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Abstract
Controlling spontaneous emission by modifying the local electromagnetic environment is of great interest for applications in optoelectronics, biosensing and energy harvesting. Although the development of devices based on one-dimensional porous silicon photonic crystals with embedded luminophores is a promising approach for applications, the efficiency of the embedded luminophores remains a key challenge because of the strong quenching of the emission due to the contact of the luminophores with the surface of porous silicon preventing the observation of interesting light–matter coupling effects. Here, we experimentally demonstrate an increase in the quantum dot (QD) spontaneous emission rate inside a porous silicon microcavity and almost an order of magnitude enhancement of QD photoluminescence intensity in the weak light–matter coupling regime. Furthermore, we have demonstrated drastic alteration of the QD spontaneous emission at the edge of the photonic band gap in porous silicon distributed Bragg reflectors and proved its dependence on the change in the density of photonic states.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The possibility to control the spontaneous emission by placing the emitters in an environment modifying the spatial distribution of electromagnetic field is of great interest due to the large number of the possible practical applications, including biosensing, fluorescence imaging, single-photon sources, and light-emitting diodes [1–4]. Light–matter interaction in the weak coupling regime leads to changes in the spectral and temporal properties of spontaneous emission due to the interaction of resonant excitation in the emitter with localized electromagnetic modes. This so-called weak coupling regime occurs when the rate of the coherent energy exchange is lower than the energy losses of both the emitter and the cavity. In this case the rate of spontaneous emission could be calculated using the Weisskopf–Wigner derivation:
where ${\Gamma _{i \to f}}(\omega )$ is the transmission probability,$i$ and f are the indices of the excited and ground states of the system, respectively, µif is the dipole matrix element between the i and f states, E0 is the electric field generated by one photon at the emitter location, and ρ(ω) is the local density of the photonic states [5]. For a single emitter, ρ(ω) is the number of electromagnetic modes per unit frequency per unit volume, and it strongly depends on the electromagnetic environment in the vicinity of the emitter.In order to alter the local electromagnetic environment of the emitter, it could be placed inside a cavity [6]. If homogeneous broadening of the luminophore emission spectrum is higher than the full width at half maximum (FWHM) of the cavity mode, enhancement of the emission at the cavity resonance wavelength could be observed along with suppression of the emission outside of the cavity mode [7]. It was supposed by Purcell in 1946 that the rate of the emission should also be changed [8]. The ratio between the emission rates of the emitter inside and outside of the cavity is called the Purcell factor. This effect has been demonstrated in numerous systems, including emitters placed inside optical and plasmonic cavities [9–11]. However, one of the most versatile ways to control the distribution of electromagnetic field is the use of photonic crystals (PhCs). PhCs are structures with a periodically changing refractive index, which results in the formation of photonic band gaps. Introducing defects into refractive index periodicity leads to the formation of localized states inside the photonic band gap. These localized states, together with the states at the edges of the photonic band gap, have an extremely high density of photonic states. A lot of studies have been performed in the field of interaction between the excited state of the emitter and localized electromagnetic field inside PhCs. However, the Purcell enhancement affects only the radiative relaxation pathway of the emitter, while the experimentally observed lifetime of the excited state is determined by the combination of both radiative and non-radiative relaxations. Thus, the suitability of the light–matter coupled system for developing fast and bright light sources is determined by the interplay between the alteration of the radiation relaxation rate, non-radiative losses, initial quantum yield of the luminophore, efficiency of the excitation, and collection of light. This last factor could also be controlled in PhCs via manipulation over the distribution of the exciting field and the spatial emission pattern. For many practical applications, one-dimensional PhCs provide the most suitable combination of the desired properties.
Today there are numerous approaches to fabrication of one-dimensional PhCs consisting of stacked layers with alternating refractive indices [12], including spin coating [13], self-assembly [14], chemical [15] and electrochemical etching [16], depending on the type of the PhC material. Formation of periodical layers of porous silicon (pSi) with different porosities and refractive indices using electrochemical etching of monocrystalline silicon [17–19] is a promising method of PhC fabrication for practical applications in drug delivery [20–25], energy storage [26,27], sensing, and biosensing [28–33]. The sensitivity of the detection strongly depends on the luminescent properties of the labels and the efficiency of signal collection [34]. A highly developed surface and oriented porous system with controllable pore sizes allows efficient embedding of probe biomolecules and detector luminophores.
There are three general mechanisms by which PhCs could enhance the emission of embedded emitters: an increase in the excitation efficiency, more efficient collection of the emitted light due to direction-confined enhanced emission, and the enhancement of the spontaneous emission rate (Purcell effect) [4,35,36]. Because the excitation wavelength is usually far from the eigenmodes of the microcavity, the first effect could be neglected [37]. In earlier studies it has already been demonstrated that embedding of luminophores into the porous structure of pSi could lead to narrowing of their photoluminescence (PL) spectra and formation of directional emission [38–41]. However, despite the strong suppression of spontaneous emission outside of the cavity resonance and its enhancement at the cavity mode wavelength, the authors doubted the weak coupling nature of the observed effects and attributed it to the optical filtration effect [38].
To the best of our knowledge, the change in the spontaneous emission rate of the luminophores embedded in one-dimensional pSi PhCs has not been demonstrated yet. We believe that the main obstacle to observing this effect was the strong quenching of the emission due to the interaction of the luminophores with the surface of pSi. We find it very promising to develop a hybrid system based on pSi PhCs with embedded luminophores, where the quenching of the emission will be suppressed, and Purcell enhancement of spontaneous emission will occur. Such structures could be effectively applied to the areas of sensing and development of compact light sources with narrow emission spectra. Furthermore, low losses of energy could lead to the strong coupling regime in systems based on pSi PhCs, promoting the use of the hybrid structures for controlling chemical reactivity and designing low-threshold coherent light sources.
Here, we have investigated the spontaneous emission of CdSe(core)/ZnS/CdS/ZnS(multishell) semiconductor quantum dots (QDs) placed inside one-dimensional pSi PhCs of two types: distributed Bragg reflectors (DBRs) and microcavities. We used QDs as emitters because of their high photostability and quantum yield, wide absorption and a relatively narrow PL spectrum [14,34,42–46]. To prevent QDs from quenching and to provide homogeneous distribution inside the PhCs, we treated the surface of porous PhCs with hexadecyltrimethoxysilane. We measured the spectral, spatial, and temporal properties of the QD emission and demonstrated enhancement of both the intensity and the rate of spontaneous emission of the QDs homogeneously distributed inside the PhCs. In addition, significant alteration of the spontaneous QD emission at the edge of the photonic band gap in distributed pSi Bragg reflectors has been observed and shown to be directly proportional to the density of photonic states in the DBR. The weak light–matter coupling nature of these effects has been demonstrated. The obtained results indicate a reliable and easily adjustable approach to controlling spontaneous luminophores emission through modification of their local electromagnetic environment in porous matrices, which paves the way to new optoelectronics, biosensing, and energy harvesting applications.
2. Results and discussion
2.1 Optical properties of fabricated samples
The porous silicon PhCs studied here were fabricated by the standard electro-chemical etching technique (see Supplement 1 for the details on fabrication). A typical DBR consisted of 5 to 25 pairs of porous layers with alternating high (75%) and low (58%) porosities. A λ/2 pSi microcavity consisted of two DBRs separated by a spacer, a high-porosity layer of the same material with a double thickness. The front DBR consisted of 5 lattice periods. The bottom DBR was fabricated using the same porosities consisting of 20 lattice periods, which resulted in a higher reflectivity and led to prevailing emission through the front mirror. Figure 1 shows scanning electron microscope (SEM) images of the front surface and the cross-section of the pSi microcavity. It could be seen that the outer surface of the microcavity is quite homogeneous, with pore diameters in the range from 10 to 20 nm, and the thickness and porosity remained unchanged over the entire depth of the microcavity.
Fig. 1. Scanning electron microscopy images of the surface (a) and cross-section (b) of the fabricated porous silicon microcavity.
For controlling the emission properties of the luminophores using light–matter coupling, emitters could be either homogeneously distributed in the porous structure or placed directly inside the spacer layer between two DBRs using the transfer-printing technique [47]. The latter option is more preferable for obtaining efficient light–matter coupling, because most emitters are in a close vicinity of the antinode of the optical mode. However, the difficulty of transferring the fragile thin film of the front pSi DBR strongly limits the scalability of this approach. On the other hand, many practical applications (e.g., in sensing) require homogeneous distribution of the emitters in porous structure in order to make it accessible for interaction with the analyte. In this case drop-casting of the solution containing emitters could be used for embedding the emitters into pSi. Although this approach seems promising, the lack of direct control over the spatial distribution and quenching of the emission are the main two obstacles for widespread application of the drop-casting technique.
The possibility to observe light–matter coupling of energy transition in emitters embedded into the microcavity strongly depends on the relationship between the coupling strength and energy losses in the systems. In the case of pSi PhCs with embedded luminophores, nonradiative losses of energy become the main issue. Due to the large surface area of the porous structure, most emitters are in a close contact with the surface of silicon, and the quantum yield of the emitters could decrease significantly. In order to prevent QDs from quenching, we thermally oxidized the pSi PhCs using the technique described in detail in the Supplement 1. As a result, we achieved deep oxidation of silicon without damaging the morphology. This led to a considerable decrease in the refractive indices of both the high- and low-porosity layers. The corresponding significant blue shift of the PhC band gap was about 120 nm, while the FWHM of the eigenmode remained unchanged. Importantly, the oxidation of the major amount of silicon not only decrease the quenching of QDs emission but also leads to the drastic drop of absorption losses for electromagnetic field propagating within the porous silicon structure in a visible range.
The pSi DBR and microcavity reflectance spectra after the oxidation are shown in Fig. 2. The high-reflection band of the DBRs was approximately 100 nm wide, spanning from 570 nm to 670 nm, and corresponded to the DBR photonic band gap.
Fig. 2. Reflectance spectra of the porous silicon distributed Bragg reflector (a) and microcavity (b) after oxidation.
To obtain interaction of the QD emission with the modes at the edge of the photonic band gap, the spectral position of the band gap was tuned to cover almost the entire emission spectra of the QDs (Fig. 3), with slight overlapping in the blue region. In order to fabricate a microcavity, a spacer with a double thickness was etched between the DBRs. This spacer has determined the localized eigenstate within the photonic band gap with an FWHM of several nanometres, corresponding to the Q-factor value between 100 and 200. The photonic band gap of the microcavity was approximately 160 nm wide (560–720 nm), with the eigenmode cantered at 620 nm. This band gap was designed to cover the emission spectra of QDs (Fig. 3) and to provide good matching between the QD emission maximum and the microcavity eigenmode.
Fig. 3. Absorption (black) and photoluminescence (PL, red) spectra of CdSe(core)/CdS/ZnS(multishell) quantum dots in a hexane solution.
2.2 Incorporation of the quantum dots into the porous silicon photonic structures
CdSe(core)/ZnS/CdS/ZnS(multishell) semiconductor QDs were fabricated using the hot injection method briefly described in Supplement 1. The absorption and PL spectra of a QD solution in hexane are shown in Fig. 3.
The PL spectrum of the QDs in the solution represents a symmetrical Gaussian peak with a maximum at about 620 nm and FWHM of about 37 nm (Fig. 3). The QDs were incorporated into the pSi photonic structures by drop-casting 5 µl of the hexane solution with a QD concentration of about 0.5 mg/ml onto the pSi substrate. Homogeneous distribution of the emitters inside the PhC was achieved by the design of the porous structure that ensured strong capillary forces [40] and by treatment of the pSi surface with hexadecyltrimethoxysilane, making it hydrophobic. The QD distribution inside the PhC was analysed using confocal microscopy, which showed homogeneous PL intensity distribution in the cross-section image of the photonic structure (see Supplement 1 for details).
After embedding of the QDs into the pSi microcavity, their PL maximum was squeezed into a peak with a FWHM of about 6 nm, corresponding to the microcavity eigenmode in shape, width, and position (Fig. 4). The FWHM of the microcavity mode at a wavelength of 620 nm was 5 nm. At the same time, the QD PL outside the PhC eigenmode was substantially suppressed.
Fig. 4. Photoluminescence (PL) spectra of the CdSe(core)/CdS/ZnS(multishell) quantum dots (QDs) and angular distribution of their PL. Panel (a): PL spectra of the QDs inside (red) and outside (black) the microcavity and microcavity reflection spectrum (blue). Panel (b): angular distribution of the QD PL inside (red) and outside (black) the microcavity.
In order to evaluate the spatial distribution of the resulting mode, we performed the measurement of the angular distribution of light emitted from QDs inside pSi PhCs and compared it with the results obtained with QDs placed onto a plain silicon surface. Figure 4 shows that the emission of QDs within the microcavity eigenmode is obviously concentrated in the direction perpendicular to the sample surface. At the same time, PL from the QD film on the silicon surface is distributed according to Lambert’s cosine law. Thus, at an angle of 30°, the PL from the QDs in the microcavity is almost vanished, while for a planar QD film its signal has an intensity of about 80% of the maximum. This distribution agrees with previous results obtained in such systems [40,48].
Narrowing of the QD PL spectra together with the change in the emission spatial confinement have been reported earlier [38]. In that study, the QDs were distributed inside the cavity region only, whereas in our system, QDs were distributed homogeneously in the entire porous structure of the PhC.
In theory, the coupling strength of the energy state of an individual emitter is proportional to the intensity of the electric field in its vicinity [7], which is not constant in the microcavity. The homogeneous distribution of QDs in the PhC should lead to poor coupling of the emitters located far from the cavity region. However, in the experiments conducted in our study, we observed a very low emission signal outside of the microcavity mode. This can be explained if we take into account the relatively deep penetration of the electromagnetic field of the eigenmode into the DBRs due to the low contrast of the refractive index between the porous layers. This behaviour of the emission of homogeneously distributed emitters could be useful for many practical applications. Furthermore, Qiao et al. claim that the observed enhancement is likely to be determined by the spatial redistribution of the emission, while the influence of the Purcell effect is doubtful [38]. Even putting aside the PL increase due to the Purcell enhancement of the emission rate, the enhancement observed in that study [38] was still three times smaller than that expected from the theoretical calculations [49–50].
In order to precisely evaluate the enhancement of the spontaneous emission, we first compared the PL spectra of the QDs inside the microcavity with those of the QDs placed inside a homogenous monolayer of pSi with a fixed porosity of about 66%, having the same thickness as the microcavity, and the same degree of oxidation (Fig. 5). Equal amounts of QDs were embedded in the microcavity and introduced in the monolayer.
Fig. 5. Quantum dot photoluminescence spectra inside the porous silicon microcavity (red) and in the porous silicon monolayer (black).
Despite the absence of a localized eigenmode in the monolayer, the PL spectrum of QDs in it is still modulated by minor oscillations of the reflection spectrum (about 20% of the amplitude) [51]. However, the peak intensity of QD PL is 7.5 times higher in the microcavity than in the monolayer, while the integral over the PL spectrum intensity is 5 times higher in the microcavity. We have already mentioned that in most previous studies the impact of the Purcell effect was neglected. However, the Purcell effect cannot be disregarded in the case when QDs are homogeneously distributed inside the pSi microcavity and their non-radiative relaxation is suppressed. Here, the eigenmode penetrating the DBR structure could change the local electromagnetic environment for most of the QDs, thus changing the rate of spontaneous emission and, subsequently, the relaxation kinetics [6,7,36,52]. Thus, the Purcell effect can play the major role in the enhancement of the spontaneous emission. In order to experimentally demonstrate this effect in our hybrid structures, we have compared the PL emission rate kinetics for the QDs located inside the microcavity with that for the QDs in the pSi monolayer, so as to exclude the influence of residual non-radiative relaxation pathways arising from the interaction with the surface of the pSi and absorption losses due to the propagation within the pSi PhC.
2.3 Spontaneous emission rate alteration
The PL kinetics was measured using the setup described in Supplement 1. For excitation, we used a 532-nm laser with a pulse length of about 350 ps. The PL decay curves were measured at the wavelength corresponding to the maximum of the PL spectra (Fig. S3 in Supplement 1). The PL decay time of QDs coupled to the microcavity mode was estimated to be about 3.8 ns, whereas in the QD monolayer it was about 6.1 ns. Hence, the ratio between the PL decay times was estimated to be about 1.6. Using the obtained PL kinetics, theoretical estimation of the enhancement factor could be done and compared with the experimental results.
The enhancement of the QDs emission (Ge) along the optical axis of a one-dimensional PhC at the eigenmode frequency is due to several factors. The first one is the redistribution of the spontaneous emission due to the multipath interference, as we have described earlier [49,50,53,54]. It can be estimated using the following equation:
2.4 Alteration of the emission spectra at the edge of the photonic band gap
Apart from the pSi microcavities, individual DBRs based on pSi are also widely used in practice [28,31,32]. We suggest that using the same technique of embedding of the QDs one could achieve the significant alteration of QDs emission spectrum due to the change in the photonic density of states (Eq. (1)). The photonic density of states inside a one-dimensional PhC, ρSi, can be determined using the following expression:
Fig. 6. Calculated reflectance spectrum of the distributed Bragg reflectors (DBRs, black) and distribution of the photonic density of states for the emitter placed into the DBR (red).
Fig. 7. Reflection of the distributed Bragg reflectors (DBRs) and photoluminescence (PL) spectra of the quantum dots (QDs) inside and outside the DBR and angular dependence of the spectral position of the enhanced PL peak. Panel (a): reflection of the distributed Bragg reflectors (DBR, black) and PL spectra of the QDs in the solution outside the DBR (blue) and homogeneously distributed in the DBR (red). Panel (b): experimental (red points) and calculated (black points) angular dependences of the spectral position of the enhanced PL peak.
Figure 7(a) shows the PL of QDs embedded in a DBR consisting of 25 pairs of pSi layers. For clear observation of the alteration of the QD emission spectrum due to the change in the photonic density of states at the edge of the photonic band gap, the maximum of the QD PL spectrum was purposely shifted into the photonic band gap, with only a small overlap of the broadened PL spectrum with the edge.
Figure 7(a) shows that a strong emission peak arose at a wavelength of 560 nm, corresponding to the edge of the photonic band gap. The intensity of this peak is slightly higher than the intensity at the wavelength of the initial PL maximum of the QD solution. PL in that region was significantly suppressed upon embedding of QDs into the cavity due to the lower photonic density of states (Fig. 6) inside the photonic band gap. The spectral redistribution of the PL intensity could be qualitatively estimated by comparing the ratios between the intensity of the PL at 560 nm and the intensity at the wavelength of the initial PL maximum of QDs in the DBR and in the solution outside the cavity. The experimental value of this ratio in the case of QDs in DBR is about 35 times higher than the corresponding value for the QD solution outside the cavity, which appears to be in excellent agreement with the theoretically predicted value of 34 corresponding to the ratio between the photonic densities of states. The minor discrepancy between the theoretically and experimentally obtained values can be explained by the difference between the calculated and experimental reflection spectra. Such a good agreement between these values allows us to speculate that the intensity of QD PL at the edge of the photonic band gap was indeed enhanced rather than merely suppressed inside the photonic band gap. Following this approach, we can estimate the enhancement at the edge of the photonic band gap from the value of the relative photonic density of states at the peak, which is about 4. In order to estimate the dependence of the PL alteration on the spectral shift of the photonic band gap edge, we measured the angular dependence of the PL of QDs embedded in the DBR, and then calculated it using the approach described in the “Calculations” section of Supplement 1.
Figure 7(b) shows that, with an increase in the angle, the enhanced PL emission peak shifts to the blue region, which corresponds to the shift of the photonic band gap. Here, the theoretical and experimental dependences are in good agreement. However, there is a minor discrepancy between the experimental and calculated spectral positions of the enhanced peak at large angles, which can be explained by the difference between the calculated and experimental reflection spectra and, in particular, the edge steepness. It could be seen from the comparison between calculated and experimental reflectance spectra (Fig. 6 and Fig. 7) that the calculated edge of the photonic bandgap is much steeper than that in the experimental reflectance spectrum. It leads to the faster decrease of the density of photonic state inside the calculated photonic bandgap and subsequent stronger suppression of the emission. As a result, the calculated enhanced peak corresponding to the edge of the photonic was shifted to the blue region relative to the measured one.
A decrease in the enhanced peak intensity was observed along with an increase in the relative emission of the main maximum of the QD PL, which remained at the same wavelength. This behaviour proves the proportionality of the emission intensity to the relative photonic density of states, which opens the way for further control over the QD emission inside the pSi PhCs. Although the increase in the emission intensity at the edge of the photonic band gap relative to the emission intensity inside it is expected theoretically, for the best of our knowledge, this effect has not been experimentally observed earlier for emitters distributed within a pSi DBR. Only a small enhancement of QD PL has been demonstrated previously upon QD deposition on the surface of the DBR, due to the high reflectivity of the substrate and more efficient signal collection [32]. Hence, the obtained results are new and important from both theoretical and practical points of view. On the one hand, the results directly demonstrate the weak-coupling origin of the modification of the QD emission spectrum upon their embedding into porous PhCs and complement the conclusions made in the previous section. Indeed, the change in the relaxation time and strong dependence on the photonic density of states are two strong arguments for the weak-coupling origin of the alteration of the PL emission spectrum. On the other hand, the developed approach can also be used for further improvement of the emission efficiency in practical applications of such hybrid systems in sensing and optoelectronics [28].
3. Conclusions
Here, we have investigated spontaneous emission of semiconductor QDs embedded in one-dimensional pSi PhCs. The spectral, spatial, and temporal characteristics of the PL emission from weakly coupled states and their dependences on the properties of PhCs have been measured. We have demonstrated a weak coupling origin of the observed modifications of the spontaneous PL emission spectra of QD. Approximately an order of magnitude enhancement of the PL of QDs located inside the pSi microcavity at the eigenmode was shown to be accompanied by an almost twofold increase in the total emission rate due to the Purcell effect. Furthermore, we have demonstrated significant alteration of spontaneous QD emission at the edge of the photonic band gap of the pSi DBR and analysed its angular distribution, which was shown to be precisely proportional to the relative photonic density of states. The ratio between the PL intensity at the wavelength corresponding to the photonic band gap edge and the intensity of the initial PL maximum has shown a 35-fold increase upon embedding of the QDs in the pSi DBR resulting from both enhancement and suppression of the PL at different wavelengths. We speculate that the placement of the QDs directly between two DBRs by the transfer-printing technique [47] could lead to further increase in the strength of interaction between light and matter and subsequent observation of the strong coupling regime in pSi-based structures. On the other hand, the simple technology of preparation of hybrid porous structures containing homogeneously distributed QDs, together with their robustness and excellent scalability, make such hybrid structures promising for applications in many fields, such as sensing, optoelectronics, and energy harvesting. We believe that our findings could be used for improving the efficiency of a wide range of devices where the sensitivity should be high enough to detect individual luminophores, when the detected analytes are rare or scattered in the large volumes of a crude probe.
Funding
Conseil régional du Grand Est; Ministère de l'Education Nationale, de l'Enseignement Superieur et de la Recherche; Russian Foundation for Fundamental Investigations (18-29-20121).
Acknowledgments
This study was supported by the Russian Foundation for Fundamental Investigations, grant no. 1829-20121. I.N. acknowledges the support from the Ministry of Higher Education, Research and Innovation of the French Republic, Conseil Régional de Grand Est and Université de Reims Champagne-Ardenne. We thank Vladimir Ushakov for the help with technical preparation of the manuscript.
Disclosures
The authors declare no conflicts of interest.
Supplementary information
See Supplement 1 for supporting content
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