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Low-Frequency Electronic Noise in Exfoliated Quasi-1D TaSe3 van Der Waals Nanowires

We report results of investigation of the low-frequency electronic excess noise in quasi-1D nanowires of TaSe3 capped with quasi-2D h-BN layers. Semi-metallic TaSe3 is a quasi-1D van der Waals material with exceptionally high breakdown current density. It was found that TaSe3 nanowires have lower levels of the normalized noise spectral density, compared to carbon nanotubes and graphene. The temperature-dependent measurements revealed that the low-frequency electronic 1/f noise becomes the 1/f^2-type as temperature increases to about 400 K, suggesting the onset of electromigration (f is the frequency). Using the Dutta- Horn random fluctuation model of the electronic noise in metals we determined that the noise activation energy for quasi-1D TaSe3 nanowires is approximately E_P=1.0 eV. In the framework of the empirical noise model for metallic interconnects, the extracted activation energy, related to electromigration, is E_A=0.88 eV, consistent with that for Cu and Al interconnects. Our results shed light on the physical mechanism of low-frequency 1/f noise in quasi-1D van der Waals semi-metals and suggest that such material systems have potential for ultimately downscaled local interconnect applications.

The investigations of the two-dimensional layers and heterostructures revealed new physics and demonstrated promising applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Starting with graphene [3][4][5], and spreading to a wide range of layered van der Waals materials [6][7][8][9][10], successful isolation of individual atomic layers from their respective bulk crystals by mechanical exfoliation led to the fast growing research activities in the 2D materials. In contrast to the layered van der Waals materials that yield 2D crystals, materials, such as TaSe3 and TiS3 [15][16][17] yield the quasi-onedimensional (1D) van der Waals crystal structures. These materials belong to the group of the transition metal trichalcogenides MX3 (where M = Mo, W, and other transition metals; X = S, Se, Te). In the monoclinic crystal structure of TaSe3, the trigonal prismatic TaSe3 units form continuous chains extending along the b axis and leading to fiber-and needle-like crystals with anisotropic semi-metallic or metallic properties. The quasi-1D atomic threads are weakly bound in bundles by the van der Waals forces. As a consequence, the mechanical exfoliation of the MX3 crystals results not in the 2D layers but rather in the quasi-1D van der Waals nanowires. We have recently demonstrated quasi-1D TaSe3 nanowires with the record high current density exceeding JB~10 MA/cm 2 , which is an order of magnitude larger than that for the Cu interconnects [18].
In this Letter, we report on the excess low-frequency electronic noise in quasi-1D nanowires of TaSe3 capped with the quasi-2D h-BN layers. The h-BN capping was used as a surface passivation protecting from environmental exposure. The measurements were performed in the temperature range from 300 K to 430 K in order to elucidate the physical mechanism of the low-frequency noise and determine the noise activation energies. The low-frequency noise is a ubiquitous phenomenon present in all kinds of electronic devices including field-effect transistors, diodes and interconnects [19][20][21]. The frequency dependence and temperature characteristics of the spectral density of the low-frequency noise have been used as reliability metrics for interconnects in Si complementary metal-oxide-semiconductor (CMOS) technology. The low-frequency noise data at elevated temperatures are directly correlated with the electromigration failure mechanisms in interconnects [22][23][24]. It was suggested that the low-frequency noise at high temperatures originates from the vacancy migration along the grain boundaries [22,25]. Hence, the noise can reveal information on the electromigration failure of interconnects and metal thin films. The noise activation energies extracted from the two commonly accepted physical models, the Dutta-Horn model [21,24] and the empirical noise model in metals [22,26,27], have shown an excellent agreement with the activation energies obtained from the industry standard electromigration mean-time-to-failure (MTF) tests. These considerations explain additional practical motivations for investigation of the lowfrequency noise in quasi-1D nanowires of TaSe3, which exhibit promise as ultimately downscaled local interconnects owing to their single-crystal atomic thread structure and exceptionally high breakdown current density [18].
The bulk TaSe3 crystals were synthesized by the chemical vapor transport (CVT) method and then were solvent exfoliated (see Methods). The high quality of both bulk and exfoliated quasi-1D TaSe3 samples has been confirmed using a variety of experimental techniques including high-resolution transmission electron microscopy, Raman spectroscopy, energy dispersive spectroscopy, powder X-ray diffraction, and electron probe micro analysis, as reported previously [18]. The devices for the low-frequency noise measurement were fabricated by the mechanical exfoliation of the quasi-1D TaSe3 nanowires on Si/SiO2 substrates. We used the dry transferred h-BN flakes to protect the quasi-1D TaSe3 nanowire channels from oxidation and chemical exposure during the fabrication processes. The devices were fabricated by standard e-beam lithography and e-beam metal evaporation [28]. In order to make an electrical connection to the quasi-1D channels we opened the contact area by dry etching the h-BN thin film and the underlying TaSe3 nanowire while leaving the edge of quasi-1D channels in contact with the metal. Figure 1 (a) shows a high-resolution transmission electron microscopy (TEM) image of TaSe3 crystal prepared by CVT method together with a schematic of the atomic plane arrangements. A scanning electron microscopy (SEM) of the long TaSe3 nanowires is presented in Figure 1 (b). Figure 1 (c) is a SEM image of representative devices used for the current voltage (I-V) and electronic noise measurements.
[ Figure 1 Figure 2 shows an optical image of a representative device used in this study. The light blue stripe between metal electrodes is the quasi-1D TaSe3 nanowire while the green region is the h-BN capping layer. The red background is the Si/SiO2 substrate.
[ Figure 2] The low-frequency noise measurements were performed both at UCR and RPI using in-house built experimental setups. The equipment included a "quiet" battery, a potentiometer biasing circuit, a low noise amplifier and a spectrum analyzer. The details of our noise measurement procedures have been reported elsewhere [28 -29]. Figure 3 (a) shows a typical normalized noise spectral density SI/I 2 ∝ 1/f  with  =1.16 (here I is the channel sourcedrain current) in theTaSe3 nanowires with the 20 nm × 110 nm cross-section. The measurements were performed at room temperature (RT). The noise spectral density was determined for the currents in the 1 A -5 µA range, which is sufficiently small to exclude the current induced effects such as electromigration. The latter is confirmed by the perfectly quadratic dependence of the noise spectral density on the sourcedrain current, i.e. SI∝ I 2 . The noise spectral density as a function of the source-drain current is shown in the inset to Figure 3 (a). The noise spectrum was collected for the two-terminal device. Since the contact resistance is very small compare to that of the channel, the contact noise was negligible.
The first interesting observation from the experimental data is that the noise level in TaSe3 nanowires is rather low in comparison with other low-dimensional materials, such as carbon nanotubes and graphene, which also have been proposed as the interconnect applications. The normalized noise spectral density, SI/I 2 , for TaSe3 nanowires as a function of the resistance is shown in Figure 3 (b). The data points for carbon nanotubes [30][31][32] and graphene [29,33] are presented for comparison. The guide line is the noise amplitude, A=SI/I 2 ×f, which was empirically obtained for the carbon nanotubes [30]. The devices with a lower resistance tend to have a lower level of the low-frequency noise. As one can see, the noise level, expressed as SI/I 2 , in quasi-1D TaSe3 nanowires is about one order of magnitude lower than that in graphene [29,33]. It is comparable to the lowest reported values for the carbon nanotubes [30][31][32]. Most of the tested carbon nanotube devices had a larger resistance and, as a result, a larger noise spectral density. The higher levels of 1/f noise typically are associated with a higher density of structural defects, as well as mechanical and electromigration damage [22,25]. The resistivity of quasi-1D TaSe3 nanowires increases with temperature, similar to other metallic materials. The inset to Figure 4 shows the resistivity change in the temperature range from 298 K to 450 K. The gradual and relatively slow resistance increase below 420 K is due to increasing electron-phonon scattering, which is common in metals. The sharp increase in resistance at the temperatures above 420 K is likely related to the onset of electromigration as commonly observed in the conventional interconnect reliability tests [24,34]. The TaSe3 nanowire noise spectral density and the frequency exponent  rapidly grows with temperature (see Figure 4). The noise level at 378 K increases by a factor of ×10 at 100 Hz and a factor of ×300 at 1 Hz compared to that at 298 K. The noise magnitude grows faster at the lower frequencies, changing the type of the frequency dependence of the normalized noise spectral density, SI/I 2 , at high temperature.
[ Figure 4] To better understand the evolution of the low-frequency noise with temperature, we plotted the frequency exponent  and the normalized noise spectral density, SI/I 2 , as the functions of temperature in the range from 298 K to 431 K. The experimental data points in Figure 5 (a-b) are shown for two representative devices with different channel cross-section areas at the frequency f=10 Hz. The frequency exponent  increases from ~1.16-1.24 at 298 K to 1.72-1.75 at 350 K. At temperatures above 350 K,  remains nearly constant at 1.71-1.75 (see Figure 5 (a)). In Figure 5 (b), one can see that the noise level increases by two orders of magnitude as temperature changes from 298 K to 400 K. The data in Figure 5 (b) suggest that the noise spectral density attains its maximum value at T=400 K and then reveal a saturation and a slowly decreasing trend. This behavior is analogous to that in thin films of Ag and Cu [35,36]. In the region of the fast growth, SI/I 2 ~T s with s=21 for the shown data set for two representative devices (see Figure 5 (b)).
[ Figure 5] We now turn to the analysis of the experimental data using two different physical models. The Dutta-Horn model describes the temperature dependent low-frequency noise by the thermally activated random fluctuations [35]. Within this model, the noise spectral density, S(f,T), can be approximated as where The temperature dependence of the frequency exponent  is expressed as [35] ( Here 0 is characteristic time constant referred to as the attempt escape time. In the original Dutta-Horn model, the time constant 0 was assumed to be ~10 -14 s which is the typical attempt escape time for random processes in solids. The exact value of 0 does not strongly affect the low-frequency noise analysis. The blue curve in Figure 5 (a) is a polynomial fit to the experimental data used in the further analysis.
In Figure 5 (b), the blue line is calculated using Eq. (2) with the approximated dependence of the frequency exponent  on temperature shown in Figure 5 (a). One can see that the Dutta-Horn model describes accurately the temperature dependence of the noise for T < 380 K. The saturation or even the decrease of noise at higher temperatures cannot be explained by this model. The latter is likely related to the onset of another low-frequency noise mechanism. For this reason, applying of the Dutta-Horn model for temperatures above ~400 K has to be done with caution. The activation energy EP, at which the distribution function D(E) attains its peak is related to temperature as The activation energy distribution calculated from the noise data in metals usually has a peak at EP≈1 eV [35]. Using the data for a representative device heated all the way to 430 K we determined that the energy distribution reaches its maximum at EP≈1.0 eV for TaSe3 nanowires as well (data set for "Device 1" in Figure 5 (b)). In a more conservative approach, increasing the temperature only to ~390 K, within the application domain of the Dutta-Horn model (data set for "Device 2" in Figure 5 (b)), we determine the low bound of the position of the maximum of the activation energy distribution function D(E). This value is somewhat smaller but still close to ~1 eV.
The noise spectral density SI/I 2 ~ 1/f  with ≈ 2 in metals is often attributed to the effects of electromigration. Although the detailed mechanism of the resistance fluctuations in metal films has not been established yet, many experiment indicate that the low-frequency noise, electromigration, and degradation in metals are related. The 1/f  noise spectral density with ≥2, which appears at high temperatures, has been widely used to extract the electromigration activation energy for interconnects. The frequency exponents as high as >4 have been reported [38]. Attributed to the vacancy migration, 1/f  noise has been proposed as a useful diagnostic tool [25]. It was found that the low-frequency noise at high temperature follows the empirical equation [22] where A is a constant, j is the biasing current density and EA is the activation energy related to  [21,23,24,37]. The noise measurements have specific advantages over the conventional reliability tests, which require time-dependent resistance measurements of interconnects under high temperature and high current stress for long periods of time (typically from 10 to 100 hours for each set). The noise measurements can be conducted in much shorter period of time. They are also be non-destructive. It was found that the noise level often increases rapidly before the sharp resistance increase, which was defined as the interconnect failure [24]. Figure 6 shows the Arrhenius plot of T×SI/I 2 vs. 1000/T for f=10 Hz. The extracted EA of 0.88 eV is within the range reported for other metal films. Table I summarizes  [ Figure 6] In conclusion, we investigated the low-frequency excess noise in quasi-1D nanowires of TaSe3  Cu with TaNTa barrier 0.76-0.78 [24] 0.79 [38] Al 0.69 [21] Al -Si (1%) 0.80 [21] Al -Cu (4%) 0.89 [21] Al thin film 1.14 [22] Al -Si (0.8%) passivated 0.74 [39] Al -Si (1%) -Cu (0.5%) passivated 0.78 [39]     Hz as the function of the channel (source-drain) current spanning from 0.2 µA to 10 µA. The quadratic dependence of the noise spectrum density SI on the channel current I indicates that the 1/f noise measured at this current level originates from the TaSe3 device itself rather than the current induced effects. (b) Normalized noise spectrum density as a function of the resistance for different low-dimensional material systems -quasi-1D TaSe3 nanowires, graphene and carbon nanotubes. For comparison, the empirical relation A=10 -11 R for the lowfrequency noise versus resistance R derived from the carbon nanotube studies [29,[31][32][33] is also shown. The noise in quasi-1D TaSe3 nanowires is about one order of magnitude lower than that in graphene.