Controlling and modulating terahertz signals is of fundamental importance to allow systems level applications. We demonstrate an innovative approach for controlling the propagation properties of terahertz (THz) radiation, through use of both the excitation optical wavelength (colour) and intensity. We accomplish this using two-dimensional (2D) layered hybrid trihalide perovskites that are deposited onto silicon substrates. The absorption properties of these materials in the visible range can be tuned by changing the number of inorganic atomic layers in between the organic cation layers. Optical absorption in 2D perovskites occurs over a broad spectral range above the bandgap, resulting in free carrier generation, as well as over a narrow spectral range near the bandedge due to exciton formation. We find that only the latter contribution gives rise to photo-induced THz absorption. By patterning multiple 2D perovskites with different optical absorption properties onto a single device, we demonstrate both colour selective modulation and focusing of THz radiation. These findings open new directions for creating active THz devices. All-optical approaches to modulate signals are of wide interest. Here the authors demonstrate the use of two-dimensional perovskites on silicon for optically controlling the propagation and attenuation of terahertz radiation in the visible by changing the number of atomic layers. Among the many device capabilities needed to create systems level applications, the ability to control and modulate signals is of fundamental importance2. Prior demonstrations of active THz modulators have utilized mechanical6, electrical12, and optical19 means for affecting change. All-optical approaches are particularly attractive because they offer the potential for high-speed modulation and switching, and can be fabricated straightforwardly on conventional semiconductor substrates. Compared to electrically controlled devices, where the need for ohmic contact adds complexity, contact-free optical modulators can be designed more simply. In such devices, modulation of THz radiation can be realized when the incident optical control beam has a photon energy above the bandgap, where the generation of charge carriers leads to increased absorption of the incident THz radiation. While this approach has been proven successful, there are limitations. The control beam wavelength is largely irrelevant as long as the photon energy is above the bandgap energy. Moreover, high peak fluence optical pulses are needed to generate sufficient photocarriers for modulating the THz response.Terahertz (THz) technologies hold great promise in the development of next-generation computing and communication systems21. The appeal arises from a combination of compelling properties that set these materials apart from conventional inorganic semiconductors: (i) a number of solution and vapor-phase deposition techniques can be used to fabricate thin films on a wide range of substrates24, (ii) changes in the chemical structure of the materials allow for tuning of the bandgap over a wide spectral range in the visible25 and (iii) recent work using methyl-ammonium based perovskites have demonstrated power conversion efficiencies exceeding 20%28.In recent years, hybrid lead-halide perovskites have been in the spotlight because of their enormous potential for developing high-performance photovoltaics3NH3PbI3 perovskites, two-dimensional (2D) perovskites self-assemble into alternating organic and inorganic layers that form natural ‘multiple-quantum wells’, with highly efficient photocurrent29 and tunable optoelectronic characteristics30. Moreover, the interlayer confinement in 2D perovskites gives rise to a large exciton binding energy of order 200 meV32. Their absorption spectrum is therefore dominated by a strong exciton band, followed by a slow increase in the absorption above the bandgap energy. These characteristics make the use of 2D perovskites for THz applications promising, although the topic remains largely unexplored33.Compared to three-dimensional (3D) CH6H5C2H4NH3)2PbI4(PEPI) – and its Ruddlesden–Popper (R–P) mixtures with CH3NH3PbI334, to enable colour selective THz modulation using plasmonic structures fabricated on a semiconductor substrate. In the R–P phase35, the alternate layers of organic cations and inorganic anion arrange to form an intercalated system of insulating and conducting layers, creating a superlattice structure. By chemically changing the number of the inorganic layers between the adjacent organic layers, the absorption band can be tuned over a wide region of the visible spectral range36. When deposited on select semiconductor substrates, we observe enhanced broadband THz absorption, as compared to the bare semiconductor. However, this only occurs when the incident radiation corresponds to the wavelength range associated with exciton absorption.Here we exploit the properties of 2D hybrid lead-trihalide perovskites –2(CH3NH3)n−1(PbI4)n where n = 1, 2, 332. Figure n = 1, 2, and 3 perovskites, where two adjacent layers of octahedral [PbI4]2− are sandwiched between [C6H5C2H4NH3]+, and [CH3NH3]+ is embedded in the [PbI4]2− framework. Thin polycrystalline films, typically ~200 nm thick, were grown via spin casting the precursor solutions onto different substrates which were pre-treated with O2 plasma. The films were annealed subsequently at 100 °C for 30 min and, once cooled, were encapsulated in a layer of poly-methyl methacrylate.The perovskites precursors were synthesized by mixing PbIn = 2) 2D perovskites deposited directly onto a high resistivity silicon wafer. Care was taken in these measurements to minimize thermal heating artifacts. The THz throughput is seen to decrease approximately uniformly from 0.1 to 1.6 THz with increasing lamp flux. In Fig. 2. What is clear from the data is the value of placing a perovskite film directly onto a silicon layer (with only a 1 nm native oxide film between the two media). It should be noted that the transmission for n = 1 and n = 3 2D perovskite/silicon samples exhibited nearly the same behavior as the n = 2 2D perovskite/silicon sample . In Fig. n = 1 to n = 3, that exhibit various bandgaps between 2.5 eV for n = 1 to 1.8 eV for n = 331. In Fig. n-variant. These PL spectra show a slight red-shift compared with the absorption bandedges. This occurs because the photoexcitations preferentially relax to the impurities of larger n-number . This agrees also with published data32, demonstrating both the quality and distinctness of each material. To better understand the excitation wavelength dependence on the THz absorption in the 2D perovskites/Si samples, we optically illuminated each sample using a series of 50 nm wide bandpass filters ranging from 450 to 800 nm. A schematic diagram of the experimental setup is shown in Fig. We synthesized three R–P phase perovskite variants, 36. However, in a superlattice structure the photoexcitations may be delocalized, which allows for tunneling between layers. The optically induced THz absorption data shown in Fig. 38. This may be an alternate explanation for increased carrier generation in the silicon substrate, where excitons are able to reach the substrate via voids between grain boundaries. Finally, we note that excitons do not dominate the absorption in 3D MAPbI3 perovskites and, thus, we do not observe an analogous wavelength (colour) selective control of the THz absorption. Instead, 3D perovskites behave much the same as conventional semiconductors for this specific application, as discussed in Interestingly, THz absorption in these samples increases appreciably only when the wavelength of the incident optical radiation corresponds to the wavelength of the exciton resonance, but not at higher energies that corresponds to band-to-band transition. To understand this phenomenon, we consider the sample structure. When a thin perovskite film is deposited onto a substrate, it consists of a stack of 2D R–P layers, each of which naturally forms a quantum well. As shown schematically in Fig. 40 in 200 nm thick aluminum thin films deposited on high resistivity silicon wafers. Subsequently, a n = 1, n = 2, or n = 3 hybrid perovskite thin film was deposited on top of the Al structure, so that it was in direct contact with the silicon only inside of each aperture, as shown schematically in Fig. n = 1 sample exhibits no optical intensity dependence when illuminated at 700 nm , since that wavelength does not correspond to photogenerated excitons in the perovskite layer. The transmission spectra are also measured as a function of the optical intensity and shown in Fig. n = 1 perovskite) through Fig. 3e (n = 3 perovskite), when illuminated using narrow-band radiation at the optimal wavelengths determined in Fig. This discovery can be used to create optical wavelength (colour) selective THz modulators. Figure 24. Thus, multiple perovskites can be deposited on different regions of the same device. To demonstrate the efficacy of this approach, we fabricated another plasmonic structure in which three separate subwavelength aperture arrays with different periodicities, though with identical aperture radius to aperture spacing ratios, were placed adjacent to one another, as shown schematically in Fig. n values on top of each region. The basic fabrication steps, shown in Fig. n = 3), ~ 0.41 THz (n = 2), and ~ 0.95 THz (n = 1).A significant advantage of perovskites over other conventional crystalline semiconductors is that thin films can be fabricated using comparatively simple solution-based and vapor-phase deposition techniques40. In contrast to the earlier demonstrations discussed above, we now use long pass optical filters to progressively reduce and ultimately erase multiple bands of resonances. Using the experimental geometry shown in Fig. n = 3 perovskite is affected. When a 600 nm long pass filter is used, only the resonance bands near 0.2 and 0.4 THz, corresponding to the n = 3 and n = 2 perovskites undergo modulation  by exciting the films on glass substrates with a 447 nm semiconductor laser (50 mW). A 500 nm long pass filter was used before the spectrometer to block the residual laser beam. UV–visible absorption spectra were carried out with Agilent Cary UV–vis Spectrophotometer (200 nm to 2.5 μ).T, and change of the transmitted probe beam (ΔT) was detected by a DLaTGS detector. The photoabsorption spectrum was calculated from measurements of the fractional change in transmission (ΔT/T) using approximately 6000 scans of the FTIR spectrometer with the pump beam on and off.Photo-induced free carrier absorption was characterized using an FTIR (Fourier transform infrared) spectrometer in various samples. A 2.8 eV (442 nm) cw diode laser was used as the optical pump and the IR probe beam was provided by the FTIR. The 2D perovskite films were deposited on Si and KBr substrates and placed in a cryostat in which the temperature could be varied from 45 to 300 K. The pump and probe beams were co-incident on the sample films, and the transmission, 2 plasma to obtain a hydrophilic surface. A thin layer of PDMS mask was then attached onto the silicon wafer before spin-coating the perovskite precursor on top. After annealing the wafer to remove the residual solvent, the uncovered part was uniformly coated with perovskite material and the PDMS mask was removed. By repeating this procedure multiple times, the silicon wafer surface was patterned with multiple 2D perovskite compounds. Finally, the prepared sample was annealed at 100 °C for 1 h to obtain polycrystalline perovskite films. The sharpness and size of the patterns were determined by the PDMS mask, with a spatial resolution of ~1 mm.The patterned multi-perovskite structures were prepared using a step-by-step spin-coating method. A silicon wafer with thin film aluminum aperture arrays were treated with O43. We used nonlinear optical crystals for both THz generation and detection stimulated by an ultrafast Ti:sapphire laser44. The broadband, linearly polarized THz radiation generated by the emitter was collected and collimated by an off-axis parabolic, such that the radiation was normally incident on the samples. A second off-axis parabolic mirror placed after the filter was used to focus the transmitted THz radiation onto the detection crystal for measurement via electro-optic sampling. For THz imaging, we used a narrow-band polarized electronic THz source operating at 0.1 THz. The transmitted radiation was imaged using a THz focal plane array.The transmission spectra were obtained using standard THz time-domain spectroscopy (THz TDS) measurementsThe data that support the findings of this study are available from the corresponding authors upon reasonable requests.Supplementary InformationPeer Review File


Thin liquid films are central to everyday life. They are ubiquitous in modern technology , consumer products  and also serve vital biological functions . A common feature in all these examples is the presence of surface-active molecules at the air-liquid interface. Though they form only molecular-thin layers, these surfactants produce complex surface stresses on the free surface, which have important consequences for the dynamics and stability of the underlying thin liquid film. Here we conduct simple thinning experiments to explore the fundamental mechanisms that allow the surfactant molecules to slow the gravity-driven drainage of the underlying film. We present a simple model that works for both soluble and insoluble surfactant systems in the limit of negligible adsorption-desorption dynamics. We show that surfactants with finite surface rheology influence bulk flow through viscoelastic interfacial stresses, while surfactants with inviscid surfaces achieve stability through opposing surface-tension induced Marangoni flows. Stability and drainage of thin surfactant films is relevant across various disciplines: industrial applications including engineered foams and emulsions , fundameThe majority of past literature has looked at the stability of thin films in presence of soluble amphiphiles, including drainage from horizontal films , 9, draiVe). A high-speed interferometer enables measurement of the varying film thickness at the apex of the film. We employ two heavily-studied commercial surfactants: 1, 2-dipalmitoyl phosphatidylcholine (DPPC), an insoluble surfactant that forms viscoelastic interfaces [immobile interface at high surface pressures, while the SDS films are more fluid-like and yield extremely mobile interfaces. The remarkably different surface properties between DPPC and SDS allow us to systematically explore the role of surface mobility on drainage dynamics.Here we utilize a simple setup  to measuterfaces , 19 and terfaces . We alsoσ), surface shear viscosity (ηs), and surface dilatational viscosity (ηd). A key assumption to note is that we assume that surfactant transport is convection-dominated , and thus neglect the adsorption-desorption dynamics for surfactants in our model.Consider a hemispherical glass dome that is raised through a bulk of liquid that results in the capture of a thinning liquid film with a complex surfactant-laden interface. Deformation of the interface leads to interfacial stresses that need to be accounted for in the hydrodynamic model capturing the evolution of this thin film. Analytical solution to this thin-film draining problem is well-established in our past work , 7. BrieH of the film at the apex, due to gravity, as a function of time:η), substrate curvature (R), density (ρ), gravitational constant (g), time (t) and initial film thickness (h0). The parameter α serves as a fitting-parameter that characterizes the fluidity of the interface and is directly coupled to the total Boussinesq number, Bq = Bqs + Bqd + Ma, where Bqs, Bqd and Ma are dimensionless numbers capturing the influence of surface shear viscosity, surface dilatational viscosity and Marangoni stresses. These numbers are defined as follows: Bqs = ηs/(ηh0), Bqd = ηd/(ηh0) and ηs, ηd are the surface shear and dilatational viscosity due to the surfactant-molecules, ∇s is the in-plane surface gradient at the air-liquid interface [From this mathematical analysis, the following single-parameter expression predicts the dimensionless thickness nterface . The totα has exact analytical values: α = 1/3 when Bq = 0 (surfactant-free interface), and α = 1/12 for Bq → ∞ (extremely viscous surfactant-laden interface) [α transitions strongly at Bq = 1 [α, thus allows us to evaluate the role of interfacial contributions, including surface viscosities  and surface-tension gradients (Ma) on the draining behavior of thin films. However, by itself, α is insufficient to inform the relative contributions of surface rheology versus Marangoni effects. Thus, we further conduct surface flow visualization experiments that help in distinguishing between these different interfacial phenomena.At the asymptotic limits of this model, the parameter terface) . Using bt Bq = 1 . This mot Bq = 1 . The purγ0 − γ, where γ and γ0 are the surface tension with and without surfactants, respectively. For DPPC films, increasing the surface pressure has the effect of increasing both the surface shear and dilatational moduli [−1 i.e., from the liquid-expanded (LE) phase to the liquid-condensed (LC) phase for DPPC, and measure the drainage of the films. A characteristic drainage experiment data-set is shown in For insoluble surfactants, it is common to connect the surface concentration through the surface pressure Π = l moduli , 21–23. −1 in H2 = (h0/h)2 is plotted as a function of τ, for different films raised at varying elevation velocities, Ve = 1–10 mm s−1. At both surface pressures, Π = 5 and 25 mN m−1, the data trends linearly, yielding extremely good fits to our simple drainage model. Using α values are shown in We further present data for Π = 5 and 25 mN m−1), α = 0.1 is in good agreement to the theoretical prediction for a no-slip interfacial boundary condition  and expected for DPPC due to its finite surface viscoelastic properties  [Bq = 0) and have no added interfacial stabilization mechanism. We observe this for pure water films as they drain almost instantly (< 50 ms), and cannot be captured using our interferometric technique. It is important to note that for DPPC, the dilatational viscosity is three orders of magnitude larger than its shear counterpart, and thus may play a more dominant role in stabilization (Bqd > Bqs) [−1), DPPC has a more fluid-like interface, and obtaining the same value of α = 0.1 hints that perhaps Marangoni stresses play a significant role in stabilization. We reinforce this observation by specifically conducting drainage experiments within the LE-LC plateau (Π = 7 mN m−1), where both the shear and dilatational moduli are negligible, and obtain a consistent value of α = 0.11  at these low surface pressures. We will later demonstrate that Marangoni effects become important for DPPC films at low surface pressures , using surface flow visualization experiments.At higher surface pressures (Π >10 mN md > >Ma) , 22. It d > >Ma) . In the α = 0.11 . Moreoveh0 of the DPPC-laden films as a function of elevation velocity (Ve) in Ca is the Capillary number defined as Ca = ηVe/γ [We also report the initial height  = ηVe/γ . Thus, tVe = 1–10 mm s−1) are conducted for two concentrations, below and above the cmc. We again plot the inverse-squared film thickness 1/H2 as a function of τ for films elevated at different Ve in α values for SDS are shown in For SDS films, elevation velocity sweeps . Thus, this stabilization has to occur via strong surface-tension gradients or Marangoni flows (Ma > 0), which will indeed be confirmed using surface flow visualization in the next section.For SDS below its cmc, we obtain surfaces , ruling α ∼ 0.3. These drainage rates have significant error bars as the films drain almost instantly and only a few data-points can be recorded—the duration of drainage is < 2 s  than the drainage times scales. Thus, α ∼ 0.10 values from our model accurately capture the role of Marangoni flows in stabilization of the SDS films below cmc.Above the cmc, SDS films are less stable and drain rapidly with  2 s see . We also 2 s see , indicath0) of the SDS films as a function of Ve in Ve > 6 mm s−1, films above the cmc concentration are relatively thinner than solutions below the cmc. Similar decreases in thickness have been observed in SDS entrainment experiments on fibers and are a consequence of micellar kinetics that reduces the Marangoni-induced stress, resulting in thinner films [Finally, we also show the initial entrained height  vs. Marangoni stresses (Ma) for DPPC and SDS films, we substitute the glass dome by an air bubble , the DPPC film is initially symmetric, with circular fringe patterns (t < 2 s). However, this stable pattern is quickly deformed by plumes of surfactant rising from the periphery. These surface flows are fundamentally similar to rising plumes in vertical soap films, commonly referred to as ‘marginal regeneration’ [t ∼ 10 s.For DPPC, both the symmetric and asymmetric drainage patterns can be observed, as its surface rheology is a strong function of surface pressure. At low surface pressures  in comparison to the thicker films that the solid dome captures (∼100μm). It is well-established that in the thinner films, the adsorption times are longer than previously discussed, which ultimately lead to stronger Marangoni flows [SDS films at 0.13 cmc and 5 cmc do not possess any measurable surface rheology . Thus, wni flows . It is wIt is common knowledge that the presence of surfactants (e.g. soap) extend the life span of thin films (e.g. bubbles). However, a systematic comparison between the drainage of soluble and insoluble surfactants has not been previously presented. We offer an experimental platform to measure the gravity-driven drainage dynamics of DPPC (insoluble) and SDS (soluble) films, as well as a simple model that can be employed to evaluate the influence of interfacial phenomena in the absence of adsorption dynamics. We show that the presence of both DPPC and SDS at the air-liquid interface increases the stability of thin films. Specifically, DPPC films are stabilized through interfacial rheology at high surface pressures, resulting in immobile surfaces and Marangoni stresses at low surface pressures, resulting in mobile surfaces. Thus, the surface pressure of DPPC serves as a control for switching surface mobility on and off. Finally, SDS films are stabilized purely through Marangoni effects, resulting in mobile surfaces both above and below cmc. We thus show that soluble and insoluble surfactant systems exploit two fundamentally unique interfacial mechanisms to achieve the same result: thin film stability.−1 glass vials. We diluted it to a concentration of 1 mg mL−1 in chloroform  and stock solutions were kept in freezer until use. To achieve a desired surface pressure, we spread DPPC at the interface, and compressed using a teflon barrier. SDS  solutions were prepared using phosphate buffer saline  to a desired concentrations of 0.28 mM and 10 mM. These particular concentrations were chosen to investigate the effect of micelles on the stability of draining films. It is important to note that the critical micelle concentration (cmc) of SDS in buffered solution is 2 mM [Two commercially available surfactants are compared: 1, 2-dipalmitoyl phosphatidylcholine (DPPC) and sodium dodecyl sulfate (SDS). DPPC is purchased from Avanti Polar Lipids Inc.  in 25 mg mL is 2 mM .−1 is observed. However, for SDS, the glass dome is initially submerged in SDS-filled trough, and the adsorption equilibrium is awaited. Once the desired surface pressure is reached in both cases, the dome is elevated using a motorized stage through the interface, and captures a thin liquid film. The thickness of this film is measured using a high speed white light interferometer  combined with a halogen light (Fiber-Lite PL-800).A photograph and a schematic of the apparatus used to characterize the drainage of thin films are shown in μm below the interface. The dome is then raised 2.5 mm at various speed, Ve, ranging from 1–10 mm s−1 and the thickness of the film, h, is captured by the interferometer. For every dataset, the height versus time data was fitted with the theoretical model to attain a characteristic value of the fitting parameter α.The following protocol was followed while conducting the experiment. The glass dome is initially positioned approximately 130 μm below the interface. The air bubble is then elevated at the speed of 0.3 mm s−1 by a vertical distance of 0.6 mm for DPPC and 1 mm for SDS. These particular vertical distances are chosen to ensure that only a fraction of the bubble cap is exposed at the interface. Under white light illumination (420–780 nm), the color interference patterns of these thin curved films (< 1 μm) are captured using a color CCD camera.To assess and visualize the interfacial and Marangoni stress-induced flows, the drainage setup was slightly modified. The elevating glass dome was replaced by an elevating air bubble  as shown in S1 Fig−1, with b corresponding to our fitting parameter α.(A) Adsorption time scales for SDS at 0.13 cmc and 5 cmc. (B) Duration of drainage for SDS films at above and below cmc. (C & D) Representative drainage results of below and above cmc of SDS at 1 mm s(TIFF)Click here for additional data file.S2 FigRaw-data showing duration of drainage (in seconds) for DPPC films at different surface pressures and elevation velocities.(TIFF)Click here for additional data file.S1 Video−1.Surface visualization flows for DPPC at 5 mN m(MOV)Click here for additional data file.S2 Video−1.Surface visualizations flows for DPPC at >25 mN m(MOV)Click here for additional data file.S3 VideoSurface visualization flows for SDS (above CMC).(MOV)Click here for additional data file.S4 VideoSurface visualization flows for SDS (below CMC).(MOV)Click here for additional data file.


Within these limits, the carbonate carbon isotope (δ13C) record becomes insensitive to changes in organic carbon burial rate, due to counterbalancing changes in the weathering of isotopically light organic carbon. This can explain the lack of secular trend in the Precambrian δ13C record, and reopens the possibility that increased biological productivity and resultant organic carbon burial drove the Great Oxidation Event.It is unclear why atmospheric oxygen remained trapped at low levels for more than 1.5 billion years following the Paleoproterozoic Great Oxidation Event. Here, we use models for erosion, weathering and biogeochemical cycling to show that this can be explained by the tectonic recycling of previously accumulated sedimentary organic carbon, combined with the oxygen sensitivity of oxidative weathering. Our results indicate a strong negative feedback regime when atmospheric oxygen concentration is of order pO 2 remained at low levels for >1.5 billion years following the Great Oxidation Event. Here, the authors show that tectonic recycling of previously accumulated sedimentary organic carbon, and oxygen sensitivity of its oxidative weathering stabilized O2 at ∼1–10% of present levels.It is unclear why atmospheric O This challenges previous inferences1015162 was ∼0.01–0.1 PAL, themselves based on models of paleosol oxidation2>0.04 PAL at ∼1.4 Ga from a lack of vanadium retention in marine sediments192062≥0.6 PAL from the appearance of Palaeozoic fossil charcoalAtmospheric oxygen pO rose fro2∼1 PAL), is short relative to geological timescales. Hence, to explain the long-term stability of pO2 requires negative feedback operating on the oxygen source(s) and/or sink(s). In the Phanerozoic, the major oxygen source is organic carbon burial (derived from oxygenic photosynthesis) and the largest sink is oxidative weathering of uplifted sedimentary organic carbon (kerogen). Models for Phanerozoic oxygen regulation1130282 (∼1 PAL), uplifted organic carbon is completely oxidized in slowly eroding soil environments2 level. However, at high erosion rates, oxidative weathering is incomplete and detrital kerogen is preserved in marine sediments33342 variations even at the present day3013C) record insensitive to changes in organic carbon burial rate, thus explaining the lack of secular trend in the Precambrian δ13C record.Identifying the mechanisms responsible for stabilizing oxygen well below present levels poses an outstanding puzzle242526Our model for the regulation of atmospheric oxygen at low Proterozoic levels hinges on an explicit consideration of the accumulation and tectonic recycling of sedimentary reduced matter over Earth history . Importa12 mol yr−1) with a smaller contribution (∼1.25 × 1012 mol yr−1) from oxidation of reduced metamorphic and volcanic gases11In the modern oxygenated environment , much of2<10−5 PAL  and 25 cm kyr−1   and removing the contributions of high-uplift regions to global sediment discharge rates (see ‘Methods' section). This can weaken the sensitivity of the global oxidative weathering flux to oxygen variation near pO2 at levels after the Great Oxidation Event402 on organic carbon burial rate , corresponding to pO2<0.01 PAL, this state loses stability and a ‘Great Deoxygenation' is predicted, because the oxygen source to the atmosphere is insufficient to counterbalance the volcanic input of reduced matter. Conversely, an increase in organic carbon burial from lower values to >25% of present is sufficient to trigger the Great Oxidation Event in the model, as the net biological source of oxygen exceeds the volcanic input of reduced matter.The relative strength of the oxidative weathering feedback is determined by its size relative to other sinks , especiaial rate . Here, w∼0.1 PAL  with oxyower pO2 . VaryingThis means that to increase atmospheric oxygen toward modern levels (∼1 PAL) requires a factor of ∼4 larger increase in organic carbon burial flux than needed for the Great Oxidation Event . This se2 with respect to short-timescale perturbations (green line).A major uncertainty in atmospheric reductant input is the contribution of thermogenic methane from organic carbon metamorphism . If thisQ∼1.5 of present, and ocean crust formation rate and high-temperature hydrothermal heat loss scaling with Q2∼2.25 of present. Metamorphic fluxes plausibly scale proportional to global heat flux (Q) and continental area, hence would be ∼1.2 of present . Mantle inputs scale as Q2 increasing both CO2 input and the seafloor hydrothermal oxygen sink (primarily serpentinisation in the low-sulfate PrecambrianSecular changes in tectonic (and solar) forcing will modify this picture13Ccarb) record. Conventionally the constancy of δ13Ccarb is taken to imply a constant ‘f-ratio' of ‘new' organic to inorganic carbon burial49502). The detail of the transient adjustment process and return to steady-state for an arbitrary decrease (and later increase) in organic carbon burial is illustrated in 13Ccarb as oxidative weathering exceeds organic carbon burial. However, after ∼10 Myr, atmospheric oxygen and oxidative weathering decrease to a new steady state, leaving δ13Ccarb unchanged from its initial value, with both the net input and output fluxes of δ13C to/from the ocean isotopically heavier than they were . Similarly, an increase in organic carbon burial results in a transient increase in δ13Ccarb and return to its initial value.Our proposed mechanism for Proterozoic oxygen regulation changes the interpretation of the Precambrian carbonate carbon isotope  is linked to continental growth, an ‘episodic continental growth' model12 mol O2 eq yr−1 . This would drop after 2.5 Ga to a net oxidation rate of ≈1.6 × 1011 mol O2 eq yr−1, which is small relative to sediment and metamorphic redox transformations (23456As our focus is on oxygen regulation after the Great Oxidation Event (rather than long-term controls on organic carbon accumulation) we have assumed that the Proterozoic rock cycle was in overall redox balancermations . However2 ∼0.01 PAL, our model predicts a reversal of the Great Oxidation Event, because although the oxidative weathering of ancient organic carbon would have become negligible, the oxygen source to the atmosphere would have been insufficient to counterbalance the volcanic/metamorphic input of reduced matter. Atmospheric oxygen then drops until the oxidation of these gases becomes kinetically-limited  at pO2<10−5 PAL  with the absence of detrital pyrite in Proterozoic sediments. Again, the one-box model behind these very low pO2 inferences2∼0.001 PAL, when instead the soil is predicted to be anoxic and reducing up to pO2∼0.1 PAL  is only appropriate in a high oxygen world where oxidative weathering of organic carbon is fairly complete, and therefore the δ13C value of carbon inputs remains fairly stable. Even today there is some compensation of changes in new organic carbon burial and pO2 by corresponding changes in the input of ancient organic carbon with the same isotopic composition.Taking into account the incomplete oxidation of organic carbon under low Proterozoic O13Ccarb excursions in the Precambrian, notably the Lomagundi event356613Ccarb excursions can also arise from changes in the inorganic carbon cycle or in δ13C fractionation. The carbon isotope decoupling observed in the Neoproterozoic δ13C record13Ccarb varies but δ13Corg is near constant) can, as previously proposed496113Corg signature will be location-dependent.There are of course long-term (>1 Myr) δThe mechanism we describe provides a potential explanation for the overall stepwise evolution of atmospheric oxygen on Earth. Recycling of sedimentary organic carbon and its kinetically limited oxidation could have sustained low Proterozoic atmospheric oxygen levels—albeit not as low as has recently been inferred11Oxidative weathering of organic carbon and pyrite was simulated using an existing 1D reaction-transport model322=1 PAL.The 1D shale model represents the steady-state balance between downwards oxygen diffusion in a porous shale and reaction with organic carbon and  pyrite. It thus quantifies the local transition between a supply-limited regime , and a kinetic-limited regime where reduced material is incompletely oxidized with the remainder eroded. The model has been calibrated against laboratory measurements constraining local kerogen32et al.−1)  . For giv2 is therefore sensitive to oxygen transport, controlled by shale porosity (n*), and reduced matter supply, controlled by organic carbon and pyrite content and the distribution of uplift rates  shale parameters. However, integration over a distribution of uplift rates results in a land-surface average with incomplete oxidation in high-uplift regions, which is very different to that of a homogeneous surface with mean uplift rate (∼5 cm kyr−1).The dependency of the land-surface integrated oxidation rate on pOft rates . As demon*=1.5). These changes were designed to maximize O2 uptake and thus establish a lower limit at which this mechanism could regulate atmospheric O2.In a sensitivity analysis  we exami2 system with no land biota and reduced solar forcing:We parameterize the COPSE model12 mol C yr−1, oxidative weathering 3.75 × 1012 mol C yr−1, metamorphic/volcanic reductant input 1.25 × 1012 mol C yr−1), to be consistent with estimates from sediment erosion rates, with carbon to sulfur ratios, and with arguments for the relative sizes of the organic carbon metamorphic and weathering sinks. Rates are comparable to those in the GEOCARB series of modelsThe rates of organic carbon burial and oxidation were set as discussed in the main text 1/2 dependency of oxidative weathering on atmospheric oxygen level in the original version of the COPSE model was replaced with the Earth-surface integrated oxidative weathering rate calculated above from the oxidative weathering model, rescaled to give oxidative weathering of koxidw=3.75 × 1012 mol C yr−1 at pO2=1 PAL.The  was removed, and solar luminosity was set at 92% of present to generate a steady-state appropriate to 1 Ga, with resulting pCOA forcing parameter ɛ was added representing the secular evolution of mechanisms  enhancing phosphorus weathering and bioavailability, and thus controlling marine organic carbon burial. The anoxia dependence of marine organic C/P burial ratio was also switched on . The authors are in the process of developing a new, release version of the COPSE model, details of which are available from the corresponding author (T.M.L.).The code for the oxidative weathering model and the code for the Precambrian COPSE model (both in MATLAB) are available from S.J.D. on request (S.Daines@exeter.ac.uk) or the corresponding author (T.M.L.) on request.The data that support the findings of this study are the input assumptions of the models (detailed in the ‘Methods' section) and the model output . These are available from S.J.D. .Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Tungsten trioxide (WO3) has been used as a source for ‘W’ while ‘Mo’ has been derived from Mo based substrate. Different experimental parameters were used in this experiment. Higher gas flow rate decreases the size of the sample flake and on other side increases the dopant concentrations. The interaction mechanism between Mo, S, W and oxygen (O) have been explored. The influence of oxygen seems to be not avoidable completely which also imposes effective growth condition for the reaction of Mo with incoming sulfur atoms. The difference in the migration energies of Mo, WO3, S clusters on the graphene and the higher reactivity of Mo clusters over other possibly formed atomic clusters on the graphene leads to the growth of W doped MoS2 monolayers. Formation of MoS2 monolayer and the nature of edge doping of ‘W’ is explained well with the crystal model using underlying nucleation principles. We believe our result provide a special route to prepare W doped MoS2 on graphene substrate in the future.In the present study, a novel method has been carried out to grow tungsten (W) doped molybdenum disulfide (MoS Molybdenum (Mo) and tungsten (W) based dichalcogenides are two such representatives of well-defined family of structurally and chemically ordered 2D compounds. The basic crystal structure of 2D TMDs materials consists of hexagonally packed atomic layers, with chalcogenide–metal–chalcogenide arrangements in the trigonal prismatic or octahedral coordination21.Recent research of two-dimensional (2D) transition metal dichalcogenides (TMDs) materials, and its successful integration into the devices opens up a new direction in applications22 and hence comparatively better than other band gap engineering processes . Isoelectronic doping can be also useful in suppressing the detrimental effect of defects created during the growth of TMDs monolayers and hence increases photoluminescence efficiency which paves the way for the TMDs materials to find its applications in opto-electronic devices23.Alloying is widely used due to its ability to accurately controlling doping concentrations which determines the physical and chemical properties of materials2). Tungsten doping into the MoS2 in a continuum compositional range MoxWx−1S2 for 0 ≤ x ≤ 1 is energetically favorable mainly due to two reasons: 1) both MoS2 and WS2 possess the same hexagonal parent structure and 2) a comparable Shannon Prewitt crystal radius, 0.790 Å (Mo4+) vs 0.800 Å (W4+) and a well-matched lattice constant24. The monolayers of MoS2 are intrinsically n-type, while WS2 and WSe2 are intrinsically p-type, and their energies are mainly contributed by their d-orbitals of tungsten. Since both Mo and W possess different d-orbitals, the band gap engineering can be done by the doping of W atoms into MoS223.In present research, we have considered W-doped molybdenum disulfide  found to be successful in the growth of large area MoS2 monolayers. In a traditional CVD setup, the sulfur (S) powder is mostly used as a reductant source. The ‘S’ vapor partially reduce volatile MoO3−x/MoO2−x/WO3−x, and increases the probability of MoS2 or WS2 monolayer formation depends on the metal precursors used28. The difference in their respective vapor pressures of Mo and W precursors establish the difficulties in achieving the controlled supply of ‘W’ atoms for the synthesis of W doped MoS2 alloy and hence extra care must be taken into an account22.Even though, W-doped MoS30, electron beam evaporation32, sputtering33 and then sulfurization continued either in the second step of experiment or in a specially designed system33, in all the cases the resulting MoS2 layers were dependent on the thickness of deposited thin films and so far, produced only MoS2 monolayers without any possible doping. In this work, the sulfurization of Mo and then doping of W into MoS2 on the graphene have been carried out in a single and simple CVD set-up  will always grow faster than S-terminated zig-zag (S-zz)41, and the relatively lower temperature would increases the differences in the rate of edge growth, and leads to the other morphologies38 than the triangles and hexagons, in this case its nanostrips  in Fig. 2 monolayers.An atomic-scale resolution ADF-STEM images of MWS-1a, MWS-1b and MWS-1c are displayed in Fig. -1a Fig. . And the-1a Fig. . The intAn atomic-scale resolution ADF-STEM images of MWS-1b is displayed in Fig. 2 (MWS-1c) are displayed in Fig. 2 monolayer clusters without W atom doping. Only one W atom was found which was marked in Fig. 2 was prepared first. The formation of MoS2 nanoflakes and monolayers are also possible in the growth temperature range of 700–750 °C, as evident from the reported elsewhere41, we suspect these small clusters might be formed during the cooling stage, at which point, Mo and S are still energetically active species to react and grow further, while W atoms does not have a chance to find its energetically active position in the already formed MoS2 structures.Atomic-scale ADF-STEM images and crystal model of some small atomic clusters of MoS3 precursor does not produce any MoS2 monolayer flakes, suggests partial pressure environment formed by the addition of W-O(x)/WSxO(3−x) is necessary for optimum experimental condition to grow MoS2. EDS mappings  derived from Mo-based substrate into the reaction and to discuss the role of oxygen in the monolayer formation mechanism, low magnification ADF-STEM images and Energy dispersive X-ray spectroscopy (EDS) mapping of as-synthesized MoS Fig. S and MoWO2 /WSxO(3−x) probably needed to reduce the complex structure as in the case of MoS and provides suitable S partial pressure environment to form two-dimensional hexagonal network of MoS2.After sulfurization (in the case of MoS sample), Mo clusters possibly forms an amorphous alloy which possess octahedral or tetrahedral co-ordination3 structures together with Mo clusters which is not oxidized. Due to the differences in the surface free energy of graphene (around 46.7 mJ/m2)49 and Mo (around 2.92–3.34 J/m2)50, metal atoms migrating on graphene is expected to form molecular clusters on graphene52, which is more reactive with sulfur and oxygen than the Mo atoms and W-O(x) clusters, and hence readily reacts with the incoming sulfur atoms (Step 3)33. The reductant source ‘S’ vapor involves simultaneously in reducing WO3. Owing to its lower vapor pressure, an intermediate compound WSxO(3−x) is expected to form (Step 3)53.In step 2, at the high temperatures between 825–875 °C, Mo get oxidized and forms thermally active MoOxO(3−x) is depicted in its simple cluster form WSO2 for an easy understanding. MoS2 monolayer in its triangular form starts to grow first and the intermediate product WSxO(3−x), together with few individual Mo and S clusters are at the near-edge site of MoS2 (Step 4). In the following reaction step, WSxO(3−x) reduces and W atoms replace Mo at its lattice sites because of the shortage of Mo due to the reduced diffusion of Mo atoms (Step 5)54.In Fig. 2 monolayer structures on graphene have been synthesized using Mo atoms (clusters) derived from Mo based substrate. Comparing to the growth temperatures, 875 °C and 825 °C, the former case provides high-quality and uniform triangular MoS2 monolayers with less concentrated W doping, while in the latter case, even though the concentration of W doping among the individual triangular monolayer structures is similar as in the case of former one, merged monolayer structures with irregular shape have been found in majority. Nucleation density is large at lower temperature, however, the probability of finding individual triangles is lesser. The size of flake grown in lower temperature experiment is also larger. Variation in carrier gas flow conditions (400 sccm) have been done to verify the tuning possibilities of dopant metal atoms into the MoS2 monolayers and found that the dopant atoms are distributed up to 60 atomic rows, while in other experiments with carrier gas flow condition of 300 sccm, the dopant atoms distribution is up to maximum of 40 atomic rows . Higher gas flow rate also decreases the size of the flakes and on other side increased the dopant concentrations. The interaction mechanism between Mo, S, W and O on the graphene and the formation of MoS2 monolayer and the nature of edge doping of ‘W’ have been briefly discussed. The influence of oxygen seems to be not avoidable completely and also impose effective growth condition for the reaction of Mo with incoming sulfur atoms. Doping is effective in all the growth conditions and in all structures irrespective of the morphologies, from small clusters to nanostrips indicate the successful nature of doping mechanism. This method of using graphene transferred TEM grid substrate could give us a new idea to prepare TMDs alloys  in the future.In summary, W-doped MoSMo) based TEM grids using a standard PMMA-assisted wet-chemistry transfer process. The TEM grids with graphene facing downwards were mounted onto a home-built ceramic carrier and 1 mg of Tungsten trioxide (WO3) precursors  placed on the silicon wafer. Quartz boat carrying silicon wafer and TEM grid at its center were loaded into the CVD chamber.Graphene films grown on polycrystalline copper foils were transferred onto molybdenum (S) source  were heated (reaches 250 °C in 2 mins) from the separate heating belt in upstream. The whole system was maintained at their respective temperatures for 15–20 mins (growth time) and then cooled down to room temperature naturally. Argon (Ar) flow was maintained throughout an experiment at the rate of 300–400 sccm. The experimental conditions to prepare set of samples is shown in Table 3 source material and the sample is named MoS and another experiment conducted using WO3 alone without sulfurization, that is, after the main temperature reaching 875 °C and the system was kept for 15 mins and naturally cooled down and the sample is named MoWO.Within a typical CVD process, the furnace was firstly heated to 300 °C in 10 mins and hold for additional 10 mins, and then increased to its growth temperature, 825 °C/875 °C in 45 mins. Just 2 mins before the main CVD furnace reaches its growth temperature, 300 mg of sulfur  was carried out on a Bruker super-X detection system.Low magnification annular dark field – scanning transmission electron microscopy (ADF-STEM) images were first obtained with FEI Technai F20 to have a preliminary check over the samples and high resolution atomic-scale ADF-STEM images were captured using FEI Chemi-STEM Titan GThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.Supplementary Information


Decadal climate predictions use initialized coupled model simulations that are typically affected by a drift toward a biased climatology determined by systematic model errors. Model drifts thus reflect a fundamental source of uncertainty in decadal climate predictions. However, their analysis has so far relied on ad-hoc assessments of empirical and subjective character. Here, we define the climate model drift as a dynamical process rather than a descriptive diagnostic. A unified statistical Bayesian framework is proposed where a state-space model is used to decompose systematic decadal climate prediction errors into an initial drift, seasonally varying climatological biases and additional effects of co-varying climate processes. An application to tropical and south Atlantic sea-surface temperatures illustrates how the method allows to evaluate and elucidate dynamic interdependencies between drift, biases, hindcast residuals and background climate. Our approach thus offers a methodology for objective, quantitative and explanatory error estimation in climate predictions. To generate an ensemble of decadal forecasts, various procedures are applied in climate models to obtain sets of initial conditions based on the observed state of the climate system at a certain time2. The observed evolution of many geophysical parameters however resides outside the climatological envelope simulated by coupled climate models used in contemporary climate prediction systems, due to the presence of large systematic model biases with respect to observations5. These affect all of mean state, seasonal cycle and interannual internal variability. Decadal climate forecasts based on full-field initialization therefore unavoidably include a growing systematic error, which corresponds with the adjustment of the simulations from the assimilated state drawn from the observed climatology towards a state consistent with the biased climatology of the model2. This signal is commonly referred to as climate model drift6.The multiannual forecast horizon inherent to decadal climate prediction requires that the complexity and uncertainties arising from the interaction between the climate response to external forcing and the evolution of internal modes of climate variability are accounted for11, but more generally they reflect our limited understanding of many of the interactions and feedbacks in the climate system and approximations and simplifications inherent to the numerical representation of climate processes . Sea-surface temperature (SST) biases are often central in the characterization of climate model biases3. Typical examples of systematic model bias are the warm and weak upwelling systems at the eastern boundaries of the tropical oceans14. Among these, the severe warm SST bias in the southeastern tropical Atlantic has been especially studied17.Model drifts and biases can result from the erroneous representation of oceanic and atmospheric processes in climate models12. The dynamical processes governing model drifts  are identical to those of the simulated climate itself, so that climate and error signals are indistinguishable by first principles. The fact that model biases and drifts often have a prominent seasonal character16 further increases the difficulty of evaluating, quantifying and understanding their impacts on the overall quality of simulated climates. Various techniques for drift mitigation have been proposed, such as anomaly initialization or flux correction18. Nonetheless, in decadal climate predictions model drifts remain most often regarded as mere biases, which are often corrected for by means of empirical techniques with varying complexity22, but rarely investigated in depth23.A multi-model analysis of SST drifts in this region highlighted that similar biases arise there in different models through a variety of locally as well as remotely growing error mechanisms24 of systematic hindcast errors  in an ensemble of decadal climate predictions. Structural decomposition refers to a process model in which temporal changes of an observable variable are attributed to the discriminant effects (or “driving forces”) underlying these changes. Accordingly, each time series of hindcast errors Dj(t) in the ensemble is represented as the sum of a systematic component Δ(t), which captures the (systematic) portion of hindcast errors common to all realizations, and a non-systematic irregular component εj(t), which is specific to the individual considered hindcast realization j. Here, Δ(t) is defined as a linear combination of systematic hindcast error δ(t) and systematic seasonal bias σ(t). In particular, δ(t) evolves as a stochastic trend with slope β(t): initially, when β(t) ≠ 0, δ(t) describes the drift; then, when β(t) ≈ 0, δ(t) corresponds to the climatological bias. Moreover, Δ(t) can incorporate the explanatory effects of a covariate X(t) representing local and/or remote processes and quantified by the associated stochastic regression coefficient γ(t) of Δ(t) on X(t). As discriminant effects are non-observable, a state-space model is built in which the state vector includes all unobserved elements and the transition matrix describes their individual dynamics (see the methods section for details).A substantial improvement in our understanding of mechanisms contributing to the generation and propagation of systematic decadal climate prediction errors may be achieved by means of a process-oriented statistical characterization of their temporal and spatial complexity and a robust quantification of associated uncertainties. Here, we propose a structural decomposition analysisj(t), for all hindcasts are accounted for conditionally on the systematic component Δ(t); the process level, where the systematic components of the bias, δ(t) and σ(t), and its constituting discriminant effects, X(t), are represented by means of a stochastic model; and the parameter level, where prior knowledge about the distributions of model errors (via the parameters τ2) is formalized.The variances of the error terms in the state-space model are unknown parameters, and inference is performed following a Bayesian approach that specifies prior distributions for them. Therefore, our modeling strategy consists of three hierarchical levels (see the methods section for details): the data level, where observational errors, ε25 (see Methods).In this contribution, we choose to illustrate our hierarchical statistical framework and its value for a robust quantification of systematic model prediction errors and their associated uncertainty by means of a specific example. We discuss the diagnosed distinctive characteristics of the different error components and use them for a reliable identification of connections between drift dynamics and the physics of the simulated climate. This study thus focuses on SST errors in the Tropical and South Atlantic Ocean estimated for an ensemble of decadal hindcasts initialized from observations, with the MiKlip prototype system for decadal climate predictionABF, the region is defined in the methods section). Empirical hindcast errors consist in large seasonal errors superposed on a warm climatological mean bias  > 0) in the first two hindcast years, which peaks at ~4 °C; a subsequent progressive weak cooling (β(t) < 0), which extends into the 7th hindcast year; and finally a transition into climatological bias conditions (β(t) ≈ 0) quantified as a bias of 3.12  °C – estimated as median and 5th–95th percentile range of δ(t = 90 …120). Annual and semiannual seasonal biases – σA(t) and σSA(t) – with amplitudes of ~1.3 °C and ~1.05 °C, respectively, interfere constructively in July/August and destructively in January/February. Further, the semiannual bias component is substantially damped during the first hindcast year, possibly highlighting the effects of the initial coupling shock. The associated Bayesian analysis .We consider the spatially averaged SST in a region of the south-eastern tropical Atlantic containing the Angola-Benguela frontal zone , i.e., the differences between Dj(t) and the Bayesian estimates of Δ(t)  from roughly the third integration year onward, indicating that our decomposition captures the bulk evolution of systematic hindcast errors. However, systematic departures from zero of the residuals are diagnosed in the first two hindcast years. The positive residuals in the first few months and the negative residuals around January of the second integration year possibly reflect unresolved issues with the seasonal error . Figure 26.The residuals rABF anomalies. The residual error signal displays an interdecadal fluctuation with predominant negative errors before the mid-1970s and predominant warm errors afterwards. This signal robustly emerges in different seasons  = PDO(t-24). The approach is applied to the full hindcast ensemble and for two equally-sized sub-ensembles defined by the period of the hindcast initialization year, i.e., 1960–1979 and 1980–1999. In the full-ensemble analysis, the stochastic regression coefficient γPDO(t) indicates that the PDO index is informative about SSTABF hindcast errors, with strongest impact in the second and third hindcast years  agree with the full-period estimate better than the corresponding estimates from a model without covariates, particularly around the peak warm error phase  suggests that this teleconnection is active also in the simulated climate; removing the effects of remote forcing from the erroneous Pacific state leads to improved estimation of the local drift component. In general, it can be concluded that the estimation of the drift and of its uncertainty depends, to some extent, on the systematic portion of hindcast errors that depends on (inter)decadal internal climate variability. Our method could therefore be used in practice to improve drift estimation by accounting for known explanatory factors of such internal climate variability.Based on this empirical analysis, the statistical model for the estimation of systematic SSTble Fig. , in lineble Fig. . The PDOABF hindcast errors when the effect of hindcast errors in selected terms of the heat budget for the local mixed layer are accounted for. The blue curves in Fig. ml). Whereas empirical estimates of systematic errors (see methods) in Qml and SSTABF are significantly correlated , the Bayesian analysis indicates that systematic SSTABF errors are largely unexplained by Qml alone, reflective of the weaker average correlation between errors of both variables in the individual hindcasts (r = −0.32) and suggesting a more complex causal association beyond the thermal state of the mixed layer.As a further example for the possibility of including explanatory covariates in the statistical model, Fig. t) and damp the estimated annual and semiannual biases  nearly vanishes from the second hindcast year onward, and the semiannual seasonal bias σSA(t) is also appreciably reduced. The larger amplitudes of σA(t) during the first years suggest decoupling of surface from subsurface errors during the initial shock phase. The posterior regression coefficient γ(t)  and 1-month lagged sea-level height (slh) reduce the error component δ((t) Fig.  correspo(t) Fig. , which i(t) Fig. .t) is obtained when the explanatory effects of hindcast errors in hfs and slh are accounted for in conjunction  has values below 1 °C for long hindcast times, indicating that the climatological bias is almost completely damped when accounting for the explanatory effects of hfs and slh. The posterior estimate of σA(t) obtained with this model configuration is phase-shifted compared to the original analysis and has larger amplitudes compared to the configuration with slh as the only covariate, which suggests concomitant effects on SST biases from misrepresented seasonal variations in hfs and slh that mutually compensate or reinforce each other depending on their phase.An even larger reduction of δ. We tested the impact of using different input data to the dynamic linear model by constructing different hindcast ensembles, from small sub-ensembles to that used in the main analysis to super-ensembles including multiple realizations for each hindcast (results not shown). Tighter constrains on τ2D are generally achieved by increasing the size of the ensemble, without significant impacts on its estimated mean. By contrast, reducing the ensemble size can lead to major discrepancies in the mean estimation. It is especially in this case that the proposed Bayesian hierarchical formulation could be valuable – through the implementation of prior knowledge about uncertainty parameters and/or explanatory factors, as shown in Fig. Figures ABF. Its analytic potential, however, is exploited more fully when it is applied simultaneously to spatially distributed data. Here, we illustrate how it may aid the characterization of the spatio-temporal complexity of decadal climate prediction errors, and assist in understanding the underlying dynamics with an application to gridded upper-ocean potential temperature data in the southern Atlantic mid-latitudes, near the Brazil–Malvinas confluence zone. The results indicate intricate variability in the sub-surface ocean for the δ(t) and σA(t) components (see supplementary movie). For instance, at  during the initial drift phase negative  errors (δ(t) < 0) are diagnosed throughout the water column down to 120 m depth, with peak negative values around 50 m depth, while errors of opposite sign characterize near-surface and subsurface evolution during the climatological bias phase  in the near-surface layers  in the field of climate research, especially to the assessment of climate model outputs. BHMs use Bayes’ theorem to incorporate information from different sources, including observations, physical theories and experts’ knowledge. They provide a flexible framework to developing consistent inference and prediction of unknown quantities under study, which overcomes single-value estimates of uncertainty.Scientific literature contains numerous studiesZ represents the data, Y represents the process and θ represents the parameters related to the data and the process model, we then have:Z|Y, θ]Data model, [Y|θ]Process model, [θ]Parameter model,  is the generic notation for the probability distribution of the random quantity A. In practice, (a) defines the statistical model representing the dependence of observations on the unknown process, (b) describes the conditional probability distribution of the process on the model parameters, and (c) describes the (prior) probability distribution of the parameters, which are treated as random quantities according to the Bayesian approach.Y and θ) with associated uncertainty through the calculation of their posterior distribution conditioned to available observations, which is allowed by the Bayes’ theorem:35.BHMs provide estimates of the unknowns (t) of the decadal climate prediction system at prediction time t is observed through differences between the predicted and the observed – or, analogously, assimilated – values (Dj(t)) from an ensemble of j = 1,…,p hindcasts initialized at different times, according to the following model:j(t) is a Gaussian white noise random error with zero mean and variance τ2D. We assume, for simplicity, that the observation error has the same variance in all hindcasts.At the data level, the systematic error Δ(t) is decomposed into two components: the drift/bias δ(t) and the seasonal bias σ(t), further split into annual (σA(t)) and semiannual (σSA(t)). Namely:At the process level, Δ(t) changes through time according to a local linear trend:δ(t) and εβ(t) are uncorrelated Gaussian white noise random errors with zero mean and variance τ2δ and τ2β, respectively. The term β(t) is a random walk. The effect of εδ(t) is to allow the level of the drift/bias to shift up and down, while εβ(t) allows the slope to change. The larger the variances, the greater the stochastic movements in the drift/bias. If τ2δ = τ2β = 0, the local linear trend collapses to a linear deterministic trend.The drift/bias δ(36. Using monthly data with k = 1 for σA(t) and k = 2 for σSA(t), the kth harmonic function takes the general formSeasonal terms are modeled using harmonic functions1k and ζ2k are constants. Like the local linear trend, the seasonal term can be built up recursively, leading to the (stochastic) model36 for both components:σ,k(t) and ε*σ,k(t) uncorrelated Gaussian noise random errors with zero mean and variance τ2σ, and * indicating the conjugate.where ζt), the model becomes:The process model (3) can be easily extended to include the effect of external factors in terms of additional explanatory variables. For one dimensional explanatory variable X(t) to vary according to a random walk:γ(t) Gaussian white noises with zero mean and variance τ2γ. Time varying coeffcients γ(t) allow us to take into account possible non stationary effects of the covariate. Again, if τ2γ = 0, the effect collapses to be constant in time. Finally, the parameter level requires the specification of the prior distribution for the unknown parameters θ = . In this study, we set τ2δ = 0 to obtain a smoothly varying error δ(t), which then better corresponds to the drift/bias. We define weakly informative lognormal (LN) priors in the form LN for all parameters.In equation  we allowY) generating the observed data (Z)37. DLMs have the general form:t is the discrete time variable representing, in our case, monthly values, Z(t) is a vector of p observations at time t, Y(t) is the underlying state vector of dimension m, G is the mxm system matrix, and F is the mxp observation matrix. We suppose that v(t)~N and w(t)~N are the observation and model Gaussian errors, respectively, that are serially and mutually uncorrelated. In this formulation, the matrices V and W contain the model parameters θ. If we suppose that the unknown parameters are random the DLM formulation is a BHM where (9) and (10) are typically referred to as observation equation and system equation, respectively.The formulation of the statistical model above allows for a straightforward implementation within the dynamic linear model (DLM) framework. DLMs are based on a state-space approach, i.e., unobservable state variables are used that allow direct modeling of the process   the observation vector is defined as Z(t) = {D1(t),…, Dp(t)}’.We have applied the DLM to spatially-averaged indices and, individually, to the model’s grid-points over the investigated domain. Following (2) and (9), and having Y(t) = {δ(t), β(t), σA(t), σA*(t), σSA(t), σSA*(t)}’. Therefore, the dimension of the state vector is m = 6. We further assume Y(0)~N, i.e., there is practically no systematic error during the assimilation. The observation matrix F is defined following (2) and (3).In the base model without explanatory covariates, following (3) and accounting for annual and semi-annual seasonalities in the decadal climate prediction errors, the state vector is defined as 37 for calculating the posterior distribution (1) inside a Monte Carlo Markov Chain algorithm. In particular, we use a slice-sampler algorithm38 to iteratively sample from the full posterior distribution of the unknown parameters θ.The sequential definition of the process model  allows to use the Kalman filter formulas28. The associated uncertainty is calculated for each hindcast time t as the unbiased sample standard deviation of the Dj(t) values from the j = 1,…,p hindcasts. Similar results are obtained using the 95% confidence interval of the standard error of the mean.The BHM results are compared with empirical estimates obtained following the guidelines for drift/bias correction by the Decadal Climate Prediction Panel for the upcoming Coupled Model Intercomparison Project phase 625 is based on the low-resolution version of the Max Planck Institute - Earth System Model (MPI-ESM-LR). MPI-ESM-LR is a conglomerate of a coupled general circulation model and subsystem models for land and vegetation, and biogeochemistry. In MPI-ESM-LR, the atmospheric general circulation model ECHAM639 uses a T63/1.9° horizontal resolution and 47 hybrid sigma pressure levels that extend up to 0.01hPa; the ocean-sea ice model MPIOM9 uses a 1.5° resolution bipolar grid with 40 z-levels. The time step for numerical integration is 600 s for ECHAM6 and 4320 s for MPIOM.The MiKlip prototype system for decadal climate predictions41.[9] describe the main oceanic biases, highlighting serious biases prevailing in the intermediate layers of the ocean, which reflect the inability of the model to maintain the correct water mass properties. In general, the ocean in MPI-ESM gets too warm and saline at intermediate levels and in the deep ocean whereas it is too cold and fresh in the upper layers. MPI-ESM-LR and similar configurations of MPI-ESM have been widely tested and used in studies of climate dynamics and variability25 based on full-field assimilation of the ORAS4 ocean reanalysis data42. The lagged initialization procedure is used to obtain the initial state from the historical assimilation run for each of the 15 ensemble members for each initialization year between 1960 and 2000. The external radiative forcing data are based on the recommendations for the Coupled Model Intercomparison Project phase 5 (CMIP5), an overview of which is outlined in25. The ensemble including the first ensemble members (“r1”) was used in the main analysis. The associated historical assimilation run is used as analog for the observational targets.We use the MiKlip decadal prediction experiments43 available at: http://research.jisao.washington.edu/pdo/PDO.latest.txt. The original monthly index was low-pass filtered with an 85-month running average (corresponding to 7 years) before analysis to smooth out ENSO influences. Adjusted surface energy flux for the mixed layer and mixed layer heat content in the ABF region are estimated following44. All empirical distributions are smoothed with a 5-point moving average with symmetric Hanning weights.Spatially-averaged indices for the Angola-Benguela front region used in the study refer to the domain spanning 10°S–20°S latitude and 10°E–15°E longitude (to the coastline). Empirical hindcast errors in monthly mean spatially-averaged SST in the Angola-Benguela front region are provided as supplementary information. The observed PDO index is the JISAO PDO indexSupplementary InformationDataset 1Supplementary Video


The enhanced exciton emission intensity can be further tuned by varying the angle of polarized incident excitation. Through controlled variation of the structural parameters of the plasmonic array in our experiment, we demonstrate modulation of the photoluminescence intensity from nearly fourfold quenching to approximately threefold enhancement. Our data indicates that the plasmonic resonance couples to optical fields at both, excitation and emission bands, and increases the spontaneous emission rate in a double spacing plasmonic array structure as compared with an equal spacing array structure. Furthermore our experimental results are supported by numerical as well as full electromagnetic wave simulations. This study can facilitate the incorporation of plasmon-enhanced transition metal dichalcogenide structures in photodetector, sensor and light emitter applications.Modulation of photoluminescence of atomically thin transition metal dichalcogenide two-dimensional materials is critical for their integration in optoelectronic and photonic device applications. By coupling with different plasmonic array geometries, we have shown that the photoluminescence intensity can be enhanced and quenched in comparison with pristine monolayer MoS It has been observed that without a separation layer between monolayer (ML) molybdenum disulfide  plasmonic NC arrays arranged on top of an atomically thin MoS2 under irradiation of incident laser excitation with different polarization angles. As a result, we are able to tune the intensity of exciton originated PL by varying the incident light polarization for the asymmetric Au NC array. Further, we show that PL intensity modulation is controlled via both optical field enhancement and spontaneous emission rate enhancement. Enhancement and quenching of luminescence from plasmonic array on ML MoS2 structure and its far field radiation profile have been studied numerically.Tuning the luminescence intensity by changing the angle of polarization of the incident excitation light would add an additional degree of freedom and flexibility to develop SPR-exciton based nanosensors. In this work, asymmetric spacing along x- and y- axes  in the plasmonic array is used to tune the intensity of induced electric field (E-field) inside ML MoS2. Double spacing Au array- lateral periodicity along y- axis is double than the lateral periodicity along x-axis, is shown in 2/Si substrate where spacings along x- and y-axes are 220 nm and 440 nm, respectively  and emission wavelength (~680 nm) as compared with equal spacing plasmonic array. It can be noted that signature of the main peaks in the absorption spectrum of ML MoS2 at ~605 nm and ~660 nm corresponding to ‘B’ and ‘A’ excitons, respectively, are present in the reflectance spectra of ML MoS2 with plasmonic array structures (2 (index ~4.5 at 680 nm) due to increase in the optical index of the medium surrounding the NC array.In our fabricated structure, the apex tip of the NC is vertically outward and the circular base is placed on top of ML MoSectively . To illuructures . SPR of 2 was deposited on top of a SiO2/Si substrate using chemical vapour deposition (CVD) as mentioned in the experimental section. A detail description about the growth process can be found elsewhere2 was carried out in two steps. In the first step, alignment markers are patterned on top of the ML MoS2 coated substrate to identify ML MoS2. The second step involves patterning of the Au NC array on selected MoS2 flake  for quantitatively determining the layer thickness and doping effects  for the equal spacing array coupled structure could be attributed to the disorder introduced in the MoS2 lattice by the Au NC array12g/A1g) has a slightly higher value for the double spacing array-coupled structure as compared with equal spacing array, which is explained later in the manuscript26Au + MoS2/EMoS2|Top view SEM images of the two Au NC arrays with different periodicities on top of ML MoS effects  and d usobserved , which ay sample , which c2 (on SiO2/Si substrate) with and without an Au plasmonic array  was performed on ML MoSic array –c to gatMo 3d3/2 . The binectively . The Mo ectively . This su00 beam) is polarized. The polarization state is horizontal with respect to the sample plane (x-y plane). However, even though high magnification (100× lens) optical alignment of polarization axis (i.e. x-axis of sample stage plane at 90° polarization angle) with the axes of the plasmonic lattice array was used, the x-, y- axes of the plasmonic array coupled structure are not aligned perfectly with respect to the polarization axis of the incident excitation due to the manual nature of the alignment procedure. It is assumed that the incident laser polarization (at 90°) axis is along some small, arbitrary angle (ψ°) with respect to the x-axis of the plasmonic Au NC array lattice. To extract the PL modulation of ML MoS2 via coupling with the SPR band of Au NCs, different areas of the samples are illuminated using the focused laser beam. The polarization and intensity of the incident laser beam are controlled by engaging a half-wave (λ/2) plate and a neutral density (ND) filter in the illumination path. An appropriate edge filter was also introduced in the collection path for recording the PL spectra. The recorded light can be directed to either a camera or the spectrometer (which are further connected to a computer) to capture the optical image or record the spectra as the case maybe. Other notations are as follows; M1, M2, M3, M4, M5: mirrors; L1 and L2: lenses as shown in schematic diagram of the experiment set-up  is shown in 2 with equal spacing array is shown in 2 sample  can be calculated using the formula36patterned/Iunpatterned) × (Ao/Abare), where Ipatterned and Iunpatterned are the PL intensities from ML MoS2 with and without the Au plasmonic array, respectively. Ao represents the excitation area of the laser spot (π × 8002 nm2) and Abare represents the area of uncovered ML MoS2 within the laser spot. The calculated value for PL enhancement factor is approximately 3.5 for the double spacing Au array. We have obtained the completely opposite result from the equal spacing array coupled ML MoS2 sample when excited with the same laser power of 50 μW. The PL intensity of ML MoS2 from equal spacing array-coupled area has been quenched significantly (4 times) when compared to pristine ML MoS2  with a 100 ×, 0.9NA objective lens. The excitation laser  and quantum efficiency (Q.E.). The intensity of PL (IPL) spectra is proportional to γ × Q.E.PL = (k × |E|2 × Q.E.), where k is a proportionality constant. Induced E- field intensity (|E|2) and Q.E. are strongly dependent on the LSPR (Purcell effect). Maximum value of simulated E-field intensity (|E|2) of the plasmonic array coupled structure divided with E-field intensity (|E0|2) without the plasmonic array structure gives the field enhancement factor. Assuming equal contribution of E-field intensity enhancement at excitation wavelength (532 nm) and emission wavelength (680 nm), the total field enhancement factor (δT) can be calculated as followsPL intensity of emitters is determined by many factors including the collection efficiency of the spectroscopy setup used for characterization, the excitation rate  is maximum. The color plot of near E-field distribution (at 680 nm) at the interface plane between the double spacing array and ML MoS2 is shown in 2  is more significant than field enhancement in the excitation band (~532 nm) for the double spacing array coupled structure. Double spacing NC array coupled structure shows significant enhancement of emission field intensity as compared to bare ML MoS2  for the double spacing array coupled structure could be the reason for higher relative intensity ratio for the Raman peaks (E12g/A1g) when compared to the single spacing array as seen in Lumerical finite-difference time-domain (FDTD) simulations were used to calculate E-field intensity distribution for different polarization angles of incident excitation  for the own in 2 . Line pl ML MoS2 , which eion band , it suff2 the quantum yield enhancement is dependent primarily on the radiative Purcell factor for spontaneous emission252 will be blocked2 emission to a higher density of Au NCs . 2” and “ML MoS2 + Au equal spacing array” cases, the patterns are symmetric and we basically have similar ellipsoidal-like shapes on both planes, where the latter has a smaller maxima, as expected from the results shown in 2 + Au double spacing array” has different patterns on the XZ- and YZ-planes due to changing periodicity along x- and y-directions. On both planes, the maximum intensity is 40% higher than the bare MoS2 case.To study the effect on the far-field radiation pattern of the two different Au NC periodic array geometries coupled with ML MoS2 by utilizing surface plasmonic resonance (SPR) and manipulating the structural parameters of an Au nanocone plasmonic arrays. Coupling of the SPR mode of the Au arrays provides a mechanism to control the emission of ML MoS2. Plasmon induced field in ML MoS2 during excitation and emission processes greatly influence the overall emission. We show that PL intensity modulation is controlled via both optical field enhancement and spontaneous emission rate enhancement. Enhancement and quenching of luminescence from plasmonic array coupled ML MoS2 structures and its far-field intensity distribution have been studied numerically by optical pumping. This method offers an important way of emission modulation from quenching to enhancement with the opportunity of polarization-based emission control for development of future optoelectronic applications.In summary, we have demonstrated enhancement (~3.5 fold) and quenching (~4 fold) in PL intensity of ML MoS3  powder was placed in a ceramic boat at the center of a 2-inch diameter furnace. In another alumina boat, sulfur  powder was placed upstream relative to the gas flow direction at a position 15 cm from the MoO3 powder. SiO2 (90 nm)/Si substrate was first sonicated in acetone and then in isopropyl alcohol (IPA) for 15 minutes each. Subsequently, it was immersed in a freshly prepared piranha solution  for 1 hour before washing with DI water and finally dried at 90 °C on a hot plate for 15 minutes. The substrate was mounted on top of the boat containing MoO3 powder with its polished surface facing downward. It was supported from the bottom by two SiO2 coated Si strips−1 with 10 sccm argon (Ar) flow. Temperature in this step was maintained at 680 °C for 5 minutes. Furnace was then switched off and the reactor was allowed to cool under the same Ar flow rate. When the temperature reached 540 °C, the flow rate of argon was increased to 300 sccm and maintained until the reactor temperature went down to room temperature.The CVD growth was performed at atmospheric pressure while flowing ultrahigh purity argon (5 N) gas. Prior to the growth, high purity MoO2 was taken to be ~0.7 nm. An additional mesh size of 0.01 nm for the MoS2 layer region was utilized making sure that enough mesh points are present inside the material. For the E-field intensity distribution2 in the xy-plane and the source excitation on top along the z-axis. The span of z-axis was such that the distance between the structure and top z-axis PML boundary was at least half of the maximum wavelength. Wavelength dependent complex permittivity of the materials were used to define their absorption. Lumerical FDTD simulations were performed on a Dell Precision workstation with the following components: Dual Intel Xeon E5 2650V3 processors (10 core) at 2.3 GHz and 128 GB DDR4 RAM.The simulations were performed using commercial software packages Lumerical FDTD2 on SiO2/Si substrate. Raith 150TWO electron beam lithography (EBL) system was used to fabricate the patterns on ML MoS2 coated SiO2/Si substrate. After monolayer MoS2 identification, alignment markers were made by standard electron beam lithography using resists (PMMA and EL-9). The detailed process flow to pattern Au plasmonic array on top of pre-defined markers on ML MoS2 is described below:Large area rectangular plasmonic arrays (22 μm × 22 μm) were patterned with monolayer MoSResist spinning for plasmonic array: The e-beam dose window was optimized for the following particular combination of bilayer PMMA. Combination of bilayer PMMA. An EBL resist (PMMA 950 K with 2% solid content dissolved in Anisole) was spun at 2500 revolutions per minute (RPM) for 45 seconds and baked 45 seconds and baked on a hot plate at 180 °C for 40 seconds. For coating of the second layer, 4% PMMA 950 K was spun on top of the first layer PMMA at 6000 RPM for 40 seconds followed by a long baking on a hot plate at 180 °C for 90 seconds.2 and 300 μC/cm2 were used for equal and double spacing array, respectively.E-beam exposure: Manual write-field alignment technique using pre-defined aligned markers was employed to perform the exposure. The writing field was set at 4000x, 25 μm. Focused beam of electrons, accelerated with an energy of 20 keV and through a 10 μm aperture (beam current: 0.034 nA) was scanned over the sample for writing arrays of equal and double spacing on bilayer PMMA coated samples. Typically, area doses of 320 μC/cm2 gas.Development: Dip in an MIBK: IPA mixture (1:3 by volume ratio) for 90 seconds at room temperature and 45–55% humidity conditions followed by rinsing in IPA for 30 seconds and finally blow dry with N−6 mbar. Au metal was deposited to obtain a total thickness of ~120 nm at a deposition rate of ~5 nm/minute.Metal deposition: Au metal was deposited on top of the patterned substrate using thermal evaporation at a base pressure of 4 × 10Lift-off: After Au deposition, the sample was immersed in an acetone bath for ~3 hours at room temperature to remove the resist and metal on top of it except the developed plasmonic array area.How to cite this article: Mukherjee, B. et al. Exciton Emission Intensity Modulation of Monolayer MoS2 via Au Plasmon Coupling. Sci. Rep.7, 41175; doi: 10.1038/srep41175 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Soft materials featuring both 3D free-form architectures and high stretchability are highly desirable for a number of engineering applications ranging from cushion modulators, soft robots to stretchable electronics; however, both the manufacturing and fundamental mechanics are largely elusive. Here, we overcome the manufacturing difficulties and report a class of mechanical metamaterials that not only features 3D free-form lattice architectures but also poses ultrahigh reversible stretchability (strain > 414%), 4 times higher than that of the existing counterparts with the similar complexity of 3D architectures. The microarchitected metamaterials, made of highly stretchable elastomers, are realized through an additive manufacturing technique, projection microstereolithography, and its postprocessing. With the fabricated metamaterials, we reveal their exotic mechanical behaviors: Under large-strain tension, their moduli follow a linear scaling relationship with their densities regardless of architecture types, in sharp contrast to the architecture-dependent modulus power-law of the existing engineering materials; under large-strain compression, they present tunable negative-stiffness that enables ultrahigh energy absorption efficiencies. To harness their extraordinary stretchability and microstructures, we demonstrate that the metamaterials open a number of application avenues in lightweight and flexible structure connectors, ultraefficient dampers, 3D meshed rehabilitation structures and stretchable electronics with designed 3D anisotropic conductivity. Soft materials with a unique combination of tailored 3D architectures, lightweight and high deformability are desirable for a diverse range of scientific and technological applications including impact absorbents1356712214151711410110From another aspect, aided with modern additive manufacturing techniques , engineers have recently demonstrated potent capability of creating exotic rigid metamaterials in highly-complex 3D micro/nano architectures to enable ultralow material density and ultrahigh mechanical efficiency242526272829303 (6% of bulk elastomer), but also ultra-stretchable with reversible strain as large as 414%, 4 times larger than that of the existing counterparts with the similar complexity of 3D architectures1Here, we propose a simple manufacturing strategy and create a class of mechanical metamaterials in nearly arbitrary 3D architectures of highly-stretchable elastomer lattices. The manufacturing strategy relies on dissolvable hollow scaffolds fabricated by projection microstereolithography and judiciously circumvents the existing roadblocks of additive manufacturing of elastomer microstructures3 that are around 6–50% of the corresponding elastomer bulk. Since the elastomer modulus is in a range of 20–400 kPa (3) by increasing the volume of the hollow scaffolds and the number of unit cells with the existing stereolithography technique combining x-y axis scanning , our elastomer lattices pose the highest reversible stretchability and compressibility . The fab2526242829305It is well known that the small-strain Young’s moduli of lattice materials scale with their relative densities in power laws as1E and Eo, ρ and ρo are Young’s moduli, density of the lattices and the solid constituents, respectively. The exponent n is strongly dependent on the architectures121bending-dominant structure, with examples including Octet-truss  to the fabricated lattices . We findμ is shear modulus, λ = 1 + ε is uniaxial stretch, I1 = λ2 + 2λ−1 is the strain invariant and λm is a parameter to characterize the maximum stretchability. Then, we systematically vary lattice densities by changing lattice beam diameters, which lead to variations of their shear moduli  elastomer Octet lattice in a cylindrical shape can support a finger to perform bending practices . With full freedom of controlling architectures, the elastomer-lattice metamaterials with tunable exotic large-strain tensile and compressive properties may open new avenues for a number of future research directions and applications. In the research field of material science, these elastomer metamaterials demonstrate a new property space which features an unprecedented combination of 3D free-form architecture, low density and ultrahigh stretchability 1; within4%. With 1165051567532331547The fabrication of elastomer lattices starts from water-soluble hollow scaffolds that are 3D-printed by a projection microstereolithography system . The phoIn compression tests, elastomer lattices are compressed by various loading rates 0.0167, 0.83 and 3.33 mm/s with a mechanical tester . The nominal stress is calculated as the loading force over the average crosssection area of the lattice. The compressive strain is directly calculated as the loading distance over the initial height of the lattice. In tensile tests, the samples are clamped on the designed stretching bars and stretched by loading rate 0.0167 mm/s. The deformation evolution is recorded by a camera (Canon EOS 70D) and the tensile strain is calculated by the real elongating length of the lattice part .0 is calculated as the volume fraction of the lattice structures, directly estimated in the SolidWorks model.The beam diameter and length of the fabricated elastomer lattices are first measured with a vernier caliper (resolution 10 μm). Then a SolidWorks model is created with the measured dimensions. The relative density ρ/ρThe elastomer foams are fabricated by curing a mixture of mold max NV14 and sugar powder  in a glass vial. The cured sample is then immerged in DI water for 6 h to dissolve the sugar, leaving a porous elastomer foam. A foam (cut in a disk with height 8 mm and diameter 8 mm) is compressed with loading rate 0.0167, 0.83 and 3.33 mm/s, respectively . Foam ba0 = 71 kPa and λm = 2.91 , an elastomer solid cubic, an HDDA lattice (ρ/ρ0 ~ 26%) and an elastomer foam (ρ/ρ0 ~ 26%) with the same sample size (8 mm × 8 mm × 8 mm) are placed on the identical HDDA shells with a very thin layer of super glue. The metal weight (~36 g) cannot break the skull (~0.16 g) by its own weight .