Correlating Electronic Transport and 1/f Noise in ${\mathrm{Mo}\mathrm{Se}}_2$ Field-Effect Transistors

Two-Dimensional Transition Metal Dichalcogenides (2D TMDCs) such as ${\mathrm{Mo}\mathrm{S}}_2$, ${\mathrm{Mo}\mathrm{Se}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{W}\mathrm{Se}}_2$ with van der Waal's type interlayer coupling are being widely explored as channel materials in a Schottky Barrier Field Effect Transistor (SB FET) configuration. While their excellent electrostatic control and high on/off ratios have been identified, a clear correlation between electronic transport and the low-frequency noise with different atomic-layer thickness is missing. For multilayer channels in ${\mathrm{Mo}\mathrm{S}}_2$ FETs, the effects of interlayer-coupling resistance on device conductance and mobility have been studied, but no systematic study has included interlayer effects in consideration of the intrinsic (channel) and extrinsic (total device) noise behavior. Here, we report the 1/f noise properties in ${\mathrm{Mo}\mathrm{Se}}_2$ FETs with varying channel thicknesses (3–40 atomic layers). Contributions of channel vs access/contact regions are extracted from current-voltage (transport) and 1/f noise measurements. The measured noise amplitude shows a direct crossover from channel- to contact-dominated noise as the gate voltage is increased. The results can be interpreted in terms of a Hooge relationship associated with the channel noise, a transition region, and a saturated high-gate-voltage regime whose characteristics are determined by a voltage-independent conductance and noise source associated with the metallurgical contact and the interlayer resistance. Both the channel Hooge coefficient and the channel/access noise amplitude decrease with increasing channel thickness over the range of 3–15 atomic layers, with the former remaining approximately constant and the latter increasing over a range of 20–40 atomic layers. The analysis can be extended to devices based on other TMDCs.

Figure 1

(a) A schematic view of ${\mathrm{Mo}\mathrm{Se}}_2$ field-effect transistor employed in the present work. ${\mathrm{Mo}\mathrm{Se}}_2$ flakes with various numbers of atomic layers are used as transistor channels. The nickel-SD-contact electrodes are fabricated on top of the back-gated channel. (b) AFM image and geometrical step profile of a ${\mathrm{Mo}\mathrm{Se}}_2$ flake within a representative field-effect-transistor channel. The thickness of the ${\mathrm{Mo}\mathrm{Se}}_2$ layer is approximately 9.7 nm, corresponding to approximately 15 layers. (c) The corresponding Raman spectrum of a ${\mathrm{Mo}\mathrm{Se}}_2$ flake is shown collected using a 532-nm excitation source. The presence of two principal peaks, A_1g and $E_{2g}^1$, confirms a bonding environment corresponding to ${\mathrm{Mo}\mathrm{Se}}_2$. The inset shows the optical microscope image of the device used in this study.

Figure 2

Characteristics of ${\mathrm{Mo}\mathrm{Se}}_2$ FETs with different layer thicknesses (N = 3, 5, 8, 10, 15, 20, and 40L), including, (a) transfer characteristics measured at V_DS = 0.2 V. (b) Intrinsic and extrinsic field-effect mobilities extracted at V_DS = 0.2 V as a function of the ${\mathrm{Mo}\mathrm{Se}}_2$ layer thickness. For the 8L device, parameters are presented for the 2-µm-channel length.

Figure 3

(a) 1/f noise-current-power-spectral density for FETs with different numbers of ${\mathrm{Mo}\mathrm{Se}}_2$ layers as a function of frequency for various numbers of layers and (b) comparison of normalized noise amplitudes (total noise, channel noise, contact/access noise) for FETs with different numbers of ${\mathrm{Mo}\mathrm{Se}}_2$ layers. Noise measurements are performed at V_GS – V_th = 7 V, frequency of 100 Hz, and at low-drain bias (V_DS = 50 mV) and channel vs contact/access contributions are extracted as described in the text.

Figure 4

(a) Measured and modeled 1/f noise response of 15L ${\mathrm{Mo}\mathrm{Se}}_2$ FET. The round symbols represent the measured data points for the normalized noise-current-power-spectral density, $f\times S_I/I_{DS}^2$ , as a function of the gate bias. The dashed lines represent the model fitting for the noise dominated by the channel contribution and the contact contribution, respectively. The green line shows the sum of both contributions. Green opened square corresponds to (g_m/I_DS)² in the right-sided y axis. The agreement between the modeled fitting and measured data indicates that the measured voltage dependence can be explained by a channel following Hooge's mobility-fluctuation model, with a transition to a contact/access-dominated regime. (b) Contact and channel components of the noise and resistance for 15L ${\mathrm{Mo}\mathrm{Se}}_2$ FET, obtained from measurements using procedure described in the text. Blue area represents “transition regime” in which channel dominates noise, but contact/access regions dominate resistance. (c) Measured, modeled 1/f noise response and (g_m/I_DS)² of 40L ${\mathrm{Mo}\mathrm{Se}}_2$ FET, using same symbols as (a). (d) Contact and channel components of the noise and resistance for 40L ${\mathrm{Mo}\mathrm{Se}}_2$ FET, using same symbols as (b). In comparison to 15L FET, the transition voltages are lower, and the width of the transition region is smaller. The noise amplitudes of the channel-dominated regime (at the same bias point) and the contact/channel-dominated regime are also larger, corresponding to a larger Hooge parameter and an increased noise contribution from interlayer resistances, respectively.

Figure 5

Comparison of noise parameters at 10-V-overdrive voltage (a) The comparison of normalized noise amplitudes (total, channel, contact/access) for FETs with different numbers of ${\mathrm{Mo}\mathrm{Se}}_2$ layers. All the noise measurements are performed at V_GS – V_th = 10 V, frequency of 100 Hz, and low-drain bias (V_DS= 50 mV). (b) Hooge's constants (α_H) as a function of number of layers in ${\mathrm{Mo}\mathrm{Se}}_2$ FETs. The inset shows schematic representation of the intrinsic and extrinsic FETs. (c) Representation of total noise originating from three independent current-noise sources, namely, contact resistance, interlayer-coupling resistance, and the channel resistance. (d) Thevenin equivalent-resistance-noise sources are shown.

Figure 6

The noise amplitudes $f\times S_I/I_{DS}^2$ and (g_m/I_DS)² as a function of overdrive voltage in 8L ${\mathrm{Mo}\mathrm{Se}}_2$ FETs. Pink, orange, and black circles represent the noise amplitude of L_ch = 0.5, 1, and 2 µm, respectively. The blue (red) dashed line indicates the model fitting for the noise in the channel (contact) regime. Green opened square corresponds to (g_m/I_DS)². Arrows indicate the appropriate axis.

Figure 7

Total resistance vs 1/(V_GS – V_th) for the extraction of series resistance (a) 15L and (b) 40L.

Figure 8

Transconductance (g_m) as a function of the overdrive voltage (V_GS – V_th) at V_DS = 0.2 V for 15L ${\mathrm{Mo}\mathrm{Se}}_2$ FET.

Figure 9

(a), (c), (e), (g), and (i): Measured and modeled 1/f noise response of ${\mathrm{Mo}\mathrm{Se}}_2$ FETs vs overdrive voltage. The round symbols represent the measured data points for the normalized noise-current-power-spectral density, $f\times S_I/I_{DS}^2$, as a function of the gate bias. The dashed lines represent the model fitting for the corresponding noise amplitude due to noise sources in the channel (blue) and the contact contribution (red). The green line shows the total modeled noise amplitude (sum of the two components). Green opened square corresponds to (g_m/I_DS)² in the right-sided y axis. (b), (d), (f), (h), and (j): Contact and channel components of the resistance-noise-power density and resistance for ${\mathrm{Mo}\mathrm{Se}}_2$ FET, obtained from measurements using procedure described in text. Blue area represents “transition regime” in which channel dominates noise, but contact/access regions dominate resistance. (a), (b) for 3L, (c), (d) for 5L, (e), (f) for 8L, (g), (h) for 10L, and (i), (j) for 20L.

Figure 10

The noise amplitudes $f\times S_I/I_{DS}^2$ and (g_m/I_DS)² as a function of overdrive voltage in 3L ${\mathrm{Mo}\mathrm{Se}}_2$ FETs. Pink, orange, and black circles represent the noise amplitude of L_ch.= 0.5, 1, and 1.9 µm, respectively. The blue (red) dashed line indicates the model fitting for the noise in the channel (contact) regime. Green opened square corresponds to (g_m/I_DS)². Arrows indicate the appropriate axis.

Figure 11

The noise parameter $(\mathrm{Area}\times S_I/I_{DS}^2)$ as a function of overdrive voltage in (a) 3L and (b) 8L ${\mathrm{Mo}\mathrm{Se}}_2$ FETs. Black circle, red square, and blue triangle represent the noise parameters of L_ch= 0.5 µm (0.5 µm), 1 µm (1 µm), and 1.9 µm (2 µm) in 3L (8L) ${\mathrm{Mo}\mathrm{Se}}_2$ FETs, respectively.