How to calculate band gap from reflectance

how to calculate band gap from reflectance

Remote Sensors

In general, the band gap of materials can be obtained from the absorption spectrum. As for non-transparent powder sample, it is difficult to obtain the absorption spectrum, and the diffuse. May 12, How to calculate band gap from Diffuse Reflectance spectroscopy (DRS) using kubelka munk functionwe will plot (F(R)hv)^2 vs hvwhere hv is the energy.

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Find more information on the Altmetric Attention Score and how the score is calculated. We investigate the origin of emission lines apparent in the low-temperature photoluminescence spectra of n-doped WS 2 monolayer embedded in hexagonal BN layers using external magnetic fields and first-principles calculations.

Apart from the neutral A exciton line, all observed emission lines are related to the negatively charged excitons. Consequently, we identify emissions due to both the bright singlet and triplet and dark spin- and momentum-forbidden negative trions as well as the phonon replicas of the latter optically inactive complexes. The semidark trions and negative biexcitons are distinguished. On the basis of their experimentally extracted and theoretically calculated g -factors, we identify three distinct families of emissions due to exciton complexes in WS 2 : bright, intravalley, and intervalley dark.

The g -factors of the cslculate subbands in both the conduction and valence bands are also determined. Whereas the former splitting is of the order of a few hundreds pes anserine bursitis how long to heal millielectronvolts, the latter equals only a few tens of millielectronvolts and can be positive or negative. Dark excitons in S-TMD ML can be divided into two subgroups because of the distinct origins of their optical inactivity, that is, intravalley spin-forbidden and intervalley momentum-forbidden complexes, which can not recombine optically due to the spin and momentum conservation rule for excitons.

Dark excitonic complexes can be also characterized by their net charge. Both neutral and charged dark excitons exist, which are bound electronhole eh pairs and the bound eh pairs with an extra carrier an electron or a holerespectively.

In this work, we investigate the low-temperature optical response of high-quality n-doped tungsten disulfide WS 2 ML encapsulated hexagonal BN hBN flakes using photoluminescence PL spectroscopy how to tear out concrete external magnetic fields.

All emission lines, observed in the PL spectrum, are due to both the bright singlet and triplet and dark spin- and momentum-forbidden negative trions as well as the phonon replicas of the latter optically inactive complexes. Moreover, the semidark trions and negative biexcitons are distinguished.

Magneto-PL hoa accompanied by first-principles calculations allow us to extract the g -factors of all transitions as well as of the spin-split subbands in both the conduction and the valence bands. The negatively charged exciton negative trion is a three-particle complex composed of an eh pair and an excess electron.

They involve correspondingly two electrons from the same valley whereas the triplet trion comprises two electrons from different valleys. For reflectannce dark optically inactive negative trions, the corresponding electrons are located in different valleys and are characterized by the antiparallel alignment of their spins.

This configuration leads to two complexes, depending on the electron involved in the recombination process: intravalley spin- Yo D and intervalley momentum-forbidden T Iwhich cannot recombine optically because of the spin and momentum conservation, respectively. Figure 1.

Schematic illustration of possible spin configurations for negatively charged excitons formed in the vicinity of so-called A exciton. T S and T T correspond to the bright singlet and triplet trions, whereas T D and T I represent the dark intravalley and intervalley complexes, respectively. Increasing the excitation power leads to the appearance of an additional emission, labeled XX . Those lines have not been reported so far in WS 2 MLs and the following is dedicated to their identification.

Figure 2. As can be appreciated in Figure 1both the intravalley spin-forbidden and intervalley momentum-forbidden negative trions share the same initial carrier configuration. The difference arises from their recombination pathway. Reflcetance effect was investigated in details in ref The observation and assignment of the emission to the intervalley momentum-forbidden negative trion is more striking. Recently, similar emission related to the momentum-forbidden dark neutral exciton was reported in the WSe 2 ML.

The origin of the T D -T I energy splitting is not clear as both the intervalley and intravalley dark trions share the same carrier configuration see Figure 1. We believe that this splitting arises from higher-order processes; the description of this is beyond the scope of our work. The similar energy separation between the intervalley and intravalley dark neutral excitons in WSe 2 ML was reported to be of about 10 meV and was ascribed to a short-range electronhole exchange interaction.

Figure 3. The solid lines represent fits according to the equation described in the text. Note the measurements were performed in the tilted configuration of the magnetic field direction in respect to the ML plane see Supporting Information for details.

Linear fits to the experimental data are also presented in the figure. The former value is consistent with our recent result reported in ref 10whereas the latter one is very similar to the g -factor reported for intervalley dark complexes in WSe 2 MLs.

The identification of four lines reflwctance in the lowest energy range of the PL spectrum see Figure 2 will be addressed in the following. One of the possibilities to fulfill the spin and momentum conservation during optical recombination of the dark trions is phonon emission. Figure 4 a shows a schematic illustration of possible recombination pathways of dark negative trions involving phonon emission. The phonon-assisted processes give rise to so-called phonon replicas of dark excitons in WSe 2 MLs.

Figure 4. The black solid lines represent the phonon emission, which tto an electron or a hole from the real subband in the CB or VB to the virtual state denoted by a dashed horizontal line. The dispersions of the relfectance phonon modes are indicated by color curves, whereas for the others it is represented by gray curves. Note that the energy axis in panel c is relative, that how to use liquid acrylic paints, in reference to the T D emission.

White dashed lines superimposed on the observed transitions are guides to the eyes. The phonon replicas of the dark trion should be red-shifted from it by the phonon energies with the redshift corresponding to the phonon emission. The calculated phonon dispersion can be therefore compared to the low-temperature PL spectrum of the WS 2 ML as presented in Figure 4 b,c.

We found that the extracted relative energies of phonon reflectqnce from the T D line are in good agreement with the reflectwnce theoretical phonon energies. To confirm the assignment of phonons shown in Figure 4 a, we analyzed their symmetries following the group theory considerations and irreducible representations IR notation from ref 26where WSe 2 ML of the same symmetry as WS 2 ML was studied.

Additionally, comparing the measured redshift how to calculate band gap from reflectance meV and the calculated phonon energy The other replicas, which involve the momentum-flip processes the spin of the electrons is conserved at the same timemust be induced by phonons from the K point.

Their calculated energies Therefore, we label the replicas apparent at about 1. The red shift of the replica at around 1. The former one should induce a spin flip, whereas the latter one preserves this symmetry and couples to a spin conserving transition. Because of the extracted g -factor value for this replica discussed in how to teach people with dyslexia next paragraphwe label it as T ZA K D.

To confirm the assignment of the how to stay cool in hot weather outside replicas, we analyze their hoow properties under circular polarized excitation and their caldulate when applying an out-of-plane magnetic field. Figure 4 d shows the helicity-resolved PL under circularly polarized excitation with the T S energy.

For the T LA Feom D line, the opposite behavior should be present, as the emission occurs at the valley which is opposite to the excitation one due to the momentum-flip of a hole in the VB. However, that replica demonstrates almost zero preservation of excitation helicity, which may be related to the scattering processes of carriers.

As can be seen in Figure 4 e, the studied lines are characterized not only fro different magnitudes of their field-induced shifts but also by ro sign. To extract their g -factors, we fitted our experimental results using the formula where E 0 is the emission how to formate your computer at zero field. We note that the corresponding semidark trion has recently been reported in WSe 2 ML.

Figure 5. Schematic illustration of a possible recombination pathway of a semidark trions made optically active due to the ee scattering and b negative biexcitons. The intensities of the PL spectra are normalized by the X B intensity. The dashed black line indicates the linear and quadratic behaviors as a guide to the czlculate. The last studied excitonic complex is a negative biexciton, denoted as XX . Its formation is possible due to the long lifetime of rflectance trions see Figure 5 bwhich was reported to be close to 0.

The XX 1 XX 2 energy separation of about 2 meV is very similar to the energy separation reported for two neutral biexcitons 2. These types of power dependence are typical for excitonic complexes composed of a single eh pair or by two eh pairs.

The g -factors for the all studied excitonic complexes are summarized in Table 1. In order to establish the g -factors of single subbands in both the CB and VB, we adapted the method proposed in ref It relies on the comparison of g -factors related to the different excitonic complexes see SI for details.

The extracted values demonstrate that the simple model commonly employed for the calculation of the excitonic g -factors using additive contribution of the spin, valley, and orbital angular momenta 36 cannot explain the single band g -factors. To verify our experimental results, we calculate theoretically g -factors using a first-principles based how to build a hydroponic greenhouse proposed in ref In this case, first the g -factors of single subbands g n calc are calculated, which are then used to determine the g -factor of a given transition g calc.

The magnitudes of g -factors can be explained in terms of the orbital and spin contributions to the angular momenta teflectance bands. The bright complexes involve the spin-conserving transitions, therefore their g calc is determined only by the orbital contribution. The momentum-forbidden complexes involve carriers from different K valleys, which give rise to the large orbital angular momentum difference and lead to a high value of g calc.

As can be appreciated in Table 2the experimental and theoretical values of g -factors are in very good agreement. We found that the extracted g -factors of all transitions may be arranged in three groups revealing a nature of electronhole recombination: bright, intravalley, and intervalley dark. We explained their signs and magnitudes with the aid of first-principles calculations. The obtained g -factors of the spin-split subbands in both the CB and VB are important for better understanding of the interlayer transitions in van der Waals heterostructures.

Such files may be downloaded by article for research use if there is a public use license linked to the relevant article, that license may permit other uses. We thank A. Slobodeniuk, M. Bieniek, and P. Faria Junior for fruitful discussions. Pasteura 5, Warsaw, Poland. More by Tomasz Kazimierczuk.

More by Piotr Kapuscinski.


How to calculate the band-gap, absorption and reflectance of any materials like graphene, doped ZnO, TiO2, ZrO2, NiOx, etc. Which software can be used and how to select the parmeters? the onset of the diffuse reflectance spectra of the powdered or bulk materials. Also the absorption edge and band gap energies of the prepared glass were determined. The optical energy gap is calculated and found to be ( - ) eV. Which is in close agreement to the one calculated for r = 1/2, i.e. the transition mechanism, is accordingly File Size: KB. where, R ? is reflectance F (R ?) is the K-M function The band gap of the samples can be estimated by using Tauc plot. (?h?) 1/n = A (h??E g).

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Natural systems display sophisticated control of light-matter interactions at multiple length scales for light harvesting, manipulation, and management, through elaborate photonic architectures and responsive material formats. Here, we combine programmable photonic function with elastomeric material composites to generate optomechanical actuators that display controllable and tunable actuation as well as complex deformation in response to simple light illumination.

The ability to topographically control photonic bandgaps allows programmable actuation of the elastomeric substrate in response to illumination. Complex three-dimensional configurations, programmable motion patterns, and phototropic movement where the material moves in response to the motion of a light source are presented.

The strategy presented here provides new opportunities for the future development of intelligent optomechanical systems that move with light on demand. These architectures have long been a source of inspiration for the development of multiple artificial optical functional materials for effective light-energy conversion 2 , 3 , 6.

Specifically interesting among these are periodic nanostructures i. These geometries have been successfully utilized as light-harvesting layers in various optical devices to enhance light-energy conversion, including photocatalysis 9 , 10 , photovoltaics 9 , 11 , light-emitting diodes 12 , 13 , and photothermal systems 14 , Another lightmatter interaction of interest converts optical energy into mechanical action, with several outcomes that add utility to applications in soft robotics 16 , 17 , biomedical devices 18 , 19 , or sensing 20 because of the ability to remotely activate devices There has been exciting progress in the development of high performance optomechanical systems based on liquid crystal networks 22 , 23 , 24 , hydrogels 25 , 26 , shape memory polymers 27 , 28 , inequivalent expansion of gradient materials 29 , 30 , inorganic materials 31 , 32 , and others Current strategies for materials for optomechanical control involve the optimization of molecular structure assembly with outcomes that cover complex movement such as folding 23 , 30 , swimming 25 , 34 , 35 , walking 31 , self-oscillation 24 , 25 , and heliotropic motion 26 , Great efforts have been devoted in finding various approaches based on photothermal and photochemical mechanisms to manage the light-energy conversion that dominate the actuation 22 , 29 , 34 , Most optomechanical devices are engineered to perform local light-energy conversion 23 , 30 , 31 , which usually involve complex and energy-intensive fabrication process or complicated setups.

We describe here a composite material exploiting both modes of lightmatter interaction in which the confluence of programmable photonic crystals with elastomeric materials enables a class of photo-responsive actuators that allow controllable and tunable actuation, and complex deformation in response to simple light illumination.

The photonic actuator is a bimorph structure consisting of a silk inverse opal SIO , doped with gold nanoparticles and polydimethylsiloxane PDMS , as illustrated in Fig.

Silk fibroin is chosen as the passive layer because of its versatility, flexibility, ease of functionalization, remarkable optical properties, nanoscale processability, and polymorphic features that allow for photonic crystal programmability 38 , Silk also possesses a negative coefficient of thermal expansion CTE 40 which is suitable to interface with PDMS as the active layer because of its large coefficient of thermal expansion, and excellent durability against repeated deformation and high temperature 41 , on top of its optical transparency.

The significant CTE difference between silk fibroin 40 and PDMS 41 allows for the generation of bending motion in response to temperature increases caused by the photothermal effect when the bimorph is exposed to light. The enlarged image shows the nanostructure of the inverse opal. The photonic structure enhances PDMS side illumination or weakens SIO side illumination the gold-nanoparticles-driven photothermal conversion by controlling light propagation within the system.

The inset is a photograph of the as-prepared photonic bilayer film, showing bright green iridescence. The image was collected in the direction perpendicular to the SIO film. The enlarged images clearly show the photonic crystal structure displayed by ordered, hollow silk fibroin structure with air holes on the wall top and the compactly contacted interface between silk and PDMS bottom.

The experimental curve is in agreement with the theoretical calculation. Inset shows a transmission electron microscopy image of the gold nanoparticles. The formation of programmable SIO films is based on colloidal assembly of polystyrene nanosphere multilayers as templates as previously described 38 , 42 , The resulting structure obtained after dissolving the polystyrene spheres in toluene consists of a free-standing gold-nanoparticle-doped SIO film with a nanostructured silk layer enlarged image in Fig.

The bimorph structure is then prepared by casting the PDMS onto the flat side of the film via spin coating and subsequent drying. The nanostructured silk layer provides a photonic crystal lattice layer which serves as an effective reflector, enhancing or weakening the interaction between gold nanoparticles and light as a function of its direction of incidence Fig.

This photonic layer only works when its stop-band matches the plasmonic absorption of gold nanoparticles. This causes larger deformation Fig. By contrast, light incident from SIO side is partially reflected and does not penetrate the gold-nanoparticle-rich layer, resulting in weaker interaction between gold nanoparticles and light and, thus, less material deformation Fig.

In order to maximize lightmatter interaction the photonic crystal layer is designed to have a stop-band that is spectrally matched to the absorption peak of gold nanoparticles. Reflectivity of the photonic structure is increased by controlling its lattice constant and the number of nanosphere layers. The resulting structure is shown in Fig.

Analysis of the interface between silk and PDMS reveals uniform contact, thereby guaranteeing effective heat transfer and stable performance. This is confirmed by analyzing the photothermal conversion of the bilayers Supplementary Fig.

Figure 2b plots the measured displacement at different illumination intensities. The displacement is defined as the straight distance at which the strip tip travels Supplementary Fig.

Consistent with the results of heating Supplementary Fig. The evaluation of displacement induced by the laser illumination time was also examined Fig. The displacement follows an exponential function when the laser is switched on and off. The response rate is evaluated from the initial slope of the displacement curve as a function of time after the light is turned on Fig. The actuation of the photonic bilayer film is reversible with no observable deterioration in displacement after cycles Fig.

Inset shows the calculation of response rate, which is defined as the slope of the tangent line. While the ability to modulate actuation with the photonic structure is remarkable, the capability to design and control the geometric distribution of its photonic bandgap position and intensity provides further degrees of control over optomechanical actuation of the photonic bilayer film.

This is first demonstrated by constructing SIOs with different nanostructures by either adjusting the number of layers and lattice constant of assembled colloidal crystals or by reconfiguring the photonic lattices after the formation of the inverse opal structure 38 Supplementary Fig. For instance, Water-vapor-treatment induces the irreversible compression of photonic lattice in the weak vertical direction of green-colored SIO, leading to the modulation of the photonic stop-band and, thus, the decrease PDMS side irradiation or increase SIO side irradiation in the displacement Fig.

Such approach leverages the ability of water vapor to direct the polymorphic transitions of amorphous silk fibroin and provides the ability to design patterned photonic lattices with different responses 38 , The displacement of PDMS side illumination increases with the increase of reflectance, while it is just the reverse for SIO side illumination.

Middle and bottom Schematics and images of the corresponding motion modes under laser illumination from SIO side: symmetrical folding e , outer bending f , twisting g , and unsymmetrical folding h. The line width changes gradually from one side to another.

The insets in e h and k show the infrared images of the patterned strips under laser irradiation with dashed line outlining the edge of the sample before laser irradiation. This photonic bandgap-dependent actuation enables the construction of complex 3D configurations by optically inducing controlled deformation of different 2D structures. As a first demonstration, a flower-like geometry was assembled using bilayers with different photonic lattices: a stamen made of a yellow SIO and six petals made of green and blue-violet SIOs Fig.

When the construct is illuminated from SIO side, the blue-violet petals bend dramatically towards the light source while the green petals only generate moderate bending Supplementary Movie 1. Another example is a wing flap of a photonic butterfly was demonstrated by patterning the photonic crystals to generate green butterfly wings with blue veins through selectively exposing part of the shaped bilayer to water vapor using stencils Fig.

When the structure is illuminated the wings close rapidly and subsequently open gradually after the light is switched off Supplementary Movie 2. The capacity to programmably pattern the photonic crystal layers by inducing molecular rearrangement in the protein matrix enables the regulation of local light propagation within the bilayer system.

This approach allows for local optomechanical actuation to realize different motion modalities. To demonstrate this idea, the photonic lattices in the bilayers were patterned as shown in Fig.

When SIO sides are illuminated by the laser beam, symmetric folding Fig. This is further verified by thermal imaging to observe temperature distribution during actuation. From the IR images, the patterned areas reach higher temperatures than the unpatterned areas. In addition to these macroscale patterning examples, it is possible to obtain finer patterning details and manipulate light on the microscale. When this structure is illuminated, asymmetric bending is generated because of the heating gradient in response to the pattern Fig.

It is worth noting that water-vapor-based non-contact patterning method presented here allows for the creation of arbitrary, high-resolution few microns patterns, of which the dimension should be determined according to the geometry of the photonic bilayer to achieve desired deformation.

While patterning photonic crystal layers effectively tailors the bandgap for controllable light manipulation, the angular dependence of the reflectivity Supplementary Fig.

This is explored by evaluating the bilayer deformation at different illumination angles Supplementary Fig. Three actuation cases can be identified: i bilayer strip rotates perpendicularly to the short axis either away from Fig. Same legend for a , b , and c. Insert in f indicates the initial state of the sunflower before illumination. Enlarged image shows the structure of one of the transfer-printed solar cells. This feature is reminiscent of the heliotropic bending and moving of sunflowers with sunlight 44 and could provide inspiration for tether free, light responsive materials that adapt and reconfigure themselves in response to moving light.

As a demonstration, a photonic sunflower with pedicel composed of a photonic bilayer film but petals and stamen composed of SIO was designed Fig. The schematics and images shown in Fig. When the irradiation ceases, the sunflower returns to its initial position. The lollipop-like geometry tracks the light source continuously with a twisting motion Supplementary Fig. This wireless, light responsive, phototropic system has utility as a light tracking device and could be used to enhance light-to-energy conversion efficiency when interfaced to photosensitive systems.

The solar cell light conversion efficiency is angle-dependent Fig. As shown in Fig. While this example is optimized for a specific wavelength, in a real-life scenario would have to be adapted to accommodate a flexible structural color filter 45 or have a broad-band photonic structure 46 in order to achieve heliotropic movement under sunlight illumination. In addition, the weight and size of the device that can be mounted in such photonic bilayer are determined by its geometry, which should be further optimized to improve its loading capacity for devices.

Finally, given the confluence of reconfigurability of photonic structures and angle dependence of stop-band, the photonic actuators could provide interesting opportunities to alternate between different motion modes and realize switchable three-dimensional configurations by only tuning the illumination angle.

The former is demonstrated by reexamining the motion modes of the patterned samples shown in Fig. Interestingly, only overall bending is generated for all the samples because of the similar light capture within the patterned and unpatterned areas Supplementary Fig. The latter is demonstrated by reshaping the photonic bilayer into a cross-shaped geometry with two symmetric sides locally patterned using water vapor Supplementary Fig. The combination of a tunable biopolymer material silk fibroin , an elastomer, and a reconfigurable photonic crystal structure provides complex modes of programmable optomechanical actuation by molding the flow of light into the composite structure.

This strategy allows controlled spectral distribution at the microscale, offering the potential for photonic microactuators with complex deformation with potential utility for microrobotic technologies. The availability of a reconfigurable photonic crystal layer for effective, angle-dependent light harvesting opens up the possibility of generating optomechanical actuators that act both as back reflectors 11 , 47 and solar trackers. The reconfigurability of the photonic crystal layer and the ease of functionalization of silk matrix can provide new avenues for optical devices with complex actuation by incorporating photothermal components with different absorption properties such as gold nanocrystals with different morphologies 48 or carbon nanotube with selective chirality distributions 32 , and by selectively matching the wavelength of light source, photonic bandgap, and the absorption band.

Considerable opportunities exist to expand this work to other optomechanical systems, like liquid-crystal elastomers, hydrogels, and shape memory polymers opening promising directions for future development of intelligent and multifunctional optomechanical devices. Citrate stabilized gold nanoparticles were synthesized using the method described in literature When the solution was a deep red color, the beaker was removed from the hotplate and allowed to cool to room temperature.

The regenerated aqueous silk fibroin solution was prepared using the established protocols

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4 thoughts on “How to calculate band gap from reflectance

  1. Yeah. they have to draw it then export it as a picture then combine them using a video editing program

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