G and V_D 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 µ_FE is further analyzed according to the conventional Matthiessen’s rule:

(6) 1 μ F E ( T ) = 1 μ P h ( T ) α + 1 μ C ( T ) β ,

where µ_Ph, µ_C, α, and β denote the optical phonon-limited mobility, Coulomb impurity scattering-limited mobility, and their power exponents, respectively (Fig. 4) [20]. To exclude channel migration effects in the fabricated ReS₂ device, we considered the µ_FE exclusively at V_D ≥ 1.0 V, in which range a single g_m peak is present. As shown in Fig. 4, the employed Matthiessen’s rule appropriately describes the V_Ddependent µ_FE for T ≤ 380 K. In this temperature regime, the dominant scattering mechanism varies from µ_C to µ_Ph, mainly because of conducting channel migration with increasing V_D. Since the SiO₂ used in this study consists of numerous positive fixed trap sites near the bottom surface of the proposed ReS₂ structure, µ_C should dominate µ_FE when the channel centroid is located near dielectrics [1,11,21]. However, as the channel centroid shifts upward to minimize the R_IT contribution to carrier transport with increasing V_D, the effect on µ_FE of µ_C (or µ_Ph) becomes weaker (or stronger), resulting in a sign reversal of the temperature exponent of µ_FE, ranging from −0.4 to 1.2.

At T ≥ 380 K, the general trend of Matthiessen’s rule fails to explain the T-dependent µ_FE, mainly because of the largely enhanced µ_FE at high temperatures, as shown in Fig. 3(d). Thus, as the contributions of the previous µ_Ph and µ_C to µ_FE are not valid for high-T regimes, we consider interlayer resistance limited mobility (µ_Int(T)) for the Tdependent µ_FE, according to the following expression:

(7) 1 μ F E ( T ) = 1 μ P h ( T ) α + 1 μ C ( T ) β + 1 μ I n t ( T ) ≈ 1 μ I n t ( T ) .

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 [22].

4. Conclusions

This study demonstrates the significant effect of R_IT on the carrier scattering mechanism in a proposed multilayer ReS₂. The Tdependent output/transfer characteristic curves, g_m/V_D, and µ_FE are presented and discussed. At relatively low temperatures (T ≤ 380 K), the conventional Matthiessen’s rule appropriately describes the T-dependent µ_FE. However, for T ≥ 380 K, the general trend of Matthiessen’s rule fails to describe the T-dependent µ_FE of the system. We attribute this anomalous behavior to the rapid suppression of R_IT at such a narrow V_G region (0 V < V_G < 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.

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