Ultrahigh sensitivity and layer-dependent sensing performance of phosphorene-based gas sensors

Two-dimensional (2D) layered materials have attracted significant attention for device applications because of their unique structures and outstanding properties. Here, a field-effect transistor (FET) sensor device is fabricated based on 2D phosphorene nanosheets (PNSs). The PNS sensor exhibits an ultrahigh sensitivity to NO2 in dry air and the sensitivity is dependent on its thickness. A maximum response is observed for 4.8-nm-thick PNS, with a sensitivity up to 190% at 20 parts per billion (p.p.b.) at room temperature. First-principles calculations combined with the statistical thermodynamics modelling predict that the adsorption density is ∼1015 cm−2 for the 4.8-nm-thick PNS when exposed to 20 p.p.b. NO2 at 300 K. Our sensitivity modelling further suggests that the dependence of sensitivity on the PNS thickness is dictated by the band gap for thinner sheets (<10 nm) and by the effective thickness on gas adsorption for thicker sheets (>10 nm).


Supplementary Note 1
To quantify the mobility degradation, we extracted the field-effect mobilities from the FET curves of a 6-nm PNS sensor before and after 10-min exposure against NO 2 in concentrations of 50 and 100 ppb ( Supplementary Fig. 6). Clearly, the field-effect carrier mobility in air 1.3 cm 2 V -1 s -1 only slightly degraded to 1.1 cm 2 V -1 s -1 upon exposure to 50 ppb NO 2 . However, it greatly reduced to 0.6 cm 2 V -1 s -1 when the gas concentration increased to 100 ppb NO 2 , implying the transition from the high-sensitive mode to the low-sensitive mode. Note that the critical gas concentration for the transition from the high-sensitive mode to the low-sensitive mode is dependent on the PNS thickness. For example, this critical gas concentration for the 6 nm PNS sensor is very similar to those of thicker films (cf. supplementary Fig. 5 for the 40 nm PNS and bulk BP) and is lower than that (~200 ppb) of the 4.8 nm PNS sensor. This is because the band gap difference (~ 0.2 eV) between 6 nm and 40 nm PNS is smaller than that (~ 0.4 eV) between 4.8 nm and 6 nm PNS 7 . Therefore, the critical gas concentration for the mode transition for the 6 nm PNS sensor is closer to that for the 40 nm PNS than that for the 4.8 nm PNS (as also shown in Fig. 5a that films with a smaller band gap will have a larger gas adsorption density upon exposure to the same gas concentration).
Note that the carrier mobilities in the supplementary E gas +E P -E gas+P where E gas , E P and E gas+P are the energies of a single gas molecule, pure phosphorene, and the complex system, respectively.

Supplementary Note 3
The phosphorus atoms form the sp 3 -like bonding, but with one dangling bond that could interact weakly with its nearest neighbors due to the puckered honeycomb structure. In contrast to the sp 2 bonding in graphene, which has only one extra electron in the p z orbital that forms the π bond responsible for NO 2 adsorption, electrons of the primitive s and p x , p y , and p z orbitals in the one dangling sp 3 orbital equivalent to one electron are also available for attracting NO 2 molecules. In other words, there are about two extra effective electrons in each phosphorus atom compared with one effective electron in each aromatic carbon atom that interacts with the NO 2 molecule.
This can also be seen by the atomic orbital-resolved density of states in Supplementary Fig. 10, in which s, p x , p y , and p z orbitals show the similar shape (i.e., suggesting the orbital hybridization), but the p z orbital is mostly populated by the charge associated with bands close to the Fermi level.

Supplementary methods
In semiconductors, the electron and hole concentrations are Here, = − is the band gap, and is the intrinsic Fermi level.
The conductivity of a semiconductor is where e is the elementary charge and ( ) is the electron (hole) mobility. We define the conductivity ratio from the electron and hole part as, for n-type or p-type semiconductors. Note that in the supplementary Eq. (5), we assume ≈ for simplicity and the difference between them is mostly less than one order of magnitude. For specific materials, this difference can be considered for better accuracy. After the following algebra, = → = and thus = ( ) = → =( ) , we obtain and for the n-type and p-type semiconductors with Fermi level and , respectively.
In conductance based gas sensors, the sensitivity for n-or p-type semiconductors is defined as where and are the conductance before and after the target gas adsorption. For low gas concentrations, the gas adsorption density is small and the gas distribution is so sparse that the gas adsorption induced scattering effect on the carrier mobility can be neglected (i.e., ≈ and ≈ ). Therefore, the supplementary Eq. (8) is then reduced to = For n-type or p-type semiconductors, ≫ or ≫ holds and thus, In a compact form, the supplementary Eq. (10) can be reformulated as Here, is charge transfer per planar unit area in the 2D film that can be determined with the knowledge of gas adsorption density (cf. Eqs. (2) and (3) in the main text) and is the film thickness.
Since the sensitivity is dependent on the PNS thickness, the sensitivity ratio can be formulated as Here is the charge transfer of the individual gas molecules. As the band gap of PNS decreases when the PNS thickness increases (especially from monolayer up to ~10 nm, then barely changes and keeps constant at the bulk value ), we divide the PNS into the thin (0.5-10 nm) and thick (>10 nm) regions. In the thin region, the carrier mobility is also thickness dependent due to the scattering effect from the substrate impurities. Eq. (2) in the main text is adopted to evaluate the gas adsorption density, and therefore ( ) For the thick PNS, as the band gap barely changes, which also holds for the binding energy (and consequently for the charge transfer and adsorption density), the supplementary Eq. (13) is reduced to Note that the thickness in the supplementary Eq. (14) should be replaced by the effective thickness, because the charge transfer upon the gas adsorption is not uniformly distributed in the entire film due to the layered 2D nature (the out-of-plane conductivity is much smaller than the in-plane one), it is instead accumulated at the surface region with certain penetration depth that would vary with respect to the PNS thickness as illustrated in the supplementary Fig. 12. Here, we empirically take this effective thickness as where is the Thomas-Fermi charge screening length, and are fitting parameters.
Then the sensitivity for thick PNS is To adopt the supplementary Eq. (16) in evaluating the sensitivity, we have to judiciously select the values of and that have distinctive physical meanings. As the penetration depth is equal to the actual PNS thickness for thin PNS, and then begins to increase but smaller than .
Thus, there exists a critical thickness . We choose = = 1 . On one hand, the gas adsorption induced carrier concentration at with respect to the surface one is reduced to (− ⁄ ) = 3.2% and thus it holds that the adsorbed gas molecules would affect the carrier concentration within the entire PNS with ; on the other hand, carrier mobility extracted from the field effect measurements shows that the mobility increases from the monolayer to thin PNS with = 1 and then slightly decreases as the PNS thickness increases 1 . The physical meaning of is that will increase with decreasing rate upon the application of source-drain current which pushes the carrier to penetrate through PNS. (=5) can be obtained by the ratio of sensitivity experimentally measured and ratio of the mobility at different PNS thicknesses.