Environmental effects in mechanical properties of few-layer black phosphorus

We report on the mechanical properties of few-layer black phosphorus (BP) nanosheets, in high vacuum and as a function of time of exposure to atmospheric conditions. BP flakes with thicknesses ranging from 4 to 30 nm suspended over circular holes are characterized by nanoindentations using an atomic force microscope tip. From measurements in high vacuum an elastic modulus of 46 ± 10 GPa and breaking strength of 2.4 ± 1 GPa are estimated. Both magnitudes are independent of the thickness of the flakes. Our results show that the exposure to air has substantial influence in the mechanical response of flakes thinner than 6 nm but small effects on thicker flakes.

The recent isolation of atomically thin materials from bulk layered crystals by mechanical or chemical exfoliation [1,2] holds promise to revolutionize the field of flexible electronics. Graphene is still by far the most studied two-dimensional crystal, however, other 2D crystals have recently gained considerable interest as they present similar mechanical performance while their electronic properties are complementary to those of graphene [3]. The lack of bandgap in graphene, for example, has motivated a surge of works on semiconducting 2D materials [4][5][6][7] which can also have a strong impact in future flexible electronics. Indeed, transition metal dichalcogenides (TMDCs) (Moand W-based dichalcogenides, mainly) have been recently used to fabricate flexible field effect transistors and photodetectors due to their high flexibility and high breaking strength [8][9][10][11].
TMDCs, however, present relatively slow photoresponse and, because of the large bandgap of Mo-and W-based compounds, they are only suited for applications in a limited part of the visible range of the electromagnetic spectrum. A material with a direct and narrow bandgap together with fast photoresponse is needed to extend the detection range accessible with 2D materials. Recently, black phosphorus thin flakes have been isolated by mechanical exfoliation of bulk synthetic crystals [12][13][14][15][16]. Bulk black phosphorus is a semiconductor with a direct bandgap of 0.35 eV with relatively high charge carrier mobilities in the order of 1000 cm 2 V −1 s −1 . Both values change with the number of layers, reaching more than 2 eV and around 1 cm 2 V −1 s −1 respectively [17,18] in its single layer form. Remarkably, strain provides another way of tuning electrical and optical properties [19][20][21]. A distinctive feature of BP is the in-plane anisotropy in its transport, optical and mechanical properties due to its puckered structure [22][23][24]. As examples (i) the in-plane anisotropy is around 64% for the electrical conductance (which is in the order of 10 μS for fewlayer BP) [24] and (ii) the prominent electronic transport direction (armchair) is orthogonal to the prominent heat transport direction (zig-zag) [25].
A significant issue in BP is its environmental instability: BP is unstable in ambient conditions in its single-and few-layer form [26]. Specifically, the presence of moisture and oxygen in air leads to the degradation of the material due to the formation of oxidized phosphorus species [27]. While some studies have already addressed environmental effects in the electronic properties of BP [26,[28][29][30][31], little is still known about its effect on the mechanical properties.
Here we investigate the role of air ambient exposition in the mechanical properties of BP. Atomic force microscopy (AFM) indentation experiments carried out in high vacuum conditions (HV, ∼10 −6 mbar) yield elastic modulus of E 3D =46±10 GPa for flake thicknesses ranging between 4 and 30 nm. Due to the geometry of our experiments (indentations at the center of BP circular membranes), the obtained E 3D is an average of the elastic modulus in both in-plane directions (zig-zag and armchair). Considering this, the measured value of E 3D is in good agreement with previous measurements in atmospheric conditions [24] and with theoretical predictions [32][33][34][35]. Our results also show that the exposure to air has a small effect on flakes thicker than 7 nm, even for time periods as long as 200 h, but substantial influence in the mechanical response of flakes thinner than 6 nm (corresponding to 10-12 layers).
For this study BP drumheads were prepared by mechanical exfoliation of bulk black phosphorus (smart elements) on SiO2 (300 nm)/Si substrates with predefined circular wells with diameters ranging from 0.5 to 3 μm (figures 1(a), (c) and supplementary information 1). The mechanical properties of the membranes were tested by indenting with an AFM tip at the center of the suspended area as sketched in figure 1(b) (details about the AFM probe can be found in supplementary information 2).
During the sample preparation procedure BP samples were not exposed to atmospheric conditions for more than 2 h (below this time no substantial degradation is appreciated [26]). Samples were kept and initially measured in a HV chamber. Subsequent to a complete characterization of their mechanical properties in HV conditions, a set of measurements in each membrane was performed while they were exposed to environment to assess the influence of ambient conditions in few-layer BP mechanical properties.
AFM indentation experiments on freely suspended BP can be modeled as clamped circular drumheads with central point loading (supplementary information 3). The force F versus indentation δ curves can be approximated by [9] ( ) ( )  nanosheet, R its radius, σ 0 the pre-tension and q=1/ (1.05 − 0.15ν − 0.16ν 2 ) is a dimensionless parameter close to 1. The first term in the equation is associated with the bending rigidity and is negligible for few layered flakes. The second term, also linear in δ, accounts for the effect of small pre-stress accumulated in the membrane during the fabrication method and varies quite randomly from drumhead to drumhead. Finally, the term in δ 3 dominates at large indentations and is governed by the intrinsic elastic modulus of the sheets. The thickness and deflection dependences reflected in equation [1] provide two complementary methods for determining E 3D . In the first method the experimental data of each indentation curve are fitted to a polynomial with terms in δ and δ 3 and the elastic modulus is extracted from the cubic coefficient. It requires large indentations but the value of E 3D can be obtained with data of exclusively one drumhead. This method automatically separates the linear coefficients from the elastic modulus, however it is not easy to apply to thick flakes where the large indentation regime is difficult to achieve. Therefore, by using this method, the elastic modulus is directly obtained from each indentation curve, however, the bending rigidity and pre-tension are not separately accessible since both contribute to the linear coefficient. The second method consists in measuring a set of flakes with different thicknesses and/or radii in the low indentation regime, where the term in δ 3 is negligible. Therefore the ∂F/∂δ (the spring constant of each flake, k flake ) scales as t 3 /R 2 [9]. Consequently, the elastic modulus is inferred by linear fitting of k flake versus t 3 /R 2 for several drumheads, according to this expression This second method is valid while the pre-tensions of all the drumheads are similar. Under that assumption, a linear fit would provide information about the Young's modulus (from the slope) and the average pre-tension of them (from the intercept).  Figure 2(b) displays a histogram of the values obtained for the elastic modulus of 39 different flakes as obtained employing the first method aforementioned. The average value for E 3D is 41±15 GPa, without any appreciable tendency with flake thickness. The prestress obtained from the linear term are in the range of 0.05 up to 0.3 N m −1 (obtained exclusively from flakes thinner than 5 nm where the bending rigidity is much lower that the pre-stress). Figure 2(c) depicts a set of experimental data points obtained in the low indentation regime, and it plots k flake versus t 3 /R 2 , following the second method described above. The obtained elastic modulus value is 52±6 GPa, within the error of the elastic modulus obtained in figure 2(b), and an average pre-tension of 0.07±0.02 N m −1 .
In order to analyze the influence of random pretensions in the flakes (which would lead to different intercepts in the linear fit of figure 2(c)), we have numerically simulated F(δ) curves with random pretensions in the low indentation regime (see supplementary information 4). Here we observe that the dispersion of the simulated data is similar to that of our experiments. This suggests that the variation of pretension among nanosheets is the main source of noise in the experimental data.
Summarizing, both methodologies yield similar results of the elastic modulus of few layered BP, being 46±10 GPa the weighted average of both values (taking into account the number of drumheads analyzed with each method).
Towards measuring the breaking strength (σ max ) of BP, some of the drumheads were indented until rupture. In order to estimate the strength we assume that it can be expressed as [36] σ max =( F break E 3D / 4πR tip t) 1/2 , where F break is the rupture force and R tip the tip radius. Figure 3  clear correlation between these two magnitudes. The average breaking strength is found to be 2.4±1 GPa. This value compares quite well with previous measurements in atmospheric conditions [24]. Figures 3(b) and (c) displays a BP membrane before and after breaking. As it can be readily seen, the crack is confined around the tip-sample contact point in contrast with other 2D materials such as MoS 2 or graphene [8,37].
Subsequent to mechanical characterization in HV conditions, measurements in ambient atmosphere were performed. Once the samples were exposed to ambient conditions, measurements separated by intervals of few hours were carried out in each membrane. The relative humidity was ≈47% and the temperature ≈22°C. This scheme allows monitoring the evolution of E 3D with the exposure time to ambient conditions. For the analysis of the nanoindentation measurements at atmospheric exposure, the first method described above was used. The results obtained from these experiments are depicted in figure 4(a), which shows the evolution of E 3D as a function of the exposure time to atmosphere.
According to our measurements BP flakes with thickness above 7 nm show a minor reduction of its elastic modulus upon ambient conditions exposure  suggesting the growth of a passivation layer. This is readily observed in the data plotted with blue, pink and green symbols in figure 4(a). We have considered a simple passivation process (see supplementary information 6). According to this model, an exponential decay fitting of these three sets of data is depicted by a dashed line. On the other hand, flakes with thickness below 6 nm show a clear tendency of decreasing elastic modulus when exposed to air (black squares and red dots in figure 4(a)), reaching a decrease of a factor of almost two at 24 h of exposure to ambient. This fast decreasing in E 3D for drumheads thinner than 6 nm can be clearly appreciated in figure 4(b), which shows several indentation curves acquired at increasing exposure time in the 5.3 nm thick flake of figure 4(a). It is plain to see that the elastic modulus decreases with time in this case. Indeed, the 4.5 nm thick flake spontaneously broke after the first 10 h of exposure. Furthermore, all the flakes studied under ambient conditions, broke at forces well below forces that were previously supported.
As previously reported [26], our AFM topographic images of BP drumheads showed significant changes as a function of time of ambient exposure. Figure 4(c) displays AFM images showing the evolution of the topography of a representative BP flake with exposure time. As a consequence of water absorption we observe a random population of protrusions increasingly covering the surface. It should be noticed the difference between bubbles, that were present immediately after sample preparation, and protrusions originated by moisture. It is also worth mentioning that the fitting errors of the indentation curves also increase with time, most probably due to the presence of these protrusions, which slightly alter the shape of these curves (see supplementary information 3).
In brief: the main conclusions derived from our latter experiments are three: (i) although exposure to air leads to substantial changes in the topography of the few-layer BP, the elastic modulus of flakes thicker than 7 nm is slightly reduced, (ii) BP flakes thinner than 6 nm, experience a significant decrease of their E 3D upon exposure to ambient conditions, and (iii) for both thickness ranges the rupture forces seem to decrease with the ambient degradation.
The elastic modulus of the flakes upon degradation yields the magnitude E 3D ·t=E 2D. For the results plotted in figure 4, the value of thickness, t, used to derive E 3D is the height of the flake measured by AFM under high vacuum conditions. Upon exposure to atmosphere this magnitude becomes experimentally inaccessible for some time, i.e. the topography of the flakes reflects a growing height due to water absorption on the flakes that does not correspond to their actual thickness. Hence, the decrease of elastic modulus observed in our measurements might be ascribed to two different physical origins: (i) an inherent decrease of the E 3D of the material and/or (ii) a decrease of the thickness of the membrane. In order to investigate these effects the samples were annealed in high vacuum at 230°C during 15 h. Following previous works, under these conditions a removal of adsorbed water occurs. This allows measuring the real thickness of the flakes. According to our AFM images before and after annealing (see supplementary information 5) the change in thickness is negligible, hence suggesting that a decrease of the intrinsic elastic constants is taking place during exposure to atmospheric conditions. This decrease in E 3D could be attributed to the passivation of the outer layers of the BP flakes leading to phosphorus oxide layers with a lower elastic modulus than that of pristine BP. Therefore, we consider the previously introduced passivation model (see supplementary information 6), in which the passivation layer depth increases at a rate that exponentially decreases with time, and the total thickness of the drumhead is constant in the whole process (as figure S7 in supplementary information 5 suggests). In order to draw conclusions from this model, determination of flake's thickness is paramount. As the real thickness of the flakes is now available, it is possible to complete the passivation model, which yields a maximum passivation depth of 9±5 nm and a passivation characteristic time of 60±20 h. The reduction factor of elastic modulus of the phosphorene oxide with respect to the one of pristine phosphorene is reported to be around 0.66 [38], leading to an elastic modulus of 30±7 GPa for fully oxidized few-layer BP (46±10 GPa was taken as elastic modulus of pristine few-layer BP). According to our model, the maximum of the elastic modulus should occur at 0 h of exposure. However, the experimental results for flakes thicker than 7 nm show an increase of E 3D for low exposure times. This behavior was theoretically predicted for phosphorene oxide in [38] and it is rationalized in terms of small relaxations of phosphorene due to chemisorbed oxygen atoms.
The presented results are in good agreement with those published by Tao et al [24] of mechanical characterization in air of thick (>14 nm) flakes but in clear disagreement with a more recent publication by Wang et al [39].
In conclusion, in this work high vacuum measurements of BP mechanical properties are reported. Indentation experiments yield elastic modulus of 46±10 GPa and breaking strength of 2.4±1 GPa. The elastic modulus barely decreases in atmospheric conditions for thick flakes but we found a clear decreasing tendency for the thinnest flakes measured in our experiments. This is attributed to a self-passivation process that saturates with time.