Role of Charge Traps in the Performance of Atomically-Thin Transistors

Transient currents in atomically thin MoTe$_2$ field-effect transistor are measured during cycles of pulses through the gate electrode. The transients are analyzed in light of a newly proposed model for charge trapping dynamics that renders a time-dependent change in threshold voltage the dominant effect on the channel hysteretic behavior over emission currents from the charge traps. The proposed model is expected to be instrumental in understanding the fundamental physics that governs the performance of atomically thin FETs and is applicable to the entire class of atomically thin-based devices. Hence, the model is vital to the intelligent design of fast and highly efficient opto-electronic devices.

The emerging family of atomically thin materials is fueling the development of conceptually new technologies 1 in highly-efficient optoelectronics 2,3 and photonic applications, 4 to name a few. The large variety of band gap values found in layered transition metal dichalcogenides (TMDC) 5,6 make these materials especially suited for transistor applications. TMDCs are compounds with the general formula MX 2 , where M is a transition metal, e.g. Mo and W, and X is an element of the chalcogen group, S, Se and Te. They appear in a layered structure where the metal forms a hexagonal plane and the chalcogenides are positioned over and under this plane in either a trigonal prismatic (2H), as shown in Fig. 1(a), or octahedral (1T) stacking configuration. 7 In the semiconducting 2H systems, the compounds show a transition from indirect band gap in bulk materials to direct band gap in single layers. 8 Single and few-layers TMDCs have been implemented in a wide range of applications, ranging from thin film transistors, 9 digital electronics and opto-electronics, 2,10,11 flexible electronics, 12 and up to energy conversion and storage devices. 13 However, the defect states in TMDCs have an ambivalent nature and can have a major positive or negative impact on the performance of atomically-thin devices. The presence of defects in photodetectors can be beneficial since it has been shown to immobilize charges at the channel which improves the gain in photodetectors 14 and produces non-volatile memory mechanisms. 15 On the other hand, large hysteresis caused, for example, by charge traps 2 and significant Schottky barriers 16 at the metal-semiconductor interface are still a major design challenge for the realisation of novel device architectures. They have been shown to cause degradation in the performance of transistors 17 and generate high levels of flicker noise. 18,19 To overcome these challenges, hysteresis is usually avoided by encapsulation 20,21 or operation under high-vacuum. 22,23 Most of the current research into surface states of TMDCs has focused on the chemical origins of charge trapping. A full understanding of their effect on the electrical properties is still lacking, hindering the optimization of functional components. While hysteresis has been shown to correlate with traps generated at the channel-dielectric interface and the channel-ambient interface, 24,25 little attention has been given to the mechanisms by which immobile charges affect the conduction characteristics of the devices, which is fundamentally different from those experienced in bulk devices.
In this communication we present the first study of the role of immobile charges on the electrical transport properties of atomically thin MoTe 2 . This TMDC is of particular interest since its direct band gap of 1eV 26,27 matches the wavelength of maximal solar emission intensity, thus making it a prime candidate for solar energy converters. MoTe 2 is intrinsically p-doped, but can exhibit ambipolar behavior, 26,28 mobility in the range of 10-30 cm 2 V −1 s −1 , 26,29 and on-off ratios of up to 10 6 . 29 A stringent quantitative analysis demonstrates that the role of trapped charges in the operation of MoTe 2 -based electronic components is a change in the threshold voltage of the field-effect transistor (FET), effectively modulating the resistivity of the entire channel. By repeating the charge capture and emission cycles in different drain biases we are able to distinguish between two sources of transient behavior in MoTe 2 -FETs. One transient is due to emission of charges from traps to the channel, and the other is due to time-dependent capacitive gating of the channel that produces a transient in the effective threshold voltage. Finally, we present a complete analytical model to support our observations. Our findings are applicable to the entire class of atomically thin-based devices and provide a thorough understanding of charge traps and carrier dynamics which is needed to facilitate the intelligent design of fast and highly efficient opto-electronic devices.
Few-layers MoTe 2 flakes were obtained by mechanical exfoliation of 2H-MoTe 2 bulk crystal (HQ graphene) onto highly doped silicon substrates, covered with 290 nm of high-quality thermally grown SiO 2 . The silicon substrate was used as a global back gate electrode, with the oxide layer acting as a gate dielectric. Standard electron beam lithography procedure was used to pattern electrodes and electrical leads. The contacts were then immediately metalized with 5 nm of Ti adhesion layer, and 50 nm of Au, using an electron beam evaporation system, working at very low pressure (∼ 10 −8 mbar) and at long working distance, to achieve high uniformity in the deposition. The devices were then annealed in dry Ar/H 2 environment at ambient pressure for 2 hours at 200 • C. Fig. 1(b) shows a schematic representation, not to scale, of the device and the circuit details. Atomic force microscopy measurements ( Fig. 1(c)), and optical contrast (not shown here) of the flakes confirm that the surface of MoTe 2 is not visibly contaminated and that the studied flakes consists of 4 number of layers.
Low noise electrical measurements were performed in a home-built Farady cage in the dark and in ambient conditions on more than five different devices, all showing a similar behavior. The drain electrode was biased using a low noise voltage source and the source electrode was kept grounded throughout the experiment. The current flowing through the source electrode was measured using a current preamplifier. An independent voltage source-meter was used to apply a bias to the gate electrode while measuring the leakage current. The response time of the system was found to be limited only by the minimal rise time of the preamplifier, which is < 5µs. (See Supporting Information) The electronic behavior of multiple devices was characterized by measuring their drain current vs.
voltage response (I ds -V ds ) and drain current vs. gate voltage transfer (I ds -V gs ) characteristics. Figure   2(a) shows the response curve of a typical MoTe 2 transistor. The curve exhibits a slight asymmetry with higher resistivity for negative applied drain bias, indicating that the metal-semiconductor contacts form a small Schottky barrier for holes. The origin of this asymmetry about V ds = 0V is in the different electrostatic potential seen by the source and drain electrodes. In the experiment the potential barrier at the MoTe 2 /source electrode interface is kept constant, as it is pinned by the gate. On the other hand, the biased drain barrier decreases (increases) in height with positive (negative) drain bias. 30 Despite the low Schottky barrier, both the linear and the log-scale of the response curve (inset in Fig 2(a)) show that the device is not rectifying and is, in fact, largely Ohmic in higher V ds values (see Supporting Information).
The device transfer characteristics are shown in Fig. 2(b), taken at V ds = 1V. The curve matches the expected behavior of an enhancement-mode p-channel transistor, showing an increase in drain current as the gate bias grows more negative beyond the threshold voltage (V th ). From the transfer curve, we can estimate the device mobility, µ p , and sub-threshold swing, SS. Using µ p = L(dI ds /dV gs )/(WC ox V ds ) in the linear regime of the curve, where L = 1µm and W = 3µm are the device length and width, respectively, and C ox = ε 0 ε r /d = 115µF m −2 is the gate dielectric capacitance, with ε 0 the vacuum permittivity and ε r the oxide relative permittivity, we find that the mobility is between 0.12 on the forward sweep and 0.14 cm 2 V −1 s −1 on the back sweep. From the sub-threshold part of the curve, we estimate a sub-threshold swing value of 4 V dec −1 using SS = d log 10 I d /dV g −1 . The low value of the mobility and the high value of the swing are indicative of the presence of mid-gap trap states. 14 .
In line with these findings, the gate sweep measurements also show a hysteretic behavior resulting in a shift in V th between the forward and backward sweeps, which changes the threshold voltage by about ∆Vth = −4V and the charge neutrality point by about −6V, see Fig. 2 To understand the physical origin of the observed changes in threshold voltage we use the well- capture process (d) when the channel is in the "off state" and "on state", respectively. E C , E V , E F , E T 1 and E T 2 are the conduction band minimum, the valance band maximum, the Fermi energy, the shallow midgap state and deep midgap state energy, respectively. known equation that describes V th in field-effect transistors: where Φ MS is the difference between the metal and semiconductor workfunctions when all the terminals are grounded, C ox is the gate dielectric capacitance, Q i is the static charge density within the dielectric, Q T is the trapped charge density at the interface between the dielectric and the conductive channel and ∆E F is the shift in the Fermi Energy, required to turn the transistor on. To gain insight on the dynamics of the charge traps, their effect on the transfer currents and their role in producing hysteretic cycles, we have monitored the transport characteristics while pulsing the gate electrode from "open" (more negative) to a "close" (more positive) value. The drain current was recorded over long periods of time (60-90 minutes) while the gate was repeatedly pulsed between V gs = −10V to open the channel and V gs = 0V to close it (Top panel in Fig. 3(a)). As the pulse on gate drives the channel from a close to an open state, a sudden rise of the current in the channel is measured followed by a fast decay. When the gate is pulsed back to the closed state, the current drops down and then slowly begins to recover. The decay in current in the open state is due to the capturing of holes in mid-gap traps that shifts the threshold voltage to a more negative value (red arrows in Fig.   2(d)), effectively closing the channel. On the other hand, the recovery in the off state is due to the holes that are emitted from the traps (blue arrow in Fig. 2(c)) shifting V th to a less negative value.
While the capture process is spontaneous and fast, the emission mechanism is thermally activated and, therefore, significantly slower then the capture rates.
Where W and L is the channel width and length, respectively, and µ p is the hole mobility. Since where all the time-independent quantities have been grouped in V th,sat for convenience. With the expression for V th (t) from Eq. 4, the expression for the transient current is readily obtained: The expression in Eq. 5 has one striking difference from the conventional expression for current transient (Eq. 2), it is linear with drain bias. Qualitatively, this is a simple manifestation of Ohm's law: as the resistance of the conductive channel changes with time, the current responds linearly, proportional to the applied bias.
In the emission segments of the gate-pulse experiment, we find that a significant increase in currents occurs on a very short time scales, while a further, slower increase is easily discernible in longer time scales. This behaviour cannot be satisfied by a single exponential fit but is in excellent agreement with adouble exponential rise equation in the form I(t) = I 0 + A 1 e −t/τ 1 + A 2 e −t/τ 2 (red line in Fig. 3(a)) suggesting that there are two types of traps 25 , a shallow trap and a deeper one, corresponding to emission coefficients τ 1 ≈ 250s and τ 2 ≈ 2, 900s. Fig. 3(b) shows the recovery currents, of charge trap spectroscopy, whether probed by temperature scans 35 or by optical means. 36 However, the added simplicity of our methodology means that it can be applied to a variety of materials and substrates, including those that are photo-active, or temperature sensitive.
Finally, we calculate the overall resistance of the device and find that the transient resistance operates in parallel to the saturation resistance: or R −1 = R −1 sat + R −1 trans which is a strong indication to the fact that both factors indeed stem from the channel itself. We note that the addition of series resistance to the circuit, such as contact resistance, does not affect the time-dependent characteristics of the model, as is discussed in details in the Supporting Information.
In conclusion, we have demonstrated a new approach to the analysis of charge trapping and transient response of TMDC-based FETs, which paves the way to a better understanding of the role of mid-gap state in the operation novel devices. Using a simple two terminal model system, we were able to distinguish between currents associated with the emission of trapped charges into the circuit and currents that evolve in time due to the changes in effective threshold voltage across the channel.
The mechanism of threshold voltage transients which we study and model is not limited to MoTe 2 but it is valid to any device based on atomically thin materials. Indeed, as long as the channel depth is much smaller than the Debye screening length, the threshold voltage will be strongly modulated by the formation of space charge regions at both the semiconductor-dielectric and -ambient interfaces.
Our model, which describes the basic physics that govern the hysteretic characteristics of atomically thin FETs, is instrumental for the design of defect-based devices, such as photodetectors and memory devices, as well as provides a new methodology to study the nature of these defects. Additional Results

MoTe 2 transfer and transient curves
The transfer curves, I ds -V gs of two additional devices are shown in Fig. S1(a) and (b). The curves show that different devices, with different resistance and quantitative gate responses show a similar qualitative behavior. For the device shown in Fig. S1(a), the mobility is 0.04 cm 2 V −1 s −1 and the sub-threshold swing is ∼ 13 V dec −1 , whereas the device in Fig. S1(b) has a mobility of 0.15 In contrast, the transient curves shown in Fig. S1 (b) and (c) are of devices with higher resistivity than that of the device discussed in the main text, as is evident from the lower currents. While in these devices, the linear trend (Fig. S1 (e) and (f)) is visible from V ds = 0.2 V onwards, the shape of the transient curves in Fig S1 (b) is quite different from those of the other reported devices. From the analysis, we find that the emission currents from the shallow traps happen at time constants, τ 1 ≈ 0.4 s, much smaller than the other reported devices, where τ 1 is in the order of a few tens of seconds.
We can, therefore, conclude that in this device, the contribution of the emission currents from the shallow traps were negligible, eliminating the initial (fast) recovery, and thus changing the shape of the transient curves. The rate of capturing holes from the valance band (R hc ) is proportional to the density of holes in the valance band (p) and the density of unoccupied traps (N T − p T ), where N T is the total density of trapping states and p T is the density of occupied states. It's important to note here that "unoccupied" from holes means occupied by electrons and electrically neutral.
Where c p is the capture coefficient for holes, and it equals the thermal velocity, v th , multiplied by the capture cross section, σ p .
The emission of holes from the traps is described using same considerations without taking into account the unoccupied states in the valance band, since it is assumed that for a non-degenerate semiconductor the emission rate is not limited by it.
Where e p is the emission rate of holes from traps to the valance band. It is therefore clear, that the total change in trap occupation is given by: With the traps saturated we can write N T = p T and the capture rate will become zero.
In a simple process where every hole added to the valance band is removed from a trap (i.e. without any further charge injection), it is clear that: Combining Eq. 11 with Eq. 10 yields Where τ = 1/e p is the decay constant per trap, and p T (0) = N T is the trap occupation at the saturation point.
In the classical case, where the entire contribution to the current transient is from charges that are emitted from the traps back into the circuit, the current transient is given by I(t) = I 0 + qR p A, Where I 0 is the steady state current, and A is the area from which charges are emitted. Using Eq. 12, one can write an explicit expression for the current transient Where I d is the drain current, W and L are the channel width and length, respectively, µ p is the mobility of the holes, C ox is the capacitance of the gate dielectric, and V th and V g are the FET threshold voltage for conduction and the gate bias, respectively. The threshold voltage is given by Where Φ MS is the difference in workfunction between the gate electrode and the conduction channel and Q T (t) = (Q 0 + qp T (t)) accounts for both the stationary charges in the oxide (Q 0 ) and the dynamic charges that are trapped and de-trapped on the channel. It is important to note here that in contrast to a conventional inversion-based FET, the MoTe 2 is an accumulation-based transistor. Therefore, the "textbook" 2φ F expression for strong inversion has been substituted here for a general ∆E F which represent the change in Fermi energy required to "open" the channel. From this equation, one can easily write an expression to describe the dynamics of the threshold voltage Using a simple model for the concentration of free charge carriers p(t) = C ox (V th (t) − V g ) /q, it's easy to see that charge is conserved in this model, p = p 0 − p T , where p 0 is the total density of holes in the valance band in equilibrium conditions and without traps, and is constant. Using the previously found expression for the emission rate, we can now write an expression for the timedependent threshold voltage Where on the right hand side, all the terms that are time-independent were grouped together into V th,sat The current then becomes Finally, to account for the case where the a resistance in series (e.g., contact resistance) plays an important role in the device performance, we add a constant resistance term, R S to Eq. 14: From this equation, we can easily isolate the current term: Which is still linear with V d , in accordance with Ohm's law. The importance of this result is clear when we examine the limits where the contact resistance is much larger than the channel resistance, i.e., when R S In this limit, the current simply reduces to I d = V d R −1 S which is time-independent. On the other limit, R S , Eq. 20 simply reduces back to Eq. 14. The dominant time-dependent characteristics of the emission currents are therefore a strong indication that the major contribution to the transient profile stems from the timedependent changes in the channel resistance.