Ever since the prospect of single gas molecule detection was first discussed with a graphene device (Schedin et al., 2007), whose high sensitivity was partially attributed to the surface nature of graphene exposing its whole volume to the gas molecule adsorbates, a gamut of 2D materials have been examined for gas sensor applications. In particular, transition metal dichalcogenides (TMDCs) have proven to be among the best materials for 2D gas sensor applications because of their tunable electronic properties and high sensitivity at room temperature (He et al., 2012; Late et al., 2014; Ko et al., 2016; Shokri and Salami, 2016; Yang et al., 2017; Pandey et al., 2020). When exposed to the target gas, a TMDC gas sensor responds to the adsorption of target gas molecules by changing its electrical conductivity. Based on the results of Hall measurements (Schedin et al., 2007), photoluminescence (PL) spectroscopy (Mouri et al., 2013; Cho et al., 2015a; Wang et al., 2019), and theoretical considerations (Leenaerts et al., 2008; Wehling et al., 2008), the molecular gas adsorption was recognized as inducing charge transfer on TMDC and modulating the charge carrier density on the 2D device. Depending on whether the electrical conductivity of the 2D sensor was increasing or decreasing, the target gas molecule would be categorized as carrier-donating or -compensating.

Experimental studies of TMDC gas sensor devices often compare the sensitivity of the device to various kinds of gas molecules, where the sensitivity is defined as the change in electrical resistance upon gas sensing, normalized to the default resistance of the device in dry air (Cho et al., 2015a; Cho et al., 2015b; Hau et al., 2021). The dry air normalization is specifically used to reduce the amount of chemical doping from redox reactions involving water vapor. The reported sensitivity involves a significant degree of reversibility correlated with the partial pressure of the target gas molecules in the gas environment. This reversibility indicates that a corresponding amount of carrier doping is induced by the physisorption of gas molecules that readily desorb upon a decrease in the partial pressure of the target gas molecules in the air.

The most frequently targeted gas molecules in TMDC gas sensor studies are nitrogen dioxide (NO₂) and ammonia (NH₃) as they are the representative p-type and n-type molecular dopants. It has consistently been reported in the experimental literature that the sensitivity of TMDC gas sensors toward NO₂ is an order of magnitude higher than for NH₃, which holds true for both n-type and p-type TMDC devices (Cho et al., 2015a, Cho et al., 2015b; Hau et al., 2021). This means that the charge carrier density in the TMDC gas sensor is much more strongly affected by the presence of NO₂ than NH₃ in the gas environment under the same partial pressure. From this, it may be concluded that NO₂ should be a dopant with a superior efficiency compared to NH₃ and other gas molecules. However, the concept of doping efficiency as used previously is rather vague because correlating the experimentally measurable sensitivity with the partial pressure of target gas molecule in the environment involves multiple processes such as molecular adsorption and charge-state transition. In the following section, we discuss the processes involved in molecular doping and introduce counter charge cluster localization, which has been seldom mentioned in the literature, despite the fact that it can potentially affect doping efficiency.

The first event that must occur in the sensing process is the adsorption of gas molecules onto the exposed TMDC surface. The adsorption energy is the thermodynamic observable estimating the surface density of target gas molecules at equilibrium. Gas molecules with lower adsorption energy would have a greater chance of affecting the electronic properties of TMDC if the number of carriers donated or compensated positively correlated with the surface density of the gas molecules. Theoretical studies of gas molecule physisorption, however, found only nonsignificant differences (less than 10 meV) in the adsorption energies of NO₂ and NH₃ on TMDC (Yue et al., 2013). Therefore, the adsorption energy alone cannot be the main cause of the large differences in sensitivity of a TMDC sensor toward NO₂ and NH₃.

In analyzing doping efficiency, we need to measure more than the surface coverage of molecular adsorbates because not all the adsorbates are activated as dopants. The dopant activation process after adsorption results in charge transfer, for which there exist multiple plausible scenarios. The so-called chemical doping occurs especially at chemically heterogeneous reactive sites of structural defects and edges of TMDC. Integer charge transfer results from redox reactions involving not only the target gas molecule and TMDC but also ambient molecules of nitrogen, oxygen, and water (Li et al., 2017; Zhao et al., 2018). Such redox reactions are strongly dependent on ambient temperature and result in charge distribution near defects and edges, producing regions of carrier depletion and double-layer potential (Gautam et al., 2021). The other viable scenario of charge transfer involves physisorption of gas molecules, which is of our interest in this report. In this case, the so-called standard model of molecular doping examines the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of gas molecules relative to the Fermi level or work function of the hosting TMDC (Peng and Cho, 2000; Wehling et al., 2008; Park et al., 2019). If the LUMO of the gas molecules is lower than the Fermi level of hosting TMDC, the molecular gas adsorbate accepts electrons from TMDC. If the HOMO is higher than the Fermi level, the gas molecules become donors of electrons to TMDC. In essence, this model follows the Schottky–Mott rule of interface band bending, which interprets electron transfer as a transport phenomenon allowing two distinct bodies of electron distribution in contact to reach equilibrium (Zhang and Yates, 2012). As this charge transfer process involves the Fermi level as an electron reservoir, the efficiency of gas molecular doping becomes a function of the Fermi level.

For conventional inorganic semiconductors where the conduction is predominantly band conduction via delocalized conduction band or the valence band, thermodynamic stability analyses of dopants at various charge states are routinely performed to address the efficiency of the dopant, such as whether it is a shallow or deep donor (Van de Walle and Neugebauer, 2004; Freysoldt et al., 2014; Alkauskas et al., 2016). However, the charged dopant stability analysis is not as frequently utilized for molecular doping of 2D materials, partly because our understanding of the conduction mechanism in TMDC gas sensors is still developing. It should be noted that electrons or holes transferred to the Fermi level of TMDC are not necessarily free-charge carriers if the Fermi level exists within the localized gap states. When the transferred charges are near the Fermi level but away from delocalized bands, they still conduct electricity via ‘hopping’ conduction (Shklovskii and Efros, 1984). In fact, this variable range hopping was reported as the governing conduction mechanism of TMDC thin films when the temperature was lower than room temperature (Qiu et al., 2013; Xue et al., 2019). Even near room temperature, the variable range hopping remained as the major channel of conduction in various 2D material thin films (Negishi et al., 2014; Kovtun et al., 2021). Considering the semi-crystalline quality of TMDC materials often adopted for gas sensor applications and research, it is plausible to assume that electrical conduction occurs through the multi-channel type of band conduction and hopping conduction, where the hopping conduction channel is rather predominant.

As outlined so far, the molecular doping of charge carriers and conduction in 2D material thin films are multifaceted phenomena. The outstanding experimental challenge preventing quantitative analysis lies in identifying the several physically distinguishable mechanisms simultaneously participating in charge transfer. Nevertheless, we can attest phenomenologically that the charge transfer between the gas molecular adsorbate and the hosting 2D material results in involves charge carriers conducting electricity along with the counter charges of the donated carriers localized upon the gas molecular adsorbate. As it is localized, the counter charge left on the adsorbate does not participate in the conduction. If anything, it would more likely hamper the mobility of the free carriers through coulomb scattering. Coulomb interactions between the free carrier and localized counter charges will affect the separation and recombination between them as well. However, as the subject of counter charge distribution has rarely been studied for molecular dopants, our understanding of how this would affect the efficiency of carrier doping is limited. As a side note, for polymer semiconductors, the effect of counter-ion size on delocalization of carriers was studied, although the subject was not the distribution of counter charges but the physical size of the counter-ions (Thomas et al., 2020).

The counter charge distribution upon charge carrier donation was first studied for conventional inorganic semiconductors, providing valuable insights toward overall understanding of carrier donation with unexpected findings (Schwingenschlögl et al., 2010). For carrier doping of conventional semiconductors of silicon and diamond, group III and group IV elements often substitute the host element to compensate or donate electrons. From the theoretical analysis of counter charge distribution upon carrier doping, it was found that the carrier donation was not executed solely by the dopant element but by the cluster of atoms composed of the dopant and nearby host atoms (Schwingenschlögl et al., 2010; 2011; Smith et al., 2017).

The additional physical understanding provided by the cluster formation model distinguishes two different types of charge transfer associated with dopant–host interaction. For the example of silicon doping using arsenic, as we look into the charge distribution between arsenic atoms and nearby silicon atoms, the electron distribution is shifted away from silicon toward arsenic because arsenic has stronger electronegativity than silicon. However, in terms of carrier doping properties, arsenic is an n-type dopant donating an electron to the silicon lattice, which contradicts the direction of charge transfer based on strength of electronegativity. The cluster formation model of carrier doping resolved this apparent inconsistency, when it was found that the electron carrier was donated to the silicon lattice not by the arsenic atom alone but by a cluster of atoms including arsenic and nearby silicon atoms. Therefore, we note two distinguishable and uncorrelated charge transfers: a local charge transfer within a cluster with electrons shifting toward arsenic from silicon and a charge transfer as carrier doping between the arsenic cluster and the silicon lattice, wherein an electron moves from the arsenic cluster to the silicon lattice.

In this paper, we describe the nature of the charge transfer between a gas molecular adsorbate and 2D TMDC material based on the counter charge cluster formation model and density functional theory. Our system of interest is 2D molybdenum disulfide (MoS₂) as the archetypal TMDC along with ammonia (-NH₃) and nitrogen dioxide (-NO₂) as the representative molecular dopants of opposing doping property. As we addressed the differences between NO₂ and NH₃ as molecular dopants, we directed our attention not to the donated charge carrier but rather to the counter charges left localized on the molecular dopant. Unlike the donated charge carrier whose spatio-temporal property keeps varying as it transports, the counter charge distribution left on the molecular dopant would be essentially constant, as long as other charge carriers were not nearby. As discussed in the following sections, the counter charge cluster formation analysis upon carrier doping by molecular dopants allowed us to determine the drastically different activities of NO₂ and NH₃. NO₂ molecular adsorbates, upon donation of a hole, form a tightly localized cluster of counter charges centered around a NO₂ molecule. On the contrary, the counter charge cluster formed by NH₃ upon electron donation is only semi-localized and exhibits a dimension that is not well defined. The implication of such a qualitative difference on the doping efficiency is conjectured and discussed.

To investigate the charge distribution in the gas molecular adsorbate complex, we used the Vienna ab initio simulation package (VASP) for the density functional theory (DFT) calculations (Hafner, 2008). Along with the exchange-correlation kernel of Perdew–Burke–Ernzerhof revised for solids (PBEsol), the projector augmented wave (PAW) pseudo-potentials for molybdenum (Mo) and sulfur(S) were adopted (Blöchl, 1994; Csonka et al., 2009). In this context, the electronic band gap energy of MoS₂ as the difference between the valence band maximum (VBM) and the conduction band minimum (CBM) in the ground state band structure was calculated to be 1.28 eV for the bilayer with a separation distance of 6.14 Å. Additional Bader charge analysis was also performed to attribute the electron distribution to each atomic and molecular entity (Tang et al., 2009). As Bader charge analysis utilizes the gradient of charge distribution, which is grid-based in VASP, a high-resolution grid between elements is necessary in charge-density calculations to reduce errors in Bader analyses. For the high-resolution grid, VASP calculations were performed with the ‘Accurate’ setting for PREC and the energy cutoff set to 420 eV, which is 1.5 times the energy cutoff used for the molybdenum pseudo-potential, to convert the charge density on gas molecules with significant figures down to two decimal places of fundamental charge.

Figure 1 shows the ground state configurations of gas molecular physisorption widely studied and reported for MoS₂ gas sensing devices. The NO₂ and NH₃ molecules are characterized as hole donors and electron donors, respectively. Such gas molecular adsorbates affect the trion peaks of photoluminescence (Tongay et al., 2013; Cho et al., 2015a), indicating variations in the carrier density. The configurations shown in Figure 1 were used to calculate the charge distribution. For charged systems, the periodic image charge interaction should affect the charge cluster confinement. Therefore, four different values of the supercell lattice constant (L) were used to address the system size dependency of charge distribution, as with L = 4a, 8a, 12a, 16a where a = 3.20 Å is the lattice constant of the MoS₂ unit cell.

The charge distribution was calculated before and after carrier donation (Schwingenschlögl et al., 2010; 2011; Smith et al., 2017). The charge transfer before carrier donation occurred locally in the dopant complex, a region of adsorbate and nearby host elements. A weak hybridization between nearby molecular orbitals rearranges the electron distribution resulting in shifting of charges. The magnitude of such charge transfer is only fractional, however. More importantly, it does not contribute to electrical conduction because transferred charges are localized at the adsorbate complex. The charge state of the overall system remains neutral because no charge leaves the adsorbate and its surroundings. On the contrary, when charge transfer happens between the adsorbate complex and the electron reservoir of the system’s Fermi level, as in carrier donation, the adsorbate complex becomes counter charged. By analyzing the distribution of this counter charge in the adsorbate complex, we investigated the formation of the counter charge cluster.

It should be noted that our interest is in charge distribution only, not on the free energy of the charged system. Addressing free energy of the various charge states of a dopant system often assumes a single isolated dopant in an infinite host, which requires corrections of various supercell artifacts (Van de Walle and Neugebauer, 2004; Persson et al., 2005; Lany and Zunger, 2008; Freysoldt et al., 2009; 2014; Alkauskas et al., 2016). For 2D charged systems of slab and surfaces, the methodological consensus is still being sought after regarding the correction of even stronger coulomb self-interactions through a vacuum (Komsa and Pasquarello, 2013; Komsa et al., 2014; Freysoldt and Neugebauer, 2018; O’Hara et al., 2019; Rutter, 2021).

As outlined in the Introduction section, the molecular doping via gas molecular physisorption goes through processes of adsorption and charge-state transition. Adsorption is a local event, while the transition in the charge state of the adsorbate is a process depending on the Fermi level of the host. Each process is accompanied by charge transfers with different characteristics and magnitudes, which are discussed separately in the following sections.

Gas sensor devices based on two-dimensional layered transition metal dichalcogenides feature desirable properties such as high sensitivity and room temperature operation. The sensing mechanism is based on the change in charge carrier density upon gas molecular adsorption. MoS₂ gas sensors show an order of magnitude higher sensitivity toward NO₂ over NH₃ (Cho et al., 2015a; Hau et al., 2021). For the case of charge carrier doping from gas molecular physisorption, the counter charge cluster formation was investigated using density functional theory calculations of charge density. The standard doping model assumes a delocalized charge carrier with a localized counter charge at the dopant, which accords well with the p-type dopant molecule, NO₂. A quarter of an elemental charge is physically distributed on the NO₂ molecule, while the remaining portion of the elemental charge is distributed over the hosting MoS₂ within the counter charge cluster.

The nature of the positive counter charge clusters formed by NH₃ upon electron donation is very different. Although the distribution of the counter charge is centered around the NH₃ adsorbate, the cluster is only semi-localized and does not have a definite size. The amount of actual counter charge possessed by NH₃ molecules is actually negligible as most of the counter charge is assumed by host atoms in the cluster. Although the effect of counter charge distribution on carrier dynamics and doping has not been systematically studied, it is conjectured that the wider distribution of semi-localized counter charge may hamper the sensitivity of gas sensors by reducing the carrier mobility through an enhanced scattering cross section and also by promoting transient recombination with the delocalized carriers.