rus
Issue #8/2021
A. I. Arzhanov, A. O. Savostianov, K. A. Magaryan, K. R. Karimullin, A. V. Naumov
Photonics of Semiconductor Quantum Dots: Basic Aspects
Photonics of Semiconductor Quantum Dots: Basic Aspects
DOI: 10.22184/1993-7296.FRos.2021.15.8.622.641
The article provides a brief overview of the works devoted to the synthesis, study of photophysical and spectral properties and analysis of applications of semiconductor nanocrystals – quantum dots. The fundamental laws connecting the morphology of quantum dots with its optical-spectral characteristics are discussed, as well as some theoretical models that allow describing various effects and processes: the quantum-dimensional effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots. The results of original experimental and theoretical studies of the temperature dependences of the spectra of colloidal quantum dots with a CdSe emitting core are presented, which made it possible to clarify the nature of the formation of the spectra of single quantum dots and their ensembles.
The article provides a brief overview of the works devoted to the synthesis, study of photophysical and spectral properties and analysis of applications of semiconductor nanocrystals – quantum dots. The fundamental laws connecting the morphology of quantum dots with its optical-spectral characteristics are discussed, as well as some theoretical models that allow describing various effects and processes: the quantum-dimensional effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots. The results of original experimental and theoretical studies of the temperature dependences of the spectra of colloidal quantum dots with a CdSe emitting core are presented, which made it possible to clarify the nature of the formation of the spectra of single quantum dots and their ensembles.
Теги: electron-phonon interaction local field effects photoluminescence blinking of single quantum dots quantum-confinement effect quantum dots квантово-размерный эффект квантовые точки мерцание фотолюминесценции одиночных квантовых точек электрон-фононное взаимодействие эффекты локального поля
Photonics of Semiconductor Quantum Dots: Basic Aspects
A. I. Arzhanov 1, 2, 3, A. O. Savostianov 1, 2, 3, K. A. Magaryan 1, K. R. Karimullin 1, 2, 3, A. V. Naumov 1, 2, 3, *
Moscow Pedagogical State University, Moscow, Russia
Institute of Spectroscopy of the Russian Academy of Sciences, Moscow, Troitsk, Russia
P. N. Lebedev Physics Institute of the Russian Academy of Sciences, Troitsk Branch, Moscow, Troitsk, Russia
The article provides a brief overview of the works devoted to the synthesis, study of photophysical and spectral properties and analysis of applications of semiconductor nanocrystals – quantum dots. The fundamental laws connecting the morphology of quantum dots with its optical-spectral characteristics are discussed, as well as some theoretical models that allow describing various effects and processes: the quantum-dimensional effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots. The results of original experimental and theoretical studies of the temperature dependences of the spectra of colloidal quantum dots with a CdSe emitting core are presented, which made it possible to clarify the nature of the formation of the spectra of single quantum dots and their ensembles.
Keywords: quantum dots, quantum-confinement effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots
The article was received: 24.11.2021
The article was accepted: 08.12.2021
Semiconductor nanocrystals (quantum dots)
Semiconductor low-dimensional structures or quantum dots (QDs) are the object of active fundamental and applied research due to their unique optical properties. The interest in such systems is based on the significant difference in their optical properties from the properties of the similar bulk materials. In particular, they are characterized by so-called quantum-confinement effects associated with the dependence of their energy states on the size of the system itself. By varying the size of a quantum dot, it is possible to change its spectrum of exciton, electronic and phonon states, control the spectrum of radiation and absorption, thereby achieving the desired characteristics.
Quantum dots were first synthesized in 1981 by A. I. Yekimov and A. A. Onushchenko in a glass matrix [1], and then in 1983 by Louis Bruce in a colloidal solution [2]. The theory of quantum dots was created by Aleksandr Efros in 1982 [3]. A. E. Ekimov, A. L. Efros and L. Bruce were awarded the R. W. Wood Prize for the discovery of quantum dots in 2006. The term “quantum dot” itself was proposed by Mark Reed [4].
Works by A. I. Ekimov, A. L. Efros and L. Bruce became the starting point for the research of a new class of physical objects with a size of units of nm. Shortly thereafter, based on studies of nanoscale semiconductor crystals, it was concluded that the electronic levels of matter were modified during the transition from bulk material to the nanoscale [3, 5, 6]. This phenomenon was named the quantum-confinement effect [7], which will be described in more detail hereafter.
The optical parameters of quantum dots are closely related to the geometric and chemical parameters of the particle. The rule which is valid for all semiconductor quantum dots states is that with a decrease in physical size, the size of the band gap will increase, which in turn will impose restrictions on the amount of quantum energy that the quantum dot is able to absorb or emit. Modern synthesis methods make it possible to fabricate quantum dots from various materials (Fig. 1). Combining materials and the various sizes of nanoparticles, it is possible to obtain a variety of configurations of optical properties. Due to that fact, quantum dots have become enormously widespread. In addition to the ability to fine-tune optical parameters, which is of great interest to fundamental science, quantum dots are in demand in technologies: solar cells and LEDs, new displays, fast optical switches, biological markers, markers for securities, quantum computer science, and communications. Not all this makes a complete list of applications of so-called “artificial atoms” – semiconductor nanocrystals.
Quantum-confinement effect
The optical properties of quantum dots are determined mainly by two factors: the band gap width of the semiconductor material and the influence of quantum-confinement effects. The combination of these factors makes it possible to produce efficient compact emitters with broadband absorption and narrow-band luminescence at a given wavelength.
The quantum-confinement effect in quantum dots is associated with the spatial restriction of the movement of charge carriers (electrons and holes) in all three directions. Such restrictions lead to a change in the energy spectrum of the material as discrete hydrogen-like levels are formed instead of a continuous distribution (Fig. 2). For this reason, quantum dots are often called artificial atoms.
The reason for such a radical restructuring of the energy structure can be understood if we consider the problem of an electron-hole pair (exciton) inside a potential well. In general, this task does not have an analytical solution, but it can be strongly simplified if a number of requirements is satisfied. So, for example, if we neglect the energy of the Coulomb interaction of an electron and a hole in comparison with the total energy of their dimensional quantization (which can be obtained by considering independently the problems of an electron and a hole in a quantum well with infinitely high walls), then we can write an expression for the exciton energy in quantum dots as follows:
. (1)
where is a bulk crystal band gap, n and l are the main and orbital quantum numbers of electrons (holes), is the n-th root of the Bessel function of the l-th order, R is a quantum dot radius, and are the effective masses of the electron and hole, respectively. This approximation is called “strong confinement”, its applicability is closely related to the concept of the Bohr exciton radius Rex. The conditions for the smallness of the Coulomb interaction are equivalent to the condition R << Rex, and therefore, knowing the values of R and Rex, it is possible to evaluate the correctness of using Equation (1). For a more correct analysis of the experimental luminescence and Raman scattering spectra in the quantum dots, however, taking into account the Coulomb interaction is still desirable. Accordingly, a summand should be added
to Equation (1) , where .
The opposite situation corresponding to the condition R >> Rex, is called “weak confinement” and actually involves considering the Vanier-Mott exciton problem in a potential well (this is already a two-particle problem, in contrast to considering a strong confinement). As can be seen from Table 1, the condition R >> Rexis rarely fulfilled for real quantum dots, which have characteristic dimensions of the order unity that are less than tens of nm.
Much more common is the so-called “intermediate confinement”, the consideration of which requires additional assumptions. For instance, in the paper [9] when considering CdS and CuBr nanocrystals, it was proposed to assume that a light electron moves freely throughout the entire volume of the quantum dot, while a much more massive hole rests in its center.
Although in the general case it is difficult to calculate the exciton energy, Equation (1) is able to qualitatively explain the regularities of the spectral properties of the quantum dots. For example, a decrease in the quantum dot radius R leads to an increase in the effective band gap and a corresponding shift of the maximum of the luminescence band to the short-wavelength region (see Fig. 3), as well as the appearance of more pronounced peaks in the absorption spectra.
The core-shell quantum dots should be noted separately. Shells act as a core passivator, reducing the number of surface defects on the core. Such defects are believed to negatively affect the optical properties of quantum dots, leading to a decrease in quantum yield, the occurrence of parasitic recombination luminescence, and the phenomenon of luminescence blinking. Quantum dots of the core-shell type can be divided into two types. The first type, which is the most widespread, is a core of a narrow-band semiconductor covered with a wide-band shell (for example, CdSe / ZnS). In such a quantum dot, the charge carriers are localized in the core. The second type (for example, CdTe / CdSe) is distinguished by the edges of the forbidden zones of the core and shell shifted relative to each other. In such quantum dots, electrons and holes are no longer localized in the cores and are located in different parts of the nanocrystal, which leads to an increase in the luminescence time, at the same time, a significant decrease in the effective bandgap allows shifting of the emission maximum to the red wavelength.
The quantum confinement effect is manifested when at least one of the geometric dimensions of a substance is reduced to tens of nanometres (Fig. 4.). Under these conditions, the electronic subsystem becomes discrete. Even later it became clear that the degree of discreteness can be controlled using chemical methods, changing the size and shape of structures. Due to this effect, semiconductor nanocrystals ranging in size from units to several tens of nanometres are capable of blocking the entire visible and near ultraviolet (UV) and infrared (IR) regions with their radiation [12].
The quantum confinement effect is characteristic not only for particles with a limited size. The effect also occurs when the material from which the particle is synthesized is changed, as well as when external fields are applied and various chemical impurities, additional shells, etc. are added. The quantum confinement effect manifests itself when electronic interaction forces (including local fields) of crystal structure occur inside the nanostructure. The ability to combine different materials in a single nanostructure provides a great opportunity for application.
Numerous examples include the combination of magnetic and optical properties in a single FePt / PbSe nanoparticle [13] or the synthesis of a Co / Fe2O3 nanostructure from two different magnetic materials [14]. As an alternative approach, inert materials can be used to increase the stability of nanostructures. An example of such an approach is the paper [15], the authors of which placed quantum dots in amorphous silicon dioxide.
It is fundamentally important to develop new methods for the synthesis of nanostructures to obtain objects of a complex predetermined shape, because the developed structure at the atomic level also contributes to the properties of the material. The improvement of the methodological and experimental base makes it possible to study the processes occurring at the level of single molecules and atoms [16], which in turn makes a huge contribution to the fundamental field of physical knowledge.
Synthesis methods, types and morphology of quantum dots
There are a number of methods for the synthesis of semiconductor nanocrystals, which are epitaxy, colloidal synthesis, laser ablation, chemical self-assembly, the mesophase growth in liquid crystal materials, etc.
To date, two methods of obtaining quantum dots have become the most frequent practice: the method of colloidal synthesis and the epitaxial method.
Epitaxial production of quantum dots can be carried out using two methods: molecular beam epitaxy [17] and metal-organic chemical vapour deposition (MOCVD) [18]. As a rule, in these processes, quantum dots are formed in thin semiconductor layers grown on well-purified single crystal substrates. A necessary condition for growth is the various constants of the lattices of the substrate and the film being built up.
Molecular beam epitaxy is an improved version of the method of thermal spraying of materials in ultrahigh vacuum conditions. Quantum dots grow on monocrystalline substrates due to the directed flow of atoms or molecules evaporated or sublimated from specially prepared sources placed in special isothermal chambers – the so-called effusion cells. The number of effusion cells is determined by the composition of the quantum dots grown and the presence of alloying impurities.
When using the metal-organic chemical vapour deposition method, the growth of the semiconductor layer is ensured by the deposition of thermal decomposition products of organic gas molecules that contain the necessary chemical elements on the substrate. Unlike molecular beam epitaxy, the process occurs at moderate pressures. The crystallization of the material occurs on a heated substrate in a reactor with cold walls when a homogeneous mixture of reagent gases with a carrier gas is passed over it. As a result of the decomposition of gas into components on a hot surface, a film of the required semiconductor material is formed on the substrate.
The properties of quantum dots obtained by means of epitaxy depend on many factors: the degree of purity of the materials used, their physic and chemical properties, the presence of defects on the crystalline substrate, the temperature at which the process is carried out. As a rule, the average monodispersity of the obtained particles does not exceed 3%. The disadvantages of nanocrystals grown in this way include the limitations of their use due to the properties of solid, often opaque substrates. This disadvantage is especially pronounced when using quantum dots as a tool for biosensorics and medical nanodiagnostics.
The modern method of colloidal synthesis originates in the pioneering works by C. Murray and M. Bawendi et alias [19]. Colloidal synthesis makes it possible to obtain nanostructures of various shapes, sizes and compositions [20].
In general, in colloidal synthesis, the reagents used are placed in a solvent, where nucleation and crystal growth occur at high temperatures (200–360 °C, the more accurate name of the method is high-temperature organometallic synthesis). Complex organic compounds are used as solvents: trioctylphosphide (TOP), trioctylphosphidoxide (TOPO), tribitylphosphine (TBP), trioctylphosphyl selenide (TOPSe) [19]. In particular, to create CdSe quantum dots, the TOPO solvent is heated to 360 °C in an argon medium. Afterward, a solution of a mixture of cadmium and selenium salts is injected into it with a syringe [21]. This method provides an opportunity to control the size of a nanocrystal in real time by measuring the wavelength of luminescence [22].
This method is widely used to synthesize quantum dots coated with a wide-band semiconductor (core-shell QDs). The fact is that the optical properties (in particular, the quantum yield of luminescence) of semiconductor nanocrystals are influenced by surface defects that occur during synthesis. These defects play the role of non-radiative recombination centres, their significant number causes a serious decrease in the quantum yield. To eliminate surface defects around the core of one semiconductor, a thin shell from another semiconductor is built up, usually with a wider band gap (for example, a ZnS shell is used for the CdSe core). The presence of such a shell makes it possible to prevent photochemical degradation of the nucleus and significantly increase the quantum yield [23]. A separate place is occupied by the so-called recombination QDs, which have a wide luminescence spectrum shifted to the red wavelength of the spectrum due to the presence of a large number of defects in the structure [24]. A great potential in applied use is expected when binding QDs with organic (macro)molecules, where energy can be transferred efficiently [25–27].
Optical and spectral characteristics
Although Equation 1 provides an opportunity to estimate the width of the effective band gap in the first approximation, and hence the wavelength of the luminescence of QDs, experiments show that the spectral properties of nanocrystals can differ significantly if there is a difference in their local environment. It should be noted herewith that the properties of the environment of nanocrystals are often dictated by the peculiarities of their practical use. Quantum dots can closely coexist with conductive polymers in photodiodes [28], metal substrates and nanoparticles in photovoltaic cells [29, 30], quartz substrates in field effect transistors [31]. The use of QDs as a means of bioimaging implies mandatory modification of the surface with the help of biocompatible polymers [32, 33], phospholipid micelles [34], silicon dioxide nanoparticles [35].
One of the important and practically significant properties of quantum dots is that their spectral characteristics depend on various parameters inherent in both the QDs and the external environment. The spectral properties of QDs depend on their size, shape, composition, and concentration in the ensemble. In addition, the spectra of QDs are influenced by temperature, pressure and the matrix in which the QDs are placed. These circumstances make it possible to control the spectral properties of QDs and materials based on them. On the other hand, QDs themselves become effective sensors of various environmental parameters. For example, QDs can act as magnetic field sensors [36].
The study of temperature-dependent luminescence spectra of QDs can provide a large amount of information about the parameters of the electron-phonon interaction, as well as about the influence of the matrix on these parameters. The temperature dependences of the parameters of the luminescence spectra of nanocomposites are investigated: the maximum position that corresponds to the width of the bandgap (exciton energy) and the spectrum width. As a rule, spectra of QDs are symmetrical bands corresponding to exciton luminescence, with a width of the order of tens of nm. Depending on the matrix basis of the composite, the spectra differ in the position of the maximum peak of exciton luminescence (exciton energy). As the temperature decreases, the maxima of exciton bands in the luminescence spectra shift to the UV region of the spectrum. Fig. 5 shows the temperature-dependent luminescence spectra of QDs of CdSe / CdS / ZnS placed in a polymeric matrix of polyisobutylene (PIB) (a) and in frozen toluene (b), in the temperature range of 4.2–300 K and the temperature dependence of the peak position and width of the exciton luminescence spectrum for CdSe / CdS / ZnS in toluene.
Temperature dependences of the band gap width for nanocomposites with QDs can be analysed within the framework of various models, for example, electron-phonon interaction [37, 38]. An analysis of the literature shows that for the first time the temperature dependence of the band gap width for bulk semiconductors was empirically described by Varshni [39] in the form:
, (2)
where Eg(0) is the bandgap width at 0 K, α is the temperature coefficient, β is the parameter associated with the Debye temperature.
Nevertheless, this ratio is not informative enough in the case of studying the parameters of the electron-phonon interaction of QDs with a matrix[40]. In the paper by O’Donnell and Chen, an [41] analytical formula was derived to describe the temperature dependence:
, (3)
which contains additional parameters characterizing the strength of the electron-phonon interaction – S (Huang-Rhys factor) and the average energy of phonons at the relaxation of electronic excitation ELO.
Describing the temperature dependences of the exciton energy obtained in the experiment using this formula, it is possible to obtain the values of the electron-phonon interaction parameters for QDs in different matrices (see Table 2).
The obtained values of S are quite different for different samples, i. e. the presence of the surrounding matrix strongly affects the parameters of the electron phonon interaction. The values of ELO also differ for different samples, which may indicate a noticeable effect of hybridization of vibrational (phonon) modes – the interaction of the emitting nucleus of a quantum dot not only with local phonons QDs, but also with the phonons of the matrix.
Differences in the parameters of the electron-phonon interaction lead to a noticeable change in the effective frequency of the local phonon, which indicates a strong influence of matrix dynamics on the spectral and luminescent properties of QDs. This is especially noticeable by the behaviour of the temperature dependence of the band gap width for QDs in frozen solutions near the temperature of phase transitions (for example, during vitrification).
The analysis of temperature-dependent luminescence spectra is an indirect method of obtaining information about the parameters of localized phonons. To confirm the data obtained, additional measurements can be performed by vibrational spectroscopy methods [42], in particular by Raman scattering [11, 38]. In these studies, bands for QDs were found in different matrices in the low-frequency spectra of Raman scattering, the frequencies of which correspond to the estimates of the ELO value from the luminescence spectra. Therefore, QDs can be used as effective and sensitive sensors of temperature and local oscillatory dynamics in various matrices.
Studies show that the spectral properties of the nanocomposite strongly depend on the concentration of QDs. For example, it was [46] found that with an increase in the concentration of QDs in solution, the luminescence spectrum shifts to the red wavelength and widens. In this regard, the concentration of QDs should be taken into account when conducting research and developing applications.
Photoluminescence of single QDs of CdSe / CdS / ZnS under the influence of external mechanical forces was studied in [47]. The experimental setup was a combined atomic force and confocal luminescent microscope. Single QDs were localized and subjected to a series of force effects using the tip of the atomic force microscope cantilever as a nanometer-sized piston. Thus, changes in photophysical characteristics under the influence of pressure were investigated at the level of single QDs. As a result of the study, it was found that the spectra of single QDs shifted either towards higher or lower radiation energies without any signs of the presence of several radiation lines induced by the action of the applied force. The direction and magnitude of these reversible spectral shifts depended on the orientation of the axes of the nanocrystals relative to the external anisotropic force. The maximum pressures in the range of several hPa utilized in this experiment are comparable to the values obtained in optical chambers with diamond anvils.
The average value of the spectral shift was about 3.0–3.5 MeV / hPa. The results obtained indicate that the luminescence spectrum of single QDs can be reversibly rearranged in a significant range of wavelengths without deterioration of their characteristics. This circumstance can be used to develop tunable sources of single photons.
Research related to the study of the kinetics of luminescence of QDs shows off its great potential. The paper [48] investigated the possibility of using colloidal QDs of CdSe / ZnS as probes to study their dielectric environment, based on data on the effect of the local refractive index on the fluorescence kinetics of these QDs. It should be noted that similar studies on microrefractometry and mapping of local fields were performed using single organic molecules in solid matrices [49]. The model of solid spheres and the Bruggeman effective medium approximation were used by authors in [48]. In the course of the study, the properties of the QD ensemble in a homogeneous solution were compared with the characteristics of single QDs placed inside different dielectric matrices. It was found that the results obtained can be described within the framework of a single model only if the point dipole emitter is located at a distance from the substrate that corresponds to the geometry of the QDs. Further, three theoretical models describing the dependence of the fluorescence decay rate on the local refractive index were analysed, and it was shown that the classical Lorentz model (virtual cavity) is the most suitable for describing the data obtained. Added to this is the fact that the authors investigated the sensitivity of QDs to environmental parameters by estimating the detection limit of the active substance using the example of streptavidin molecules. In doing so, it is shown that QDs can be used as effective sensors for studying the parameters of the local environment and serve as a basis for creating nanosensors to determine the content of various substances in ultra-low concentrations.
Spectromicroscopy
of single quantum dots
Upon study of single quantum dots, unique effects are discovered that are invisible when studying bulk crystals of semiconductors. One of these effects is the phenomenon of luminescence blinking, which occurs when a single quantum dot undergoes continuous laser irradiation. An example of this behaviour is shown on the Figure 6.
Stochastic transitions between the state, in which the quantum dot emits luminescence (the so-called “on-states”) and the state in which the emission stops under direct irradiation (“off-state”), reduce the total quantum yield of the particle. This circumstance imposes restrictions on the potential use of semiconductor quantum dots as track markers and biological sensors, and especially as non-classical light sources. Many research groups that conduct independent studies came to the following conclusions: alternation of on-state and off-state depend on the size of quantum dots, the material from which they are synthesized, and configuration (quantum dot, thread, well, the presence or absence of shell, etc.). The existence of so-called “grey” states, intermediate states, in which the luminescence intensity is less than that in on-state, and more than in off-state, the duration of radiative and nonradiative states is affected by the intensity of the exciting radiation, and temperature and other parameters of the environment that surrounds a quantum dot [50, 51].
There are various approaches to describing this phenomenon. The first model describing the dynamics in a quantum dot was developed by Efros and Rosen and called as “charge model” [53]. Upon absorption of a photon by a quantum dot, an electron-hole (e-h) pair with a strong bond (exciton) is formed. In QDs, there are energy levels that can be occupied by an electron and a hole, which form an exciton. The annihilation of such an e-h pair leads to the emission of a luminescence photon and the transition of the QD to the ground state. The characteristic lifetime of an exciton, for example, in a CdSe QD is several ns. In addition, there are defects on the surface of a quantum dot (violation of the ideal crystal structure), which have their own long-lived energy levels, which are different from the exciton levels of the QD. As a result of internal ionization, an electron or a hole can be “trapped” at these defect levels (so-called trap states), and an uncompensated charge remains in the QD core. Further, with the subsequent absorption of a photon and the creation of an e-h pair, the Auger recombination process becomes decisive – the transfer of energy from the recombining pair to an uncompensated charge with subsequent nonradiative relaxation, thus the QD does not emit in a trapped state. The lifetime of an electron (hole) in the trap significantly exceeds the time during which the exciton decays; for this reason, the QD does not emit luminescence for a long time (from microseconds to hours) (it is in the off state). After tunneling the charge from the trap back to the core, the system goes over to the radiative on-state. This model does not describe the power law of the distribution of on- and off-time intervals, which was recorded by various scientific teams [54], which is taken into account by the following models
In the model of multiple recombination centres (MRC model) [55], the existence of multiple recombination centres for charge carriers is considered. The presence of such recombination centres leads to fluctuations in the rate of nonradiative transitions, which in turn affects the change in the total luminescence intensity and as a result leads to the flicker effect.
There is a model that was named as combined, using the advantages of the charge model and model of the tunneling two-level systems (TLS) [56]. According to the model, transitions from the radiative state to the non-radiative state are associated with the processes of Auger ionization and subsequent Auger neutralization and / or tunnelling of the charge back into the nucleus, similar to the mechanism in the charge model. The existence of low-amplitude transitions in both on and off states is explained by analogy with the TLS model [57]. Such transitions are caused by fluctuations in the probability of nonradiative transitions associated with the dynamics of atoms on the surface of the nucleus of a quantum dot (which, in a generalized sense, is described in the MRC model). It is interesting that information can be extracted even for blinking characteristic times longer than both blind times and time slots between them. [58]
When spectroscopic studies of the effect of blinking luminescence of a single quantum dot were under way, it became clear that intensity fluctuations are also associated with the so-called spectral diffusion [52]. This is a phenomenon in which the position of the spectral band changes continuously between two (and sometimes more) values on the frequency scale. The dynamics of this process is observed in experiments with high temporal resolution, with long-term studies leading to a significant broadening of the luminescence spectral contour.
Such temporal behaviour analysis provides an opportunity to characterize dynamic processes in a single quantum dot. Such dynamics is described within the framework of a model [52] that takes into account both processes – luminescence blinking and spectral diffusion. In [43], in particular, a model of electron-phonon interaction with a fluctuating coupling strength coefficient was developed, which leads to a synchronous abrupt change in the position and width of the luminescence spectrum (exciton peak) over time (Fig. 6).
As can be seen, upon the research of individual quantum dots, new unique effects are discovered that are invisible when studying an ensemble of particles. Features that manifest themselves only at the level of single objects have a great potential for application. In particular, photostability and high quantum yield of luminescence have become the basis of numerous applications of QDs in optoelectronics, and the highest sensitivity of the optical-spectral characteristics of QDs to external parameters provides them an opportunity to be used as spectral nanoprobes.
Acknowledgement
The work was carried out within the framework of the State Assignment of the Moscow Pedagogical State University (MPSU) “Physics of Nanostructured Materials: Fundamental Research and Applications in Materials Science, Nanotechnology and Photonics” with the support of the Ministry of Education of the Russian Federation (AAAA-A20-120061890084-9) together with the Centre for Collective Use “Structural Diagnostics of Materials” of the Federal Research Centre of the Russian Academy of Sciences “Crystallography and Photonics”. The authors of the article are members of the leading scientific school of the Russian Federation “Optical-spectral nanoscopy of quantum objects and diagnostics of promising materials” (project NSh-776.2022.1.2).
All the unique photo-physical properties of quantum dots open a way for exciting applications (light sources, re-emitters and light converters, biomarkers, lasers, photovoltaics etc.) which will be considered in the next issue of PHOTONICS RUSSIA.
A. I. Arzhanov 1, 2, 3, A. O. Savostianov 1, 2, 3, K. A. Magaryan 1, K. R. Karimullin 1, 2, 3, A. V. Naumov 1, 2, 3, *
Moscow Pedagogical State University, Moscow, Russia
Institute of Spectroscopy of the Russian Academy of Sciences, Moscow, Troitsk, Russia
P. N. Lebedev Physics Institute of the Russian Academy of Sciences, Troitsk Branch, Moscow, Troitsk, Russia
The article provides a brief overview of the works devoted to the synthesis, study of photophysical and spectral properties and analysis of applications of semiconductor nanocrystals – quantum dots. The fundamental laws connecting the morphology of quantum dots with its optical-spectral characteristics are discussed, as well as some theoretical models that allow describing various effects and processes: the quantum-dimensional effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots. The results of original experimental and theoretical studies of the temperature dependences of the spectra of colloidal quantum dots with a CdSe emitting core are presented, which made it possible to clarify the nature of the formation of the spectra of single quantum dots and their ensembles.
Keywords: quantum dots, quantum-confinement effect, electron-phonon interaction, local field effects, photoluminescence blinking of single quantum dots
The article was received: 24.11.2021
The article was accepted: 08.12.2021
Semiconductor nanocrystals (quantum dots)
Semiconductor low-dimensional structures or quantum dots (QDs) are the object of active fundamental and applied research due to their unique optical properties. The interest in such systems is based on the significant difference in their optical properties from the properties of the similar bulk materials. In particular, they are characterized by so-called quantum-confinement effects associated with the dependence of their energy states on the size of the system itself. By varying the size of a quantum dot, it is possible to change its spectrum of exciton, electronic and phonon states, control the spectrum of radiation and absorption, thereby achieving the desired characteristics.
Quantum dots were first synthesized in 1981 by A. I. Yekimov and A. A. Onushchenko in a glass matrix [1], and then in 1983 by Louis Bruce in a colloidal solution [2]. The theory of quantum dots was created by Aleksandr Efros in 1982 [3]. A. E. Ekimov, A. L. Efros and L. Bruce were awarded the R. W. Wood Prize for the discovery of quantum dots in 2006. The term “quantum dot” itself was proposed by Mark Reed [4].
Works by A. I. Ekimov, A. L. Efros and L. Bruce became the starting point for the research of a new class of physical objects with a size of units of nm. Shortly thereafter, based on studies of nanoscale semiconductor crystals, it was concluded that the electronic levels of matter were modified during the transition from bulk material to the nanoscale [3, 5, 6]. This phenomenon was named the quantum-confinement effect [7], which will be described in more detail hereafter.
The optical parameters of quantum dots are closely related to the geometric and chemical parameters of the particle. The rule which is valid for all semiconductor quantum dots states is that with a decrease in physical size, the size of the band gap will increase, which in turn will impose restrictions on the amount of quantum energy that the quantum dot is able to absorb or emit. Modern synthesis methods make it possible to fabricate quantum dots from various materials (Fig. 1). Combining materials and the various sizes of nanoparticles, it is possible to obtain a variety of configurations of optical properties. Due to that fact, quantum dots have become enormously widespread. In addition to the ability to fine-tune optical parameters, which is of great interest to fundamental science, quantum dots are in demand in technologies: solar cells and LEDs, new displays, fast optical switches, biological markers, markers for securities, quantum computer science, and communications. Not all this makes a complete list of applications of so-called “artificial atoms” – semiconductor nanocrystals.
Quantum-confinement effect
The optical properties of quantum dots are determined mainly by two factors: the band gap width of the semiconductor material and the influence of quantum-confinement effects. The combination of these factors makes it possible to produce efficient compact emitters with broadband absorption and narrow-band luminescence at a given wavelength.
The quantum-confinement effect in quantum dots is associated with the spatial restriction of the movement of charge carriers (electrons and holes) in all three directions. Such restrictions lead to a change in the energy spectrum of the material as discrete hydrogen-like levels are formed instead of a continuous distribution (Fig. 2). For this reason, quantum dots are often called artificial atoms.
The reason for such a radical restructuring of the energy structure can be understood if we consider the problem of an electron-hole pair (exciton) inside a potential well. In general, this task does not have an analytical solution, but it can be strongly simplified if a number of requirements is satisfied. So, for example, if we neglect the energy of the Coulomb interaction of an electron and a hole in comparison with the total energy of their dimensional quantization (which can be obtained by considering independently the problems of an electron and a hole in a quantum well with infinitely high walls), then we can write an expression for the exciton energy in quantum dots as follows:
. (1)
where is a bulk crystal band gap, n and l are the main and orbital quantum numbers of electrons (holes), is the n-th root of the Bessel function of the l-th order, R is a quantum dot radius, and are the effective masses of the electron and hole, respectively. This approximation is called “strong confinement”, its applicability is closely related to the concept of the Bohr exciton radius Rex. The conditions for the smallness of the Coulomb interaction are equivalent to the condition R << Rex, and therefore, knowing the values of R and Rex, it is possible to evaluate the correctness of using Equation (1). For a more correct analysis of the experimental luminescence and Raman scattering spectra in the quantum dots, however, taking into account the Coulomb interaction is still desirable. Accordingly, a summand should be added
to Equation (1) , where .
The opposite situation corresponding to the condition R >> Rex, is called “weak confinement” and actually involves considering the Vanier-Mott exciton problem in a potential well (this is already a two-particle problem, in contrast to considering a strong confinement). As can be seen from Table 1, the condition R >> Rexis rarely fulfilled for real quantum dots, which have characteristic dimensions of the order unity that are less than tens of nm.
Much more common is the so-called “intermediate confinement”, the consideration of which requires additional assumptions. For instance, in the paper [9] when considering CdS and CuBr nanocrystals, it was proposed to assume that a light electron moves freely throughout the entire volume of the quantum dot, while a much more massive hole rests in its center.
Although in the general case it is difficult to calculate the exciton energy, Equation (1) is able to qualitatively explain the regularities of the spectral properties of the quantum dots. For example, a decrease in the quantum dot radius R leads to an increase in the effective band gap and a corresponding shift of the maximum of the luminescence band to the short-wavelength region (see Fig. 3), as well as the appearance of more pronounced peaks in the absorption spectra.
The core-shell quantum dots should be noted separately. Shells act as a core passivator, reducing the number of surface defects on the core. Such defects are believed to negatively affect the optical properties of quantum dots, leading to a decrease in quantum yield, the occurrence of parasitic recombination luminescence, and the phenomenon of luminescence blinking. Quantum dots of the core-shell type can be divided into two types. The first type, which is the most widespread, is a core of a narrow-band semiconductor covered with a wide-band shell (for example, CdSe / ZnS). In such a quantum dot, the charge carriers are localized in the core. The second type (for example, CdTe / CdSe) is distinguished by the edges of the forbidden zones of the core and shell shifted relative to each other. In such quantum dots, electrons and holes are no longer localized in the cores and are located in different parts of the nanocrystal, which leads to an increase in the luminescence time, at the same time, a significant decrease in the effective bandgap allows shifting of the emission maximum to the red wavelength.
The quantum confinement effect is manifested when at least one of the geometric dimensions of a substance is reduced to tens of nanometres (Fig. 4.). Under these conditions, the electronic subsystem becomes discrete. Even later it became clear that the degree of discreteness can be controlled using chemical methods, changing the size and shape of structures. Due to this effect, semiconductor nanocrystals ranging in size from units to several tens of nanometres are capable of blocking the entire visible and near ultraviolet (UV) and infrared (IR) regions with their radiation [12].
The quantum confinement effect is characteristic not only for particles with a limited size. The effect also occurs when the material from which the particle is synthesized is changed, as well as when external fields are applied and various chemical impurities, additional shells, etc. are added. The quantum confinement effect manifests itself when electronic interaction forces (including local fields) of crystal structure occur inside the nanostructure. The ability to combine different materials in a single nanostructure provides a great opportunity for application.
Numerous examples include the combination of magnetic and optical properties in a single FePt / PbSe nanoparticle [13] or the synthesis of a Co / Fe2O3 nanostructure from two different magnetic materials [14]. As an alternative approach, inert materials can be used to increase the stability of nanostructures. An example of such an approach is the paper [15], the authors of which placed quantum dots in amorphous silicon dioxide.
It is fundamentally important to develop new methods for the synthesis of nanostructures to obtain objects of a complex predetermined shape, because the developed structure at the atomic level also contributes to the properties of the material. The improvement of the methodological and experimental base makes it possible to study the processes occurring at the level of single molecules and atoms [16], which in turn makes a huge contribution to the fundamental field of physical knowledge.
Synthesis methods, types and morphology of quantum dots
There are a number of methods for the synthesis of semiconductor nanocrystals, which are epitaxy, colloidal synthesis, laser ablation, chemical self-assembly, the mesophase growth in liquid crystal materials, etc.
To date, two methods of obtaining quantum dots have become the most frequent practice: the method of colloidal synthesis and the epitaxial method.
Epitaxial production of quantum dots can be carried out using two methods: molecular beam epitaxy [17] and metal-organic chemical vapour deposition (MOCVD) [18]. As a rule, in these processes, quantum dots are formed in thin semiconductor layers grown on well-purified single crystal substrates. A necessary condition for growth is the various constants of the lattices of the substrate and the film being built up.
Molecular beam epitaxy is an improved version of the method of thermal spraying of materials in ultrahigh vacuum conditions. Quantum dots grow on monocrystalline substrates due to the directed flow of atoms or molecules evaporated or sublimated from specially prepared sources placed in special isothermal chambers – the so-called effusion cells. The number of effusion cells is determined by the composition of the quantum dots grown and the presence of alloying impurities.
When using the metal-organic chemical vapour deposition method, the growth of the semiconductor layer is ensured by the deposition of thermal decomposition products of organic gas molecules that contain the necessary chemical elements on the substrate. Unlike molecular beam epitaxy, the process occurs at moderate pressures. The crystallization of the material occurs on a heated substrate in a reactor with cold walls when a homogeneous mixture of reagent gases with a carrier gas is passed over it. As a result of the decomposition of gas into components on a hot surface, a film of the required semiconductor material is formed on the substrate.
The properties of quantum dots obtained by means of epitaxy depend on many factors: the degree of purity of the materials used, their physic and chemical properties, the presence of defects on the crystalline substrate, the temperature at which the process is carried out. As a rule, the average monodispersity of the obtained particles does not exceed 3%. The disadvantages of nanocrystals grown in this way include the limitations of their use due to the properties of solid, often opaque substrates. This disadvantage is especially pronounced when using quantum dots as a tool for biosensorics and medical nanodiagnostics.
The modern method of colloidal synthesis originates in the pioneering works by C. Murray and M. Bawendi et alias [19]. Colloidal synthesis makes it possible to obtain nanostructures of various shapes, sizes and compositions [20].
In general, in colloidal synthesis, the reagents used are placed in a solvent, where nucleation and crystal growth occur at high temperatures (200–360 °C, the more accurate name of the method is high-temperature organometallic synthesis). Complex organic compounds are used as solvents: trioctylphosphide (TOP), trioctylphosphidoxide (TOPO), tribitylphosphine (TBP), trioctylphosphyl selenide (TOPSe) [19]. In particular, to create CdSe quantum dots, the TOPO solvent is heated to 360 °C in an argon medium. Afterward, a solution of a mixture of cadmium and selenium salts is injected into it with a syringe [21]. This method provides an opportunity to control the size of a nanocrystal in real time by measuring the wavelength of luminescence [22].
This method is widely used to synthesize quantum dots coated with a wide-band semiconductor (core-shell QDs). The fact is that the optical properties (in particular, the quantum yield of luminescence) of semiconductor nanocrystals are influenced by surface defects that occur during synthesis. These defects play the role of non-radiative recombination centres, their significant number causes a serious decrease in the quantum yield. To eliminate surface defects around the core of one semiconductor, a thin shell from another semiconductor is built up, usually with a wider band gap (for example, a ZnS shell is used for the CdSe core). The presence of such a shell makes it possible to prevent photochemical degradation of the nucleus and significantly increase the quantum yield [23]. A separate place is occupied by the so-called recombination QDs, which have a wide luminescence spectrum shifted to the red wavelength of the spectrum due to the presence of a large number of defects in the structure [24]. A great potential in applied use is expected when binding QDs with organic (macro)molecules, where energy can be transferred efficiently [25–27].
Optical and spectral characteristics
Although Equation 1 provides an opportunity to estimate the width of the effective band gap in the first approximation, and hence the wavelength of the luminescence of QDs, experiments show that the spectral properties of nanocrystals can differ significantly if there is a difference in their local environment. It should be noted herewith that the properties of the environment of nanocrystals are often dictated by the peculiarities of their practical use. Quantum dots can closely coexist with conductive polymers in photodiodes [28], metal substrates and nanoparticles in photovoltaic cells [29, 30], quartz substrates in field effect transistors [31]. The use of QDs as a means of bioimaging implies mandatory modification of the surface with the help of biocompatible polymers [32, 33], phospholipid micelles [34], silicon dioxide nanoparticles [35].
One of the important and practically significant properties of quantum dots is that their spectral characteristics depend on various parameters inherent in both the QDs and the external environment. The spectral properties of QDs depend on their size, shape, composition, and concentration in the ensemble. In addition, the spectra of QDs are influenced by temperature, pressure and the matrix in which the QDs are placed. These circumstances make it possible to control the spectral properties of QDs and materials based on them. On the other hand, QDs themselves become effective sensors of various environmental parameters. For example, QDs can act as magnetic field sensors [36].
The study of temperature-dependent luminescence spectra of QDs can provide a large amount of information about the parameters of the electron-phonon interaction, as well as about the influence of the matrix on these parameters. The temperature dependences of the parameters of the luminescence spectra of nanocomposites are investigated: the maximum position that corresponds to the width of the bandgap (exciton energy) and the spectrum width. As a rule, spectra of QDs are symmetrical bands corresponding to exciton luminescence, with a width of the order of tens of nm. Depending on the matrix basis of the composite, the spectra differ in the position of the maximum peak of exciton luminescence (exciton energy). As the temperature decreases, the maxima of exciton bands in the luminescence spectra shift to the UV region of the spectrum. Fig. 5 shows the temperature-dependent luminescence spectra of QDs of CdSe / CdS / ZnS placed in a polymeric matrix of polyisobutylene (PIB) (a) and in frozen toluene (b), in the temperature range of 4.2–300 K and the temperature dependence of the peak position and width of the exciton luminescence spectrum for CdSe / CdS / ZnS in toluene.
Temperature dependences of the band gap width for nanocomposites with QDs can be analysed within the framework of various models, for example, electron-phonon interaction [37, 38]. An analysis of the literature shows that for the first time the temperature dependence of the band gap width for bulk semiconductors was empirically described by Varshni [39] in the form:
, (2)
where Eg(0) is the bandgap width at 0 K, α is the temperature coefficient, β is the parameter associated with the Debye temperature.
Nevertheless, this ratio is not informative enough in the case of studying the parameters of the electron-phonon interaction of QDs with a matrix[40]. In the paper by O’Donnell and Chen, an [41] analytical formula was derived to describe the temperature dependence:
, (3)
which contains additional parameters characterizing the strength of the electron-phonon interaction – S (Huang-Rhys factor) and the average energy of phonons at the relaxation of electronic excitation ELO.
Describing the temperature dependences of the exciton energy obtained in the experiment using this formula, it is possible to obtain the values of the electron-phonon interaction parameters for QDs in different matrices (see Table 2).
The obtained values of S are quite different for different samples, i. e. the presence of the surrounding matrix strongly affects the parameters of the electron phonon interaction. The values of ELO also differ for different samples, which may indicate a noticeable effect of hybridization of vibrational (phonon) modes – the interaction of the emitting nucleus of a quantum dot not only with local phonons QDs, but also with the phonons of the matrix.
Differences in the parameters of the electron-phonon interaction lead to a noticeable change in the effective frequency of the local phonon, which indicates a strong influence of matrix dynamics on the spectral and luminescent properties of QDs. This is especially noticeable by the behaviour of the temperature dependence of the band gap width for QDs in frozen solutions near the temperature of phase transitions (for example, during vitrification).
The analysis of temperature-dependent luminescence spectra is an indirect method of obtaining information about the parameters of localized phonons. To confirm the data obtained, additional measurements can be performed by vibrational spectroscopy methods [42], in particular by Raman scattering [11, 38]. In these studies, bands for QDs were found in different matrices in the low-frequency spectra of Raman scattering, the frequencies of which correspond to the estimates of the ELO value from the luminescence spectra. Therefore, QDs can be used as effective and sensitive sensors of temperature and local oscillatory dynamics in various matrices.
Studies show that the spectral properties of the nanocomposite strongly depend on the concentration of QDs. For example, it was [46] found that with an increase in the concentration of QDs in solution, the luminescence spectrum shifts to the red wavelength and widens. In this regard, the concentration of QDs should be taken into account when conducting research and developing applications.
Photoluminescence of single QDs of CdSe / CdS / ZnS under the influence of external mechanical forces was studied in [47]. The experimental setup was a combined atomic force and confocal luminescent microscope. Single QDs were localized and subjected to a series of force effects using the tip of the atomic force microscope cantilever as a nanometer-sized piston. Thus, changes in photophysical characteristics under the influence of pressure were investigated at the level of single QDs. As a result of the study, it was found that the spectra of single QDs shifted either towards higher or lower radiation energies without any signs of the presence of several radiation lines induced by the action of the applied force. The direction and magnitude of these reversible spectral shifts depended on the orientation of the axes of the nanocrystals relative to the external anisotropic force. The maximum pressures in the range of several hPa utilized in this experiment are comparable to the values obtained in optical chambers with diamond anvils.
The average value of the spectral shift was about 3.0–3.5 MeV / hPa. The results obtained indicate that the luminescence spectrum of single QDs can be reversibly rearranged in a significant range of wavelengths without deterioration of their characteristics. This circumstance can be used to develop tunable sources of single photons.
Research related to the study of the kinetics of luminescence of QDs shows off its great potential. The paper [48] investigated the possibility of using colloidal QDs of CdSe / ZnS as probes to study their dielectric environment, based on data on the effect of the local refractive index on the fluorescence kinetics of these QDs. It should be noted that similar studies on microrefractometry and mapping of local fields were performed using single organic molecules in solid matrices [49]. The model of solid spheres and the Bruggeman effective medium approximation were used by authors in [48]. In the course of the study, the properties of the QD ensemble in a homogeneous solution were compared with the characteristics of single QDs placed inside different dielectric matrices. It was found that the results obtained can be described within the framework of a single model only if the point dipole emitter is located at a distance from the substrate that corresponds to the geometry of the QDs. Further, three theoretical models describing the dependence of the fluorescence decay rate on the local refractive index were analysed, and it was shown that the classical Lorentz model (virtual cavity) is the most suitable for describing the data obtained. Added to this is the fact that the authors investigated the sensitivity of QDs to environmental parameters by estimating the detection limit of the active substance using the example of streptavidin molecules. In doing so, it is shown that QDs can be used as effective sensors for studying the parameters of the local environment and serve as a basis for creating nanosensors to determine the content of various substances in ultra-low concentrations.
Spectromicroscopy
of single quantum dots
Upon study of single quantum dots, unique effects are discovered that are invisible when studying bulk crystals of semiconductors. One of these effects is the phenomenon of luminescence blinking, which occurs when a single quantum dot undergoes continuous laser irradiation. An example of this behaviour is shown on the Figure 6.
Stochastic transitions between the state, in which the quantum dot emits luminescence (the so-called “on-states”) and the state in which the emission stops under direct irradiation (“off-state”), reduce the total quantum yield of the particle. This circumstance imposes restrictions on the potential use of semiconductor quantum dots as track markers and biological sensors, and especially as non-classical light sources. Many research groups that conduct independent studies came to the following conclusions: alternation of on-state and off-state depend on the size of quantum dots, the material from which they are synthesized, and configuration (quantum dot, thread, well, the presence or absence of shell, etc.). The existence of so-called “grey” states, intermediate states, in which the luminescence intensity is less than that in on-state, and more than in off-state, the duration of radiative and nonradiative states is affected by the intensity of the exciting radiation, and temperature and other parameters of the environment that surrounds a quantum dot [50, 51].
There are various approaches to describing this phenomenon. The first model describing the dynamics in a quantum dot was developed by Efros and Rosen and called as “charge model” [53]. Upon absorption of a photon by a quantum dot, an electron-hole (e-h) pair with a strong bond (exciton) is formed. In QDs, there are energy levels that can be occupied by an electron and a hole, which form an exciton. The annihilation of such an e-h pair leads to the emission of a luminescence photon and the transition of the QD to the ground state. The characteristic lifetime of an exciton, for example, in a CdSe QD is several ns. In addition, there are defects on the surface of a quantum dot (violation of the ideal crystal structure), which have their own long-lived energy levels, which are different from the exciton levels of the QD. As a result of internal ionization, an electron or a hole can be “trapped” at these defect levels (so-called trap states), and an uncompensated charge remains in the QD core. Further, with the subsequent absorption of a photon and the creation of an e-h pair, the Auger recombination process becomes decisive – the transfer of energy from the recombining pair to an uncompensated charge with subsequent nonradiative relaxation, thus the QD does not emit in a trapped state. The lifetime of an electron (hole) in the trap significantly exceeds the time during which the exciton decays; for this reason, the QD does not emit luminescence for a long time (from microseconds to hours) (it is in the off state). After tunneling the charge from the trap back to the core, the system goes over to the radiative on-state. This model does not describe the power law of the distribution of on- and off-time intervals, which was recorded by various scientific teams [54], which is taken into account by the following models
In the model of multiple recombination centres (MRC model) [55], the existence of multiple recombination centres for charge carriers is considered. The presence of such recombination centres leads to fluctuations in the rate of nonradiative transitions, which in turn affects the change in the total luminescence intensity and as a result leads to the flicker effect.
There is a model that was named as combined, using the advantages of the charge model and model of the tunneling two-level systems (TLS) [56]. According to the model, transitions from the radiative state to the non-radiative state are associated with the processes of Auger ionization and subsequent Auger neutralization and / or tunnelling of the charge back into the nucleus, similar to the mechanism in the charge model. The existence of low-amplitude transitions in both on and off states is explained by analogy with the TLS model [57]. Such transitions are caused by fluctuations in the probability of nonradiative transitions associated with the dynamics of atoms on the surface of the nucleus of a quantum dot (which, in a generalized sense, is described in the MRC model). It is interesting that information can be extracted even for blinking characteristic times longer than both blind times and time slots between them. [58]
When spectroscopic studies of the effect of blinking luminescence of a single quantum dot were under way, it became clear that intensity fluctuations are also associated with the so-called spectral diffusion [52]. This is a phenomenon in which the position of the spectral band changes continuously between two (and sometimes more) values on the frequency scale. The dynamics of this process is observed in experiments with high temporal resolution, with long-term studies leading to a significant broadening of the luminescence spectral contour.
Such temporal behaviour analysis provides an opportunity to characterize dynamic processes in a single quantum dot. Such dynamics is described within the framework of a model [52] that takes into account both processes – luminescence blinking and spectral diffusion. In [43], in particular, a model of electron-phonon interaction with a fluctuating coupling strength coefficient was developed, which leads to a synchronous abrupt change in the position and width of the luminescence spectrum (exciton peak) over time (Fig. 6).
As can be seen, upon the research of individual quantum dots, new unique effects are discovered that are invisible when studying an ensemble of particles. Features that manifest themselves only at the level of single objects have a great potential for application. In particular, photostability and high quantum yield of luminescence have become the basis of numerous applications of QDs in optoelectronics, and the highest sensitivity of the optical-spectral characteristics of QDs to external parameters provides them an opportunity to be used as spectral nanoprobes.
Acknowledgement
The work was carried out within the framework of the State Assignment of the Moscow Pedagogical State University (MPSU) “Physics of Nanostructured Materials: Fundamental Research and Applications in Materials Science, Nanotechnology and Photonics” with the support of the Ministry of Education of the Russian Federation (AAAA-A20-120061890084-9) together with the Centre for Collective Use “Structural Diagnostics of Materials” of the Federal Research Centre of the Russian Academy of Sciences “Crystallography and Photonics”. The authors of the article are members of the leading scientific school of the Russian Federation “Optical-spectral nanoscopy of quantum objects and diagnostics of promising materials” (project NSh-776.2022.1.2).
All the unique photo-physical properties of quantum dots open a way for exciting applications (light sources, re-emitters and light converters, biomarkers, lasers, photovoltaics etc.) which will be considered in the next issue of PHOTONICS RUSSIA.
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