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Yi-Te Lee, Yu-Ting Huang, Shao-Pin Chiu, Ruey-Tay Wang, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Raman Sankar, Chi-Te Liang, Wei-Hua Wang, Sheng-Shiuan Yeh, Juhn-Jong Lin

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Applied Materials & Interfaces, copyright ©  2023 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acsami.3c14312.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Determining the Electron Scattering from Interfacial Coulomb Scatterers in Two-Dimensional Transistors](https://mdr.nims.go.jp/datasets/5fbd9a6d-bd85-4ad3-b43b-0eacba985fbc)

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Microsoft Word - Manuscript 2023 11 201  Determining the electron scattering from interfacial Coulomb scatterers in two-dimensional transistors Yi-Te Lee1, Yu-Ting Huang2,3, Shao-Pin Chiu1, Ruey-Tay Wang1, Takashi Taniguchi4, Kenji Watanabe5, Raman Sankar6, Chi-Te Liang3, Wei-Hua Wang2,*, Sheng-Shiuan Yeh7,8 *, Juhn-Jong Lin1 1Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan 2Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan 3Department of Physics, National Taiwan University, Taipei 106, Taiwan 4Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 5Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 6Institute of Physics, Academia Sinica, Taipei 106, Taiwan 7Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan 8International College of Semiconductor Technology, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan   2  ABSTRACT  Two-dimensional (2D) transistors are promising for potential applications in next-generation semiconductor chips. Owing to the atomically thin thickness of 2D materials, the carrier scattering from interfacial Coulomb scatterers greatly suppresses the carrier mobility and hampers transistor performance. However, a feasible method to quantitatively determine relevant Coulomb scattering parameters from interfacial long-range scatterers is largely lacking. Here, we demonstrate a method to determine the Coulomb scattering strength and the density of Coulomb scattering centers in InSe transistors by comprehensively analyzing low-frequency noise and transport characteristics. Moreover, the relative contribution from long-range and short-range scattering in the InSe transistors can be distinguished. This method is employed to InSe transistors consisting of various interfaces as a model system, revealing profound effects of different scattering sources on the transport characteristics and the low-frequency noise. Quantitatively accessing the scattering parameters of 2D transistors provides valuable insight into engineering the interfaces of a wide spectrum of ultrathin-body transistors for high-performance electronics.  KEYWORDS: electron scattering, 2D materials, Coulomb scattering strength, low-frequency noise, indium selenide, interfacial Coulomb scatterers, 2D transistors 3  MANUSCRIPT TEXT Introduction Ultrathin-body field-effect transistors (FETs), including silicon-on-insulator (SOI)-FETs and Fin-FETs, exhibit a small gate screening length and have effectively facilitated the continuation of miniaturization to sub-10-nm technology.1 To achieve shorter gate lengths, alternative technologies to further reduce the channel thickness are required.1, 2 In particular, the dangling-bond-free surface and atomic-scale thickness of two-dimensional (2D) materials make them promising for downscaling dimensions for further miniaturization of microelectronics.3 As the channel thickness of 2D transistors is decreased, the charge carriers are greatly scattered by the interfacial Coulomb scatterers, resulting in significant mobility degradation.4-9 The Coulomb scattering is further intensified in 2D transistors when their channel approaches atomically thin thickness. Thus, in-depth knowledge of the Coulomb scattering parameters is crucial for designing high-performance 2D transistors. Previous studies regarding Coulomb scattering have demonstrated reduced Coulomb scattering effects and enhanced mobility via interface engineering,10 dielectric modification, and layer thickness control.11-13 However, a quantitative understanding of the interaction strength between charge carriers and Coulomb scatterers at interfaces, as well as the density of these long-range scattering centers, is still lacking. This knowledge gap indicates that a suitable method to directly probe these Coulomb scattering parameters is essential. In this work, we report a unique method to determine the Coulomb scattering strength and the density of Coulomb scattering centers of 2D transistors. Our method relies on low-frequency 1 𝑓⁄  noise, where 𝑓 is the frequency, and electrical transport measurements without any assumptions. We apply this method to study InSe FETs with various interfaces as a model system to elucidate 4  the effect of Coulomb scatterers on the electrical transport and 1 𝑓⁄  noise characteristics. Ohmic contact and high-quality electrical properties are realized in the InSe FETs, allowing us to explicitly study the transport characteristics of the semiconducting channel. Our method can be widely applied to various defect- and interface-engineered low-dimensional systems14, 15 to obtain quantitative knowledge of these microscopic interfacial characteristics. We fabricated InSe FETs with hexamethyldisilazane (HMDS)-treated SiO2/Si, a hexagonal boron nitride (h-BN) interlayer, and a native SiO2/Si substrate, which are designated samples A, B, and C, respectively. Figure 1a shows a schematic of our InSe FETs. The inset of Figure 1a shows an optical micrograph of a typical InSe FET with the h-BN interlayer. The topology of the InSe devices was characterized by atomic force microscopy (AFM), where an AFM image of sample B is shown in Supporting Information S1. The thickness of our InSe channels is approximately 18–30 nm. The channel thickness of InSe transistors is selected by optimizing the carrier mobility. The InSe transistors with the channel thickness of approximately 10 nm is found to exhibit high carrier density, resulting greater efficiency to screening Coulomb impurities from the adjacent interfaces. Similar thickness dependence of the performance of 2D transistors has been studied in literature.4 On the other hand, the chosen channel thickness of InSe transistors is thin enough to allow us to probe and study the effect of carrier scatterers at the interfaces. Thee relevant parameters of the three InSe FETs studied in this work are listed in Supporting Information S2. The circuit for the electrical transport and low-frequency noise measurements is depicted in Figure 1a. Notably, the source-drain current (𝐼 ) and frequency-dependent current noise power spectral density (PSD) 𝑆 𝑓  are measured simultaneously, enabling quantitative determination of each parameter and their correlation. 5  Figure 1. (a) Schematic of an InSe FET with the electrical circuit for transport characteristic and 1 𝑓⁄  noise measurements. Inset: optical micrograph of a typical InSe FET with the h-BN interlayer. (b) Field-effect mobility 𝜇  of sample A as a function of Δ𝑉  at four different 𝑇. (c) Normalized noise 𝑆 𝐼⁄  as a function of frequency for sample A at various 𝑉  and 𝑇 130 K. The dashed line indicates a 1 𝑓⁄  relation and is a guide to the eye. (d) 𝑓𝑆  as a function of 𝐼  for sample A at 𝑇 170 and 210 K. The solid lines are the linear fits to the data. Inset: 𝐼  versus 𝑉  of sample A at different 𝑇. The solid lines are the linear fits to the data.  0 10 20 30 40100101102 90 K 130 K 170 K 210 K FE (cm2 /Vs)Vg (V)a c d 10-1 100 10110-1110-1010-910-810-7f -1T = 130 K  Vg = 50 V Vg = 70 V Vg = 90 V SId / I d2  (Hz-1)f (Hz)b 0 2 4 6 8 1002468T = 170 KT = 210 KVg = 100 V fSI d (10-18 A2)Id 2 (10-10A2)0.0 0.2 0.40102030  90 K 130 K 170 K 210 KI d (A)Vd (V)InSe h-BN In/Au 10 µm SiO 2 6  The transfer characteristics (𝐼  as a function of gate voltage 𝑉 ) of samples A, B, and C reveal n-type behavior, as shown in Supporting Information S3. Figure 1b shows the field-effect mobility 𝜇 𝑔 𝐿 𝐶 𝑉 𝑊⁄  of sample A as a function of Δ𝑉 𝑉 𝑉 , where 𝑔 𝑑𝐼 𝑑𝑉⁄  is the transconductance, 𝐿  (𝑊 ) is the length (width) of the InSe channel, 𝐶  is the specific gate capacitance, 𝑉  is the source-drain voltage, and 𝑉  is the threshold voltage. To reflect the transition from weak to strong inversion, we used the match-point method16, 17 to determine the threshold voltage 𝑉  (Supporting Information S3). For a small Δ𝑉 , 𝜇  increases with Δ𝑉 , which can be attributed to the increased charge carrier (electron) density and stronger Coulomb screening effect as the carrier density (𝑛) increases. 𝜇  saturates at larger Δ𝑉  when the Coulomb scattering rate decreases and is overtaken by short-range scattering and electron-phonon scattering, which are not affected by the electron screening effect. 𝜇  increases with decreasing temperature (𝑇) for Δ𝑉7 V, validating the intrinsic behavior of InSe at high 𝑛, which is consistent with our previous observation.18 Figure 1c shows the normalized noise 𝑆 𝐼⁄  as a function of frequency for sample A at different 𝑉  and 𝑇 130 K. 𝑆  exhibits a power law 𝑆 ∝ 𝑓 , with 𝛽 1.0 0.1 in the range of 𝑓 0.06 10 Hz. The noise data for all InSe FETs at different 𝑇 show the same 1 𝑓⁄  behavior. All measured 𝑆  values are larger than the background noise by at least one order of magnitude to ensure reliable noise data from the InSe FETs instead of from extrinsic sources. The background noise in our system mostly originates from the Johnson-Nyquist noise and the noise of the current preamplifier.19 We then calculated the average 𝑓𝑆 , where 𝑓𝑆 ∑ 𝑓𝑆 , 𝑁⁄ ,20 with 𝑖 and 𝑁 denoting the index and number of discrete data points of the measured 𝑆 𝑓 , respectively. Figure 1d shows 𝑓𝑆  as a function of 𝐼  for sample A at 𝑇 170 and 210 K, indicating that 7  𝑓𝑆 ∝ 𝐼 . Moreover, the inset of Figure 1d shows the output curve, indicating ohmic behavior 𝐼 𝑉 𝑅⁄  for T ranging from 90 to 210 K.18 Consequently, the resistance fluctuations δ𝑅 of our InSe FETs lead to current fluctuations 𝛿𝐼 𝛿𝑅 𝑅⁄ 𝐼  with an applied 𝑉 , yielding 𝑆 ∝ 𝐼  when considering the definition 𝑆 ∝ 𝛿𝐼 . Therefore, the observed linear relation of 𝑓𝑆  as a function of 𝐼  confirms that (i) our InSe FETs exhibit ohmic behavior, (ii) the noise originates from intrinsic resistance fluctuations,21 and (iii) no extra resistance fluctuations are activated by the bias voltage. 20 40 60 80 100 120 140 160 180 20005101520 90 K  130 K  170 K 210 KfSId 0.5/gm (mV)Id /gm (V)1.33 18.2 10.4 0.99 65.8 Id /gm (V) I II a c 0 500246 fSId 0.5 /gm (mV)Id /gm (V)1 1010-1510-1410-13  fSId 0.5/Id  sCNF sCMFfSId 0.5/I d (Hz-1)Id /gm (V)b d 10 100104105106107108T = 130 K (Vs/C)Vg (V) Vg-3.38  Figure 2. (a) Schematic showing the trap states, static Coulomb scatterers, and short-range scatterers in an InSe FET. The blue gradient color represents the electron density, signifying a higher electron density near the Si back gate. (b) 𝑓𝑆/𝑔  as a function of 𝐼 𝑔⁄  for sample A at different 𝑇. Inset: 𝑓𝑆/𝑔  as a function of 𝐼 𝑔⁄  for a small 𝐼 𝑔⁄  range to show the large variation in 𝑓𝑆/𝑔 . (c) Comparison of 𝑓𝑆⁄𝐼 , 𝑠  and 𝑠  as a function of 𝐼 𝑔⁄  for sample A. (d) Extracted 𝛼 as a function of Δ𝑉  for sample A at 130 K in a double logarithmic plot. The corresponding 𝐼 𝑔⁄  values are indicated on the top x-axis. The solid line is a fit to the power law dependence 𝛼 ∝ Δ𝑉 .  We now discuss a method to quantitatively determine the strength of carrier scattering from interfacial Coulomb scatterers (𝛼) and the area density of interfacial trap states (i.e., surface traps) at the Fermi energy (𝑛 ). Here, 𝛼 is defined as 𝜇 , 𝛼𝑒𝑛 ,22, 23 where 𝑒 is the electronic charge, 𝑛  is the area density of trapped charges at interfaces, and 𝜇 ,  is the mobility limited by these traps. The Coulomb scattering strength 𝛼 is proportional to the scattering rate of carriers from unit Coulomb scatterers, which is derived by using Fermi’s golden rule. It is assumed that 𝛼 is an average Coulomb scattering strength for interfacial Coulomb scatterers, thus the total scattering rate of carriers is proportional to 𝛼𝑛  based on the Matthiessen's rule. To derive 𝛼 from the noise analysis, we employed the carrier number fluctuation–correlated mobility fluctuation (CNF-CMF) model,22, 23 which has been applied to understand the low-frequency resistance noise in 2D semiconductor devices.24-28 Neither Hooge mobility fluctuations29, 30 nor carrier number fluctuations31, 32 are applicable to the low-frequency noise in our InSe FETs (Supporting Information S4), suggesting the validity of the CNF-CMF mechanism. The schematic in Figure 2a 9  depicts major charge scattering sources, including trap states, static Coulomb, and short-range scatterers. The trapping/detrapping processes of charge carriers cause not only carrier number fluctuations but also correlated mobility fluctuations. Under an applied 𝑉 , both the carrier number and correlated mobility fluctuations contribute to the fluctuations in 𝐼 . Assuming that the trapping/detrapping processes of charge carriers are governed by the quantum tunneling process, the normalized current noise PSD can be written as33 𝑆 1 𝛼𝜇 𝐶 ,      (1) where 𝑆 𝑒 𝑘 𝑇𝑁 𝐿𝑊𝐶 𝑓⁄  is the PSD of the flat-band voltage noise, and 𝑘  is Boltzmann’s constant. The first and second terms in parentheses on the right-hand side correspond to CNF and CMF terms, respectively. We now quantitatively evaluate the 𝛼 and 𝑁  values in InSe FETs by employing the CNF-CMF model. For comparison with experimental data, we rewrite Eq. (1) as 〈𝑓𝑆 〉 ⁄ 𝑔⁄𝑓𝑆/1 𝛼𝜇 𝐶 𝐼 𝑔⁄ , designated as Eq. (1A). Figure 2b shows 𝑓𝑆/𝑔  as a function of 𝐼 𝑔⁄  for sample A. For 𝐼 𝑔⁄ 10 V, 𝑓𝑆/𝑔  linearly increases with 𝐼 𝑔⁄ , suggesting that 𝛼𝜇  is a constant of 𝐼 𝑔⁄  in this regime. Importantly, the linear dependence of 𝑓𝑆/𝑔  on 𝐼 𝑔⁄  at high 𝐼 𝑔⁄  allows us to determine the 𝑁  value, which can be extracted from the intercept 𝑓𝑆/𝑒 𝑘 𝑇𝑁 𝐿𝑊𝐶⁄⁄ of the linear fitting. Moreover, we can rewrite Eq. (1) to obtain the square root of the normalized measured noise PSD, 〈𝑓𝑆 〉 𝐼 𝑓𝑆⁄𝐼 𝑔⁄ 𝑓𝑆⁄𝛼𝜇 𝐶 ≡ 𝑠 𝑠 ,       (2) 10  where 𝑠 𝑓𝑆⁄𝐼 𝑔⁄  and 𝑠 𝑓𝑆⁄𝛼𝜇 𝐶  (2A) are the noise caused by CNFs and CMFs, respectively. 𝑁 , and thus 𝑠 , can be extracted from the data, followed by the determination of 𝑠  based on 𝑠 〈𝑓𝑆 〉 𝐼 𝑠 . Figure 2c compares 〈𝑓𝑆 〉 𝐼 , 𝑠  and 𝑠  as a function of 𝐼 𝑔⁄ , indicating that the 𝑠  noise significantly contributes to the measured noise 〈𝑓𝑆 〉 𝐼 . We can now extract the Coulomb scattering strength 𝛼 according to Eq. 2A, which is one of the central goals of this work. The determination of both 𝛼 and 𝑁  in this method does not require any assumptions, as the remaining parameters can be determined from the 1 𝑓⁄  noise and transport measurements. Figure 2d shows the extracted 𝛼 as a function of Δ𝑉  for sample A at 𝑇 130 K in a double logarithmic plot, exhibiting a monotonically decreasing trend with increasing Δ𝑉 . The Δ𝑉  dependence of 𝛼 can be characterized into two distinct regimes: At low Δ𝑉  (Δ𝑉 30 V, regime I), 𝛼 rapidly decreases with Δ𝑉 . At high Δ𝑉  (Δ𝑉 30 V, regime II), the Δ𝑉  dependence of 𝛼 becomes relatively weak. Notably, 𝛼 varies by four orders of magnitude with Δ𝑉  ranging from 1 V to 80 V. In regime I, the carrier density increases with increasing 𝑉 , leading to enhanced Coulomb screening and a rapid decrease in 𝛼 with 𝑉 .34 𝛼 follows the power law 𝛼 ∝ Δ𝑉 .  for 3 V Δ𝑉 30 V. In previous reports, a power law of 𝛼 ∝ 𝑛  was assumed to describe the carrier density dependence of 𝛼,24-28 where 𝜈 1.2–1.6 and 𝜈 0.9 were reported for MoTe224 and WS2 devices,25 respectively. The comparatively large exponent of 3.3 indicates a very strong screening effect, which may be qualitatively understood in terms of a significantly induced electron density in InSe35 compared with other 2D semiconductors. To further discuss the rapid decrease in 𝛼  with increasing Δ𝑉 , we plot 𝑓𝑆/𝑔  in the small 𝐼 𝑔⁄  range (inset of 11  Figure 2b). 𝛼 is inferred to drastically decrease with increasing 𝐼 𝑔⁄  to overtake the trend of 𝜇  (Supporting Information S5), further supporting the very large Δ𝑉  dependence in regime I. In regime II, 𝛼  weakly decreases with Δ𝑉  compared with the trend in regime I and gradually saturates, which may be ascribed to saturation of the screening effect from Coulomb scatters in this regime.  Figure 3. (a) Comparison of 𝛼 as a function of Δ𝑉  for samples A, B, and C at 𝑇 130 K. Sample B exhibits very small Coulomb scattering in InSe FETs with the h-BN interlayer. Inset: 𝑁  as a function of 𝑇 for samples A, B, and C. (b) Schematics illustrating the distribution of the trap states 0 10 20 30 40103104105106107108109sample Asample Bsample C (Vs/C)Vg (V)0 10 20 30 4010-710-610-510-410-310-210-1100101 sample A sample B sample CfSI dLW/I d2 (Hz-1m2 )Vg (V)0 10 20 30 40100101102103sample A sample Bsample C FE (cm2/Vs)Vg (V)100 2001010101110121013Nst (eV-1cm-2)T (K)0 20 4010-710-610-510-410-3 sample A sample C      (scaled) fSI dLW/I d2  (Hz-1m2 )Vg (V)a c b d 12  and their relative distance 𝑟 to the charge carriers in the InSe channel for samples A, B, and C. The blue gradient color represents the electron density, signifying a higher electron density near the Si back gate. (c) Comparison of the field-effect mobility 𝜇  as a function of Δ𝑉  for samples A, B, and C at 𝑇 130 K. (d) Area-normalized noise PSD 𝑓𝑆 𝐿𝑊 𝐼⁄  as a function of Δ𝑉  for samples A, B, and C at 𝑇 130 K. Inset: comparison of the 𝑓𝑆 𝐿𝑊 𝐼⁄  of sample A and the scaled noise PSD of sample C at 𝑇 130 K.  Having established the method to determine 𝛼 and 𝑁 , we now apply it to elucidate the effect of the interfacial properties of the InSe FETs by comparing the Coulomb scattering parameters of samples A, B, and C. Figure 3a compares the measured 𝛼 values for samples A, B, and C at 130 K, which all exhibit similar behavior as those for sample A, as discussed in Figure 2d. The 𝛼 values for samples A and C are comparable for the range of all measured Δ𝑉 . 𝛼  characterizes the Coulomb scattering rate, and thus, 𝛼 ∝ 𝑉  according to Fermi’s golden rule, where 𝑉  is the Coulomb potential that depends on the carrier density and the distance between the charge carrier and the interfacial impurity (𝑟). For samples A and C, the major trap sites reside at the InSe/SiO2 interface, as depicted in Figure 3b; thus, 𝑉  is similar in the two samples. Therefore, the Δ𝑉  dependences of 𝛼 for these two samples being comparable is reasonable. Remarkably, the 𝛼 determined for sample B is smaller than that for samples A and C by four orders of magnitude at Δ𝑉 0, indicating very small Coulomb scattering for the InSe FETs with the h-BN interlayer. As depicted in Figure 3b, the distance 𝑟 for samples A and C can be assumed to be on the order of 0.1 nm by noting that the interaction between the InSe channel and the substrate is governed by the van der Waal force36 and that the dominant carriers are induced adjacent to the InSe/SiO2 interface under an applied 𝑉 .37 In contrast, while the bottom InSe 13  interface of sample B is pristine, polydimethylsiloxane (PDMS) residue can be present on the top InSe interface,5 suggesting that the 𝑟 in sample B can be approximated by the thickness of the InSe channel, which is on the order of 10 nm (Supporting Information S1). At Δ𝑉 0, 𝑛 0, and the Coulomb screening effect is negligible; the Coulomb potential is 𝑉 ∝ 𝜀 𝑟 , where 𝜀  is the dielectric constant. For sample B, 𝑟 is larger than that for samples A and C by two orders of magnitude. Therefore, we can estimate that the 𝛼 for sample B is smaller than that for samples A and C by four orders of magnitude, which is in reasonable agreement with the experimental data. Importantly, clean InSe/h-BN interfaces adjacent to the dominant carriers are achieved, which has a profound effect on reducing 𝛼. Furthermore, the Δ𝑉  dependence of 𝛼 at low Δ𝑉  of sample B is much weaker than that of samples A and C. Considering that the 𝑛 near the top InSe interface is low and that the Coulomb screening of the scatterers at this interface is much weaker, 𝛼 likely exhibits a small variation with Δ𝑉 . The inset of Figure 3a shows 𝑁  as a function of 𝑇 for samples A, B, and C. The average 𝑁  of sample A (HMDS-treated SiO2) is on the order of 1010 eV-1 cm-2 and is smaller than that of sample C (intrinsic SiO2) by two orders of magnitude. Because the HMDS-treated SiO2 yields a hydrophobic surface that greatly reduces the number of adsorbates,38 the large difference in 𝑁  suggests that the trap states may be attributed to the water molecules absorbed at the InSe/SiO2 interface. This ascription of trap states is in line with previous reports for single-crystal pentacene FETs39 and MoS2 FETs.40 As a comparison, a high 𝑁  on the order of 1011 1013 eV-1 cm-2 was commonly observed in MoTe2 and MoS2 devices when the surface of substrates was not pretreated,24, 26-28 indicating the importance of the hydrophobic surface treatment. The 𝑁 ∼1 1012 eV-1 cm-2 for sample B is high, which may originate from the PDMS residue on the top InSe interface.5 14  Figure 3c compares 𝜇  as a function of Δ𝑉  for samples A, B, and C. The 𝜇  of sample C increases as Δ𝑉  increases and saturates when Δ𝑉 20 V, showing a trend similar to that for sample A, as discussed in Figure 1b. Moreover, the 𝜇  of sample A is higher than that of sample C, which can be accounted for by a lower interfacial density of static Coulomb scatters in sample A caused by surface treatment (Supporting Information S2), considering that 𝛼 is comparable in these two samples. Sample B exhibits higher 𝜇  than samples A and C, which is consistent with the lower value of 𝛼. Interestingly, the 𝜇  in sample B is high despite its large 𝑁 , indicating the dominant role of the long-range Coulomb scattering strength 𝛼 in determining 𝜇 . The 𝜇  of sample B monotonically decreases with Δ𝑉 , revealing different behavior compared with samples A and C. Because 𝛼 is very small in sample B, Coulomb scattering can be overtaken by other scattering mechanisms. The atypical behavior of the 𝜇  of sample B may be attributed to surface roughness scattering,41 which becomes stronger with increasing number of induced carriers, resulting in 𝜇  decreasing with increasing Δ𝑉 . We now discuss the noise properties of the InSe FETs by further examining the associated 𝑁  and 𝛼. Figure 3d shows the area-normalized noise PSD 𝑓𝑆 𝐿𝑊 𝐼⁄  for samples A, B, and C. The normalized noise PSD of sample A is smaller than that of sample C by approximately two orders of magnitude. This difference can be understood by referring to Eq. (1): the 𝛼 values are comparable for samples A and C, as shown in Figure 3a, while the 𝑁  values in sample A are smaller than those in sample C by approximately two orders of magnitude. Additionally, we scale the normalized noise PSD of sample C by the 𝑁  ratio, as shown in the inset of Figure 3d. The scaled data of sample C collapse onto those of sample A, suggesting the validity of our analysis. Therefore, the largely suppressed noise in sample A can be attributed to a great reduction in 𝑁  due to the HMDS treatment. In addition, by comparing the area-normalized noise of the three 15  samples, the trap centers are inferred to be located at interfaces instead of in the bulk of the InSe channel (Supporting Information S6). Finally, we discuss the density of interfacial Coulomb scatterers 𝑛  and the mobility associated with different scattering mechanisms given that 𝛼 is determined. The mobility corresponding to Coulomb scattering 𝜇  can be written as22 𝜇 𝛼′𝑒𝑛 . (3) The factor 𝛼′ in Eq. (3) corresponds to both static and dynamic Coulomb scatterers, while the 𝛼 in Eq. (1) is only associated with the trap states. In this work, we presume that both static and dynamic Coulomb scatterers reside at the same interface, resulting in the same 𝛼 value for both scattering sources, and thus, ′  . The effective mobility 𝜇 𝜇  and can be expressed as ℎ,      (4) where 𝜇  and 𝜇  are the mobilities corresponding to short-range scattering and electron-phonon scattering, respectively. Because at low Δ𝑉 , where electron screening is weak, Coulomb scattering is strong and dominant,9 we can assume 𝜇 𝜇  in this regime. We then estimate 𝑛  at low Δ𝑉  based on Eq. (3), yielding 𝑛  values of 1.4 10  and 3.0 10  cm-2 for samples A and C at 𝑇  130 K, respectively. With the extracted 𝑛 , we can then calculate the Δ𝑉  dependence of 𝜇  based on Eq. (3). Figure 4a compares 𝜇 Δ𝑉  and 𝜇 Δ𝑉  for sample A at 130 K. For Δ𝑉 5 V, 𝜇  increases slower and deviates from the trend of 𝜇 . This suppression of 𝜇  can be qualitatively understood because when Coulomb scattering is strongly screened at higher Δ𝑉 , other scattering mechanisms, i.e., short-range scattering (𝜇 ) and phonon scattering (𝜇 ), become dominant in the regime. 16   Figure 4. (a) Comparison of 𝜇  and  𝜇  as a function of Δ𝑉  for sample A at 𝑇 130 K. The area density of interfacial Coulomb scatterers 𝑛  is estimated in a regime dominated by Coulomb scattering. (b) 𝑇 dependence of the mobility limited by the short-range and phonon scattering 𝜇 𝜇  of sample A at Δ𝑉 30 V. Inset: plot of 𝜇 𝜇  as a function of Δ𝑉  at different 𝑇 for sample A. (c) Comparison of 𝜇 𝜇  for samples A, B, and C at 𝑇 130 K. Sample B exhibits the highest mobility corresponding to the fewest short-range scattering centers at interface compared with samples A and C.  To further distinguish the contributions from different scattering mechanisms, we subtracted 𝜇  from 𝜇  according to Eq. (4). The inset of Figure 4b plots 𝜇 𝜇  as a function of Δ𝑉  at various 𝑇 for sample A. For a given 𝑇, 𝜇 𝜇  slightly decreases with 𝑛, which may be attributed to the screening of the remote interfacial phonon scattering at large 𝑛.42, 43 𝜇𝜇  saturates for Δ𝑉 30 V due to weakening electron screening. When 𝑇 decreases from 210 K to 90 K, 𝜇 𝜇  decreases by a factor of approximately  5. Figure 4b plots the 𝑇 50 100 150 2000100200300(1/s+1/ ph)-1 (cm2/V s)T (K)0 10 20 3010-1100101102103104105 FE  c (cm2 /Vs)Vg (V)sample AT = 130 K10 20 30 4010-210-1 90 K 130 K 170 K 210 K s-1+ ph-1 (cm-2 V s)Vg (V)0200400600800CB(1/s+1/ ph)-1 (cm2 /V s)AT = 130 Ksamplea c b 17  dependence of the mobility corresponding to the short-range and electron-phonon scattering 𝜇 𝜇  at Δ𝑉 30 V . 𝜇 𝜇  increases with decreasing 𝑇  because the electron-phonon scattering rate is suppressed. 𝜇 𝜇  approaches a constant value at lower 𝑇 as electron-phonon scattering becomes negligible, enabling determination of the mobility for short-range scattering. Figure 4c compares the 𝜇 𝜇  for samples A, B, and C at 130 K. The assumption that the 𝜇  and 𝜇  corresponding to the bulk short-range scatterers are comparable in these devices is reasonable, considering the same measured 𝑇 and source bulk crystal. Therefore, the value of 𝜇 𝜇  reflects the number of short-range scatterers at the interfaces for these samples. Sample B exhibits the highest 𝜇 𝜇 , which can be attributed to fewer short-range scattering centers at InSe/h-BN interface compared with that of InSe/SiO2 interface. In summary, we demonstrated a method to quantitatively extract the Coulomb and short-range scattering parameters in 2D transistors by combining the low-frequency 1 𝑓⁄  noise behavior and the transfer characteristics. The extracted long-range Coulomb scattering strength of 2D transistors is found to be a nontrivial function of the carrier density, as opposed to the previous understanding of a simple power law. We applied our method to study InSe FETs with different interfaces and obtained comprehensive correlations between the relevant Coulomb scattering parameters. In particular, InSe FETs with the h-BN interlayer exhibit high mobility and low noise, which can be attributed to the clean InSe/h-BN interfaces and the very low Coulomb scattering strength measured. This method can be applied to a wide spectrum of 2D FETs with different channel materials and various interfaces as well as ultrathin-body FETs to understanding the role of Coulomb scattering. This in-depth knowledge of the Coulomb scattering strength and its key 18  influences on the transport characteristics and low-frequency noise properties are highly useful for tailoring the interface and developing high-performance electronics.    19  METHODS 2D InSe FETs fabrications. The InSe and hexagonal boron nitride (h-BN) flakes are mechanically exfoliated onto the Si substrate with a 300-nm-thick SiO2 dielectric layer. The high-quality InSe crystals are grown by Bridgman method. The mechanical exfoliation of InSe flakes was performed in ambient condition. We then annealed the InSe samples in a furnace at 300 °C with Ar 95% and H2 5% forming gas to remove the PDMS residues. The InSe samples were then loaded into an e-beam evaporation system in high vacuum to deposit the contact metal. To achieve clean interface, the InSe samples were kept in a vacuum of 1 10  Torr for 15 h before In/Au (3 nm/80 nm) metallic films was deposited as the electrical contacts at a base pressure of 1 10  Torr. We fabricated three types of samples with different interfaces, including hexamethyldisilazane (HMDS)-treated SiO2, h-BN interlayer, and intrinsic SiO2/Si substrates. For the samples with HMDS treatment, ambient adsorbates such as water molecules can be greatly reduced compared with unprocessed SiO2 surface.38 For the samples with an h-BN interlayer, the exfoliated InSe crystals were transferred onto h-BN flakes, which were pre-exfoliated on a SiO2/Si substrates. Back gate voltage is applied to Si substrates to tune the carrier density in InSe. Electrical measurements. In the measurement, all InSe devices are enclosed in a sample space of a cryostat which is immersed in liquid nitrogen. The sample space is filled with helium gas. The devices are connected by twisted-pair measurement wires to suppress the magnetically induced current noise originated from the electromagnetic fluctuations in the laboratory environment. The electrical measurement circuit for transfer characteristic (the drain current dI  as a function of gate voltage gV ) and low-frequency noise is schematically depicted in Figure 1(a) in the main text. The gate voltage gV  is applied to the heavily doped (p++) Si substrate. Two sourcemeters (Keithley 6430) are used to apply the gV  and the source-drain voltage dV . The drain current as a function of 20  time  dI t  is amplified and converted to voltage by the current preamplifier (Stanford Research Systems model SR570) and then measured by the dynamic spectrum analyzer (Stanford Research Systems model SR785). The SR785 probes the signal with a sampling rate of 1024 Hz and measurement time of 30 s and stored the readings in the buffers.19 A computer fetches the data from the buffers, divide them by the gain of the SR570 and calculates the source-drain current noise power spectrum density (PSD) ( )dIS f  using a LabVIEW program. The ( )dIS f  and the dI  are measured simultaneously. For each gV , the ( )dIS f  is measured 10 times and is averaged to minimize the uncertainty of the noise. The InSe FETs were mounted in a cryostat and cooled with liquid nitrogen to study the T  dependence of transport property and low-frequency noise from 300 K to 80 K. The measurement is performed in a helium atmosphere. The sample temperature is monitored with a calibrated silicon diode thermometer.  ASSOCIATED CONTENT Supporting Information. Characterization of the InSe channel by atomic force microscopy. Comparison of the density of interfacial trap states 𝑁  and area density of Coulomb impurities 𝑛  among samples A, B, and C. Transfer characteristics for samples A, B, and C. Mechanism of the low-frequency noise in the InSe FETs. Correlation between 𝐼 𝑔⁄  and 𝑉 𝑉 . Consideration of interfacial and bulk trap defects.  AUTHOR INFORMATION Corresponding Author 21  *Wei-Hua Wang Tel: +886 2 2366 8208  E-mail: wwang@sinica.edu.tw †Sheng-Shiuan Yeh Tel: +886 978 098 108 E-mail: ssyeh@nycu.edu.tw  Author Contributions Y.T.L., W.H.W., S.S.Y., and J.J.L. conceived the experiment. Y.T.H. fabricated and characterized the InSe FETs with the assistance from W.H.W. and C.T.L. Y.T.L. and S.S.Y. performed the experimental measurements with assistance from S.P.C. and R.T.W. T.T. and K.W. synthesized the h-BN crystals. R.S. synthesized the InSe crystals. Y.T.L., W.H.W., S.S.Y., and J.J.L. analyzed and explained the data. S.S.Y., W.H.W., J.J.L., and C.T.L. wrote the manuscript. All the authors discussed the data and the manuscript.  ACKNOWLEDGMENT This work was supported by the National Science and Technology Council (NSTC) of Taiwan through Grant Nos. 110-2112-M-A49-015 and 111-2119- M-007-005 (J.J.L.), 110-2112-M-A49-033-MY3 (S.S.Y.), 112-2119-M-002-014 (C.T.L.), and 109-2112-M-001-041-MY3 (W.H.W). R. S. acknowledges the financial support provided by the NSTC under project number 110-2112-M-001-065-MY3 and Academia Sinica for the budget of AS-iMATE-109-13. S.S.Y. is grateful to the support by Taiwan Ministry of Education through the Higher Education Sprout Project of the NYCU. 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