We report measurement of low frequency 1/f noise in molybdenum di-sulphide (MoS2) field-effect transistors in multiple device configurations including MoS2 on silicon dioxide as well as MoS2-hexagonal boron nitride (hBN) heterostructures. All as-fabricated devices show similar magnitude of noise with number fluctuation as the dominant mechanism at high temperatures and density, although the calculated density of traps is two orders of magnitude higher than that at the SiO2 interface. Measurements on the heterostructure devices with vacuum annealing and dual gated configuration reveals that along with the channel, metal-MoS2 contacts also play a significant role in determining noise magnitude in these devices.

Atomically thin films of MoS2 have emerged as a promising platform for transparent flexible electronics. In the field-effect geometry, MoS2 offers several advantages that include large on-off ratio, immunity against short channel effects, and small subthreshold swing.1,2 These promise MoS2-based logic devices3,4 and energy-efficient field-effect transistor,5–7 although presence of localized band tail due to disorder,8 and metal-MoS2 Schottky barriers1,9 at the contacts were found to severely affect the performance, i.e., mobility of these devices. Low frequency noise, on the other hand, is also considered as one of the basic performance limiting factors in electronic devices, but the effect of the above-mentioned factors on noise is not clearly understood till date. Several groups have recently studied low frequency noise in MoS2. Sangwan et al.10 showed that noise magnitude increases by two orders of magnitude on exposure to ambient condition, whereas Renteria et al.11 has demonstrated that the noise level considerably increases with prolong exposure to atmospheric condition. Xie et al.12 have performed noise measurement in MoS2 devices before and after annealing in high vacuum, and showed that noise decreases by a factor of 20 after annealing. These studies mainly focus on the effect of external adsorbates on 1/f noise, and a proper understanding of the origin of noise in terms of both internal and external disorder along with contact induced effects is still lacking.

In this letter, we show that along with the channel, contacts also play a crucial role in determining the overall noise magnitude in MoS2 transistor devices. To show this, we systematically study 1/f noise measurement in MoS2 devices at high vacuum (∼ 2 × 10−6 mbar) where the effect of atmospheric water vapour is minimal. In order to find the effect of lithographic contaminations and residual water vapour, we fabricate MoS2 devices protected with hexagonal boron nitride. Comparison of 1/f noise measurement in protected and unprotected devices before and after annealing indicate that the lithographic polymer, and residual water vapour play a minimal role whereas the transparency of contacts significantly affects the total magnitude of noise in these devices. We also comment on the channel contribution to total noise from our measurement in dual-gated MoS2 devices.

Bulk MoS2 crystals were obtained from SPI supplies, and were characterized thoroughly with X-ray photoemission spectroscopy (XPS) and Raman spectroscopy (see Sec. I of the supplementary material13). In this work, we study two different classes of devices: (1) MoS2 devices on Si/SiO2 substrate, and (2) MoS2-hBN heterostructure devices. In case of the former, single and bilayer MoS2 flakes were exfoliated on 285 nm Si/SiO2 wafer using the scotch tape technique. Heterostructure devices were fabricated using well known Van der Waals assembly process14,15 (see Sec. II of the supplementary material13). Two different types of heterostructure devices were prepared with MoS2 being placed either on hBN, or below. We consider the latter as “protected device” since in these devices the channel is never exposed to lithographic polymer residues, and presence of water vapour at the MoS2-hBN interface is minimal as the transfer process was performed at 120 °C. The degenerately doped Si was used as backgate. Contact pads were designed using standard ebeam lithography, and thermal evaporation of Au (without any adhesive layer, such as Ti or Cr) (see Sec. II of the supplementary material13). An optical micrograph of a typical device is shown in bottom-right inset of Fig. 1(a). In all devices (see Table I), the current-voltage (IDSVDS) characteristics were linear at low source-drain bias VDS ⩽ 100 mV, and high back gate voltage (VBG) around room temperature (see Fig. S2 of the supplementary material13). We restricted the excitation bias to VDS ⩽ 100 mV to ensure measurements in linear regime. Both conductivity, and noise measurement were performed in two-probe configuration due to high resistance of the samples using current mode of lock-in amplifier. For noise measurement the sample was biased with an ac voltage ≈10mV (rms) at 777 Hz. The sample current was passed through a low noise preamplifier and measured using lock-in technique.16 The current fluctuation data were recorded as a function of time as illustrated in the inset of Fig. 1(b), and was Fourier transformed to obtain current noise power spectral density SI/I2 as a function of frequency f. For all devices I2 dependence was checked at every temperature before measurement to avoid any heating induced effect (see Fig. S3 of the supplementary material13). Due to linearity, the current power spectral density could be converted to conductivity fluctuation power spectral density Sσ2 using the relation Sσ2 = SI/I2.

FIG. 1.

(a) Conductivity (σ) as a function of backgate voltage (VBG) at different temperature (VDS = 10 mV) for a SiO2- supported single layer device. Inset: Source-drain current (IDS) as a function of VBG at room temperature in log-linear scale (upper left). Optical micrograph of a typical single layer device on Si/SiO2 substrate. Scale bar 10 μm (lower right). (b) 1/f power spectrum of conductivity fluctuations at three different VBG. The inset shows corresponding conductivity fluctuations as a function of time at the same gate voltages. (c) Gate voltage dependence of noise power spectral density Sσ2 at various T for a typical single layer device. (d) Non-monotonic T dependence of both Sσ2 at three different VBG. The localized regime was observed below 240 K, and the weak metallic regime for T > 240 K. Inset: Non-monotonic T dependence of σ at the same VBG.

FIG. 1.

(a) Conductivity (σ) as a function of backgate voltage (VBG) at different temperature (VDS = 10 mV) for a SiO2- supported single layer device. Inset: Source-drain current (IDS) as a function of VBG at room temperature in log-linear scale (upper left). Optical micrograph of a typical single layer device on Si/SiO2 substrate. Scale bar 10 μm (lower right). (b) 1/f power spectrum of conductivity fluctuations at three different VBG. The inset shows corresponding conductivity fluctuations as a function of time at the same gate voltages. (c) Gate voltage dependence of noise power spectral density Sσ2 at various T for a typical single layer device. (d) Non-monotonic T dependence of both Sσ2 at three different VBG. The localized regime was observed below 240 K, and the weak metallic regime for T > 240 K. Inset: Non-monotonic T dependence of σ at the same VBG.

Close modal
TABLE I.

Details of the devices.

DeviceLayer numberDevice area (L×W)aMobility(μFE)b
1L-1 2 × 2.5 
1L-2 5 × 8 
1L-3 0.8 × 4 
2L-1 2.8 × 2.5 22 
2L-2 3 × 4.9 11 
2L-3 1.9 × 2.2 10 
2L-BN 0.8 × 1.8 
4L-BN 1.7 × 2.7 20 
1L-P 3 × 4 
DeviceLayer numberDevice area (L×W)aMobility(μFE)b
1L-1 2 × 2.5 
1L-2 5 × 8 
1L-3 0.8 × 4 
2L-1 2.8 × 2.5 22 
2L-2 3 × 4.9 11 
2L-3 1.9 × 2.2 10 
2L-BN 0.8 × 1.8 
4L-BN 1.7 × 2.7 20 
1L-P 3 × 4 
a

Both dimensions in μm.

b

In cm2/V s near room temperature and ΔVBG ∼ 60V.

The backgate transfer characteristics of a typical single layer device at various temperatures are shown in Fig. 1(a). We find that from 120 K to 240 K conductivity (σ) increases with increasing temperature indicating a localized transport in this regime.8 Above 240 K, temperature dependence of conductivity reverses which indicates localized to weak metallic transition (see inset Fig. 1(d)).9,17 Low frequency noise in our devices showed 1/f-type power spectrum (Fig. 1(b)) in the entire gate voltage range down to 80 K. The gate voltage dependence of Sσ2 is shown in Fig. 1(c). We observed that Sσ2 decreases monotonically with increasing gate voltage at a fixed temperature. Temperature dependence of Sσ2 at three different VBG is shown in Fig. 1(d). We observed that noise, like conductivity, is also non-monotonic in temperature. It increases sharply with decreasing temperature below 240 K which can be attributed to the localized state transport, where an exponential increase in noise is predicted due to the broad distribution of the waiting time of the carriers between successive hops.18 On the other hand, for T > 240 K, where σ displays a metal-like transport,9,17 the noise magnitude slowly increases with increasing temperature similar to diffusive quasi-metallic systems.19 

In the subsequent sections, we will only discuss the noise behaviour in the diffusive, i.e., high density and temperature regime which is of technological relevance. We first discuss the carrier density dependence of noise in MoS2 devices on SiO2 substrate. To obtain carrier density (n), we define VON (top-left inset of Fig. 1(a)) as the backgate voltage at which the current through the device became measurable (≈1 pA) at T = 300 K. The parameter ΔVBG = VBGVON is then approximately proportional to carrier density (n) particularly at high ΔVBG. In Fig. 2(a), we plot ΔVBG dependence of noise for 1L-2 device at various temperature. We find that the dependence slowly becomes 1/(ΔVBG)2 as temperature approaches to room temperature. In Fig. 2(b), we plot carrier density dependence of room temperature noise for three different devices on Si/SiO2 substrate. We observe that at low ΔVBG, the variation differs from one sample to another and may be connected to the details of electron localization. However, at large ΔVBG, all devices show

$S_{\sigma }/\sigma ^2 \propto 1/\Delta V_{BG}^2$
Sσ/σ21/ΔVBG2⁠, which is a characteristic feature of number fluctuation in semiconductor channels.20 The interfacial trap states in the SiO2 substrate close to channel has been quantitatively shown to cause similar scenario in graphene-on-SiO221,22 and Si-MOSFETs.23 In order to check whether the oxide traps can account for the observed noise, we calculate interfacial trap density Dit from observed noise magnitude using24 

\begin{equation}S_I=\frac{g_m^2q^2k_BTD_{it}}{WLC_{ox}^2f},\end{equation}
SI=gm2q2kBTDitWLCox2f,
(1)

where gm, L, and W are device transconductance, length, and width, respectively, q is electronic charge, Cox is gate oxide capacitance per unit area. The application of the number fluctuation model here is justified by the observation of nearly constant

$S_I/g_m^2$
SI/gm2 in our devices,25 which also suggests that at high ΔVBG resistance at the MoS2-Au interface could be mainly due to randomly distributed defects states, rather than a conventional Schottky barriers at the metal-semiconductor interface. Similar conclusion was reached in tunneling spectroscopic study as well.26 The calculated Dit which ranges between 6×1010 and 1 × 1012 cm−2 eV−1 has been plotted in the inset of Fig. 2(b) for three different devices on SiO2 substrate. We observe that Dit is approximately one to two orders of magnitude higher than SiO2 trap density24 (see Sec. VI of the supplementary material for details13). Recent studies of noise,11 as well as space charge limited conductivity,27 yield very similar magnitude of trap density in MoS2 thin film transistors.

FIG. 2.

(a) Carrier density dependence of Sσ2 for a single layer device at different temperature. The dependence evolves to

$1/ \Delta V_{BG}^2$
1/ΔVBG2 as T approaches room temperature. (b)
$1/ \Delta V_{BG}^2$
1/ΔVBG2
dependence of Sσ2 at high VBG and near room temperature for three different MoS2 devices on SiO2 substrate. Inset: Calculated trap density Dit as a function of VBG for 1L-2, 2L-1, and 2L-2 devices on SiO2 substrate. The SiO2 interface trap density is indicated by the gray band.

FIG. 2.

(a) Carrier density dependence of Sσ2 for a single layer device at different temperature. The dependence evolves to

$1/ \Delta V_{BG}^2$
1/ΔVBG2 as T approaches room temperature. (b)
$1/ \Delta V_{BG}^2$
1/ΔVBG2
dependence of Sσ2 at high VBG and near room temperature for three different MoS2 devices on SiO2 substrate. Inset: Calculated trap density Dit as a function of VBG for 1L-2, 2L-1, and 2L-2 devices on SiO2 substrate. The SiO2 interface trap density is indicated by the gray band.

Close modal

For further understanding on the defects states, we fabricated MoS2 transistor on crystalline hexagonal boron nitride (hBN) substrate known to be free from surface trap states and dangling bonds.28 This device architecture eliminates the SiO2 trap states as a mean to exchange carriers with the channel. Noise measurements on two “MoS2 on hBN” devices are shown in Fig. 3(a) which also follow

$1/\Delta V_{BG}^2$
1/ΔVBG2 dependence at high ΔVBG. The area normalized noise magnitude for these two devices are compared with SiO2-supported devices as a function of carrier density in Fig. 3(b). We find that the noise level in both kinds of devices is similar which indicates that only the interfacial trap charges cannot account for the observed noise magnitude.

FIG. 3.

(a)

$1/ \Delta V_{BG}^2$
1/ΔVBG2 dependence of Sσ2 at high VBG in MoS2 on hBN substrate. The inset shows the optical micrograph of an MoS2 on hBN device. Scale bar 8 μm. (b) Comparison of area-normalized noise magnitude in MoS2 devices on SiO2 and hBN substrate at 300 K.

FIG. 3.

(a)

$1/ \Delta V_{BG}^2$
1/ΔVBG2 dependence of Sσ2 at high VBG in MoS2 on hBN substrate. The inset shows the optical micrograph of an MoS2 on hBN device. Scale bar 8 μm. (b) Comparison of area-normalized noise magnitude in MoS2 devices on SiO2 and hBN substrate at 300 K.

Close modal

The high noise level in as-fabricated devices, as discussed above, can be attributed to several factors. Lithographic polymer residues can act as additional trapping-detrapping source. Localized trap states inside the channel due to sulphur vacancies can slowly exchange carrier to contribute to noise.20,29–31 Moreover, as mentioned earlier, all our devices were measured in high vacuum which ensures significant, but not entire, removal of the adsorbed water vapour from the surface of channel, and thus, remaining adsorbate can also affect the noise level. Conductivity fluctuations can also happen at the contact due to presence of spatially inhomogeneous Schottky barrier.32 In order to address the contribution from the above-mentioned factors, we fabricate devices by transferring a thin (∼20 nm) single crystalline layer of hBN on top of the MoS2 flake prior to lithography processes. Such encapsulation protects the channel from acrylic residues, and the possibility of the presence of water vapor is also minimal as the transfer was done at 120 °C. Here we present the data from a typical device where two 2-probe channels were fabricated on the same MoS2 flake. A schematic and an optical micrograph of the device is shown in Figs. 4(a) and 4(b), respectively. The channel between probe 1 and probe 2 was exposed to fabrication-induced atmospheric contaminations, whereas the part between 2 and 3 was protected by hBN. We could not perform noise measurement in ambient condition in the unprotected channel due to large relaxation of IDS in the time scale of noise data acquisition (see Fig. S4 of the supplementary material13). Therefore, we evacuated the cryostat to ≈10−6 mbar vacuum, and performed conductivity and noise measurement (see Fig. S5 of the supplementary material13 for transfer characteristics). The carrier mobilities of the protected and unprotected channels were ∼ 4 and ∼ 3 cm2/Vs, respectively. The noise magnitude normalized by the device area in both channels are compared at similar carrier density in Fig. 4(c). We observe that the noise from unprotected channel is only slightly (≲ 50%) higher than that from the protected channel. This may be because of the contribution from acrylic residues, and residual water vapour remaining on the as-fabricated unprotected channel. In the next step, we anneal the device at 150 °C for 2 h in high vacuum condition. The conductivity and noise measurements were performed after cooling the device to room temperature. The transfer characteristics for both channels after annealing are shown in the supplementary material13 (see Fig. S5). We found that in all cases, the VON shifted towards large (< −60 V) negative gate voltages after annealing. This has been observed previously, but the reason behind this remain controversial.17 The noise behavior of unprotected, and protected channels before and after annealing are plotted in Figs. 4(d) and 4(e), respectively. For comparison, we plot Sσ2 normalized to its magnitude at ΔVBG ≈10 V as a function of ΔVBG. We observe that both the channels, in spite of having very different surface conditions, show 10 − 30 times decrease in noise magnitude after annealing. Assuming that annealing at 150 °C can only remove residual water vapour, adsorbed molecules, and not polymer residues, such large change cannot be accounted for by the desorption of atmospheric contaminants.

FIG. 4.

(a) Schematic and (b) optical micrograph of a device consists of two 2-probe channels on the same flake. The region between 1 and 2 was exposed to external trapping-detrapping agents. The region between 2 and 3 was protected with hBN. (c) Comparison of area-normalized noise magnitude of 1 and 2, and 2 and 3 regions as a function of carrier density before annealing. Comparison of noise magnitude before and after annealing for (d) 1 and 2 (e) 2 and 3 channel regions. The Sσ2 was normalized with its values at ΔVBG = 10V and 16 V in Figs. 4(d) and 4(e), respectively. The black dashed lines indicate |$1/\Delta V_{BG}^2$|1/ΔVBG2. (f) Sσ2 as a function of top gate voltage at different VBG = 0, 20, 40 V. Inset: Drain-source current as a function of top gate voltage at fixed VBG = 40 V.

FIG. 4.

(a) Schematic and (b) optical micrograph of a device consists of two 2-probe channels on the same flake. The region between 1 and 2 was exposed to external trapping-detrapping agents. The region between 2 and 3 was protected with hBN. (c) Comparison of area-normalized noise magnitude of 1 and 2, and 2 and 3 regions as a function of carrier density before annealing. Comparison of noise magnitude before and after annealing for (d) 1 and 2 (e) 2 and 3 channel regions. The Sσ2 was normalized with its values at ΔVBG = 10V and 16 V in Figs. 4(d) and 4(e), respectively. The black dashed lines indicate |$1/\Delta V_{BG}^2$|1/ΔVBG2. (f) Sσ2 as a function of top gate voltage at different VBG = 0, 20, 40 V. Inset: Drain-source current as a function of top gate voltage at fixed VBG = 40 V.

Close modal

We now discuss two possibilities that may account for the large decrease in noise on annealing: (1) reduction in the localized trap states inside the channel and (2) modifications in the metal-MoS2 contacts. It is well-known that the defects in MoS2 arises due to sulphur vacancies and interstitial,26 and are stable till ∼1000°C.17 Therefore, we exclude the former as the mechanism of noise reduction by annealing. On the other hand, it is well-established that, in the space-charge region of metal-semiconductor interface, random occupancy of the trap states can lead to low-frequency noise, for example, via fluctuations in the Schottky barrier height.33 In case of MoS2, however, the defect states created at the metal-MoS2 interface has been suggested to be intrinsic in nature that could also cause a strong lowering of the local Schottky barrier.26,29 The sensitivity of transport to annealing indicated these to be significantly lower in energy, the reduction of traps on annealing increases both the transparency of the contacts,1,9 as well as the overall noise level in these devices.

To obtain a more direct evidence of the role of contacts, we measure the noise in MoS2 devices with both backgate and top gate (denoted as TG in Fig. 4(b)). The thin (20 nm) hBN layer played the role of top gate dielectric apart from surface protection. The noise measurements were performed as a function of top gate voltage (VTG) keeping the backgate at a constant voltage. The backgate induces carriers in MoS2 both below the contact pads and the channel region between the contacts, and we used VBG to change the transparency of the contacts. The top gate, on the other hand, influences only the channel region between the contacts, and can drive the transistor on/off due to its stronger capacitative coupling. The transfer characteristics of the device as a function of top gate voltage keeping VBG = 40 V is shown in the inset of Fig. 4(f). We observe that the transfer characteristics saturates at high VTG due to contact resistance. The variation of noise as a function of VTG at three different VBG are shown in Fig. 4(f). We observe that at high carrier density, where the transfer characteristics is dominated by the contacts, noise becomes a weak function of VTG.11 The data at VBG = 0, 20, and 40 V (Fig. 4(f)) clearly indicate that the transparency of the contacts significantly affects the measured noise, and can lift the noise level even by orders of magnitude in these devices. Alternatively, in the low VTG regime (for example, VTG < −2 V at VBG = 40 V), where the channel resistance dominate over contact resistance, we find that even though the contact barriers are highly transparent due to high VBG, noise magnitude increases rapidly with decreasing VTG. This indicates that the channel contribution to noise is dominant in this regime which may originate due to strong localization of carriers in the channel.8,29

In conclusion, we investigate the origin of the low frequency 1/f noise in MoS2 devices. Our measurement suggest that, along with the external trapping-detrapping centers, metal-MoS2 contacts play a significant role in determining the noise magnitude in these devices. The dramatic decrease in noise after vacuum annealing is probably due to large increase in the transparency of the contacts rather than the removal of surface contaminations. We conclude that highly transparent contact along with channel encapsulation is essential to implement MoS2 in low noise applications.

We thank Dr. Paromita Kundu and Prof. N. Ravishankar for their useful discussions. We thank DST, Govt. of India for a sponsored project under Nano Mission. S.G. thanks CSIR for financial support.

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