Article pubs.acs.org/JPCC
Theoretical Studies on Understanding the Feasibility of PorphyrinSensitized Graphene Quantum Dot Solar Cell Bikash Mandal,† Sunandan Sarkar,†,‡ and Pranab Sarkar*,† †
Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India ABSTRACT: We present results of our theoretical investigation on the electronic structure of porphyrin functionalized graphene quantum dots(GQDs). We put our emphasis on how the electronic energy levels of GQDs are modified because of the functionalization by porphyrin molecules. Our study shows that the HOMO−LUMO gap of the GQD-porphyrin hybrid material is lower as compared to GQD of same size. The possibility of forming type-II nanohybrids is explored by varying either the size of the QD or by attaching different functional groups to the porphyrin moiety. We also analyzed the absorption spectra of one model GQD-porphyrin nanocomposite. We found that GQD-porphyrin hybrid material form type-II band alignment for GQD of smaller size. The hybrid material with larger QDs show type-I band alignment however they can be made type-II by proper attachment of the electron donating group to the porphyrin molecule. The type-II band alignment lowers the chance of electron−hole recombination. The free energy of electron injection, that is, the energy gap between LUMO of porphyrin and LUMO of GQD increases with increasing the size of the GQD. So, on the basis of our theoretical study, we suggest that the GQD-porphyrin nanohybrid material with larger GQD may be a good candidate for the application in solar cell.
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INTRODUCTION During the last couple of decades, the research on semiconductor quantum dots (QDs) has seen an explosive growth because of their diverse applications in various fields ranging from optoelectronic devices to third generation solar cells.1−6 In the recent time, the research on nanohybrid materials composing two different materials become the subject of extensive research. It is now established that the nanohybrid materials have superior properties as compared to the individual components from which they are made. This class of materials are particularly suitable for use in designing solar cell because of the capability of efficient photo electron transfer from one material to other. In this context various inorganic− organic nanohybrids composed of inorganic semiconductor quantum dots and organic components such as carbon nanotube, fullerene, graphene have been studied extensively from both experimental7−16 and theoretical17−21 point of view. These studies confirmed that these hybrid systems exhibit better photovoltaic performance as compared to individual semiconductor materials. Graphene, consisting of a single atomic layer of carbon atoms arranged in a two-dimensional hexagonal lattice is one of the latest important materials discovered only in 200422 and have shown many fascinating properties because of its unique structure. Porphyrin, the pigments of life form a great variety of complexes with metal ions and nonmetals.23,24 The extensive 2D π electron framework and large extinction coefficient in the visible range makes porphyrin molecule a suitable candidate to be used in optoelectronics. In the recent time, the research on porphyrin molecule has seen an explosive growth because of their excellent light-harvesting properties mimicking natural photo© XXXX American Chemical Society
synthesis and hence their use in the fabrication of dyesensitized solar cell.25−27 However, porphyrin alone suffers from poor device performance because of their nearly planar structure favoring the formation of dye aggregates. One solution of the problem is the implementation of cosensitization with other dye or light absorbing materials. In this respect the nanohybrids made up of combining graphene with optoelectronically active porphyrin has the promise of showing multifunctional properties. There are many experimental investigation on the synthesis of porphyrin functionalized graphene hybrid materials.28−35 Chen and co-workers28 have synthesized porphyrin-graphene nanohybrid and showed that this nanohybrid material has superior optical limiting properties and the authors argued that this nanohybrid may be new entry in the realm of light harvesting devices. Zhang et al.30 have reported a facile method for for the synthesis of porphyrin functionalized graphene hybrid nanosheets which can be used as sensor for adenosine triphosphate (ATP) detection. Kiessling et al.31 in a very recent article reports the synthesis of nanographene/porphyrin hybrids and have demonstrated the applicability of these nanohybrids in solar cells. Li et al.36 through their pioneering work in 2010 have shown that periodic graphene can also be realized in the form of QDs. The so-called graphene quantum dots (GQDs) since then become the focus of recent research.37−45 Because of large Bohr exciton radius, the quantum confinement effect in graphene can be observed at any finite size of the QDs. Thus, one can tune Received: November 13, 2014 Revised: January 17, 2015
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Figure 1. Optimized geometries of GQD-porphyrin nanocomposites (hexagonal (a) and trigonal (b)) having the number of carbon atoms 114 and 126, respectively, in hexagonal and trigonal GQD.
particular shape. We have then cut this smallest unit from the graphene sheet. By maintaining the particular symmetry, we have cut a larger QDs from the graphene sheet to generate GQDs of larger size. In this way, we have generated GQDs up to 10 nm in size retaining their symmetry. To model the GQDporphyrin nanocomposites we have attached the porphyrin molecule with GQD through amide linkage. Porphyrin molecules contain four phenyl groups, one of them involve in formation of amide linkage and the remaining are utilized during functionalization of porphyrin molecule. Functional groups are placed at the para position of those phenyl ring by removing their para hydrogens. The total energy calculation of these GQD-porphyrin nanocompositess have been performed by self-consistentcharge density-functional tight-binding (SCC-DFTB) method,49−54 as implemented in the dftb+ code by employing large supercells, including a large vacuum region in all directions to isolate the nanocomposites from their periodic replicas. As the porphyrin moiety is attached to the GQD through a single C− C linkage, the interaction between porphyrin and GQD would be better understood by inclusion of dispersion correction. So, we have also included the dispersion interaction through Slater−Kirkwood model, using the previously derived set of parameters for H and C.50,54 We used the conjugate gradient algorithm for geometry optimization until the forces on each atoms are below 0.001 eV/Å. The optimized structure of two representative porphyrin functionalized graphene QDs (triangular and hexagonal) are shown in Figure 1. In this context it is to be noted that the system, which is considered for calculation of absorption spectra, contains only one porphyrin moiety.
the HOMO−LUMO gap over a wide range of wavelengths from the ultraviolet through the visible into the infrared by just varying their size. By using time-dependent density-functional theory, Schumacher46 elucidated the optical selection rules in isolated graphene QDs and their relation to the system symmetry. Voznyy et al.47 have studied the effect of reconstruction and passivation of zigzag edges on the electronic and magnetic properties of triangular graphene QDs. In a very recent article, by using density-functional theory and timedependent density-functional calculation Mahasin et al.48 have shown that the phtotoluminescence of GQD can be sensitively tuned by controlling its size, shape, edge configuration, chemical functionalization, and doping hetero atoms. Graphene quantum dot, as mentioned above, is a very new member of the QD synthesized only in 2010, and because of its large exciton radius, it exhibits properties that can be widely tuned by varying both size and shape of the quantum dots. So, one can expect better tunability of the electronic structure of graphene QD-porphyrin nanohybrid systems as compared to graphene-porphyrin hybrid systems. In view of this, we here performed density-functional tight-binding calculation on the electronic structure of porphyrin functionalized graphene QDs. We will put emphasis on how the functionalization of the graphene QD with porphyrin molecule modifies the electronic structure of graphene QD and whether the electronic energy levels of the resulting nanohybrids have proper band energy alignment for the efficient transfer of photoexcited electrons or have favorable spatial charge separation for lower recombination of the charge carriers.
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COMPUTATIONAL METHODS In the present work, we employed the self-consistent charge density-functional based tight-binding (SCC-DFTB) method to study the electronic structure of GQD-porphyrin composite systems. This method has been described in detail elsewhere.49−54 We have used Slater-type orbitals (STOs) as basis sets and Perdew−Burke−Ernzerhof (PBE)55 exchange correlation energy functional. The GQDs of different sizes have been modeled as follows. We have first built up a large graphene sheet and then have chosen a smallest graphene QDs of a
RESULTS AND DISCUSSION One of the major goals in studying electronic structure of materials is to find out the way to engineer the HOMO− LUMO gap. It is now well established that functionalization of nanostructures with organic molecule in addition to size and shape plays an important role in tuning the electronic energy levels of the nanostructures. However, in one of our previous study and studies of others showed that the functionalization with small organic molecules has very little effect on the B
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The Journal of Physical Chemistry C HOMO−LUMO gap of the GQDs.36,38,38,45 Now to see whether the functionalization of graphene QD with porphyrin molecule can bring a change in the HOMO−LUMO gap we have shown the variation of HOMO−LUMO gap as a function of the size of the GQD in Figure 2. We have considered both
Figure 2. Variation of energy gap against number of conjugated carbon atoms (N) of GQD for hybrid systems as well as for GQDs. Blue line with circle and triangle (down) used for hexagonal GQD and hexagonal composite, respectively, while red line with triangle (up) and star used for triangular GQD and triangular nanocomposites, respectively.
triangular and hexagonal GQDs in Figure 2. From the figure it is seen that the HOMO−LUMO gap of the porphyrinfunctionalized GQD for a smaller size of the QD is smaller as compared to GQD itself. So, the GQD-porphyrin nanocomposite will show red shift in its absorption spectra as compared to GQD. This red shift in absorption spectra is in good agreement with experimental study on porphyringraphene nanohybrid of Xu et al.28 However, the HOMO− LUMO gap of the GQD-porphyrin composite system for large size GQD are the same as that of GQD itself. Thus, we conclude that the HOMO−LUMO gap of the nanocomposites for larger GQD is controlled by the electronic energy levels of GQD. Now to understand the details of the electronic energy levels of the composite systems and the contribution of the GQDs and porphyrin molecule we have plotted the projected density of states (PDOS) of GQD-porphyrin nanocomposites with hexagonal GQD in Figure 3. In the same figure we have also shown the density of states of GQDs and porphyrin molecule. From the figure it is seen that HOMO of GQDs shifts to higher energy while that of LUMO shifts to lower energy with increase of the size of GQD. In the nanocomposites the positions of the HOMO and LUMO of porphyrin remain unchanged whatever may be the size of the GQDs. Thus, we conclude that in the composite system only the electronic energy levels of GQD is perturbed while there is no significant effect on those of porphyrin molecule. This conclusion of our theoretical study get supports from the experimental results of Xu et al. on porphyrin-graphene nanocomposites.28 The most interesting observation is that this particular nanocomposite with smaller sized GQD exhibits type-II band energy alignment; the HOMO of the composite system is controlled by porphyrin, while the LUMO is controlled by GQD. However, for nanocomposites with GQD of moderate size the HOMO has contribution from both GQD and porphyrin it is seen from DOS graphs (c) and (d). The nanocomposites with larger GQD (graph (e)) show type-I band alignment. So there is a transition from type-II to type-I
Figure 3. Projected density of states (PDOS) of five different hexagonal nanohybrids having number of conjugated carbon atoms 114 (a), 222 (b), 366 (c), 546 (d), and 762 (e) in GQDs. Blue shaded region represent the total density of states of nanocomposites, while the region under red and green line represent the contribution of GQD and porphyrin, respectively. The dotted line represent the Fermi level.
band alignment with the increase in size of the GQD. Thus, for nanocomposites with smaller QDs, there is spatial charge separation and as a consequence of that the chance of recombination of charge carriers is low. So, we conclude that this nanocomposite may be suitable to be used as building blocks of third generation solar cell. A careful inspection of the DOSs reveal that the energy gap between the LUMO of porphyrin and that of GQD increases with increase in size of the GQD. Thus, the rate of electron transfer from porphyrin to GQD will increase with increasing size of the GQD. This feature is same for both triangular and hexagonal GQDs. To understand the spatial charge separation in GQDporphyrin nanocomposite as mentioned in the last section we plotted the HOMO and LUMO densities of GQD-porphyrin nanocomposites in Figure 4 for three different GQD sizes. The figure clearly indicates that for nanocomposite of smaller GQD the LUMO is localized on porphyrin and HOMO density is localized on GQD. So there is a clear charge separation in GQD-porphyrin nanocomposite with smaller GQD. However, nanocomposites with larger GQD both HOMO and LUMO densities are on GQD (Figure 3e,f). This spatial charge C
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Figure 4. HOMO (red) and LUMO (blue) charge density of hexagonal composite systems with carbon atoms in GQD 114 (a and b), 546 (c and d), and 762 (e and f), respectively. Isovalue = 0.0001 is used for plotting.
composites. We also found the same feature for −NH2 functionalized porphyrin-GQD nanocomposites. Thus, the functionalization of porphyrin with electron donating group such as −OCH3 and −NH2 results in forming type-II band energy alignment. The functionalization with electron donating group raises the energy of HOMO of porphyrin molecule above the HOMO energy of GQD. Thus, we found that nanocomposites with larger size of GQD which was type-I become type-II with functionalization of porphyrin molecule with electron donating group such as −OCH3 and −NH2. Another interesting feature of this nanocomposites as evident from the density of states (not shown here) is that the energy gap between LUMO of porphyrin and that of GQD which controls the electron injection efficiency from porphyrin to GQD increases when electron donating group is attached to the porphyrin molecule as compared to nonfunctionalized nanocomposites. So, the GQD-porphyrin nanocomposite with either smaller or larger GQD (with some modification) can form type-II band energy alignment. This kind of energy alignment as mentioned earlier hinders the process of recombination of charge carriers. The nanocomposites with larger GQDs also have a large energy gap between the LUMO of the porphyrin and LUMO of the GQD; thus, the free energy change for the electron injection from porphyrin to GQD is high. Following the Marcus theory,56 one can write down the rate of charge recombination as follows:
separation has very important consequence in the recombination dynamics of charge carriers and will be discussed later. We know apart from other factors the efficiency of a photovoltaic cell depends mainly on two factors: one is the efficient electron transfer from dye to the QD and other is spatial separation of the charge carriers that lowers the electron−hole recombination rate. Now from the discussion in the preceding paragraph we noticed two contrasting events. The electron injection efficiency which depends on the difference in energies between the LUMO of the porphyrin and GQD will increase with nanocomposites of larger size. But the nanocomposites with larger QD show type-I band energy alignment that is both HOMO and LUMO are in the same material. So the recombination of charge carriers will be much faster that essentially reduced the photovoltaic efficiency. Now the question is by some chemical modification of the nanocomposites with larger QD is it possible to attain type-II band energy alignment retaining the faster electron injection rate. The functionalization with organic functional groups is one of the many ways through which one can tune the electronic structure of nanoparticles. We functionalized the porphyrin molecule by electron donating groups −OCH3 and −NH2 with a goal to achieve type-II band alignment. To understand the effect of functionalization on the charge separation at the interface of the composite system, the wave functions corresponding to the HOMO and LUMO of one representative system (GQD-porphyrin nanocomposite functionalized with −OCH3) are presented in Figure 5. From the figure it is evident that HOMO is localized only on one porphyrin molecule, while the LUMO is localized only on GQD. So, there is distinct charge separation in the nano-
k= D
2π ℏ
⎡ (λ + ΔG)2 ⎤ H2 exp⎢ − ⎥ 4λkBT ⎦ ⎣ 4πλkBT
(1)
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Figure 5. HOMO (red) and LUMO (blue) charge density of largest size hexagonal nanohybrid with unsubstituted (a and b) and −OCH3 substituted (c and d) porphyrin moiety.
where k is the recombination rate constant, H is the electronic coupling strength, λ is the total reorganization energy, and ΔG is the driving force. Although this equation is strictly valid for a molecule, we can use it for qualitative prediction of the charge recombination of our nanocomposites. From the equation it is clear that the charge recombination rate greatly depends on H which in turn depends on the overlap of HOMO and LUMO wave functions of the composite system. As it is found from both Figure 4a,b and Figure 5 that the electron and hole wave functions are localized on two different components of the composite system so there is negligible overlap in the composite system. So, we can conclude at least qualitatively that, for this particular composite system, the charge recombination rate is low and will be found suitable for application in dye-sensitized solar cell. Our theoretical prediction is in line with the experimental study of Kiessling et al.31 These authors have synthesized the novel nanographene/porphyrin hybrids and explore the possibility of application of these nanohybrids in solar cell. These authors have shown that the presence of nanographene in the nanohybrid causes the implementation of a Schottky barrier, thus, reducing the rate of recombination process, and this leads to a significant boost of the overall device performance. Finally, we have calculated the absorption spectra few representative porphyrin-GQD nanocomposites and are shown in Figure 6. For the calculation of absorption spectra we have first performed DFT ground state calculation of the studied systems using plane wave ab initio program ABINIT57−59 with the Troullier-Martins norm-conserving pseudopotentials with a cutoff energy equal to 20 hartree and
Figure 6. Optical absorption spectra of hybrid (a) system as well as −OCH3 (c) and −NH2 (e) functionalized nanocomposite containing 42 carbon atoms in the GQD. The PDOS of the corresponding systems are shown in the right panel of the figure.
GGA-PBE exchange correlation functional. The Kohn−Sham eigenvalues and eigenvectors are used as starting point for the TDDFT linear response calculation as implemented in DP code60 with number of shells of G vectors up to 6 and number of shells of plane waves equal to 15. The interesting point to note is that the first absorption peak as calculated by ab initio calculation matches almost exactly with the band gap calculated E
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GQD exhibit type-I band energy alignment. There is charge separation in the system with type-II band alignment and thus for these systems the recombination of charge carriers is low. So we suggest that porphyrin-GQD nanocomposites with smaller GQD will have better photovoltaic performances. We also extend our study to explore the possibility of achieving type-II band alignment in porphyrin-GQD nanocomposite with larger GQDs. To that end, we have functionalized the porphyrin molecule with an electron donating group, such as −OCH3 and −NH2, and we found that the resulting nanocomposites exhibit type-II alignment. The detail analysis of the DOSs of the nanocomposites reveal that the energy gap between the LUMO of porphyrin and that of GQD, which is a measure of ΔG for the electron injection efficiency from the photoexcited porphyrin to GQD increases with increase in size of the GQD. Thus, the rate of electron transfer from porphyrin to GQD will increase with increasing size of the GQD. So, we suggest that the porphyrin-GQD nanocomposite may be a good building block for the realization of a dye-sensitized solar cell, and we hope that our theoretical results will certainly motivate the experimentalist for exploration of this new form of nanohybrids.
by the SCC-DFTB method thereby give support to our SCCDFTB results. The absorption of porphyrin-GQD nanocomposites with electron donating group shows a clear red shift as compared to unsubstituted porphyrin-GQD nanocomposite. In order to explain the absorption spectra, we have plotted PDOS of the system on the right panel of Figure 6 and tried to find out the most probable electronic transitions that are responsible for absorption peaks. The lowest energy absorption peak (p1) for unsubstituted GQD-porphyrin nanocomposite observed at 1.67 eV in the hybrid system, arises due to electronic transitions from d1 to e1 (d1 → e1), which are localized on the porphyrin moiety. The first higher energy absorption peak (p2) at 1.92 eV is originated from d2 → e1. The next higher energy absorption peak (p3) at 2.28 eV, which is basically the band gap transition of GQD, is intensified by the high energy transition of porphyrin. As can be seen from the PDOS that d4, d3, and e1 originated simultaneously from GQD and porphyrin, thus, the transitions d3 → e1 and d4 → e1 give rise to a higher intensity absorption peaks p3 and p4, respectively. As the porphyrin moiety is functionalized by −OCH3 group, energy states of porphyrin moiety shift toward higher energy, but shifting of HOMO is much higher than LUMO, which results from a clear red-shift of the lowest energy absorption peak (p1) to 1.63 eV arises from the localized transition d1 → e1 in porphyrin. The d2 → e1 transition is forbidden, thus, the absorption peak, p2 of the unsubstituted hybrid system disappears here. The intensity of the band gap absorption peak of GQD, p2, slightly decreased due to a decrease of the contribution from porphyrin. A huge change of PDOS of porphyrin is observed due to functionalization, mainly for d3 and d4, which is manifested as a wide and highly intense double hump p3 peak, arises from d3 → e1 and d4 → e1 transitions. As energy states of porphyrin shift toward higher energy, d3 and d4 accumulate more intensity from porhyrin, which is responsible for the more intense peak p3. A major shift of HOMO of porphyrin is observed when it is functionalized by −NH2 group, and the effect is manifested as a huge shift of lowest energy bright absorption (p1), found to be 1.49 eV, originated from d1 → e2, which is localized on porphyrin. There is no intense peak observed in between p1 and p2, so we can say that d2 → e2 is not an allowed transition in this system. Due to functionalization by −NH2, d3 appears as a separate state fully localized on porphyrin, and a transition from d3 to e2 gives rise to a new highly intese peak p2. The band gap transition peak of GQD is suppressed under p3, which basically comes from band gap transition of GQD and electronic excitation from porphyrin of d4 to e2. Thus, from the above analysis, it is clear that the lowest energy bright absorption (p1) shifted toward red region with increasing the power of electron donating group.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ‡
Department of Physical Chemistry, Regional Centre of Advance Technologies and Materials, Faculty of Science, Palacký University Olomouc, tř. 17. Listopadu 12, 771 46 Olomouc, Czech Republic.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The financial support from CSIR, New Delhi [ 01(2744)/13/ EMR-II] through research grant is gratefully acknowledged. B.M. is grateful to CSIR, New Delhi, for the award of Senior Research Fellowship (SRF).
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CONCLUSION In summary, by using density-functional method we explored the electronic structure of graphene QD-porphyrin nanocomposites with an objective to have qualitative understanding of the applicability of this nanohybrid for solar cell application. The analysis of the electronic energy levels reveals that depending on the size of the QD the nanocomposites may show either type-I or type-II band energy alignment. This particular nanocomposite with smaller sized GQD show type-II band energy alignment. The HOMO of the composite system is controlled by the porphyrin molecule while the LUMO is controlled by GQD. However, composite systems with larger F
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