Relation between film thickness and surface doping of MoS₂ based field effect transistors

Molybdenum disulfide (MoS₂), a representative member of the transition metal dichalcogenides family, continues to attract attention. In this material, the two-dimensional layers are bonded by weak van der Waals forces allowing easy separation into ultra-thin films without inducing dangling bonds. Given these properties and its semiconductive nature, MoS₂ has demonstrated to be of interest for applications ranging from low power logic devices, spintronic, valleytronic up to photo-voltaic devices.^1–5 Nevertheless, MoS₂ based devices still face several challenges that need to be addressed. One of the major problems is the limited control of the MoS₂ film doping. By doping the MoS₂ film, the sheet resistance (R_SH) can be reduced, thereby reducing the contact resistance (R_C) to metals. Moreover, doping is also of interest for creating p-n junctions and to tune MoS₂ superconductivity.^6,7

Several strategies have been studied for the doping of MoS₂ films. Among them, substitutional doping and surface doping are the most interesting routes. In substitutional doping, sulphur atoms of the MoS₂ layers are replaced by the dopant atoms. According to the type of doping required, dopants with excess or deficit of electrons can be employed.^6,8–11 However, replacing the atoms induces damage to the MoS₂ lattice, causing an increase in carrier scattering and hence reduced mobility. On the other hand, in the case of surface doping, the dopant is physically adsorbed on the surface of the film without disrupting the MoS₂ lattice. Doping thus takes place through a combination of the partial charge transfer and interaction of the dipoles of the adsorbate molecules with the MoS₂ film.^12–16 In this manner, the carrier concentration is increased without greatly affecting the carrier mobility. The effect of film thickness on the subthreshold swing has been previously reported for Nb substitutionally doped MoS₂ devices where a constant dopant distribution across the MoS₂ film was assumed.⁹ Nevertheless, for surface doping, the dopant is adsorbed on the surface of the film. and thus the distribution of the added carriers in the MoS₂ film will greatly depend also on the thickness. For that reason, the effect of doping induced by the adsorbate on different MoS₂ film thicknesses need to be understood, in order to identify the optimal thickness for improved electrical performance.

In this work, we built 4-probe devices with MoS₂ films of different thicknesses and systematically characterized them before and after surface doping. The results are then analyzed by comparing the carrier mobility with the ratio between the on drain current and the off drain current (I_ON/OFF) before and after doping the devices. Finally, the observed behavior is corroborated using a semi-classical model, and the optimal thickness for the surface doped devices is identified.

MoS₂ flakes were mechanically exfoliated and transferred to Si substrates covered with 20 nm SiO₂. The thickness of the flakes was evaluated using atomic force microscopy (AFM), and three flakes with thicknesses (t_sc) of 3.6 nm, 5.0 nm, and 8.5 nm were used to build 4-probe back gated field effect transistors (FETs). 20 nm of Ni with 30 nm of Au was used as metal contacts. The devices were then electrically characterized in a N₂ atmosphere to reduce the known impact of water and air exposure.¹⁷ A potential difference (⁠$VDS=1$ V) was applied between the source (S) and the drain (D) of the devices, and the current flowing through the drain (⁠$ID$⁠) was measured as a function of the applied gate potential (⁠$VGS$⁠). this, a potential difference (V_DS = 1 V) between the source (S) and the drain (D) of the devices and measuring the current flowing through the drain (I_D) as a function of the applied gate potential (V_GS). The potential drop across the probes P1 and P2 (V_CH) was measured to extract the potential drop in the channel without the contact effect. A sketch of the characterization structure and biasing conditions that were used can be seen in the inset of Fig. 1. After the as-built devices were characterized, they were functionalized with poly(vinyl-alcohol) (PVA) by submerging the samples for 1 h in 1% PVA solution of water and then spun at 2000 rpm for 45 s to form a thin film. Annealing for 30 $min$ at 90 °C inside a N₂ atmosphere dehydrated the film. The samples were then electrically characterized in the same fashion as previously described. The resulting transfer characteristics for the device with t_sc = 3.6 nm before and after doping with PVA are shown in Fig. 1.

Subthreshold swing (SS), mobility (μ_FE), and 2D carrier concentration (n₀) at V_GS = 0 V were extracted for the devices. SS was extracted as $SS=dVGS/d[log(ID)]$ from the first three decades of the subthreshold regime of the device. For μ_FE and n₀, first the sheet conductance of the device was obtained as $GSH=(ID/VCH)×(LCH/WCH)$⁠. Then the mobility was obtained as $μ=1/COX×dGSH/dVGS$⁠, where C_OX is the gate oxide capacitance from parallel plate capacitance. The 2D carrier concentration was then obtained as n₀ = G_SH/(qμ) at $VGS$ = 0 V, where q represents the electron charge. The extracted parameters can be seen in Table I.

PVA has been demonstrated previously to be an effective n-dopant.¹⁸ This is clearly manifested in the increase of the on current in Fig. 1 after doping and the increase of n₀ after doping by an average of 2.4 $×1012$ cm⁻² with a standard deviation of 0.6 $×1012$ cm⁻² among the three devices (Table I). This increase in the carrier concentration is a result of the charge transfer from the PVA to the MoS₂ film given the low electron affinity of electrons in PVA as compared to MoS₂.¹⁹ It is also important to notice that no current is expected to flow through the PVA layer. As expected, the doping does not degrade the mobility of the device but rather increases it. This can be explained by both, Coulomb impurity screening and surface optical phonon quenching as observed previously.¹⁸ 

As a result of the increase in carrier concentration and mobility, an increase in the on state current by a factor of 1.75 and 1.82 (for the same gate over-drive voltage before and after doping) was observed for the devices with t_sc = 3.6 nm and 5.0 nm. This increase is in agreement with previously reported enhancements from PVA doping for films of similar thickness. Nevertheless, for the device with the thick film (t_sc = 8.5 nm), the improvement is reduced to a factor of 1.5. This can be understood from the fact that for this technique, the dopant induces carriers on the surface, and thus the doping effect will have a finite extension inside the MoS₂ layer. In thinner films, the doping increases the carrier density along the complete film thickness including the region where the current flows. However, for thicker films, the induced carriers will only affect a portion of the thickness region. Furthermore, the I_ON/OFF ratio (for the same V_GS window) of the devices decreases as the MoS₂ film gets thicker (Fig. 2). Before doping, the gradual degradation in the I_ON/OFF ratio with increased film thickness can be explained by the reduction in the electrostatic control of the gate over the channel. This is also corroborated by the monotonic increase of the subthreshold swing for the devices as the thickness increases. However, after the PVA doping, a steep decrease is observed from the device with t_sc = 3.6 nm to the device with 5.0 nm. Interestingly, between the devices with the film thicknesses of 5.0 nm and 8.5 nm, almost no difference in the I_ON/OFF ratio was observed. In order to better understand these observations, the spatial distribution of the induced carriers inside the MoS₂ film is of great interest.

For this purpose, a semi-classical model was used to simulate the device with t_sc = 3.6 nm and 8.5 nm. For the model, the same 2D geometry depicted in the inset of Fig. 1 was implemented using Sentaurus Structure Editor$Ⓡ$⁠, while the electrical simulations were carried out using Sentaurus Device$Ⓡ$⁠. In order to compute the electrostatics for the MoS₂ film, a two-dimensional effective density of states (2D-DOS) was used for the semiconductive slab in place of a three-dimensional DOS. Additionally, field-emission and thermionic assisted field emission of the electron in the Metal/MoS₂ interface was modeled using a non-local tunneling model and Schottky barrier boundaries conditions.²⁰ The model is tuned with the parameters extracted for the undoped devices as shown in Table I. Additionally, the effective Schottky barrier height for the Ni/MoS₂ interface was taken to be 0.3 eV,^20,21 and the density of interface states was varied till a good fit was obtained with the subthreshold transfer characteristics of the measured devices.

First, the undoped devices were simulated and then the effect of the PVA doping was introduced by positioning a 2D charge layer at the interface between the MoS₂ film and the vacuum for both the devices. A charge density of 2.4 $×1012$ cm⁻² as experimentally observed for the doped devices was used for the 2D charge layer. Additionally, the mobility for the devices after doping was also modified according to the experimentally extracted values. In Fig. 1, the solid lines represent the results of the simulated transfer characteristics for the device with t_sc = 3.6 nm. A very good agreement between the simulated and experimental transfer characteristics was observed, for both, the device before and after PVA doping.

Figure 3 shows the surface plot of the carrier density in the channel cross section for both devices (t_sc = 3.6 nm and 8.5 nm) after doping. The biasing conditions were V_GS = 0 V and V_DS = 1 V. Clearly, for the 3.6 nm thick device, the PVA induced charge is distributed across the complete film and the 3D carrier concentration is very high (about 1 $×1020$ cm⁻³). On the other hand, for the 8.5 nm thick MoS₂ film, the carriers are accumulated mostly at the top of the film near the PVA/MoS₂ interface and away from the MoS₂/SiO₂ interface. Thus, in the thicker films, it will be more difficult for the gate to deplete the charges induced by the PVA. This explains the strong decrease in the I_ON/OFF ratio for thick devices after doping. Additionally, the band diagram and carrier concentration across the channel (cross section A in Fig. 3) are shown in Fig. 4. For the device with t_sc = 3.6 nm [Fig. 4(a)], the conduction band is overpassed by the quasi-Fermi level energy (ϕ_Fe) at the PVA/MoS₂ interface (Y = −3.6 nm) indicating a highly doped semiconductor. Interestingly, after doping, the conduction band across the MoS₂ film is closer to the ϕ_Fe than that of the undoped device, indicating the presence of doping effect through the complete film. Additionally, when a negative potential is applied to the gate (V_GS = −3 V), the complete channel is depleted, and the conduction band is farther from the ϕ_Fe than the undoped device. These changes in the band diagrams are manifested in the carrier concentration (n_2D) distribution along the thickness of the film. Clearly, a rather uniform increase in carrier density is observed after doping with PVA across the complete film, and this charge is successfully depleted when a negative potential is applied to the gate, to levels below the initial state (before PVA functionalization). In contrast, for the device with t_sc = 8.5 nm, even though after doping the conduction band reaches its minimum at the PVA interface, it does not remain lower than the level of the conduction band before doping, throughout the whole film. At about 5.2 nm from the PVA interface (Y = −3.3 nm), the level of the conduction band before and after doping is the same. This indicates the penetration depth of carriers induced by the PVA film. Moreover, after applying a negative potential in the gate (V_GS = −3 V), only the charge close to the MoS₂/SiO₂ interface (Y = 0 nm) is depleted, while a great amount of free carriers still remain in the region close to the PVA/MoS₂ interface (Y = −8.5 nm).

The results of this semi-classical simulations support the experimental observation seen in Fig. 2. From the carrier concentration before and after doping, shown in Fig. 4(b), it is seen that the penetration length of the carriers induced by the PVA on the surface of the MoS₂ film will be approximately 5.2 nm. Thus, for thicker films, the 1% PVA surface functionalization will only increase carriers in the first 5.2 nm and not the complete channel as is the case for films thinner than 5.2 nm. Moreover, in the film with t_sc = 3.6 nm, given the proximity of PVA induced charges to the MoS₂/SiO₂ interface, it is easier for the gate stack to deplete the charges when a negative potential is applied. In contrast, for thick films (t_sc = 5.0 nm and 8.5 nm), the induced charges will be farther from the MoS₂/SiO₂ interface, and thus it will be much more difficult to deplete the charges.

In summary, we demonstrate the effect of the surface dopant for different MoS₂ film thicknesses. The film thickness will affect both the electrostatic control of the device and the overall performance enhancement of the ON state of the device. The thinner the semiconductor film, the more uniform will be the dopant induced charge in the channel. For thick films, the increase in the carrier concentration will be limited to the first 5.2 nm near the PVA/MoS₂ interface. Additionally, for thicker films, the induced charge will be farther from the gate stack, and thus less electrostatic control will make turning off the device more difficult. For the case of thin devices, even if the film is heavily doped, the depletion of the charge by a negative gate potential can be achieved due to the closeness of the induced charge to the gate that allows for better electrostatic control.

See supplementary material for transfer characteristics of additional devices and a control device to demonstrate effect of doping from PVA and not from humidity.

The authors thank N. Pinna, K. Baumans, and J. De Cooman for their technical work and the Beyond CMOS program at imec for financial support.