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Abstract
Interested in the recent development of the building up of photovoltaic devices using graphene-like quantum dots as a novel electron acceptor; we study in this work the optoelectronic properties of edge-functionalized SiC quantum dots using the first principles density functional. For an accurate quantitative estimation of key parameters, a many-body perturbation theory within GW approximation is also performmed. We examine the ability to tailor the electronic gap and optical absorption of the new class of QDs through hydroxylation and carboxylation of seam atoms, in order to improve their photovoltaic efficiency. The HOMO-LUMO energy gap was significantly altered in terms of the type, the concentration and the position of functional groups. The spatial charge separation and charge transfer characterizing our systems seem very prominent to use as dye-sensitized solar cells. Furthermore, the optical band gap of all our compounds is in the NIR-visible energy window, and exhibits a magnitude smaller than that calculated in the pristine case, which enhances the photovoltaic efficiency. Likewise, absorption curves, exciton binding energy and singlet-triplet energy splitting have been broadly modified by functionalization confirming the great luminescent yield of SiCQDs. Depending on the size, SiC quantum dots absorb light from the visible to the near-infrared region of the solar spectrum, making them suitable for third generation solar cells.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past decades, research on energy-related applications has seen explosive progress [1–4]. Indeed, the harvesting of primary solar energy through photovoltaic technologies is one of the most promising applications used today, owing to the abundance of sunlight. The optimization of new materials to achieve high-efficiency solar cells based on the improvement of the optoelectronic properties, such as the absorption coefficient, the band gap, the exciton binding energy and the carrier mobilities [5–8]. Organic solar cells and dye-sensitized solar cells (DSSC) have drawn enormous attention due to their high power conversion efficiency (PCE) and their low production cost [9–12], helping to sustain the huge demand for clean energy [13,14].
DSSC, which is an analogous concept to photosynthesis, is a prominent successor to p-n junction photovoltaic devices [15]. In recent years, much effort has been devoted to the design and synthesis of highly efficient sensitizers such as organic dyes and quantum dots (QDs) [16]. Because of their absorption in the near ultraviolet (NUV) to the visible region, their remarkable photostability, their structural flexibility and their rapid electron injection, porphyrin organic dyes are very suitable as sensitizers for DSSC [17]. Moreover, organic phenoxazine dyes showed interesting electrochemical characteristics like strong electron-donating ability which implies their possible integration as dye sensitizers [18]. However, organic dyes alone suffer from limitations such as poor absorption.
QDs present emergent materials for use as a sensitizer due to their unique optoelectronic features, like prominent quantum confinement, tunable energy gap, strong absorption, good photostability, high PCE and low manufacturing cost [19]. Among the different solar cells QDs, graphene quantum dots (GQDs) are the most commonly investigated as they can play the role of different components of DSSC, namely the photoanode, the counter electrode and the sensitizer. Indeed, GQDs can be employed as co-sensitizers in the hybrid DSSC, which enhances their performance [20]. More precisely, the use of GQDs considerably improves the absorption as the harvesting of visible light increases the photogenerated electron transfer and reduces the electron-hole recombination [21]. Otherwise, GQDs could be used as modifiers for photoanodes to tune the DSSC performance. The incorporation of GQDs into TiO$_{2}$-based photoanodes significantly increased their PCE to 29.31% [22]. Moreover, these nanostructures have been employed as an effective substituent to platinum in DSSC, enabling the fabrication of Pt-free count electrodes [23].
Interestingly, the nanocomposites obtained through the functionalization of GQDs with organic ligands showed better photoelectronic properties compared to the individual components from which they are made. Theoretically, porphyrin-functionalized GQDs exhibit high efficiency and strong photovoltaic response [24] and the increment in the amount of QDs in nanocomposites improves their optical absorption ability [25]. The modification of GQDs with small functional groups like carboxyl (-COOH) manipulates their orientation on the semiconductior metal oxides substrate which helps determe their performance in DSSC [26].
Obviously, GQDs exhibit potential and suitable characteristics for the DSSC. This promising finding encouraged the study of new QDs-based conformers with novel optical properties to innovate the current DSSC. QDs derived from the two-dimensional silicon carbide sheet (SiC) present a pioneer alternative since, unlike graphene, SiC sheets are characterized by a large band gap and significant optoelectronic and excitonic features [27,28]. hydrothermal route, and were found to have a well-defined chemical structure and strong photoluminescence. SiCQDs have been profitably employed for cellular imaging and the intracellular transporter [29]. Our previous theoretical study revealed the high structural and chemical stability of SiCQDs as well as their adjustable optoelectronic features that are strongly dependent on size variation [14,30].
Like GQDs, which have been successfully fabricated using a variety of top-down and bottom-up methods [31–35], SiCQDs have also recently been synthesized by employing a facile hydro-thermal route that achieves efficiently the desired shape and size [29]. This strategy allows control of the QDs’ size, which plays an essential role in improving of the open-circuit voltage $(V_{oc})$ of the device and the lapses of the short circuit current $(J_{sc})$ [36]. However, well implementation of quantum dots based 2d materials in solar cells at large scale, with a uniform size and in a high yield and low-cost way, remains challenging [37].
Aware that the efficiency of the DSSC depends mainly on two factors, namely the electron transfer and the charge spatial separation [13,38–40], we focus in this work on the complete and partial edge-functionalization process to ensure the occurrence of charge transfer. Based on the good results obtained for hydroxylated and carboxylated GQDs and SiQDs reported in our previous work [41], we chose -OH and -COOH as molecular substituents to modify the structural, electronic and optical properties of SiCQDs. We found that our systems are energetically stable and exhibit substantial resistance to mechanical deformations induced by functional groups. Furthermore, we have demonstrated that chemical reactivity can be modulated by the edge-functionalization. The energy gap was found to be strongly dependent on the position, concentration and the nature of functional groups. Complete functionalization induced remarkable decrement in the energy gap. Whereas, the situation was different for half-functionalization since the variation in energy gap relied mostly on the functional group position and type. This broad variety of electronic behavior is attributed to the hybridization of frontier molecular orbitals. The correction of the ground state energy gap through the GW approximation has increased greatly due to the electron-electron (e-e) interaction. Likewise, the inclusion of excitonic effects via the GW+BSE method has greatly tailored the position and intensities of optical curves, exciton binding energies and singlet-triplet energy splitting (STES). Optical curves have been shifted toward lower energies occupying the visible-near infrared (NIR) of the solar spectrum. Besides, binding energy values were shifted-up owing to the large charge transfer from the Si/C skeleton to molecular substituents. The estimated considerable luminescent yield for our structures was deduced from the calculation of STES, showing that SiCQDs present a new class of QDs with promising properties for emergent photovoltaic technologies, optoelectronic devices and nanomedical applications.
Our paper is organized as follows. Section 2 reports the computational methods and structural properties of QDs. The obtained results of structural stability, global reactivity, electronic and optical properties were discussed in section 3. Finally, we summarize and conclude our main results in section 4.
2. Computational and structural details
2.1 Numerical methods
Numerical simulations reported in the present paper were carried out employing a three-step procedure. The starting point is ground-state density functional theory (DFT) calculations performed using a plane-wave approach, within the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [42], as implemented in Quantum Espresso (QE) simulation package [43]. A norm-conserving pseudo-potential was employed to describe the electron-electron interaction with kinetic energy cutoff set at 60 Ry. The investigation of isolated systems required avoiding the non-physical interactions between periodic images through using a vacuum of 20 $\mathring {A}$ in all three dimensions. Owing to the zero dimensional nature of QDs, only gamma point is taken into account in all the calculations. All the configurations considered here were fully relaxed under stress and forces until the components of all forces are less than $10^{-3}eV$ . In order to improve our calculations and obtain results in agreement with experiments, we calculate the self-energy of quasiparticles $\Sigma (E)$ in term of Green’s function and screened coulomb potential using many-body perturbation theory (MBPT) via GW approximation and therefore, we estimate the quasiparticle corrections to the DFT-GGA eigenvalues by solving the following equation [44]:
where $E_{KS}^{QP}$ and $\psi _{nk}$ are the the Kohn-Sham (KS) energy and wavefunction respectively, $\Sigma (E_{nk}^{QP})$ is the self-energy operator and $V_{xc}^{KS}$ is the exchange-correlation potential. Noting that a total of 600 bands were used to construct the dielectric matrix and self-energy operator of all studied SiCQDs. Following [48], we calculate the global reactivity indices that are expressed in terms of ionisation potential $IP$ and electron affinity $EA$ as follows: where $IP=-E_{HOMO}$ and $EA=-E_{LUMO}.$The last step consists on analysing the excitonic properties of all the systems presented in this work through solving the Bethe-Salpeter equation (BSE) [45]. The obtained excitation energies and exciton wave functions allow calculating the imaginary part of the dielectric function using the following formula [46]:
2.2 Structural properties
Figure 1 displays the optimized geometry of the investigated QDs. Figure 1 (b) and (e) represent a complete functionalization of seam atoms with -OH and -COOH respectively, while the configurations (c), (d), (f) and (g) illustrate the half decoration of seam atoms, namely either C or Si atoms are functionalized. Notice that two different sizes of diamond-shaped (DS) quantum dots (QDs) derived from the 2D SiC sheet are considered in this work. Small sized pristine QDs contain 26 atoms, 10 of which are hydrogen (H) atoms, while 16 are shared equally between carbon (C) and silicon (Si) atoms. The large configurations contain a total of 44 atoms including 14 H, 15 C and 15 Si atoms. Each configuration brings together zigzag edges and armchair corners passivated with hydrogen atoms. It is noteworthy that SiCQDs, having various sizes and thickness, were successfully synthesized through hydrothermal route [29]. Their analyzis shows a well-defined hexagonal structure like their counterpart 2D SiC sheet.
The molecular geometry of the pristine structure reveals that SiCQDs are characterized by planar geometry where C and Si atoms are $sp^{2}$ hybridized according to the measured bond angles ranging between 118$^{\circ }$ and 121$^{\circ }$. Concerning edge-functionalized SiQDs, only the seam atoms connecting the zigzag edges to the armchair corners are decorated with -OH and -COOH functional groups. The complete and half decoration of the considered seam atoms generated 12 configurations. Structural distortions were evaluated by measuring the summit angles $D_{1}=(1,2,3)$ and $D_{2}=(4,5,6)$ illustrated in Fig. 1. The values obtained for $D_{1}$ and $D_{2}$ are reported in Table 1. One can deduce that for all functionalized structures, only -OH functional group has introduced negligible deformations at the summit angles and this is due to the significant electronegativity of the oxygen atom O with respect to C and Si. This result confirms that the SiCQDs have inherited substantial resistance to mechanical deformations and chemical corrosion from of their analogous 2D SiC sheets [29].
Fig. 1. Optimized geometry structures corresponding to a) pristine and b-g) edge-functionalized SiCQDs with -OH and -COOH molecules. Yellow, cyan, purple and red spheres represent carbon, silicon, hydrogen and oxygen atoms respectively. In b) and e), the four hydrogenated seam atoms are functionalized. In c) and f) only carbon seam atoms are functionalized and in d) and g) only silicon atoms are decorated.
Table 1. Calculated values of QDs: the summit angles $D_{1}$ and $D_{2}$, the global reactivity descriptors: hardness $\eta$, chemical potential $ \mu$ and electrophilicity $ \omega$. The calculated energies: Binding energy $E_{B}$, HOMO-LUMO energy gaps $E_{g}^{GGA}$ and $E_{g}^{GW}$ at DFT and GW level respectively. All the energies are in eV.
3. Results and discussion
This section details key results for edge-functionalized SiCQDs including energetic stability, global reactivity and optoelectronic behaviours.
3.1 Stability
The thermodynamic stability of QDs is examined through the analysis of their formation energies listed in Table 1. Negative values reveal the energetic stability of the configurations. Large-sized structures are more stable than smaller ones, and the complete edges-functionalization makes QDs more stable compared to partially functionalized structures. The most stable are the hydroxylated $Si_{8}C_{8}H_{10}$ and $Si_{15}C_{15}H_{14}$ QDs due to the strong electronegative effect of oxygen adsorbate in OH-functional group as well as its direct bond to the SiC skeleton in contrast to the COOH-molecule. This result is in accordance with [53,54], and is also confirmed through the chemical stability and the global reactivity descriptors, namely global hardness ($\eta$), chemical potential ($\mu$) and global electrophilicity index ($\omega$).
The measurements listed in Table 1 and the variation of hardness and electophilicity index plotted in Fig. 2 revealed that small sized QDs are harder and less reactive. Moreover, the type, the concentration and the position of molecular substituents have noticeably modified the global hardness of QDs, and result in slightly softening some structures making them more polarizable and easy to be excited. Regardless the size, we can note that the hydroxylation of only Si atoms as well as the carboxylation of only C atoms enhance the global hardness with respect to pristine QDs because of the significant drop of electron affinity (EA) with respect to ionisation potential (IP). Whereas, the small difference between EA and IP in OH-$C_{8}Si_{8}H_{10}$ and OH-$C_{15}Si_{15}H_{14}$ increases the electrophilicity index of pristine QDs, and therefore brings more stabilization to these configurations. For the remaining hydroxylated structures, the EA/IP difference sounds remarkable compared to pristine structures, leading to a decreased electrophilicity. In contrast, -COOH substituents enhance the chemical reactivity making the new QDs strong electrophiles except COOH-$C_{8}Si_{8}H_{10}$ and COOH-C$_{15}$Si$_{15}$H$_{14}$. This result can be attributed to the significant gap between IP and EA found for the two structures and not observed for the leftover -COOH configurations. Therefore the increased electrophilicity values indicates the improved capacity of our systems to gain additional electronic charge, especially in carboxylated structures, enhancing thus their stabilization in energy. Furthermore, in spite of the morphological and chemical modification, the variation of both reactivity indices maintains the minimum hardness and the maximum electrophilicity principles [49].
Fig. 2. Hardness (dotted) and electrophilicity index (dashed) of a) hydroxylated and b) carboxylated SiCQDs with (X=OH, COOH).
3.2 Energy gap and charge density analysis
The effect of type, concentration and position of edge-molecular substituents on energy gap is investigated by employing two different theoretical approaches, namely DFT formalism and GW approximation. GGA-DFT calculations reveal that complete functionalization of seam atoms results in decreasing the HOMO-LUMO (H-L) energy gap of pristine QDs as listed in Table 1. In the case of half decoration of seam atoms, the variation of the energy gap is clearly dependent on the position of the functional groups. Interestingly, the hydroxylation of only silicon seam atoms or the carboxylation of their carbon matches induced a marked increase of the H-L energy gap. Whereas, a decreasing in the energy gap is observed in structures with only hydroxylated carbon seam atoms or only carboxylated silicon ones. Among the two cases in which the H-L gap has decreased, half functionalization resulted in the most significant drop. This finding is attributed to the hybridization of frontier molecular orbitals, in particular the increment of HOMO or LUMO energies upon different functionalization. To shed more light on this argument, we analyse the charge density distribution plotted in Fig. 3. Clearly, the HOMO and LUMO densities are localized on zigzag edges and armchair corners for all the configurations. More precisely, the LUMO originates mostly from the contribution of Si atoms while the HOMO is largely dominated by C atoms, with a pronounced charge density carried by the seam atoms [41,55]. It is noticeable that edge-functionalized SiCQDs maintained practically the same charge distribution as pristine configurations, with an obvious contribution originated from molecular substituents, excepting OH-$Si_{8}C_{8}H_{10}$ and OH-$Si_{15}C_{15}H_{14}$ where the contribution of -OH to the HOMO is almost absent, also COOH-$C_{8}Si_{8}H_{10}$ and COOH-$Si_{15}C_{15}H_{14}$ that showed a negligible participation of -COOH in the LUMO. This outcomes the shift-up in the H-L energy gap aforementioned. Furthermore, SiCQDs are characterized by a favourable spacial charge separation that lowers the recombination of charge carriers and thus enhances the photovoltaic efficiency. This property sounds more prominent in carboxylated SiCQDs, making them promising candidates for use as sensitizers in third generation solar cells.
In order to take into account the e-e interaction and predict the self-energy corrections to the GGA-DFT energy gaps, many body perturbation theory using GW approximation is also employed. According to Table 1, the quasiparticle corrections are in the range of 3.02-3.34 eV and 2.02-2.74 eV for small and large sized SiCQDs respectively, showing a crucial tunability depending on quantum confinement characterizing QDs and size effects. The GW-gap energies are in good agreement with measured gaps for graphene QDs which demonstrates the accuracy of our results compared with experimental values [56,57].
3.3 Absorption profile and excitonic effects
The optical behaviour of SiCQDs is studied using the BSE approximation conjugated with GW method. The effects of the functionalization of the seam atoms on the absorption spectrum are plotted in Fig. 4. For incident light polarized along the x-axis, edge-functionalization has strongly altered the optical profile of H-passivated SiCQDs. The absorption curves are shifted toward lower energies upon hydroxylation and carboxylation of seam atoms. In the case of SiCQDs with a complete functionalization of seam atoms, -OH functional exhibit the greatest impact on the absorption spectra. Similarly, the optical properties of structures with decorated C atoms are mainly affected by hydroxylation more than carboxylation. However, for configurations with decorated Si atoms, -COOH show the most remarkable effect on absorption curves. Notice that the optical absorption peaks corresponding to large sized SiCQDs are more red-shifted compared to smaller structures, and their intensities are significantly increased. As summarized in Table 2, the optical gaps are in the range of $2.59-0.59$ eV. It follows that, except OH-$Si_{15}C_{15}H_{14},$ OH-$Si_{15}C_{15}H_{14}$-OH and COOH-$Si_{15}C_{15}H_{14},$ functionalized QDs show a range absorption profile in the visible energy window which is a crucial property required for materials designed for use in photovoltaic and solar cell devices. This finding confirms the emergence of our SiCQDs in photovoltaic applications.
Fig. 4. Optical absorption spectra of edge-functionalized SiCQDs at GW+BSE level as a function of size and molecular substituents X=H, OH, COOH. a-c) small sized and d-e) large sized SiCQDs.
Table 2. Calculated values of QDs: The charge transfer from SiC skeleton to functional groups (X = OH, COOH). The exciton binding energy $E_{b}^{X}$, the optical gap $E_{opt}^{X}$ and the singlet-triplet energy splitting $\Delta _{S-T}^{X}$. All the energies are in eV.
Unlike bulk materials, the difference between optical band gap and electronic band gap is large due to the reduced electron screening effects and quantum confinement in low-dimensional semiconducting materials. This results in a large binding energy. More precisely, except COOH-$Si_{8}C_{8}H_{10}$-COOH and COOH-$Si_{8}C_{8}H_{10}$ configurations that show an abnormality, all functionalized SiCQDs exhibit a strongly bound exciton, which are significantly larger than those found for pristine structures, and this is attributed to the fact that -OH and -COOH functional group withdraw electrons from SiC skeleton (Table 2) leading to a drop in the density of charge carriers which enhances the e-h interaction and thus increase $E_{b}^{X}$. The decrement in $E_{b}^{X}$ values observed in COOH-$Si_{8}C_{8}H_{10}$-COOH and COOH-$Si_{8}C_{8}H_{10},$ despite the remarkable charge transfer from SiC skeleton to -COOH , is originated from the H$\rightarrow$L electronic transitions of the first bright exciton in these configurations. Here, the incident light polarized along the y-axis is not considered because of the isotropic behaviour of optical properties in all the structures as showed in our previous work [14]. The spacial distribution of the first bright exciton in OH-$C_{8}Si_{8}H_{10}$ is quite similar to pristine Si$_{8}$C$_{8}$ QDs. Except this configuration, all small sized QDs diplayed the electron-hole pairs that are mainly delocalized over the SiC skeleton especially Si atoms including all or some of the molecular substituents. As plotted in Fig. 5, the situation is slightly different for large configurations, since the electron-hole pairs are dispersed along to the upper moiety of SiC basal plane including the functional groups, except for COOH-$C_{15}Si_{15}H_{14}$ in consistence with charge density associated to LUMO presented in Fig. 3. The strong charge distribution localized around the hole found for small structures certified the pronounced excitonic effects in these SiCQDs with respect to larger one.
To investigate the photophysical processes occurring in edge-functionalized QDs and examine their luminescence yield, the singlet-triplet energy splitting $\Delta _{S-T}^{X}$ is reported in Table 2 for the first bright exciton. Complete and half decorations of seam atoms exhibit a noticeable impact on the photophysical processes of pristine SiCQDs as illustrated in the $\Delta _{S-T}^{X}$ modification. Additionally, the reported values reveal the remarkable role of quantum confinement in tuning the luminescence, since the functionalization enhances $\Delta _{S-T}^{X}$ in large-sized structure and diminishes that of smaller configurations. The energy splitting ranges between $0.5$ and $1$ eV indicating a high fluorescence luminescent yield in decorated QDs [58]. Furthermore, some QDs structures are thermally activated delayed fluoresence (TADF) with an exchange splitting less or equal to 0.37 eV. This assigns the structures the ability to harvest 100% triplet excitons through facilitated reversed intersystem crossing. It follows that TADF QDs are Characterized by their improved external quantum efficiency and the long diffusion lengths of their excitons prior to the dissociation. Compared to other nanostructures, known to exhibit significant quantum confinement and exchange splitting, such as carbon nanotubes [50], silicon nanowires [51] and silicon QDs [52], the calculated $\Delta _{S-T}^{X}$ values are found to be larger. This confirms the high potential of photoluminescent SiCQDs which as emergent candidates for optoelectronic and photovoltaic applications.
Fig. 5. Spatial distribution corresponding to the first bright exciton for SiCQDs. The hole is fixed at the center as indicated by the black point.
4. Conclusion
In summary, we employed the first principles DFT and GW+BSE simulations to examine the viability of edge -hydroxylated and -carboxylated SiCQDs for use in DSSC. More precisely, we investigate their electronic and optical properties. The structural geometry of the SiCQDs has shown remarkable resistance to potential distortions brought by the edge-functionalization. Moreover, all configurations appear to be thermodynamically stable according to binding energy values, especially small sized SiCQDs with complete hydroxylation, which showed crucial energy stability over their larger counterparts. Likewise, global reactivity descriptors indicated that the chemical reactivity of SiCQDs was strongly tailored by varying the position, concentration and type of molecular substituents. With respect to the electronic properties, the complete functionalization of the seam atoms leads to a decrease in the H-L gap, while for a half decoration, the variation of the energy gap depends on the molecular substituents position. This finding is attributed to the hybridization of the frontier molecular orbitals, resulting in diverse electronic behaviors as a function of the adopted edge-functionalization process. Furthermore, it is shown that most of the configurations are characterized by spatial charge separation, significant charge transfer, low optical bandgap and NIR- absorptions which are very required to improve DSSC performance. Finally, this work shows that edge functionalization is a valuable tool for tailoring chemical stability, reactivity, H-L gap and splitting of SiCQDs, which makes them promising for photovoltaic, optoelectronic and nanomedical applications.
Acknowledgement
The authors would like to acknowledge the "Académie Hassan II des Sciences et Techniques"-Morocco for its financial support. They also thank the LPHE-MS, Faculty of Sciences, Mohammed V University in Rabat, Morocco for the technical support through computer facilities, where all the calculations have been performed. L. B. Drissi acknowledges the Alexander von Humboldt Foundation for the research fellowship Ref 3.4 - MAR - 1202992 - GF-E.
Disclosures
The authors declare no conflicts of interest.
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