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Optoelectronic properties of phosphorene quantum dots functionalized with free base porphyrins
Computational Materials Science 171 (2020) 109278
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Optoelectronic properties of phosphorene quantum dots functionalized with free base porphyrins A. Samiaa, E. Feddia, C.A. Duqueb, M.E. Mora-Ramosc, V. Akimovd, J.D. Corread,
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a
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSET, Mohammed V University in Rabat, Rabat, Morocco Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia c Centro de Investigación en Ciencias-IICBA, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos, Mexico d Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia b
A R T I C LE I N FO
A B S T R A C T
Keywords: DFT Quantum-dots Phosphorene Optical
Electronic and optical properties of phosphorene quantum dots functionalized with an organic molecule, porphyrin, are investigated using density functional theory with two different van der Waals functionals. The electronic structure of this complex is obtained and with this information, the real and imaginary parts of the dielectric function are calculated, from which, the interband optical response can be determined. Depending on the size of the quantum dot and the relative orientation between the dot and the organic molecule, it is found that the porphyrin physisorption leads to important modifications of the energy spectrum of the functionalized blue phosphorene quantum dots. These changes reflect in the optical response of the complex which shows features that come from both the blue phosphorene structure and the organic molecule. It is also found that the rotations of the molecule with respect to the phosphorene quantum dot do not practically alter the value of the binding energy.
1. Introduction The subject of two-dimensional (2D) systems has captured the interest of the scientific community in the last ten to fifteen years [1–4]. These materials present new physical properties that make them candidates for promising applications [3]. For instance, 2D materials would be largely suitable for optoelectronics, spintronics, catalysts, chemical, and biological sensing, supercapacitors, solar cells, and efficient long endurance batteries [2]. Some 2D nanostructures were theoretically put forward, and then they have been synthesized [4]. Among the distinct synthesis processes employed to produce 2D nanostructures, it is possible to mention micromechanical exfoliation, liquid exfoliation, chemical vapor deposition, van der Waals epitaxial growth, and hydrothermal synthesis [3]. Unlike the well-known semiconductor low-dimensional structures known as quantum wells, which provide a kind of 2D confinement to the electron gas through a layered structure of bulk crystals with covalent bonds in all three dimensions, the new 2D materials often form nanostructures, including layered systems. In the case of the multilayer configuration, the involved atomic layers interact with van der Waals forces [1,5].
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In this work, we are going to deal with the theoretical study of a system based on phosphorene, a 2D phosphorus allotrope named in analogy to graphene, a material consisting of a single atomic layer of carbon that extends periodically in two-dimensions [6,7]. Unlike to graphene, phosphorene exhibits a band gap that allows to treat it as a semiconductor material [5,8], for which a number of important prospective applications – some of them thought to be even more spectacular than their graphene-based counterparts – are foreseen [9]. The particular allotropic form to be considered is the one named as blue phosphorene (BP) [10]. To be more specific, we have investigated BPbased quantum dots (QDs). The synthesis and properties of BPQDs appear reviewed in very recent publications [11,12]. Besides, reports on structural, electronic, and optical properties of BP can be found in Refs. [13–16]. Applications in gas sensing and photocatalysis of these nanostructures have also been investigated using first-principles calculations [14,17,18]. On the other hand, the porphyrin molecules have received attention concerning their role in biological processes as well as to their prospective use in catalysis, nanosensors, and electronics (tetraphenyl porphyrin thin film transistors have been fabricated [19]). The optical response of a hybrid system containing porphyrin adsorbed in porous
Corresponding author. E-mail address: [email protected] (J.D. Correa).
https://doi.org/10.1016/j.commatsci.2019.109278 Received 7 June 2019; Received in revised form 9 September 2019; Accepted 10 September 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 171 (2020) 109278
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silicon was reported in [20]. The adsorption of porphyrins onto a metal surface is governed by van der Waals forces and is capable of causing significant changes in the molecular density of states [21]. Porphyrin adsorbed onto semiconductors and dielectrics – including oxide nanoparticles – are reported as well [22–24]. Also, several theoretical works have explored the possibilities provided by the compounds formed of 2D quantum dots and porphyrins to act as photovoltaic materials [25–28]. On the other hand, a recent study has shown that a nanocomposite formed by phosphorene quantum dots functionalized with fullerenes is a prominent candidate for future generation solar energy harvester[29]. In particular, we are interested in characterizing the complex of a phosphorene quantum dot interacting via van der Waals coupling with an organic molecule – free base porphyrin –; in terms of its energy structure as well as its linear optoelectronic properties. Besides, we are aimed at investigating its stability under the influence of such factors as mutual spatial shift and rotation. The method chosen for that purpose is the calculation within the density functional theory (DFT). In particular, we make use of SIESTA density functional theory package. The article contains the following sections: Section 2 is devoted to presenting the theoretical environment of the work; Section 3 includes the discussion of obtained results, and in Section 4 we present the corresponding conclusions.
investigate a number of distinct configurations, related to the position of the adsorbed H2P molecule with respect to the BPQD. The latter is chosen to be the smaller, P24 H14 , one. The configurations are identified as P1-P4 , and they are schematically depicted in Fig. 2. It is possible to use the positions of the free base porphyrin N atoms as a guide for the eyes in order to identify the relative orientation between the components in each case.
2. Calculation method and geometric structure
3. Results and discussion
To obtain the electronic structure of the complex made of an Hpassivated blue phosphorene quantum dot and a free base porphyrin molecule, we perform DFT calculations using SIESTA package [30]. We employ norm-conserving pseudopotentials and localized atomic orbitals as basis set (double-ζ , single polarized in the present work) In each case, the unit cell is taken in a way that ensures a distance of 10 Å between the system images. This separation avoids spurious interactions. All calculations were made at the Γ point. The structures were relaxed until the atomic forces were smaller than 0.04 eV/Å. The inclusion of van der Waals (vdW) interaction in DFT calculations has shown that the chemical accuracy of the results depends on the selected exchange functional [31]. In accordance, with the aim to perform a proper comparison, we make use of two different vdW exchange-correlation functionals: i) the vdW-KBM one, which shows a good description for S22 dataset [31] and ii) the vdW-BH functional, which has been intensively used yielding appropriate results for solids, layered materials, and aromatic molecules [32]. Then, based on the calculated ground state of the system, the imaginary part of the dielectric function, ε2 (ω) can be evaluated and, from it, the interband optical absorption coefficient is evaluated as a function of the frequency α (ω) = ω ε2 (ω)/ c nr , where c is the speed of light in vacuum and nr is the static refractive index. The latter can be known from the zero-frequency limit of n (ω) , obtained after the real part of the dielectric function is determined through the Kramers-Krönig relations (see, for instance, Ref. [33]). As known, blue phosphorene (BP) consists of a quasi-planar isotropic hexagonal array of phosphorus (P) atoms, where P atoms are covalently bonded with three others located in the other plane at an average distance of 1.2 Å forming a puckered honeycomb structure [5]. To obtain a blue phosphorene quantum dot (BPQD), this one is cut from the BP monolayer and assume that the P atoms at the edges are bond to hydrogen atoms in order to ensure the appropriate coordination at these sites. We shall consider different BPQD structures. To mention two examples, the one labeled as P24 H12 is composed by seven phosphorene rings with an overall average diameter of 12.2 Å, while the P54 H18 , with nineteen phosphorene rings, has an overall diameter of 18.6 Å. The free base porphyrin molecule of the formula C20 H14 N4 (H 2P ) has an average diameter of 10.7 Å. In Fig. 1 we present the relaxed geometric structure of P54 H18 and C20 H14 N4 . Besides, for the case of the BPQD-H2P complex, we have chosen to
The Fig. 3 contains the energy spectra related to several BPQDs as well as the one corresponding to the free base porphyrin H2P. The distinct BP-based structures correspond to different QD sizes, as indicated. It can be noticed that small QD systems have wider energy band gaps whilst for the larger structures this quantity tends to stabilize and approaches the value reported for the BP extended monolayer. The complex BPQD-H2P resulting from the adsorption of the free base porphyrin on the blue phosphorene QD substrate shows noticeable modifications in its energy spectrum. These modifications will depend on the BPQD size and also on the particular P1-P4 orientational configuration. In our case, the DFT calculation of the energy spectrum has been carried out using two different vdW exchange-correlation functionals (vdW-BH and vdW-KBM) to ensure the inclusion of the interaction between BPQD and H2P. In this context, Table 1 contains information on the structure and binding energies of different BPQD-H2P complexes. There, the calculated minimum adsorption distance, d, between the porphyrin and the BPQD is reported together with the corresponding complex binding energy, Eb . The general trend observed – except for a single case for each approach – is that both vdW-BH and vdW-KBM results for d are larger in the case of the P24 H12 -H2P complex, compared to the P54 H18 -H2P one, whereas the magnitude of the binding energies for the latter is always greater than its counterparts in the smaller size system. Furthermore, the more considerable differences between the vdW-BH and vdW-KBM calculated properties appear precisely in Eb , with the vdW-KBM being significantly larger in magnitude. In the Figs. 4 and 5 we are presenting the calculated energy level distribution in P24 H12 -H2P and P54 H18 -H2P complexes in the four P1-P4 relative orientation configurations, together with the spectra of isolated BPQD and free porphyrin for the sake of comparison. The choice of such small structures is justified by the fact that the calculation for larger systems does not result in significant variations of properties such as the energy band gap. In Fig. 4 the results were obtained using the vdW-BH functional and those appearing in Fig. 5 correspond to the calculation the made use of the vdW-KBM functional. It can be observed that in each case, the adsorption of the H 2P molecule produces a rather strong modification of the energy spectrum. Analyzing case by case, we have that: (i) In the P24 H12 -H 2P complex, the greater change takes place in the energies located below the Fermi level. In that energy range, the H 2P has several energy levels located within the BPQD forbidden gap, as is observed in the projected density
Fig. 1. Geometric structure of phosphorene quantum dots and free basis porphyrin (a) P54 H18 phosphorene quantum dot, and (b) free basis porphyrin.
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Fig. 2. Geometric structure of relaxed complex P24 H12 -H2P for different positions of the free-base porphyrin over the P24 H12 . These positions are chosen, taking into account: P1 corresponds to a slight rotation of the structure depicted in Fig. 1(b) that naturally appears when the relaxation is achieved; P2, is a rotation of around 60° with two N atoms of the H-N bond are located on top of P atoms. P3 has a rotation of ∼ 120°; and P4, in which the angle of rotation is ∼ 150°.
of the BPQD and the BPQD-H 2P complex appear in the region located above the Fermi level. First, it can be observed that the whole “conduction” spectrum is significantly shifted down. In the second place, it is possible to see that, in all cases, that part of the spectrum becomes denser than its counterpart in the pristine BPQD. That is, the effect of the adsorbed organic molecule causes that a large number of levels appear in that interval, as if they were pulled down by the interaction. On the other hand, the part of the spectrum located below the Fermi level – the “valence” region – shows only a minimal shift upwards in the case of the upper levels; but for the lower ones, the shift is stronger, and a larger number of levels tend to accumulate within the region. The differences in the use of the two different van der Waals functionals can also be appreciated. Taking as a reference the case of the smaller system, P24 H12 -H 2P , one may observe from Fig. 5(a) that in the region below the Fermi level, the vdW-KBM-calculated “valence” edge energies have lower values compared to the vdW-KBM ones [Fig. 4(a)]. This can also be seen in the case of the P54 H18-H 2P complex, in which it is also possible to detect that the vdW-KBM “valence” spectrum has a larger density of levels per unit energy than it vdW-BM counterpart. Going over to the “conduction”-like states – above the Fermi energy – we notice that the descent of the level induced by the porphyrin physisorption on the BPQD is more pronounced when the calculation is performed using the vdW-KBM functional. With regard to the energy bandgap it is possible to observe that, in general, the differences between the description that uses the BH functional and that employing the KBM functional are, at most, of 6–7 meV for the smaller -P24 H12 -H 2P - QD and of 15–20 meV for the P54 H18 -H 2P . The rotated configurations differ from each other in a few meV, as can be seen in the rightmost columns of Table 1. Changes associated with the modification of the relative orientation of the adsorbed molecule with respect to the BPQD substrate can be noticed as well. They are seen throughout the entire range of energies reported. However, in order to have a first impression, it is sufficient to look at the relative displacements of the gap edges when comparing the P1-P4 results. Then, one may observe that for distinct P1-P4 orientations, the edge levels in both the “valence” and “conduction” regions shift in slightly different ways. As commented, the spectrum of allowed energy states of the BPQDH2P systems arises from the interaction that takes place during physisorption. In order to have a more comprehensive view of its features, we have depicted in Fig. 6 the vdW-KBM energy level structure of P24 H12 -H2P-P1 together with a representation of the local density of states (LDOS) in the complex. Each depicted configuration corresponds to a given allowed energy state, indicated by an arrow. It can be noticed that for some of the states, the LDOS is largely localized on the H 2P molecule whereas in some others it is predominantly localized on the BPQD. However, there are others, such as the lowest level in the “valence” energy region, for which the LDOS distributes more evenly between the QD and the organic molecule. This gives the idea of rather complex nature of the spectrum, mainly in the vicinity of the band gap region. Let us now comment on the calculated optical response of the
Fig. 3. Calculated energy levels of several pristine phosphorene quantum dots and isolated free basis porphyrin.
Table 1 Calculated minimum adsorption distance (d,) binding energy (Eb ), and energy band gap (Egap ) for blue phosphorene quantum dot plus free base porphyrin complexes. Two different quantum dot sizes and four distinct relative orientations between the dot substrate and the adsorbed molecule are considered (see Fig. 2). (a) results obtained with the use of van der Waals-BH functional, (b) results obtained with the use of van der Waals-KBM functional. System
P24 H12 − H 2P − P1 P24 H12 − H 2P − P 2 P24 H12 − H 2P − P 3 P24 H12 − H 2P − P 4 P54 H12 − H 2P − P1 P54 H12 − H 2P − P 2 P54 H12 − H 2P − P 3 P54 H12 − H 2P − P 4
d (Å) a
3.476 , 3.426a, 3.447a, 3.434a, 3.299a, 3.397a, 3.454a, 3.391a,
Eb (eV) b
3.294 3.313b 3.332b 3.285b 3.346b 3.307b 3.114b 3.240b
−0.743 , −0.737a, −0.730a, −0.739a, −1.066a, −1.064a, −1.052a, −1.059a, a
Egap (eV)
−0.941 −0.924b −0.913b −0.921b −1.230b −1.276b −1.242b −1.271b b
1.851a, 1.862a, 1.864a, 1.876a, 1.830a, 1.850a, 1.855a, 1.838a,
1.845b 1.855b 1.858b 1.878b 1.812b 1.844b 1.836b 1.818b
of states (PDOS) on Figs. 4 and 5. The interaction with these molecule states acts in a way that pulls up the QD energies with the upper value tending to level with the corresponding one of the organic molecule. This phenomenon also reflects in a denser energy level distribution, compared with the pristine BPQD case. For the same complex, the modification occurring in the energy range above the Fermi level is less pronounced although in all case one may notice a slight shift downwards of the lower states and the opening of a secondary gap of about 0.5 eV between these states and those immediately above. This is something that is not present in the pristine BPQD and resembles the large inter-level separation of the isolated H 2P molecule in that energy interval. (ii) The spectra of P54 H18 -H 2P complexes exhibit quite noticeable modifications as well, compared to those of the pristine QD and the isolated molecule. In this case, although the energy band gap also decreases, the larger differences between the energy level distribution 3
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Fig. 4. Calculated energy levels of P24 H12 -H 2P (a) and P54 H18 -H 2P complexes (b) and projected density of states over QD (red lines) and H 2P (blue lines) for P24 H12 -H 2P (c) and P54 H18 -H 2P complexes (d). The results are obtained using the van der Waals vdW-BH functional. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
change in the incident light polarization practically does not affect the lower energy response, but one may notice important differences in the corresponding ε2 (E ) curves at high photon energies. To understand the features of the BPQD-related results in Fig. 7, the information about the allowed energies spectra depicted in Fig. 3 is crucial. Clearly, the response corresponding to the pristine BPQDs has strong differences with the BP monolayer one when the size of the quantum dot is small. The signal from the P24 H12 shows large amplitudes at energies well above the position of the main peak of the BP monolayer. As long as the size of the dot augments, there is a greater resemblance of the calculated imaginary part of the dielectric function
BPQD-H2P structures. Fig. 7 contains the imaginary part of the dielectric function plotted versus the energy of the incident photon. The curves correspond to isolated H 2P and pristine BPQDs of different sizes. For the sake of comparison, the result for the BP monolayer is included. Two distinct incident light polarizations have been considered in the calculation regarding the H 2P molecule. We first comment on the features of the H2P-related response. It can be seen from Fig. 7 that the stronger response associates with inter-level transitions around 2 eV. They involve the allowed molecule levels that appeared depicted in Fig. 3 immediately below and above the Fermi energy. Higher energy transitions show much smaller amplitudes. The
Fig. 5. Calculated energy levels of P24 H12 -H 2P (a) and P54 H18 -H 2P (b) complexes and projected density of states over QD (red lines) and H 2P (blue lines) for P24 H12 -H 2P (c) and P54 H18 -H 2P complexes (d). The results are obtained using the van der Waals vdW-KBM functional. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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functional, and correspond to the higher energy values considered (above 4.5 eV) which certainly involve states resulting from the coupling of QD states with higher H2P levels. The change in light polarization also produces a small shift in the signal. It can be more clearly noticed by observing the peaks around the mentioned low-energy H2P feature, and it is more apparent in the case that uses vdW-KBM functional in the calculation. On the other hand, the interaction between the QD and H2P appears in the ε2 as small transitions in the 2.2 –2.7 eV range. These transitions show a stronger H2P position dependence for both vdW functionals considered. The analysis of the optical properties for the P54 H18 -H 2P depicted in Fig. 9, and more of its related conclusions follow the same line of smaller QD case. That is, it is based in the previously commented results for the energy spectrum and the characteristics of the corresponding optical response from the pristine BPQD and the isolated porphyrin molecule. However, in this situation one may observe that a stronger reduction of the low-energy ε2 amplitude of the physisorbed complex compared to the isolated H2P one, whereas the amplitude of the high energy response can be approximately equal than its low-energy counterpart thus differing from the P24 H12 -H 2P results and somehow resembling the BP monolayer response appearing in Fig. 7. In the Supplementary material, we are presenting the calculated real part of the dielectric function and the light absorption coefficient as functions of the incident photon energy for the different BPQD sizes that have been considered in the present work (Fig. S1), and for complex P24 H12 -H2P (Fig. S2), and P54 H18 -H2P (Fig. S3). For both P24 H12 -H2P and P54 H18 -H2P complexes, it comes out that in the calculated optical absorption response, the amplitude of the corresponding resonant absorption peaks associated to the H2P-related feature is smaller than the amplitudes of the high-energy absorption peaks. This has to do with the presence of the ω = E/ℏ factor, which makes the absorption amplitude directly proportional to the resonant peak energy. Since the H2P-related peaks appear at lower energies, this factor quenches the overall amplitude of the absorption close to the light absorption threshold while it enhances the amplitude for high enough energies. That is, the ω = E/ℏ resonant factor dominates over the contribution coming from the ε2 variation with the incident light energy.
Fig. 6. The vdW-KBM energy level structure of P24 H12 -H 2P − P1 together with a representation of the local density of states in the complex. Each depicted configuration corresponds to a given allowed energy state, indicated by an arrow.
4. Conclusions
Fig. 7. Imaginary part of the dielectric function for several pristine blue phosphorene quantum dots and the free basis porphyrin. The filled lines correspond to a blue-phosphorene monolayer. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
In this work, we have investigated the properties of the energy spectrum of blue phosphorene quantum dots with H-passivated edges on which an organic molecule – free base porphyrin – is adsorbed. The theoretical study makes use of density functional calculations, including different descriptions of the van der Waals quantum dot-porphyrin interaction via the BH and KBM functionals. Distinct quantum dot sizes, as well as four different quantum dot-porphyrin relative orientations, were considered. With the outcome of the energy spectrum at hand, it was possible to determine the real and imaginary parts of the dielectric function related to interband transitions. Besides, the interband-related optical absorption coefficient is evaluated, as well. It turns out that both the energy structure and the optical response (including two different linear polarizations of the incident light) of the physisorbed complexes show significant changes concerning those of the blue phosphorene quantum dot and free base porphyrin separately. In particular, it is shown with the help of a single example that according to the calculation of the local density of states, the resulting energy spectrum combines rather intricately the quantum dot and organic molecule contributions. The features of the optical response also reflect such intricacy. Using one functional or the other produces values of the binding energy that significantly differ. However, only small differences appear in the physisorption distance and the energy bandgap, as a rule. For the latter, these changes amount at most 20 meV and manifest mainly in the case of the phosphorene quantum dot with the larger size. Another aspect to be highlighted is that the rotations of the molecule with
to that of the monolayer case, with a reduction of the signal’s blueshift, although some higher energy transitions are still detected. By observing Fig. 3(b) one may ratify this fact. Actually, the absorption coefficient for small BPQDs shows peaks of high amplitude in the ultraviolet range. What happens to the optical response when the BPQD-H 2P complex forms? To comment on that we again choose the two cases P24 H12 -H2P (Fig. 8) and P54 H18 -H 2P (Fig. 9). In both cases, the P1-P4 orientational configurations and the x and y polarizations are considered. Both vdWBH and vdW-KBM results are reported for BPQD size. The analysis for ε2 in the P24 H12 -H 2P -P1-P4 case shows the prominent H 2P -related feature (refer to Fig. 7) around 2 eV, which suffers slight modifications in its position when going from the free isolated molecule to the BPQD-H2P adsorbed complex. Also, this feature becomes smaller in amplitude in the P1-P4 complex (with small variations from one orientation to another) with respect to the single H 2P system. For higher energies, the comparison is worth to be made with respect to the pristine QD case. It is possible to notice some changes in the imaginary part of the dielectric function, most of them related to amplitude rather than the position of the appearing peaks. In fact, the energy positions of the physisorbed complexes are only slightly modified in comparison to the pristine BPQD. The greater departures from the pristine QD structure are obtained with the use of vdW-BH 5
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Fig. 8. Calculated imaginary part of the dielectric function of the blue phosphorene quantum dot P24 H12 with free base H 2P porphyrin adsorbed as a function of the photon energy, for several relative orientations P1-P4 (see Fig. 2 for illustration). The results for the pristine quantum dot and the free molecule are included for comparison. Graphics are depicted for x and y incident light polarization and both van der Waals functionals vdW-BH (a), (b), and vdW-KBM (c), (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 9. Calculated imaginary part of the dielectric function of the blue phosphorene quantum dot P54 H18 with free base H 2P porphyrin adsorbed as a function of the photon energy, for several relative orientations P1-P4 (see Fig. 2 for illustration). The results for the pristine quantum dot and the free molecule are included for comparison. Graphics are depicted for x and y incident light polarization and both van der Waals functionals vdW-BH (a), (b), and vdW-KBM (c), (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 6
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respect to the phosphorene quantum dot do not practically alter the value of the binding energy. Hence, one may conclude that such a quantity remains almost unchanged no matter the relative orientation of the physisorbed porphyrin molecule for the dot.
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CRediT authorship contribution statement A. Samia: Software, Investigation. E. Feddi: Formal analysis. C.A. Duque: Writing - review & editing. M.E. Mora-Ramos: Writing - original draft. V. Akimov: Formal analysis. J.D. Correa: Methodology, Conceptualization, Writing - original draft. Acknowledgments The authors thank the Laboratorio de Simulación y Computación Científica of Universidad de Medellín for computational facilities. MEMR thanks the colleagues at the Universidad de Medellín, for hospitality during the preparation of this work. C.A.D. is grateful to the Colombian Agencies: CODI-Universidad de Antioquia (Estrategia de Sostenibilidad de la Universidad de Antioquia and projects “Propiedades magneto-ópticas y óptica no lineal en superredes de Grafeno” and “Estudio de propiedades ópticas en sistemas semiconductores de dimensiones nanoscópicas”), and Facultad de Ciencias Exactas y Naturales-Universidad de Antioquia (CAD exclusive dedication projects 2018-2019). He also acknowledges the financial support from “El Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación Francisco José de Caldas” (project 80740-173-2019). The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.commatsci.2019.109278. References [1] A.K. Geim, I.V. Grigorieva, Van der Waals heterostructures, Nature 499 (7459) (2013) 419–425, https://doi.org/10.1038/nature12385 URL: http://www.nature. com/doifinder/10.1038/nature12385. [2] M. Xu, T. Liang, M. Shi, H. Chen, Graphene-like two-dimensional materials, Chem. Rev. 113 (5) (2013) 3766–3798, https://doi.org/10.1021/cr300263a URL: http:// pubs.acs.org/doi/abs/10.1021/cr300263a. [3] A. Gupta, T. Sakthivel, S. Seal, Recent development in 2D materials beyond graphene, Prog. Mater Sci. 73 (2015) 44–126, https://doi.org/10.1016/j.pmatsci. 2015.02.002. [4] S.Z. Butler, S.M. Hollen, L. Cao, Y. Cui, J.A. Gupta, H.R. Gutiérrez, T.F. Heinz, S.S. Hong, J. Huang, A.F. Ismach, E. Johnston-Halperin, M. Kuno, V.V. Plashnitsa, R.D. Robinson, R.S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M.G. Spencer, M. Terrones, W. Windl, J.E. Goldberger, Progress, challenges, and opportunities in two-dimensional materials beyond graphene, ACS Nano 7 (4) (2013) 2898–2926, https://doi. org/10.1021/nn400280c URL: http://pubs.acs.org/doi/abs/10.1021/nn400280c. [5] H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, Phosphorene: an unexplored 2D semiconductor with a high hole mobility, ACS Nano 8 (4) (2014) 4033–4041, https://doi.org/10.1021/nn501226z URL: http://pubs.acs.org/doi/ abs/10.1021/nn501226z. [6] H.P. Boehm, A. Clauss, G.O. Fischer, U. Hofmann, Dünnste kohlenstoff-folien (thin carbon leaves), Zeitschrift für Naturforschung B 17 (1961) 150–152. [7] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (5696) (2004) 666–669, https://doi.org/10.1126/science.1102896. [8] L. Kou, C. Chen, S.C. Smith, Phosphorene: fabrication, properties, and applications, J. Phys. Chem. Lett. 6 (14) (2015) 2794–2805, https://doi.org/10.1021/acs.jpclett. 5b01094 URL: http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.5b01094. [9] A. Carvalho, M. Wang, X. Zhu, A.S. Rodin, H. Su, A.H. Castro Neto, Phosphorene: from theory to applications, Nat. Rev. Mater. 1 (2016) 16061 review Article.https://doi.org/10.1038/natrevmats.2016.61.
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Optoelectronic properties of phosphorene quantum dots functionalized with free base porphyrins A. Samiaa, E. Feddia, C.A. Duqueb, M.E. Mora-Ramosc, V. Akimovd, J.D. Corread,
T
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a
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSET, Mohammed V University in Rabat, Rabat, Morocco Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia c Centro de Investigación en Ciencias-IICBA, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos, Mexico d Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia b
A R T I C LE I N FO
A B S T R A C T
Keywords: DFT Quantum-dots Phosphorene Optical
Electronic and optical properties of phosphorene quantum dots functionalized with an organic molecule, porphyrin, are investigated using density functional theory with two different van der Waals functionals. The electronic structure of this complex is obtained and with this information, the real and imaginary parts of the dielectric function are calculated, from which, the interband optical response can be determined. Depending on the size of the quantum dot and the relative orientation between the dot and the organic molecule, it is found that the porphyrin physisorption leads to important modifications of the energy spectrum of the functionalized blue phosphorene quantum dots. These changes reflect in the optical response of the complex which shows features that come from both the blue phosphorene structure and the organic molecule. It is also found that the rotations of the molecule with respect to the phosphorene quantum dot do not practically alter the value of the binding energy.
1. Introduction The subject of two-dimensional (2D) systems has captured the interest of the scientific community in the last ten to fifteen years [1–4]. These materials present new physical properties that make them candidates for promising applications [3]. For instance, 2D materials would be largely suitable for optoelectronics, spintronics, catalysts, chemical, and biological sensing, supercapacitors, solar cells, and efficient long endurance batteries [2]. Some 2D nanostructures were theoretically put forward, and then they have been synthesized [4]. Among the distinct synthesis processes employed to produce 2D nanostructures, it is possible to mention micromechanical exfoliation, liquid exfoliation, chemical vapor deposition, van der Waals epitaxial growth, and hydrothermal synthesis [3]. Unlike the well-known semiconductor low-dimensional structures known as quantum wells, which provide a kind of 2D confinement to the electron gas through a layered structure of bulk crystals with covalent bonds in all three dimensions, the new 2D materials often form nanostructures, including layered systems. In the case of the multilayer configuration, the involved atomic layers interact with van der Waals forces [1,5].
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In this work, we are going to deal with the theoretical study of a system based on phosphorene, a 2D phosphorus allotrope named in analogy to graphene, a material consisting of a single atomic layer of carbon that extends periodically in two-dimensions [6,7]. Unlike to graphene, phosphorene exhibits a band gap that allows to treat it as a semiconductor material [5,8], for which a number of important prospective applications – some of them thought to be even more spectacular than their graphene-based counterparts – are foreseen [9]. The particular allotropic form to be considered is the one named as blue phosphorene (BP) [10]. To be more specific, we have investigated BPbased quantum dots (QDs). The synthesis and properties of BPQDs appear reviewed in very recent publications [11,12]. Besides, reports on structural, electronic, and optical properties of BP can be found in Refs. [13–16]. Applications in gas sensing and photocatalysis of these nanostructures have also been investigated using first-principles calculations [14,17,18]. On the other hand, the porphyrin molecules have received attention concerning their role in biological processes as well as to their prospective use in catalysis, nanosensors, and electronics (tetraphenyl porphyrin thin film transistors have been fabricated [19]). The optical response of a hybrid system containing porphyrin adsorbed in porous
Corresponding author. E-mail address: [email protected] (J.D. Correa).
https://doi.org/10.1016/j.commatsci.2019.109278 Received 7 June 2019; Received in revised form 9 September 2019; Accepted 10 September 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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silicon was reported in [20]. The adsorption of porphyrins onto a metal surface is governed by van der Waals forces and is capable of causing significant changes in the molecular density of states [21]. Porphyrin adsorbed onto semiconductors and dielectrics – including oxide nanoparticles – are reported as well [22–24]. Also, several theoretical works have explored the possibilities provided by the compounds formed of 2D quantum dots and porphyrins to act as photovoltaic materials [25–28]. On the other hand, a recent study has shown that a nanocomposite formed by phosphorene quantum dots functionalized with fullerenes is a prominent candidate for future generation solar energy harvester[29]. In particular, we are interested in characterizing the complex of a phosphorene quantum dot interacting via van der Waals coupling with an organic molecule – free base porphyrin –; in terms of its energy structure as well as its linear optoelectronic properties. Besides, we are aimed at investigating its stability under the influence of such factors as mutual spatial shift and rotation. The method chosen for that purpose is the calculation within the density functional theory (DFT). In particular, we make use of SIESTA density functional theory package. The article contains the following sections: Section 2 is devoted to presenting the theoretical environment of the work; Section 3 includes the discussion of obtained results, and in Section 4 we present the corresponding conclusions.
investigate a number of distinct configurations, related to the position of the adsorbed H2P molecule with respect to the BPQD. The latter is chosen to be the smaller, P24 H14 , one. The configurations are identified as P1-P4 , and they are schematically depicted in Fig. 2. It is possible to use the positions of the free base porphyrin N atoms as a guide for the eyes in order to identify the relative orientation between the components in each case.
2. Calculation method and geometric structure
3. Results and discussion
To obtain the electronic structure of the complex made of an Hpassivated blue phosphorene quantum dot and a free base porphyrin molecule, we perform DFT calculations using SIESTA package [30]. We employ norm-conserving pseudopotentials and localized atomic orbitals as basis set (double-ζ , single polarized in the present work) In each case, the unit cell is taken in a way that ensures a distance of 10 Å between the system images. This separation avoids spurious interactions. All calculations were made at the Γ point. The structures were relaxed until the atomic forces were smaller than 0.04 eV/Å. The inclusion of van der Waals (vdW) interaction in DFT calculations has shown that the chemical accuracy of the results depends on the selected exchange functional [31]. In accordance, with the aim to perform a proper comparison, we make use of two different vdW exchange-correlation functionals: i) the vdW-KBM one, which shows a good description for S22 dataset [31] and ii) the vdW-BH functional, which has been intensively used yielding appropriate results for solids, layered materials, and aromatic molecules [32]. Then, based on the calculated ground state of the system, the imaginary part of the dielectric function, ε2 (ω) can be evaluated and, from it, the interband optical absorption coefficient is evaluated as a function of the frequency α (ω) = ω ε2 (ω)/ c nr , where c is the speed of light in vacuum and nr is the static refractive index. The latter can be known from the zero-frequency limit of n (ω) , obtained after the real part of the dielectric function is determined through the Kramers-Krönig relations (see, for instance, Ref. [33]). As known, blue phosphorene (BP) consists of a quasi-planar isotropic hexagonal array of phosphorus (P) atoms, where P atoms are covalently bonded with three others located in the other plane at an average distance of 1.2 Å forming a puckered honeycomb structure [5]. To obtain a blue phosphorene quantum dot (BPQD), this one is cut from the BP monolayer and assume that the P atoms at the edges are bond to hydrogen atoms in order to ensure the appropriate coordination at these sites. We shall consider different BPQD structures. To mention two examples, the one labeled as P24 H12 is composed by seven phosphorene rings with an overall average diameter of 12.2 Å, while the P54 H18 , with nineteen phosphorene rings, has an overall diameter of 18.6 Å. The free base porphyrin molecule of the formula C20 H14 N4 (H 2P ) has an average diameter of 10.7 Å. In Fig. 1 we present the relaxed geometric structure of P54 H18 and C20 H14 N4 . Besides, for the case of the BPQD-H2P complex, we have chosen to
The Fig. 3 contains the energy spectra related to several BPQDs as well as the one corresponding to the free base porphyrin H2P. The distinct BP-based structures correspond to different QD sizes, as indicated. It can be noticed that small QD systems have wider energy band gaps whilst for the larger structures this quantity tends to stabilize and approaches the value reported for the BP extended monolayer. The complex BPQD-H2P resulting from the adsorption of the free base porphyrin on the blue phosphorene QD substrate shows noticeable modifications in its energy spectrum. These modifications will depend on the BPQD size and also on the particular P1-P4 orientational configuration. In our case, the DFT calculation of the energy spectrum has been carried out using two different vdW exchange-correlation functionals (vdW-BH and vdW-KBM) to ensure the inclusion of the interaction between BPQD and H2P. In this context, Table 1 contains information on the structure and binding energies of different BPQD-H2P complexes. There, the calculated minimum adsorption distance, d, between the porphyrin and the BPQD is reported together with the corresponding complex binding energy, Eb . The general trend observed – except for a single case for each approach – is that both vdW-BH and vdW-KBM results for d are larger in the case of the P24 H12 -H2P complex, compared to the P54 H18 -H2P one, whereas the magnitude of the binding energies for the latter is always greater than its counterparts in the smaller size system. Furthermore, the more considerable differences between the vdW-BH and vdW-KBM calculated properties appear precisely in Eb , with the vdW-KBM being significantly larger in magnitude. In the Figs. 4 and 5 we are presenting the calculated energy level distribution in P24 H12 -H2P and P54 H18 -H2P complexes in the four P1-P4 relative orientation configurations, together with the spectra of isolated BPQD and free porphyrin for the sake of comparison. The choice of such small structures is justified by the fact that the calculation for larger systems does not result in significant variations of properties such as the energy band gap. In Fig. 4 the results were obtained using the vdW-BH functional and those appearing in Fig. 5 correspond to the calculation the made use of the vdW-KBM functional. It can be observed that in each case, the adsorption of the H 2P molecule produces a rather strong modification of the energy spectrum. Analyzing case by case, we have that: (i) In the P24 H12 -H 2P complex, the greater change takes place in the energies located below the Fermi level. In that energy range, the H 2P has several energy levels located within the BPQD forbidden gap, as is observed in the projected density
Fig. 1. Geometric structure of phosphorene quantum dots and free basis porphyrin (a) P54 H18 phosphorene quantum dot, and (b) free basis porphyrin.
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Fig. 2. Geometric structure of relaxed complex P24 H12 -H2P for different positions of the free-base porphyrin over the P24 H12 . These positions are chosen, taking into account: P1 corresponds to a slight rotation of the structure depicted in Fig. 1(b) that naturally appears when the relaxation is achieved; P2, is a rotation of around 60° with two N atoms of the H-N bond are located on top of P atoms. P3 has a rotation of ∼ 120°; and P4, in which the angle of rotation is ∼ 150°.
of the BPQD and the BPQD-H 2P complex appear in the region located above the Fermi level. First, it can be observed that the whole “conduction” spectrum is significantly shifted down. In the second place, it is possible to see that, in all cases, that part of the spectrum becomes denser than its counterpart in the pristine BPQD. That is, the effect of the adsorbed organic molecule causes that a large number of levels appear in that interval, as if they were pulled down by the interaction. On the other hand, the part of the spectrum located below the Fermi level – the “valence” region – shows only a minimal shift upwards in the case of the upper levels; but for the lower ones, the shift is stronger, and a larger number of levels tend to accumulate within the region. The differences in the use of the two different van der Waals functionals can also be appreciated. Taking as a reference the case of the smaller system, P24 H12 -H 2P , one may observe from Fig. 5(a) that in the region below the Fermi level, the vdW-KBM-calculated “valence” edge energies have lower values compared to the vdW-KBM ones [Fig. 4(a)]. This can also be seen in the case of the P54 H18-H 2P complex, in which it is also possible to detect that the vdW-KBM “valence” spectrum has a larger density of levels per unit energy than it vdW-BM counterpart. Going over to the “conduction”-like states – above the Fermi energy – we notice that the descent of the level induced by the porphyrin physisorption on the BPQD is more pronounced when the calculation is performed using the vdW-KBM functional. With regard to the energy bandgap it is possible to observe that, in general, the differences between the description that uses the BH functional and that employing the KBM functional are, at most, of 6–7 meV for the smaller -P24 H12 -H 2P - QD and of 15–20 meV for the P54 H18 -H 2P . The rotated configurations differ from each other in a few meV, as can be seen in the rightmost columns of Table 1. Changes associated with the modification of the relative orientation of the adsorbed molecule with respect to the BPQD substrate can be noticed as well. They are seen throughout the entire range of energies reported. However, in order to have a first impression, it is sufficient to look at the relative displacements of the gap edges when comparing the P1-P4 results. Then, one may observe that for distinct P1-P4 orientations, the edge levels in both the “valence” and “conduction” regions shift in slightly different ways. As commented, the spectrum of allowed energy states of the BPQDH2P systems arises from the interaction that takes place during physisorption. In order to have a more comprehensive view of its features, we have depicted in Fig. 6 the vdW-KBM energy level structure of P24 H12 -H2P-P1 together with a representation of the local density of states (LDOS) in the complex. Each depicted configuration corresponds to a given allowed energy state, indicated by an arrow. It can be noticed that for some of the states, the LDOS is largely localized on the H 2P molecule whereas in some others it is predominantly localized on the BPQD. However, there are others, such as the lowest level in the “valence” energy region, for which the LDOS distributes more evenly between the QD and the organic molecule. This gives the idea of rather complex nature of the spectrum, mainly in the vicinity of the band gap region. Let us now comment on the calculated optical response of the
Fig. 3. Calculated energy levels of several pristine phosphorene quantum dots and isolated free basis porphyrin.
Table 1 Calculated minimum adsorption distance (d,) binding energy (Eb ), and energy band gap (Egap ) for blue phosphorene quantum dot plus free base porphyrin complexes. Two different quantum dot sizes and four distinct relative orientations between the dot substrate and the adsorbed molecule are considered (see Fig. 2). (a) results obtained with the use of van der Waals-BH functional, (b) results obtained with the use of van der Waals-KBM functional. System
P24 H12 − H 2P − P1 P24 H12 − H 2P − P 2 P24 H12 − H 2P − P 3 P24 H12 − H 2P − P 4 P54 H12 − H 2P − P1 P54 H12 − H 2P − P 2 P54 H12 − H 2P − P 3 P54 H12 − H 2P − P 4
d (Å) a
3.476 , 3.426a, 3.447a, 3.434a, 3.299a, 3.397a, 3.454a, 3.391a,
Eb (eV) b
3.294 3.313b 3.332b 3.285b 3.346b 3.307b 3.114b 3.240b
−0.743 , −0.737a, −0.730a, −0.739a, −1.066a, −1.064a, −1.052a, −1.059a, a
Egap (eV)
−0.941 −0.924b −0.913b −0.921b −1.230b −1.276b −1.242b −1.271b b
1.851a, 1.862a, 1.864a, 1.876a, 1.830a, 1.850a, 1.855a, 1.838a,
1.845b 1.855b 1.858b 1.878b 1.812b 1.844b 1.836b 1.818b
of states (PDOS) on Figs. 4 and 5. The interaction with these molecule states acts in a way that pulls up the QD energies with the upper value tending to level with the corresponding one of the organic molecule. This phenomenon also reflects in a denser energy level distribution, compared with the pristine BPQD case. For the same complex, the modification occurring in the energy range above the Fermi level is less pronounced although in all case one may notice a slight shift downwards of the lower states and the opening of a secondary gap of about 0.5 eV between these states and those immediately above. This is something that is not present in the pristine BPQD and resembles the large inter-level separation of the isolated H 2P molecule in that energy interval. (ii) The spectra of P54 H18 -H 2P complexes exhibit quite noticeable modifications as well, compared to those of the pristine QD and the isolated molecule. In this case, although the energy band gap also decreases, the larger differences between the energy level distribution 3
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Fig. 4. Calculated energy levels of P24 H12 -H 2P (a) and P54 H18 -H 2P complexes (b) and projected density of states over QD (red lines) and H 2P (blue lines) for P24 H12 -H 2P (c) and P54 H18 -H 2P complexes (d). The results are obtained using the van der Waals vdW-BH functional. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
change in the incident light polarization practically does not affect the lower energy response, but one may notice important differences in the corresponding ε2 (E ) curves at high photon energies. To understand the features of the BPQD-related results in Fig. 7, the information about the allowed energies spectra depicted in Fig. 3 is crucial. Clearly, the response corresponding to the pristine BPQDs has strong differences with the BP monolayer one when the size of the quantum dot is small. The signal from the P24 H12 shows large amplitudes at energies well above the position of the main peak of the BP monolayer. As long as the size of the dot augments, there is a greater resemblance of the calculated imaginary part of the dielectric function
BPQD-H2P structures. Fig. 7 contains the imaginary part of the dielectric function plotted versus the energy of the incident photon. The curves correspond to isolated H 2P and pristine BPQDs of different sizes. For the sake of comparison, the result for the BP monolayer is included. Two distinct incident light polarizations have been considered in the calculation regarding the H 2P molecule. We first comment on the features of the H2P-related response. It can be seen from Fig. 7 that the stronger response associates with inter-level transitions around 2 eV. They involve the allowed molecule levels that appeared depicted in Fig. 3 immediately below and above the Fermi energy. Higher energy transitions show much smaller amplitudes. The
Fig. 5. Calculated energy levels of P24 H12 -H 2P (a) and P54 H18 -H 2P (b) complexes and projected density of states over QD (red lines) and H 2P (blue lines) for P24 H12 -H 2P (c) and P54 H18 -H 2P complexes (d). The results are obtained using the van der Waals vdW-KBM functional. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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functional, and correspond to the higher energy values considered (above 4.5 eV) which certainly involve states resulting from the coupling of QD states with higher H2P levels. The change in light polarization also produces a small shift in the signal. It can be more clearly noticed by observing the peaks around the mentioned low-energy H2P feature, and it is more apparent in the case that uses vdW-KBM functional in the calculation. On the other hand, the interaction between the QD and H2P appears in the ε2 as small transitions in the 2.2 –2.7 eV range. These transitions show a stronger H2P position dependence for both vdW functionals considered. The analysis of the optical properties for the P54 H18 -H 2P depicted in Fig. 9, and more of its related conclusions follow the same line of smaller QD case. That is, it is based in the previously commented results for the energy spectrum and the characteristics of the corresponding optical response from the pristine BPQD and the isolated porphyrin molecule. However, in this situation one may observe that a stronger reduction of the low-energy ε2 amplitude of the physisorbed complex compared to the isolated H2P one, whereas the amplitude of the high energy response can be approximately equal than its low-energy counterpart thus differing from the P24 H12 -H 2P results and somehow resembling the BP monolayer response appearing in Fig. 7. In the Supplementary material, we are presenting the calculated real part of the dielectric function and the light absorption coefficient as functions of the incident photon energy for the different BPQD sizes that have been considered in the present work (Fig. S1), and for complex P24 H12 -H2P (Fig. S2), and P54 H18 -H2P (Fig. S3). For both P24 H12 -H2P and P54 H18 -H2P complexes, it comes out that in the calculated optical absorption response, the amplitude of the corresponding resonant absorption peaks associated to the H2P-related feature is smaller than the amplitudes of the high-energy absorption peaks. This has to do with the presence of the ω = E/ℏ factor, which makes the absorption amplitude directly proportional to the resonant peak energy. Since the H2P-related peaks appear at lower energies, this factor quenches the overall amplitude of the absorption close to the light absorption threshold while it enhances the amplitude for high enough energies. That is, the ω = E/ℏ resonant factor dominates over the contribution coming from the ε2 variation with the incident light energy.
Fig. 6. The vdW-KBM energy level structure of P24 H12 -H 2P − P1 together with a representation of the local density of states in the complex. Each depicted configuration corresponds to a given allowed energy state, indicated by an arrow.
4. Conclusions
Fig. 7. Imaginary part of the dielectric function for several pristine blue phosphorene quantum dots and the free basis porphyrin. The filled lines correspond to a blue-phosphorene monolayer. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
In this work, we have investigated the properties of the energy spectrum of blue phosphorene quantum dots with H-passivated edges on which an organic molecule – free base porphyrin – is adsorbed. The theoretical study makes use of density functional calculations, including different descriptions of the van der Waals quantum dot-porphyrin interaction via the BH and KBM functionals. Distinct quantum dot sizes, as well as four different quantum dot-porphyrin relative orientations, were considered. With the outcome of the energy spectrum at hand, it was possible to determine the real and imaginary parts of the dielectric function related to interband transitions. Besides, the interband-related optical absorption coefficient is evaluated, as well. It turns out that both the energy structure and the optical response (including two different linear polarizations of the incident light) of the physisorbed complexes show significant changes concerning those of the blue phosphorene quantum dot and free base porphyrin separately. In particular, it is shown with the help of a single example that according to the calculation of the local density of states, the resulting energy spectrum combines rather intricately the quantum dot and organic molecule contributions. The features of the optical response also reflect such intricacy. Using one functional or the other produces values of the binding energy that significantly differ. However, only small differences appear in the physisorption distance and the energy bandgap, as a rule. For the latter, these changes amount at most 20 meV and manifest mainly in the case of the phosphorene quantum dot with the larger size. Another aspect to be highlighted is that the rotations of the molecule with
to that of the monolayer case, with a reduction of the signal’s blueshift, although some higher energy transitions are still detected. By observing Fig. 3(b) one may ratify this fact. Actually, the absorption coefficient for small BPQDs shows peaks of high amplitude in the ultraviolet range. What happens to the optical response when the BPQD-H 2P complex forms? To comment on that we again choose the two cases P24 H12 -H2P (Fig. 8) and P54 H18 -H 2P (Fig. 9). In both cases, the P1-P4 orientational configurations and the x and y polarizations are considered. Both vdWBH and vdW-KBM results are reported for BPQD size. The analysis for ε2 in the P24 H12 -H 2P -P1-P4 case shows the prominent H 2P -related feature (refer to Fig. 7) around 2 eV, which suffers slight modifications in its position when going from the free isolated molecule to the BPQD-H2P adsorbed complex. Also, this feature becomes smaller in amplitude in the P1-P4 complex (with small variations from one orientation to another) with respect to the single H 2P system. For higher energies, the comparison is worth to be made with respect to the pristine QD case. It is possible to notice some changes in the imaginary part of the dielectric function, most of them related to amplitude rather than the position of the appearing peaks. In fact, the energy positions of the physisorbed complexes are only slightly modified in comparison to the pristine BPQD. The greater departures from the pristine QD structure are obtained with the use of vdW-BH 5
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Fig. 8. Calculated imaginary part of the dielectric function of the blue phosphorene quantum dot P24 H12 with free base H 2P porphyrin adsorbed as a function of the photon energy, for several relative orientations P1-P4 (see Fig. 2 for illustration). The results for the pristine quantum dot and the free molecule are included for comparison. Graphics are depicted for x and y incident light polarization and both van der Waals functionals vdW-BH (a), (b), and vdW-KBM (c), (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 9. Calculated imaginary part of the dielectric function of the blue phosphorene quantum dot P54 H18 with free base H 2P porphyrin adsorbed as a function of the photon energy, for several relative orientations P1-P4 (see Fig. 2 for illustration). The results for the pristine quantum dot and the free molecule are included for comparison. Graphics are depicted for x and y incident light polarization and both van der Waals functionals vdW-BH (a), (b), and vdW-KBM (c), (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 6
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respect to the phosphorene quantum dot do not practically alter the value of the binding energy. Hence, one may conclude that such a quantity remains almost unchanged no matter the relative orientation of the physisorbed porphyrin molecule for the dot.
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CRediT authorship contribution statement A. Samia: Software, Investigation. E. Feddi: Formal analysis. C.A. Duque: Writing - review & editing. M.E. Mora-Ramos: Writing - original draft. V. Akimov: Formal analysis. J.D. Correa: Methodology, Conceptualization, Writing - original draft. Acknowledgments The authors thank the Laboratorio de Simulación y Computación Científica of Universidad de Medellín for computational facilities. MEMR thanks the colleagues at the Universidad de Medellín, for hospitality during the preparation of this work. C.A.D. is grateful to the Colombian Agencies: CODI-Universidad de Antioquia (Estrategia de Sostenibilidad de la Universidad de Antioquia and projects “Propiedades magneto-ópticas y óptica no lineal en superredes de Grafeno” and “Estudio de propiedades ópticas en sistemas semiconductores de dimensiones nanoscópicas”), and Facultad de Ciencias Exactas y Naturales-Universidad de Antioquia (CAD exclusive dedication projects 2018-2019). He also acknowledges the financial support from “El Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación Francisco José de Caldas” (project 80740-173-2019). The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.commatsci.2019.109278. References [1] A.K. Geim, I.V. Grigorieva, Van der Waals heterostructures, Nature 499 (7459) (2013) 419–425, https://doi.org/10.1038/nature12385 URL: http://www.nature. com/doifinder/10.1038/nature12385. [2] M. Xu, T. Liang, M. Shi, H. Chen, Graphene-like two-dimensional materials, Chem. Rev. 113 (5) (2013) 3766–3798, https://doi.org/10.1021/cr300263a URL: http:// pubs.acs.org/doi/abs/10.1021/cr300263a. [3] A. Gupta, T. Sakthivel, S. Seal, Recent development in 2D materials beyond graphene, Prog. Mater Sci. 73 (2015) 44–126, https://doi.org/10.1016/j.pmatsci. 2015.02.002. [4] S.Z. Butler, S.M. Hollen, L. Cao, Y. Cui, J.A. Gupta, H.R. Gutiérrez, T.F. Heinz, S.S. Hong, J. Huang, A.F. Ismach, E. Johnston-Halperin, M. Kuno, V.V. Plashnitsa, R.D. Robinson, R.S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M.G. Spencer, M. Terrones, W. Windl, J.E. Goldberger, Progress, challenges, and opportunities in two-dimensional materials beyond graphene, ACS Nano 7 (4) (2013) 2898–2926, https://doi. org/10.1021/nn400280c URL: http://pubs.acs.org/doi/abs/10.1021/nn400280c. [5] H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, Phosphorene: an unexplored 2D semiconductor with a high hole mobility, ACS Nano 8 (4) (2014) 4033–4041, https://doi.org/10.1021/nn501226z URL: http://pubs.acs.org/doi/ abs/10.1021/nn501226z. [6] H.P. Boehm, A. Clauss, G.O. Fischer, U. Hofmann, Dünnste kohlenstoff-folien (thin carbon leaves), Zeitschrift für Naturforschung B 17 (1961) 150–152. [7] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (5696) (2004) 666–669, https://doi.org/10.1126/science.1102896. [8] L. Kou, C. Chen, S.C. Smith, Phosphorene: fabrication, properties, and applications, J. Phys. Chem. Lett. 6 (14) (2015) 2794–2805, https://doi.org/10.1021/acs.jpclett. 5b01094 URL: http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.5b01094. [9] A. Carvalho, M. Wang, X. Zhu, A.S. Rodin, H. Su, A.H. Castro Neto, Phosphorene: from theory to applications, Nat. Rev. Mater. 1 (2016) 16061 review Article.https://doi.org/10.1038/natrevmats.2016.61.
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