Spin-Dependent Phenomena in Semiconductor Micro-and Nanoparticles—From Fundamentals to Applications

The present overview of spin-dependent phenomena in nonmagnetic semiconductor microparticles (MPs) and nanoparticles (NPs) with interacting nuclear and electron spins is aimed at covering a gap between the basic properties of spin behavior in solid-state systems and a tremendous growth of the experimental results on biomedical applications of those particles. The first part of the review represents modern achievements of spin-dependent phenomena in the bulk semiconductors from the theory of optical spin orientation under indirect optical injection of carriers and spins in the bulk crystalline silicon (c-Si)—via numerous insightful findings in the realm of characterization and control through the spin polarization—to the design and verification of nuclear spin hyperpolarization in semiconductor MPs and NPs for magnetic resonance imaging (MRI) diagnostics. The second part of the review is focused on the electron spin-dependent phenomena in Si-based nanostructures, including the photosensitized generation of singlet oxygen in porous Si and design of Si NPs with unpaired electron spins as prospective contrast agents in MRI. The experimental results are analyzed by considering both the quantum mechanical approach and several phenomenological models for the spin behavior in semiconductor/molecular systems. Advancements and perspectives of the biomedical applications of spin-dependent properties of Si NPs for diagnostics and therapy of cancer are discussed.


Introduction
Semiconductor microparticles (MPs) and nanoparticles (NPs) exhibit interesting electronic, optical and magnetic properties, which depend on a preferential orientation of electron and nuclear spins in those particles. These properties are essential for their biomedical applications. Spatial confinement of charge carriers (electron and holes) in a semiconductor nanostructure results in an increase of the spin-lattice relaxation time. Going from itinerant to immobile, fully-localized electrons, while inducing the hyperfine dephasing, can be also beneficial in quenching the spin-lattice relaxation. The dynamic electrons, while inducing the hyperfine dephasing, can be also beneficial in quenching the spin-lattice relaxation. The dynamic nuclear polarization in semiconductor nano-and microstructures opens fascinating prospects for creation of new efficient contrast agents in magnetic resonance imaging (MRI), which is a powerful diagnostic tool in biomedicine. Perspective applications of silicon (Si) MPs and NPs in hyperpolarized 29 Si MRI are discussed in Reference [1] Si nanocrystals (nc-Si) in electrochemically prepared porous Si are found to be a sensitizer of the photoinduced generation of singlet oxygen, which is a highly reactive form of molecular oxygen. The photosensitized singlet oxygen generation by nc-Si with adsorbed molecular oxygen is explained by spin-dependent energy transfer from excitons confined in nc-Si to molecular oxygen in the ground triplet state. This type of oxygen generation is promising for application of nc-Si based NPs and MPs in photodynamic therapy (PDT) of cancer [2]. Both the bioimaging and therapeutic functionality of Si NPs can be combined in an approach called as theranostics (therapy + diagnostics) of cancer, which is recently an urgent task of modern nanomedicine [3].
Importantly, nanostructuring of semiconductor materials provides an avenue for a significant control over the dynamic characteristics [4,5], including those which determine the spin relaxation [6]. For instance, spin-lattice relaxation times derived in germanium quantum wells (Ge QWs) ( Figure  1) approach 5 µs and are substantially longer than the one reported for conduction electrons in bulk Ge at the same temperatures (0.02 to 0.9 µs). By spatially separating conduction band electrons residing in the Ge QW from their parent donor atoms embedded in the SiGe barriers, the impurityinduced bottleneck pertaining to experiments utilizing bulk Ge wafers was prevented and long-lived spins were resolved despite the low temperature operation. As emphasized in Reference [7], the relative strength of modulation of the hyperfine coupling with nuclei by lattice vibrations and the spin-orbit interaction are different for various materials. In Si, where the spin-orbit interaction is much weaker than in GaAs, the dominant spin-flip mechanism in the case of the phonon-assisted transitions between the Zeeman levels of the usual impurity was found to be the modulation of the hyperfine coupling with nuclei by lattice vibrations. The magnitude of the calculated spin-phonon relaxation rates in parabolic lens-shaped III-V quantum dots due to the phonon modulation of the spin-orbit interaction in presence of an external magnetic field through the deformation-potential and piezoelectric electron-phonon couplings increases when the dot size is As emphasized in Reference [7], the relative strength of modulation of the hyperfine coupling with nuclei by lattice vibrations and the spin-orbit interaction are different for various materials. In Si, where the spin-orbit interaction is much weaker than in GaAs, the dominant spin-flip mechanism in the case of the phonon-assisted transitions between the Zeeman levels of the usual impurity was found to be the modulation of the hyperfine coupling with nuclei by lattice vibrations. The magnitude of the calculated spin-phonon relaxation rates in parabolic lens-shaped III-V quantum dots due to the phonon modulation of the spin-orbit interaction in presence of an external magnetic field through the deformation-potential

Principle of DNP
The process of DNP occurred by off-center irradiation of the resonance of paramagnetic centers, which were present at low concentration in the sample [9]. Its importance was shown to far exceed that of the other methods of nuclear polarization.
Spin-temperature theory was initially suggested for the investigation of nuclear magnetism in solids and then evolved into an important tool for the explanation of NMR in solids. A first extension of the theory to extremely low temperatures, for systems of nuclear spins at normal concentrations, led to the understanding of nuclear magnetic cooperative ordering. A second extension of the spintemperature theory, to dilute electronic spin systems both at high and low temperatures, led to the unveiling of several physical mechanisms contributing to dynamic polarization.
The basic hypothesis in the spin-temperature theory is that the evolution of an isolated system of a big number of interacting spins leads to an equilibrium state characterized by a temperature. In fact, spin systems are never completely isolated. Therefore, the concept of spin temperature is meaningful only if the rate of achievement of internal equilibrium in the spin system is much faster than the spin-lattice relaxation rate. Variation of polarization and of dipolar inverse temperature as a function of irradiation frequency for a spin system in a high field according to spin-temperature theory is provided in Figure 3. The basic hypothesis in the spin-temperature theory is that the evolution of an isolated system of a big number of interacting spins leads to an equilibrium state characterized by a temperature. In fact, spin systems are never completely isolated. Therefore, the concept of spin temperature is meaningful only if the rate of achievement of internal equilibrium in the spin system is much faster than the spin-lattice relaxation rate. Variation of polarization and of dipolar inverse temperature as a function of irradiation frequency for a spin system in a high field according to spin-temperature theory is provided in Figure 3.  Reproduced with permission. All rights reserved).

Fundamentals of the Optically Induced DNP
Photoexcitation of electrons in a semiconductor under irradiation with unpolarized light (the case of circular polarization is considered in Appendix) produces an equal number of electrons with spin up and down. After that, the Overhauser effect [16] occurs on 29 Si nuclei in the bulk crystalline silicon (c-Si): the dynamic enhancement of the nuclear polarization, obtained by maintaining the electronic polarization off its equilibrium value. The essence of the Overhauser effect consists in the following.

Fundamentals of the Optically Induced DNP
Photoexcitation of electrons in a semiconductor under irradiation with unpolarized light (the case of circular polarization is considered in Appendix) produces an equal number of electrons with spin up and down. After that, the Overhauser effect [16] occurs on 29 Si nuclei in the bulk crystalline silicon (c-Si): the dynamic enhancement of the nuclear polarization, obtained by maintaining the electronic polarization off its equilibrium value. The essence of the Overhauser effect consists in the following.
A metal sample is placed in a constant magnetic field B 0 , which creates the polarization of electron spins. The electron energy in this field E = F − µ e ·B 0 , is expressed in terms of F is the Fermi energy F and the magnetic moment of the electron spin S : µ e = −g e µ Be S, where µ Be = e 2m e is the Bohr magneton and g e is the electron g-factor ( [17], p. 420). It has two eigenvalues where g e is taken as 2. The electron spins tend to be aligned with the field. The resulting difference in spatial density of electrons with spins down and up D ≡ N ↓ − N ↑ is selected as a measure of the electron spin magnetization S z ≡ µ Be D. In thermal equilibrium under relatively weak magnetic fields, the value of D takes on the form ( [17], pp. 421 and 435)

at low lemperatures;
Nµ Be B 0 kT at high temperatures.
The metal sample is subjected, furthermore, to a perpendicular alternating magnetic field (in particular, of the microwave radiation) B ac = 2B 1 cos(ωt), whose frequency satisfies the electron spin resonance (electron paramagnetic resonance) criterion ( [17], p. 488) where 2µ Be B 0 is the distance between the eigenenergies given by Equation (1). 2µ Be B 0 / is the precession frequency for the electron spin magnetic moment µ e around the magnetic field B 0 . Such a radiation leads to the transitions between electronic states. As a consequence, two kinds of processes take place in the sample-first, relaxation drives the magnetization to its equilibrium value S z0 ≡ µ Be D 0 with a typical spin relaxation time T 1 ; second, the alternating field induces more transitions with the photoinduced relaxation time τ from the state with a higher population and therefore leads to a decrease of the magnetization: In a stationary state, dD dt = 1, the both processes are counterbalancing each other, what gives rise to the steady-state magnetization At strong alternating magnetic fields, the resonance is saturated, that is D = 0. In the general case, a saturation parameter changes from 0 when there is no alternating magnetic field to 1 when it is strong. It is a function of the ratio T 1 /τ only: Appl. Sci. 2020, 10, 4992 6 of 45 The amplitude of the microwave field that is necessary to saturate the resonance is inversely proportional to the geometric mean value of the spin relaxation time T 1 and the transverse relaxation time T 2 , which is determined by the integrated width of the resonance line w through w = π /T 2 [16]. Using NMR of 29 Si, the spin-lattice relaxation time was determined as a function of mobile carrier concentration (sample resistivity) [18]. T 1 was established to be inversely proportional to the carrier concentration for the high-conductivity samples, approaching an asymptotic value in the purer samples ( Figure 4).  Analysis of relaxation times in semiconductors [19] led to the conclusion that the relaxation of 29 Si in the exhaustion and intrinsic ranges should be accomplished by the hyperfine interaction between the nuclear spins and the spins of the mobile electrons or holes. However, there was a significant uncertainty in the density of mobile carriers. No differences were observed because of the crystal growth conditions (some crystals were pulled from quartz crucibles, some zone-refined without crucibles). The asymptotic values of p-and n-type Si were substantially different.
The low-field relaxation of nuclear hyperpolarization was studied in undoped and highly doped Si MPs at room temperature following removal from high field [20]. For nominally undoped particles (Figure 5a), two relaxation time scales were identified for ambient fields above 0.2 mT. The slower, T1,s, was roughly independent of ambient field; the faster, T1,f , decreased with increasing ambient field. A model assumed the nuclear spin relaxation to occur at the Si MPs surface via a 2-electron mechanism in a good agreement with the experimental data in what concerns the magnetic-field Analysis of relaxation times in semiconductors [19] led to the conclusion that the relaxation of 29 Si in the exhaustion and intrinsic ranges should be accomplished by the hyperfine interaction between the nuclear spins and the spins of the mobile electrons or holes. However, there was a significant uncertainty in the density of mobile carriers. No differences were observed because of the crystal growth conditions (some crystals were pulled from quartz crucibles, some zone-refined without crucibles). The asymptotic values of pand n-type Si were substantially different.
The low-field relaxation of nuclear hyperpolarization was studied in undoped and highly doped Si MPs at room temperature following removal from high field [20]. For nominally undoped particles (Figure 5a), two relaxation time scales were identified for ambient fields above 0.2 mT. The slower, T 1,s , was roughly independent of ambient field; the faster, T 1,f , decreased with increasing ambient field. A model assumed the nuclear spin relaxation to occur at the Si MPs surface via a 2-electron mechanism in a good agreement with the experimental data in what concerns the magnetic-field independence of the slow relaxation time. For boron-doped particles (Figure 5b), a single relaxation time scale was observed. This suggested that for doped particles, mobile carriers and bulk ionized acceptor sites, rather than paramagnetic surface states, were the dominant relaxation mechanisms. Relaxation times for the undoped particles were not affected by tumbling in a liquid solution [20]. Nuclei in the core region of the particle relax by transferring their magnetization to the nuclei in the shell region, nearer to the surface, by spin diffusion. The nuclei near the surface can relax quickly due to strong dipolar coupling to paramagnetic defects at the Si/SiO2 interface. (b) Rate model showing dominant nuclear relaxation pathways of direct relaxation on mobile holes and short diffusion to nonionized B (i.e., bound holes) throughout the bulk of the boron-doped particle. Long-distance spin diffusion to surface impurities is relatively slow and direct coupling of the nuclei to the lattice is weak. Nuclear polarization is most efficiently performed via the hyperfine interaction with electrons localized in a donor impurity [21]. The key issue is the hyperfine dipolar interaction between the magnetic moments of electron and nucleus = ( = ℏ ) separated in space by a vector = − Here, and (for nuclei with = ½) are the nuclear spin angular moment and nuclear Bohr magneton, respectively. As shown in Figure 6, the action of the hyperfine interaction is twofold. (i) Every nucleus is subjected, next to the applied magnetic fields, to a magnetic field of polarized electron spins fluctuating due to the aforementioned processes of spin relaxation. The magnitude of this field is proportional to the average (over the fluctuations) electron spin. The nuclear spin relaxation time due to the hyperfine interaction is (ii) Every electron is subjected, next to the Nuclei in the core region of the particle relax by transferring their magnetization to the nuclei in the shell region, nearer to the surface, by spin diffusion. The nuclei near the surface can relax quickly due to strong dipolar coupling to paramagnetic defects at the Si/SiO 2 interface. (b) Rate model showing dominant nuclear relaxation pathways of direct relaxation on mobile holes and short diffusion to non-ionized B (i.e., bound holes) throughout the bulk of the boron-doped particle. Long-distance spin diffusion to surface impurities is relatively slow and direct coupling of the nuclei to the lattice is weak. Nuclear polarization is most efficiently performed via the hyperfine interaction with electrons localized in a donor impurity [21]. The key issue is the hyperfine dipolar interaction between the magnetic moments of electron µ e and nucleus µ n = µ Bn g n I (µ Bn = e 2m n C ) separated in space by a vector r Here, I and µ Bn (for nuclei with I = 1 2 ) are the nuclear spin angular moment and nuclear Bohr magneton, respectively. As shown in Figure 6, the action of the hyperfine interaction is twofold. (i) Every nucleus is subjected, next to the applied magnetic fields, to a magnetic field of polarized electron spins fluctuating due to the aforementioned processes of spin relaxation. The magnitude of this field is proportional to the average (over the fluctuations) electron spin. The nuclear spin relaxation time due to the hyperfine interaction is T n (ii) Every electron is subjected, next to the applied magnetic fields, to the total magnetic field of all polarized nuclei. These two magnetic fields are comparable because electrons at low energy levels interact with a large number of nuclei. The electron spin relaxation time due to the hyperfine interaction is T 1 . As a consequence, there occurs a feedback, which leads to a steady-state polarization of both electron and nuclear spins. There has been a renewed interest in the hole-nuclei hyperfine interaction in semiconductor quantum dots [22]. The main effect arises from the coupling of the nuclear spin with the hole wavefunction within the same unit cell, that is, the short-range part of the dipole-dipole interaction [12]. The potential effect of large inhomogeneous elastic strain in nanostructures (like quantum dots) on the microscopic Bloch hole wave function is considered as a possible route to engineer the hyperfine coupling.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 47 same unit cell, that is, the short-range part of the dipole-dipole interaction [12]. The potential effect of large inhomogeneous elastic strain in nanostructures (like quantum dots) on the microscopic Bloch hole wave function is considered as a possible route to engineer the hyperfine coupling. Figure 6. Feedback coupling of the electron spin system (ESS) and the nuclear spin system (NSS) in a semiconductor. Optically oriented electrons polarize the nuclei (arrow polarization) Because of the polarization, an effective magnetic field arises, which, in its turn, affects the electron orientation and hence the luminescence polarization. (Reprinted from Reference [21],  (1984), with permission from Elsevier).
Similar to the electron spins, the difference in numbers of nuclei (with spin I=1/2, like 29 Si) possessing spins up and down D = ↑ − ↓ is selected as a measure of the nuclear spin magnetization ≡ /2. At arbitrary value of the nuclear spin I, D denotes the difference between the populations of the adjacent nuclear spin states. The total number of nuclear spins is supposed to be equal to = ↑ + ↓ . (or the sum of all available spin eigenvalues at arbitrary I). The thermal equilibrium value of the difference D at the nuclear spin value I is the following: [23] ∆ = ℬ (2 + 1) .
The corresponding steady-state magnetization on nuclei with spin I=1/2 is = ∆ /2. In terms of the gyromagnetic ratios, that is, = − / , = , the relative magnetization of nuclei takes on the form (see Section IX C in Reference [12]): In analogue to the Overhauser effect [16], the steady-state nuclear polarization is enhanced as if the nuclear gyromagnetic ratio would be increased by | |. Near the saturation, when s is close to 1, this increase theoretically may be as large as | |/ =3310 in 29 Si [17, p. 489]. The experimentally observed nuclear spin polarization enhancement extrapolated to an infinite time of continuous irradiation by an unpolarized light constitutes 〈 〉/I0 = −5.6 [14]. According to Equation (10), this implies the saturation parameter s~2 × 10 −3 .
The nuclear magnetization (Figure 2a) produced by optical pumping in a field of 1G (extrapolated to infinite time of continuous irradiation) corresponded to the equilibrium polarization in a field of 28 kG at 77 K and constituted 〈 〉=3.7 × 10 −6 . Thus, the enhanced nuclear polarization as high as 2.8 × 10 4 due to the optical pumping was experimentally demonstrated [14]. . Feedback coupling of the electron spin system (ESS) and the nuclear spin system (NSS) in a semiconductor. Optically oriented electrons polarize the nuclei (arrow polarization) Because of the polarization, an effective magnetic field arises, which, in its turn, affects the electron orientation and hence the luminescence polarization. (Reprinted from Reference [21], © (1984), with permission from Elsevier).
Similar to the electron spins, the difference in numbers of nuclei (with spin I=1/2, like 29 Si) possessing spins up and down = M ↑ − M ↓ is selected as a measure of the nuclear spin magnetization I z ≡ ∆/2. At arbitrary value of the nuclear spin I, ∆ denotes the difference between the populations of the adjacent nuclear spin states. The total number of nuclear spins is supposed to be equal to N = M ↑ + M ↓ . (or the sum of all available spin eigenvalues at arbitrary I). The thermal equilibrium value of the difference ∆ atI is the fo the nuclear spin value llowing: [23] The corresponding steady-state magnetization on nuclei with spin I = 1/2 is I 0 = ∆ 0 /2. In terms of the gyromagnetic ratios, that is, γ e = − µ Be 1/2 , γ n = µ Bn I , the relative magnetization of nuclei takes on the form (see Section IX C in Reference [12]): In analogue to the Overhauser effect [16], the steady-state nuclear polarization is enhanced as if the nuclear gyromagnetic ratio γ n would be increased by s γ e . Near the saturation, when s is close to 1, this increase theoretically may be as large as γ e /γ n = 3310 in 29 Si [17], (p. 489). The experimentally observed nuclear spin polarization enhancement extrapolated to an infinite time of continuous irradiation by an Appl. Sci. 2020, 10, 4992 9 of 45 unpolarized light constitutes I z /I 0 = −5.6 [14]. According to Equation (10), this implies the saturation parameter s~2 × 10 −3 .
The nuclear magnetization (Figure 2a) produced by optical pumping in a field of 1G (extrapolated to infinite time of continuous irradiation) corresponded to the equilibrium polarization in a field of 28 kG at 77 K and constituted I z = 3.7 × 10 −6 . Thus, the enhanced nuclear polarization as high as 2.8 × 10 4 due to the optical pumping was experimentally demonstrated [14].
Polarized electronic spins are produced by optical pumping with circularly polarized light. Both spin directions are created in the conduction band. However, the unequal proportions G + and G − of transitions to spin-up and spin-down states lead to a net electronic polarization much larger than its equilibrium value (see Equation (VI.7) in Reference [15]): where the first term in the parentheses is due to the optical pumping, while the second one is the saturation term [14]. As long as under optical pumping the latter is much smaller than the former and I 0 I z and taking into account that [14]), the steady-state nuclear spin polarization turns to It depends on matrix-element ratios describing electronic transitions between valence and conduction bands, as well as on electronic recombination and relaxation rates. Therefore, for this mechanism the value of the obtained nuclear spin polarization is of key importance rather than the enhancement of the relative nuclear spin polarization. A direct measurement of T 1 /τ performed in Reference [14] demonstrated that only 0.4% was achieved of the magnetization that could be expected if only one kind of electronic spin had been created. This was due to the matrix elements between the valence and conduction bands in Si, which is an indirect bandgap material.
A theory proposed in Reference [24] established the first link between the degrees of spin polarization of electrons and the circular polarization for each of the dominant phonon-assisted optical transitions, which was crucial for the subsequent development of applications. A method of hyperpolarizing Si MPs and NPs demonstrated an increase of the 29 Si MR signal by up to 3-5 orders of magnitude via the enhanced nuclear spin alignment, while retaining this improved signal for tens of minutes [25,26].

Optical Spin Orientation in Various Semiconductors
Since the first successful experiment [14], discussed in the previous Subsection, there has been a steady interest in theoretical and experimental investigation of optical spin orientation in various semiconductors. Among them, c-Si is an advantageous material for spintronics because of its long spin relaxation time and dominating technology. The dynamic polarization of 29 Si nuclei in phosphorus-doped (N d = 1.5 × 10 13 cm −3 ) n-type c-Si induced by optical pumping was investigated in Reference [27]. During illumination of c-Si, the magnetization of 29 Si nuclei becomes gradually established, following an exponential law with a time constant equal to the spin-lattice relaxation time T l of 29 Si nuclei. Limiting relative polarization of the 29 Si nuclei obeyed the following equation [27]: With the concentrations n ph of photoexcited and n 0 of thermal electrons, correspondingly. Without light, the nuclear magnetization equaled its equilibrium value. When the concentrations of photoexcited electrons was much higher than that of thermal electrons, the saturation value was described by Equation (13) in agreement with experiment (see Figure 7). The limiting degree of nuclear polarization was determined by the spin polarization of both the photoexcited and thermal electrons in the conduction band. The presence of rare earth impurities (Gd) in combination with shallow impurities (P) resulted in increased optical pumping efficiency, because the rare earth impurities increased the ionization energy of the shallow impurities [28]. More recently, the dynamic-nuclear-polarization capabilities of optical pumping at 4 K and a magnetic field of 7 T were investigated with a 29 Si-enriched sample. Using NMR spectroscopy, the 29 Si polarization as high as up to 0.25% was demonstrated [29]. The investigations of above-bandgap excitations look promising for further enhancement of 29 Si polarization in the sample area close to the exposed surface. However, c-Si is an indirect bandgap semiconductor and it was soon clear that higher nuclear polarizations could be generated in direct bandgap materials. The main focus of solid-state optical pumping therefore shifted to direct bandgap semiconductors soon after the pioneering experiment of Lampel [14], which was analyzed in Section 2.1.3. The stationary spin orientation of photoelectrons excited by circularly polarized light in GaxAl1-xAs, as detected by the degree of the circular polarization of photoluminescence, was determined by the value of the nuclear magnetization [30]. The optical method manifested a very high sensitivity (signal-to-noise ratio of the order of 100:1 when the total number of photoelectrons constituted 10 9 ) and could be applied to samples at microscale. Optically-pumped, directly-detected NMR experiments on the bulk crystalline InP (c-InP) were performed [31] by using irradiation of a sample of undoped c-InP wafer from a diode laser to enhance the spin polarization of 31 P nuclei near the sample surface. The spin polarization was found to depend on the light polarization. The spin polarization magnitude and polarization transfer efficiency of the from the semiconductor substrate to the overlayer ( Figure 8) were high enough to permit solid state NMR measurements on sub-nanomole quantities of molecules in the overlayer [31]. The optically induced dynamic nuclear polarization in CdS was observed by radio-frequency detection of the 113 Cd nuclear magnetic resonance signal for T < 2 K. At this temperature, the optically induced spin polarization was negative when compared to the thermal polarization, irrespective of the helicity of the pumping light [32]. By increasing the depth of the donor levels ( Figure 9), a very significant nuclear polarization was achieved because of the increase of the electron spin relaxation time. However, c-Si is an indirect bandgap semiconductor and it was soon clear that higher nuclear polarizations could be generated in direct bandgap materials. The main focus of solid-state optical pumping therefore shifted to direct bandgap semiconductors soon after the pioneering experiment of Lampel [14], which was analyzed in Section 2.1.3. The stationary spin orientation of photoelectrons excited by circularly polarized light in Ga x Al 1-x As, as detected by the degree of the circular polarization of photoluminescence, was determined by the value of the nuclear magnetization [30]. The optical method manifested a very high sensitivity (signal-to-noise ratio of the order of 100:1 when the total number of photoelectrons constituted 10 9 ) and could be applied to samples at microscale. Optically-pumped, directly-detected NMR experiments on the bulk crystalline InP (c-InP) were performed [31] by using irradiation of a sample of undoped c-InP wafer from a diode laser to enhance the spin polarization of 31 P nuclei near the sample surface. The spin polarization was found to depend on the light polarization. The spin polarization magnitude and polarization transfer efficiency of the from the semiconductor substrate to the overlayer ( Figure 8) were high enough to permit solid state NMR measurements on sub-nanomole quantities of molecules in the overlayer [31]. The optically induced dynamic nuclear polarization in CdS was observed by radio-frequency detection of the 113 Cd nuclear magnetic resonance signal for T < 2 K. At this temperature, the optically induced spin polarization was negative when compared to the thermal polarization, irrespective of the helicity of the pumping light [32]. By increasing the depth of the donor levels ( Figure 9), a very significant nuclear polarization was achieved because of the increase of the electron spin relaxation time.
NMR measurements on sub-nanomole quantities of molecules in the overlayer [31]. The optically induced dynamic nuclear polarization in CdS was observed by radio-frequency detection of the 113 Cd nuclear magnetic resonance signal for T < 2 K. At this temperature, the optically induced spin polarization was negative when compared to the thermal polarization, irrespective of the helicity of the pumping light [32]. By increasing the depth of the donor levels ( Figure 9), a very significant nuclear polarization was achieved because of the increase of the electron spin relaxation time. Figure 8. Dependence of the 31 P optically-pumped nuclear magnetic resonance (NMR) lineshape on the period during which the shutter is closed , with the period during which the shutter is open =120 s. At short , the lineshape is dominated by signal from the optically-pumped surface-layer. At long , the lineshape is dominated by signal from the bulk of the InP sample which increases due to spin-lattice relaxation. (Reprinted from Reference [31],  (1998), with permission from Elsevier). At long τ D , the lineshape is dominated by signal from the bulk of the InP sample which increases due to spin-lattice relaxation. (Reprinted from Reference [31], © (1998), with permission from Elsevier). The mechanism of optical pumping can be considerably more complicated and less well understood. Both contact hyperfine and dipolar hyperfine interactions can contribute appreciably to cross-relaxation. The spin polarization of the photoexcited electrons may depend on the pumping wavelength and the magnetic field. The precise nature of the photoexcitation that dominate optical pumping, which are expected to be localized excitations, may be unknown. The roles of photogenerated holes, doped carriers and radiationless transitions to a metastable excited state after the initial absorption of a photon are to be clarified [31].
A theory of the optical spin orientation under indirect optical injection of carriers and spins in bulk Si, proposed in Reference [33], predicted the maximum degree of spin polarization as high as 25% at low temperatures and 15% at high temperatures. These values of the degree of the spin polarization implied the term "optically induced spin hyperpolarization" for the phenomenon, which is the main objective of the present review. The theory of Reference [33] was immediately applied to analyze two-photon indirect optical injection of carriers and spins and two-color coherent control in bulk Si [34]. Measurements of the electron spin lifetime and optical orientation efficiency were also carried out in Ge by using electrical detection of radio frequency modulated spin polarization [35]. The optical spin injection and spin lifetime in Ge heterostructures were experimentally investigated The mechanism of optical pumping can be considerably more complicated and less well understood. Both contact hyperfine and dipolar hyperfine interactions can contribute appreciably to cross-relaxation. The spin polarization of the photoexcited electrons may depend on the pumping wavelength and the magnetic field. The precise nature of the photoexcitation that dominate optical pumping, which are expected to be localized excitations, may be unknown. The roles of photogenerated holes, doped carriers and radiationless transitions to a metastable excited state after the initial absorption of a photon are to be clarified [31].
A theory of the optical spin orientation under indirect optical injection of carriers and spins in bulk Si, proposed in Reference [33], predicted the maximum degree of spin polarization as high as 25% at low temperatures and 15% at high temperatures. These values of the degree of the spin polarization implied the term "optically induced spin hyperpolarization" for the phenomenon, which is the main objective of the present review. The theory of Reference [33] was immediately applied to analyze two-photon indirect optical injection of carriers and spins and two-color coherent control in bulk Si [34]. Measurements of the electron spin lifetime and optical orientation efficiency were also carried out in Ge by using electrical detection of radio frequency modulated spin polarization [35]. The optical spin injection and spin lifetime in Ge heterostructures were experimentally investigated in Reference [36]. Th valley-dependent spin polarization and long-lived electron spins were detected in Ge [37]. Spin-dependent optical properties were investigated as a function of strain in Si and Ge [38]. Theory of spin-dependent intravalley and intervalley electron-phonon scatterings was developed for Ge [39]. The optical spin-selection rules in bulk Si and Ge/Si quantum dots were experimentally unveiled in Reference [40]. Two optical routes of cold carrier injection in Si were revealed by time-resolved excitation spectroscopy [41]. The optical generation of pure spin currents was detected at the indirect gap of bulk Si [42]. Hot phonon and carrier relaxation in Si single crystalline wafers with the (100) crystallographic orientation were determined by transient extreme ultraviolet spectroscopy [43].
The spin-to-charge conversion for hot photoexcited electrons was experimentally detected in Ge [44]. The successful optical generation of a net spin polarization of electrons in the strained Ge 1-x Sn x alloy, which manifests hybridization of the spin properties of Ge with the peculiar electronic states offered by α-Sn, was demonstrated by recording PL spectra, the optical spin orientation being robust over a wide temperature range up to room temperature [45]. The spin coherence time of photoexcited spin-polarized electrons was found to decay from 12 ns to 6 ns when increasing the magnetic field from 0 to 53.5 mT owing to g-factor fluctuations as long as spin dephasing was triggered by the cooling process, during which optically generated electrons underwent momentum relaxation under random effective magnetic fields due to local changes in the alloy composition and strain [45].

Microwave-Induced Optical Nuclear Polarization
The hyperpolarization of 29 Si nuclear spins is usually generated by solid-state DNP at low temperatures and high magnetic fields to spin-polarize an electron to near unity. This spin polarization is then transferred to nearby nuclear spins through microwave-mediated dipolar interactions, similar to those occurring in the liquid phase with 13 C [46].
A combination of the DNP and the photoexcitation of the electron-pair spin to the triplet state is known as microwave-induced optical nuclear polarization [47]. The polarization from the electron triplet states is transferred via microwaves to the nuclear spins. The hyperpolarization of electron spins can be prepared at low magnetic fields, since it is generated due to selectivity in crossing from excited singlet states to hyperpolarized triplet states. Because the triplet states have a longer relaxation time as compared to the singlet state, the hyperpolarized nuclear spins can be generated by DNP at room temperature. Feasibility of the nuclear hyperpolarization at low magnetic field and room temperature provides an advantage to microwave-induced optical nuclear polarization as compared to the DNP. The unpaired electron spins do not perturb the NMR signals because the decay time of the triplet state to the diamagnetic state is shorter than the relaxation time of the longitudinal nuclear magnetization [47]. While the microwave-induced optical nuclear polarization was demonstrated for organics as fluorene C 13 H 10 crystals [48], it seems to be a possible mechanism for inorganic semiconductor systems as NP/MPs with nc-Si, where triplet excitonic state are rather probable (see Section 3).

29 Si Surface-Enhanced NMR Spectroscopy
Fast characterization of the distribution of surface bonding modes and interactions in a series of functionalized materials was achieved via surface-enhanced nuclear magnetic resonance spectroscopy using DNP [49]. Surface-enhanced 29 Si DNP NMR spectra were obtained by using incipient wetness impregnation of the sample with a solution containing a polarizing radical (TOTAPOL). The bonding topology of functional groups was identified in materials obtained via a sol-gel process and in materials prepared by post-grafting reactions [49].
The remarkable gain in time provided by surface-enhanced NMR Spectroscopy using DNP, which is of the order of 400, allows for a facile acquisition of 2D correlation spectra for characterization of the distribution of the surface bonding modes/interactions ( Figure 10) in functionalized materials [49].

Long T1 Nanoparticles for Hyperpolarized 29 Si MRI
The synthesis, materials characterization and DNP of amorphous and crystalline Si NPs for use as hyperpolarized MRI agents were represented in Reference [26]. The Si NPs of ~10 nm size were synthesized by a metathesis reaction and surface functionalized with a variety of passivating ligands. Because of the long size-adjusted nuclear spin-lattice relaxation time T1 > 600 s ( Figure 11), Si NPs can be hyperpolarized by low-temperature DNP ( Figure 12) and retain the polarization for > 300 s [26].

Long T 1 Nanoparticles for Hyperpolarized 29 Si MRI
The synthesis, materials characterization and DNP of amorphous and crystalline Si NPs for use as hyperpolarized MRI agents were represented in Reference [26]. The Si NPs of~10 nm size were synthesized by a metathesis reaction and surface functionalized with a variety of passivating ligands. Because of the long size-adjusted nuclear spin-lattice relaxation time T 1 > 600 s ( Figure 11), Si NPs can be hyperpolarized by low-temperature DNP ( Figure 12) and retain the polarization for >300 s [26]. Figure 11. Nuclear spin relaxation (T1) times at 2.9 T and 300 K as a function of particle diameter d for Si NPs. Previously reported T1 measurements of other Si particles are shown as a reference. Simulations of the nuclear relaxation based on a spin diffusion model are also shown. Vertical error bars are from exponential fits to relaxation data; horizontal error bars are from size distributions. (Reprinted with permission from Reference [26]. © 2013 American Chemical Society).  29 Si nuclear polarization as a function of microwave frequency under DNP conditions. (c) 29 Si NMR spectra obtained under DNP conditions. (Reprinted with permission from Reference [26]. © 2013 American Chemical Society).
In solid-state spin-1/2 materials, such as Si, the primary source of nuclear spin-lattice relaxation is the interaction with unbonded electrons or holes, which occur in the form of free charge carriers or paramagnetic centers either at lattice defect sites or at the surface. In pure materials, the nuclear spin polarization is to a significant extent protected from sources of relaxation, resulting in bulk relaxation times of many hours [11,12,18]. A transition to the nanoscale resulted in spin relaxation times that depend on the particle size, purity and density of defects [11].The colloidal synthesis of Si NPs with average diameters of∼10 nm at room temperature provided spin relaxation times that exceed 600 s. This resulted in fabrication of NPs that revealed significantly longer size-adjusted 29 Si nuclear spin relaxation times T1 than commercially available Si particles [11] and diamond NPs of similar sizes Figure 11. Nuclear spin relaxation (T 1 ) times at 2.9 T and 300 K as a function of particle diameter d for Si NPs. Previously reported T 1 measurements of other Si particles are shown as a reference. Simulations of the nuclear relaxation based on a spin diffusion model are also shown. Vertical error bars are from exponential fits to relaxation data; horizontal error bars are from size distributions. (Reprinted with permission from Reference [26]. © 2013 American Chemical Society).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 47 Figure 11. Nuclear spin relaxation (T1) times at 2.9 T and 300 K as a function of particle diameter d for Si NPs. Previously reported T1 measurements of other Si particles are shown as a reference.
Simulations of the nuclear relaxation based on a spin diffusion model are also shown. Vertical error bars are from exponential fits to relaxation data; horizontal error bars are from size distributions.
(Reprinted with permission from Reference [26]. © 2013 American Chemical Society).  29 Si nuclear polarization as a function of microwave frequency under DNP conditions. (c) 29 Si NMR spectra obtained under DNP conditions. (Reprinted with permission from Reference [26]. © 2013 American Chemical Society).
In solid-state spin-1/2 materials, such as Si, the primary source of nuclear spin-lattice relaxation is the interaction with unbonded electrons or holes, which occur in the form of free charge carriers or paramagnetic centers either at lattice defect sites or at the surface. In pure materials, the nuclear spin polarization is to a significant extent protected from sources of relaxation, resulting in bulk relaxation times of many hours [11,12,18]. A transition to the nanoscale resulted in spin relaxation times that depend on the particle size, purity and density of defects [11].The colloidal synthesis of Si NPs with average diameters of∼10 nm at room temperature provided spin relaxation times that exceed 600 s. This resulted in fabrication of NPs that revealed significantly longer size-adjusted 29 Si nuclear spin relaxation times T1 than commercially available Si particles [11] and diamond NPs of similar sizes  29 Si nuclear polarization as a function of microwave frequency under DNP conditions. (c) 29 Si NMR spectra obtained under DNP conditions. (Reprinted with permission from Reference [26]. © 2013 American Chemical Society).
In solid-state spin-1/2 materials, such as Si, the primary source of nuclear spin-lattice relaxation is the interaction with unbonded electrons or holes, which occur in the form of free charge carriers or paramagnetic centers either at lattice defect sites or at the surface. In pure materials, the nuclear spin polarization is to a significant extent protected from sources of relaxation, resulting in bulk relaxation times of many hours [11,12,18]. A transition to the nanoscale resulted in spin relaxation times that depend on the particle size, purity and density of defects [11]. The colloidal synthesis of Si NPs with average diameters of ∼10 nm at room temperature provided spin relaxation times that exceed 600 s. This resulted in fabrication of NPs that revealed significantly longer size-adjusted 29 Si nuclear spin relaxation times T 1 than commercially available Si particles [11] and diamond NPs of similar sizes [50]. These Si NPs are the smallest characterized for hyperpolarization applications. Due to their size and long T 1 times, they are perspective as in vivo imaging agents, which are suitable for intracellular investigations and for crossing the blood-brain barrier [26].

DNP in Si Microparticles
High 29 Si spin polarization was achieved using DNP in microcrystalline Si powder [51]. Unpaired electrons in the powder are related to Si DBs in the amorphous region of microcrystalline grains. Nuclei in the amorphous region become polarized by forced electron-nuclear spin flips induced by off-resonant microwave radiation ( Figure 13). Nuclei in the crystalline region are polarized by spin diffusion across crystalline boundaries. Hyperpolarized Si MPs have long T 1 ( Figure 14) and hence can be used as tracers for MRI [51].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 47 [50].These Si NPs are the smallest characterized for hyperpolarization applications. Due to their size and long T1 times, they are perspective as in vivo imaging agents, which are suitable for intracellular investigations and for crossing the blood-brain barrier [26].

DNP in Si Microparticles
High 29 Si spin polarization was achieved using DNP in microcrystalline Si powder [51]. Unpaired electrons in the powder are related to Si DBs in the amorphous region of microcrystalline grains. Nuclei in the amorphous region become polarized by forced electron-nuclear spin flips induced by off-resonant microwave radiation ( Figure 13). Nuclei in the crystalline region are polarized by spin diffusion across crystalline boundaries. Hyperpolarized Si MPs have long T1 ( Figure 14) and hence can be used as tracers for MRI [51].   Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 47 [50].These Si NPs are the smallest characterized for hyperpolarization applications. Due to their size and long T1 times, they are perspective as in vivo imaging agents, which are suitable for intracellular investigations and for crossing the blood-brain barrier [26].

DNP in Si Microparticles
High 29 Si spin polarization was achieved using DNP in microcrystalline Si powder [51]. Unpaired electrons in the powder are related to Si DBs in the amorphous region of microcrystalline grains. Nuclei in the amorphous region become polarized by forced electron-nuclear spin flips induced by off-resonant microwave radiation ( Figure 13). Nuclei in the crystalline region are polarized by spin diffusion across crystalline boundaries. Hyperpolarized Si MPs have long T1 ( Figure 14) and hence can be used as tracers for MRI [51].

In Vivo MRI of Hyperpolarized Si Particles
Natural physical properties of Si ( Figure 15) provide surface electronic states for DNP, long depolarization times, insensitivity to the in vivo environment and surfaces favorable for functionalization. In vivo imaging of hyperpolarized 29 Si in Si MPs and NPs by MRI is perspective for applications to gastrointestinal, intravascular and tumor perfusion imaging at sub-picometer concentrations ( Figure 16) [25].

In Vivo MRI of Hyperpolarized Si Particles
Natural physical properties of Si ( Figure 15) provide surface electronic states for DNP, long depolarization times, insensitivity to the in vivo environment and surfaces favorable for functionalization. In vivo imaging of hyperpolarized 29 Si in Si MPs and NPs by MRI is perspective for applications to gastrointestinal, intravascular and tumor perfusion imaging at sub-picometer concentrations ( Figure 16) [25].   2.2.6. Si Nanoparticles for Hyperpolarized MRI MRI of hyperpolarized nuclei was shown to provide a very high image contrast with little or no background signal [11]. To date, in vivo applications of pre-hyperpolarized materials have been limited by relatively short nuclear spin relaxation times. Si NPs were proposed as a new type of hyperpolarized MRI agent. Nuclear spin relaxation times for a variety of Si NPs were found to be extremely long, ranging from many minutes to hours at room temperature ( Figure 17), allowing hyperpolarized NPs to be transported, administered and imaged on practical time scales [11]. Additionally, Si NPs can be surface functionalized using techniques common to other biologically targeted NP systems. These results suggest that Si NPs can be used as a targetable, hyperpolarized MRI agent ( Figure 18) with a large range of potential applications.    . NMR Properties of Si particles. Nuclear spin relaxation (T1) times at 2.9 T as a function of particle diameter d0 for various Si particles. Vertical error bars are from exponential fits to relaxation data; horizontal error bars represent the dispersion of size distributions. Inset: Fourier-transform NMR peak amplitude, A, as a function of polarization time for the ball-milled high-resistivity particles with d0 = 0.17 m. T1 values were measured using a saturation recovery spin echo pulse sequence.
(Reprinted with permission from Reference [11]. © (2009) American Chemical Society). Micrometer-sized Si MPs, which reveal the longest known relaxation times up to 136 min at room temperature at 2.9 T [20], are difficult to administer and impossible to handle in-vivo. A new window for MRI applications was opened in Reference [52], where it was demonstrated that 29 Si NPs in powder synthesized from a gas phase using a laser-assisted technique, with average particle size of 55 ± 12 nm can be hyperpolarized with superior properties, that is, maximal polarization about 12.6% with a long T1 relaxation time of 42.3 ± 0.1 min at room temperature ( Figure 19A). Such a long depolarization time enabled the observation of 29 Si NMR signal more than 5 h after transfer to the imaging system ( Figures 19B,C). The presence of PEG polymer on the surface of the nanoparticles resulted in shortening of T1 relaxation times at room temperature from 42.3 ± 0.1 min to 34.0 ± 0.3 min ( Figure 19A), while no change in the polarization level was observed. A further significant increase in the polarization level is proposed by lowering the temperature (to < 2 K) in the course of the DNP process, using a dedicated long-run helium bath or helium-free cryostat, boosting the obtainable 29 Si polarization. Conducting the DNP process at higher magnetic fields is also expected to increase final Micrometer-sized Si MPs, which reveal the longest known relaxation times up to 136 min at room temperature at 2.9 T [20], are difficult to administer and impossible to handle in-vivo. A new window for MRI applications was opened in Reference [52], where it was demonstrated that 29 Si NPs in powder synthesized from a gas phase using a laser-assisted technique, with average particle size of 55 ± 12 nm can be hyperpolarized with superior properties, that is, maximal polarization about 12.6% with a long T 1 relaxation time of 42.3 ± 0.1 min at room temperature ( Figure 19A). Such a long depolarization time enabled the observation of 29 Si NMR signal more than 5 h after transfer to the imaging system ( Figure 19B,C). The presence of PEG polymer on the surface of the nanoparticles resulted in shortening of T 1 relaxation times at room temperature from 42.3 ± 0.1 min to 34.0 ± 0.3 min ( Figure 19A), while no change in the polarization level was observed. A further significant increase in the polarization level is proposed by lowering the temperature (to <2 K) in the course of the DNP process, using a dedicated long-run helium bath or helium-free cryostat, boosting the obtainable 29 Si polarization. Conducting the DNP process at higher magnetic fields is also expected to increase final nuclear polarization. The limited availability of high-power microwave sources operating in the frequency range above 100 GHz is presently the major difficulty.   Optimal physical and chemical conditions, including surface-defect concentration adjusted to the particle size, are necessary to achieve a high level of DNP enhancement [10]. Real-time MRI-guided catheter tracking using hyperpolarized 29 Si particles (polycrystalline/amorphous; average mean diameter~2 µm) was demonstrated [53]. The increased signal of the 29 Si particles is generated via low-temperature, solid-state DNP and the particles retain their enhanced signal for ≥40 min, thus allowing imaging experiments over extended time durations in phantoms and live mice. The measured hyperpolarized relaxation rate of the 29 Si particles was~25 min at 7 T and room temperature.
A variety of particle sizes (20 nm to 2 µm) were found to have hyperpolarized relaxation times ranging from ∼10 to 50 min [54,55]. The addition of different functional groups to the Si particle surface was shown to provide no effect on the hyperpolarization buildup or decay rates and allowed for in vivo imaging over long time-scales. Hyperpolarized Si particles were demonstrated to be available agents for targeted, noninvasive and nonradioactive molecular imaging of various cancer systems [54] and a powerful theragnostic deep tissue imaging platform [55]. In vivo studies examined diverse particle administration routes in mice, including intraperitoneal injection, rectal enema and oral gavage [54]. Incorporating exogenous radicals (e.g., 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO)) into Si NPs suspensions is proposed order to improve the characteristics of hyperpolarization of 29 Si nuclear spins to levels sufficient for in vivo MRI [56] (Figure 20). Without any added radical, T 1 values ranged from ∼23 min (30 nm particles) to ∼36 min (200 nm particles). This size-dependence of T 1 is largely expected given the spin-diffusion model [20] for the relaxation of core nuclei to the surface. At optimal TEMPO concentrations (30-60 mM), the shortened T 1 values of the Si particles were overshadowed by the significant increase in the 29 Si MR signal [56].  29 Si T1 decay for NPs indicated in (a), measured at room temperature and under 7 T. Inset: 29 Si MRI of the Si NP sample (70 nm/30 mM TEMPO) within its sample tube following the corresponding decay study in (b); the MRI was taken 65 min after DNP and after exciting the phantom with a 10° pulse every 5 min to acquire the 29 Si spectra used for the T1 calculation. Photograph to right of 29 Si MRI shows sample. (Reprinted with permission from Reference [56]. © (2018) American Chemical Society).

Excitons in Si Nanocrystals
The same optical pumping of the electronic system of semiconductor MPs and NPs, which is used for the nuclear spin orientation (see Section 2), can also initiate the electron-spin-dependent processes, which are highly sensitive to both the size of semiconductor particles and their molecular environment. Besides the quantum confinement effect, which results in an increase of the forbidden  29 Si T 1 decay for NPs indicated in (a), measured at room temperature and under 7 T. Inset: 29 Si MRI of the Si NP sample (70 nm/30 mM TEMPO) within its sample tube following the corresponding decay study in (b); the MRI was taken 65 min after DNP and after exciting the phantom with a 10 • pulse every 5 min to acquire the 29 Si spectra used for the T 1 calculation. Photograph to right of 29 Si MRI shows sample. (Reprinted with permission from Reference [56]. © (2018) American Chemical Society).

Excitons in Si Nanocrystals
The same optical pumping of the electronic system of semiconductor MPs and NPs, which is used for the nuclear spin orientation (see Section 2), can also initiate the electron-spin-dependent processes, which are highly sensitive to both the size of semiconductor particles and their molecular environment. Besides the quantum confinement effect, which results in an increase of the forbidden gap and optical transition energies in nc-Si of different dimensionally and characteristic sizes from 1 to 10 nm [57,58], the Coulomb interaction between photoexcited electrons and holes in nc-Si promotes the existence of excitons with relatively large binding energies up to 100-200 meV [57] that ensures stability for the excitons at room temperature. Furthermore, the exchange interaction in an exciton can remove the spin degeneracy for the exciton states [59]. It results in two possible spin configurations for the exciton states in nc-Si, which consist of optically active spin-singlet states and optically inactive spin-triplet ones. The triplet exciton state is lowered in energy in respect to the singlet state because of the electron-hole exchange interaction as it was experimentally demonstrated for small nc-Si in electrochemically prepared porous Si (por-Si) [60]. Despite a small singlet-triplet splitting being in the range from 1 to 30 meV the main part of excitons in nc-Si can be in the threefold degenerated triplet state even at elevated temperatures [61].
The relatively long radiative lifetime of the excitons in nc-Si is due to both a contribution of the indirect optical transitions [61] and the spin-conservation rule [59][60][61]. In particular, the triplet exciton states are more populated and the corresponding radiative times of the order of several milliseconds and it is detected as the long-lived exciton PL of nc-Si at cryogenic temperatures [60,61]. At room temperature the radiative lifetimes of excitons in nc-Si are partially controlled by the singlet exciton states, which exhibit the radiative lifetimes varied from 10 to 100 µs, depending on nc-Si dimensions [61]. Because small nc-Si possess a huge accessible internal surface area up to~1000 m 2 /cm 3 , the electronic surface states and adsorbed molecules can influence the excitons and therefore the photoluminescent properties of nc-Si [62].

Photosensitized Generation of Singlet Oxygen
Since there is a similarity between the electronic structure of excitons in nc-Si and that of many organic molecules as dyes, the energy transfer through spin-split states of the latter can be also probable for the former. A bright example of the spin-dependent energy transfer from photoexcited dye molecules to molecular oxygen in its triplet state followed with its transformation into the singlet oxygen, that is, (1) O 2 where (1) in the superscript indicates the electron spin degeneracy, which is used in the photodynamic therapy (PDT) [63]. It was found that nc-Si in por-Si layer and powder can act as a photosensitizer of the (1) O 2 generation [64]. The observed photosensitization was explained by the spin-dependent energy transfer from excitons in nc-Si with sizes of 1-10 nm to O 2 molecules adsorbed on the nc-Si surface [65].
According to the quantum mechanics the relaxation of (1) O 2 back to the ground (triplet) state is "spin-forbidden" and thus a (1) O 2 molecule is characterized by rather long lifetime [66], which is favorable for transferring the excitation energy to oxidation reactions. The latter can be used for the detection and application of (1) O 2 [67]. The latter is known to be an electronically excited state of molecular oxygen [67] and it influences oxidative biochemical processes in living systems [68]. The 1 O 2 -mediated reaction, which is employed in PDT of cancer, consists of a drug, that is, photosensitizer of (1) O 2 , administration followed with resonant photoexcitation of the drug [63].
The efficient 1 O 2 photosensitization by nc-Si is promoted by its huge specific surface area up to 10 3 m 2 /g [62] and by long radiative lifetimes (10 −5 -10 −3 s) of the triplet excitons confined in nc-Si [61]. The (1) O 2 generation by photoexcited nc-Si can be quantified by measuring the quenching of the exciton photoluminescence (PL) of nc-Si [64] and by analyzing the radiative decay of (1) O 2 molecules at 0.98 eV (1270 nm) as it is usually used for molecular sensitizer [68,69]. In fact, the (1) O 2 photosensitization by por-Si was successfully monitored by means of the PL spectroscopy of (1) O 2 emission at 0.98 eV [70]. While the (1) O 2 luminescence indicates a high efficiency of the photosensitization process [71], a strong deactivation (quenching) of (1) O 2 molecules in nc-Si assemblies is revealed from a comparison of the photosensitizing efficiency of the standard molecular sensitizer as porphyrin molecules and nc-Si [72]. It can be explained by considering a process of the nonradiative collisional quenching of (1) O 2 molecules on the nc-Si surfaces in por-Si layer and powder. The (1) O 2 quenching acts as a limiting factor to achieve high concentration of (1) O 2 due to the photosensitized generation in por-Si MPs [73].
A method of the electron paramagnetic resonance (EPR) is well known to detect (1) O 2 in gaseous ambient [67]. The conventional X-band EPR spectroscopy of photoexcited por-Si in O 2 atmosphere allowed us to estimate the (1) O 2 concentration photosensitized by nc-Si to be of the order of 10 19 cm −3 under excitation with photon flux about 10 20 cm −2 [74]. Similar results were obtained by means of the Q-band EPR spectroscopy, which demonstrated a conversion of about 30% of O 2 molecules in the singlet state upon excitation of por-Si powder in oxygen atmosphere [75]. The (1) O 2 photosensitization was shown to be also possible for por-Si dispersed in different oxygen-saturated organic and inorganic liquids [70] as well in water [76].
The quantum theory describes the ground energy state of a O 2 molecule as two different molecular orbitals located at two different oxygen atoms with the total spin equals to 1, which is denoted as 3 Σ state. The electronically excited states are singlet ones and they are characterized by the energy excess of about 0.98 eV ( 1 ∆ state) and 1.63 eV ( 1 Σ state) in respect to the ground one. The electron transition from the (3) O 2 state to (1) O 2 one is a spin-flip process and the direct state conversion via absorption of photons is spin-forbidden according to the spin-selection rule. Since the photon absorption and emission are mirror-like processes the pure radiative decay lifetimes of the 1 ∆ and 1 Σ states are extremely long-about 45 min and 7 s respectively [66]. Note, the observed lifetimes of the singlet states are considerably shorter in condensed phases (~10 −9 s and~10 −3 s for the 1 Σ and 1 ∆ states respectively) because of collisions of (1) O 2 with other molecules [68].
For the first time, the strong interaction of oxygen molecules with photoexcited nc-Si in por-Si was observed at cryogenic temperatures [64] and it was further studied in more details at different excitation conditions and temperatures including room temperature [65]. The investigated samples of por-Si were prepared by standard electrochemical etching of c-Si wafers in a solution of hydrofluoric acid [77]. In References [64,65] free standing por-Si layers were dried in air for several hours and a part of the prepared por-Si was milled to get powder of MPs assembled from nc-Si and their agglomerates. The samples were kept in a vacuum chamber in oil-free vacuum with a residual pressure of about 10 −5 Torr. The exciton PL spectrum of nc-Si measured in vacuum at low temperature is characterized by a broad, featureless emission band located in the visible region (dashed line in Figure 21). The spectral position and bandwidth reflect the wide band-gap distribution of the nc-Si assembly. Intrinsic defects commonly attributed to Si dangling bonds (DBs) are responsible for the infrared PL band below 1 eV [61]. The adsorption of O 2 on nc-Si surface resulted in a strong suppression of both the exciton PL and the defect PL band [65]. The PL quenching by O 2 adsorption is maximal for the PL photon energies above 1.63 eV (Figure 21). The latter value corresponds to the 3 Σ → 1 Σ transition energy in O 2 molecule. At the same time, the PL line at 0.98 eV, which is related to the radiative transition 1 ∆ → 1 Σ, appeared after oxygen adsorption in por-Si (inset in Figure 21). These spectroscopic data manifest the (1) O 2 photosensitization by the energy transfer from excitons in nc-Si [65].
suppression of both the exciton PL and the defect PL band [65]. The PL quenching by O2 adsorption is maximal for the PL photon energies above 1.63 eV (Figure 21). The latter value corresponds to the 3   1  transition energy in O2 molecule. At the same time, the PL line at 0.98 eV, which is related to the radiative transition 1   1 , appeared after oxygen adsorption in por-Si (inset in Figure 21). These spectroscopic data manifest the (1) O2 photosensitization by the energy transfer from excitons in nc-Si [65]. Detailed description of the energy-transfer mechanism responsible for the photosensitized generation of 1 O2 can be obtained from the spectral dependence of the PL quenching strength, which can be defined as follows [65]: where IPL vac and IPL ox are the exciton PL intensities of nc-Si in vacuum and in oxygen ambient, respectively. The spectra of Q(hPL) and its second derivative are shown in Figure 22. Besides the strongest quenching at 1.63 eV there is an additional maximum at hPL of about 57 meV below the 1  state energy and numerous maxima separated by energy of about 63 meV. These maxima correspond to the energy transfer from nc-Si with band gaps, which do not satisfy to the resonance with the excitation energies of (1) O2. A local maximum separated by 57 meV from the main maximum at 1.63 eV is an evidence of the indirect radiative transition in nc-Si, where the participation of the momentum conserving TO phonon with energy of 57 meV is required [61]. The excess of the exciton energy with respect to the energies of the 1  and 1  states is compensated by emission of the TO phonons with energy of 63 meV [64,65]. Detailed description of the energy-transfer mechanism responsible for the photosensitized generation of 1 O 2 can be obtained from the spectral dependence of the PL quenching strength, which can be defined as follows [65]: where I PL vac and I PL ox are the exciton PL intensities of nc-Si in vacuum and in oxygen ambient, respectively.
The spectra of Q(hν PL ) and its second derivative are shown in Figure 22. Besides the strongest quenching at 1.63 eV there is an additional maximum at hν PL of about 57 meV below the 1 Σ state energy and numerous maxima separated by energy of about 63 meV. These maxima correspond to the energy transfer from nc-Si with band gaps, which do not satisfy to the resonance with the excitation energies of (1) O 2 . A local maximum separated by 57 meV from the main maximum at 1.63 eV is an evidence of the indirect radiative transition in nc-Si, where the participation of the momentum conserving TO phonon with energy of 57 meV is required [61]. The excess of the exciton energy with respect to the energies of the 1 ∆ and 1 Σ states is compensated by emission of the TO phonons with energy of 63 meV [64,65]. The dynamics of the energy transfer is deduced from the PL transients of por-Si in the presence of adsorbed O2 molecules [65]. The PL spectra of por-Si at different quenching level by the energy transfer to O2 at low temperatures and the corresponding PL decay times PL are shown in Figure 23. In vacuum PL is approximately equal to the radiative lifetime of excitons ex of the order of 10 −3 s and The dynamics of the energy transfer is deduced from the PL transients of por-Si in the presence of adsorbed O 2 molecules [65]. The PL spectra of por-Si at different quenching level by the energy transfer to O 2 at low temperatures and the corresponding PL decay times τ PL are shown in Figure 23. In vacuum τ PL is approximately equal to the radiative lifetime of excitons τ ex of the order of 10 −3 s and it does not depend on the photon energy (see Figure 23). The PL quenching by O 2 adsorption is accompanied by a significant decrease of the PL decay time because the adsorbed O 2 molecules on the nc-Si surface represent a channel for the nonradiative recombination of the excitons. The spectral dependence of τ PL follows the quenching strength spectrum. The shortest τ PL is observed at the PL photon energies, which correspond the strongest PL quenching. Increasing the concentration of adsorbed O 2 molecules results in a stronger PL quenching and further decrease of τ PL [65]. The time resolved PL studies performed with nanosecond time resolution confirm this spectral behavior of the exciton lifetime [71]. Figure 22. Spectral dependence of the PL quenching strength of por-Si with adsorbed O2 molecules at T = 5 K. Inset shows the second derivative of the PL quenching strength. For convenient presentation, the data are partially scaled by the indicated multiplication factor. Vertical dotted lines are guide for the eye. (From Reference [65]).
The dynamics of the energy transfer is deduced from the PL transients of por-Si in the presence of adsorbed O2 molecules [65]. The PL spectra of por-Si at different quenching level by the energy transfer to O2 at low temperatures and the corresponding PL decay times PL are shown in Figure 23. In vacuum PL is approximately equal to the radiative lifetime of excitons ex of the order of 10 −3 s and it does not depend on the photon energy (see Figure 23). The PL quenching by O2 adsorption is accompanied by a significant decrease of the PL decay time because the adsorbed O2 molecules on the nc-Si surface represent a channel for the nonradiative recombination of the excitons. The spectral dependence of PL follows the quenching strength spectrum. The shortest PL is observed at the PL photon energies, which correspond the strongest PL quenching. Increasing the concentration of adsorbed O2 molecules results in a stronger PL quenching and further decrease of PL [65]. The time resolved PL studies performed with nanosecond time resolution confirm this spectral behavior of the exciton lifetime [71]. The average time of the energy transfer from excitons in nc-Si assembly to O 2 molecules can be calculated from the following expression [65]: In the regime of the strongest quenching the values of τ ET for the 1 ∆ and 1 Σ states are 50 to 100 µs and <3 µs, respectively. A uniform concentration of O 2 molecules for all nc-Si would result in a quenching strength that scales as τ ex /τ PL . Obviously this simple relation is not valid. A decay time longer than that expected from the quenching strength is observed because of statistical fluctuations of the number of adsorbed O 2 molecules-while mainly the slowest PL emission from nc-Si with a small number of the adsorbed molecules contributes to the PL decay, the PL intensity spectrum reflects the response of all nanocrystals [65].
A mechanism of the direct electron exchange between nc-Si and O 2 molecule is explained the triplet-triplet annihilation of excitons accompanied by spin-flip excitation of an O 2 molecule and followed by the (1) O 2 formation [65]. The energy transfer rate is supposed to be determined by the spatial overlap of the electronic wave functions of the interacting species and depends exponentially on the donor-acceptor distance [78]. The latter parameter controls the energy transfer probability, which is larger for nc-Si in as-prepared por-Si with hydrogen-terminated surface [65]. For oxidized nc-Si the increased spacing between confined excitons and adsorbed O 2 molecules is of the order of double the length of the Si-O bond (~3 Å). This critically affects the efficiency of the electron exchange interaction. Contrary to a strong coupling for hydrogen-terminated nanocrystals, the PL quenching efficiency is reduced by orders of magnitude if a thin oxide barrier is present. The degree of spatial overlap of the electronic wave functions of confined excitons and adsorbed oxygen molecules depends on the size of nc-Si. For smaller nc-Si the overlap becomes better and the probability for energy transfer is higher. On the other hand, for smaller NPs a larger number of emitted phonons is required to conserve the energy, which lowers the probability for energy exchange. The interplay between these two tendencies results in an almost spectrally constant efficiency of the energy transfer. While the involved transitions are spin forbidden in isolated nc-Si and O 2 molecules, they become allowed through exchange interaction [65].
To demonstrate the role of the electron spin statistics for the energy transfer rate, the magnetic-field dependence of the PL quenching efficiency was studied [65]. A magnetic field introduces the quantization axis for electron spins and it results in the lifting of the energy state degeneracy in both O 2 molecules and nc-Si. In general, the number of possible states participating in the electron exchange is reduced and the decreased energy transfer rate results in a weaker PL quenching. At low temperature the magnetic field results in preferential occupation of "spin-down" states for both O 2 and excitons, while to proceed with energy exchange "spin-up states" are required. The PL quenching was observed at temperature of 10 K in magnetic fields up to 10 T as shown in Figure 24. For the spectral region above the 1 Σ state, the high quenching level of the PL intensity prevented the observation of magnetic field effects within the experimental detection sensitivity.
triplet-triplet annihilation of excitons accompanied by spin-flip excitation of an O2 molecule and followed by the (1) O2 formation [65]. The energy transfer rate is supposed to be determined by the spatial overlap of the electronic wave functions of the interacting species and depends exponentially on the donor-acceptor distance [78]. The latter parameter controls the energy transfer probability, which is larger for nc-Si in as-prepared por-Si with hydrogen-terminated surface [65]. For oxidized nc-Si the increased spacing between confined excitons and adsorbed O2 molecules is of the order of double the length of the Si-O bond (~3 Å). This critically affects the efficiency of the electron exchange interaction. Contrary to a strong coupling for hydrogen-terminated nanocrystals, the PL quenching efficiency is reduced by orders of magnitude if a thin oxide barrier is present. The degree of spatial overlap of the electronic wave functions of confined excitons and adsorbed oxygen molecules depends on the size of nc-Si. For smaller nc-Si the overlap becomes better and the probability for energy transfer is higher. On the other hand, for smaller NPs a larger number of emitted phonons is required to conserve the energy, which lowers the probability for energy exchange. The interplay between these two tendencies results in an almost spectrally constant efficiency of the energy transfer. While the involved transitions are spin forbidden in isolated nc-Si and O2 molecules, they become allowed through exchange interaction [65].
To demonstrate the role of the electron spin statistics for the energy transfer rate, the magneticfield dependence of the PL quenching efficiency was studied [65]. A magnetic field introduces the quantization axis for electron spins and it results in the lifting of the energy state degeneracy in both O2 molecules and nc-Si. In general, the number of possible states participating in the electron exchange is reduced and the decreased energy transfer rate results in a weaker PL quenching. At low temperature the magnetic field results in preferential occupation of "spin-down" states for both O2 and excitons, while to proceed with energy exchange "spin-up states" are required. The PL quenching was observed at temperature of 10 K in magnetic fields up to 10 T as shown in Figure 24. For the spectral region above the 1  state, the high quenching level of the PL intensity prevented the observation of magnetic field effects within the experimental detection sensitivity.  Besides the quenching of exciton PL, the photosensitized generation of (1) O 2 can be observed by measuring the infrared PL related to the (1) O 2 radiative de-excitation [64,65]. The relevant time scale of the infrared PL was determined from time-resolved measurements. In the presence of adsorbed O 2 molecules the radiative decay of the 1 ∆ state of (1) O 2 was observed at detection energy of 0.953 eV. The initial fast decay is attributed to the defect-related PL background. The slow component with the lifetime τ ∆ ≈ 0.5 ms accounts for the 1 ∆ → 3 Σ transition in O 2 . This lifetime is significantly shorter that the radiative lifetime of a free O 2 molecule. The shortening of τ ∆ can be explained by the interaction of the 1 ∆ state of (1) O 2 with nc-Si surface. The same interaction should also influence the radiative lifetime τ r of adsorbed (1) O 2 molecules. Firstly, the quantum yield η r ≈ 7·10 −5 of the radiative decay of the 1 ∆ state is estimated from the comparison from the integral intensity of the exciton PL band. The radiative lifetime of (1) O 2 τ r ≈ 7 s is obtained by using the simple relation τ r = τ ∆ /η r . On the one hand, the obtained τ r is much shorter than the intrinsic radiative lifetime~50 min. On the other hand, τ r ≈ 7 s is close to the 1 ∆ radiative lifetimes of (1) O 2 in different liquids. Therefore, the photoexcited Si nanocrystals contribute simultaneously to the photosensitization process and to the quenching of (1) O 2 in por-Si layers and MPs.

Phenomenological Model of the Photosensitization by Si Nanocrystals
The photosensitized generation of (1) O 2 in nc-Si ensembles is quantitatively explained by using a model based on the rate equations for excitons and oxygen molecules [65,79]. In brief, the number of excitons in the nc-Si ensemble at low temperatures is limited due to the long radiative lifetime of excitons and efficient nonradiative Auger recombination in nc-Si [80]. According to the experimental data the PL intensity of por-Si in vacuum increases linearly with the excitation intensity up to 0.01 W/cm 2 as shown in Figure 25 [65]. At higher excitation intensities an occupation of each nc-Si by two electron-hole pairs can be achieved and the nonradiative Auger recombination results in a saturation behavior of the emission intensity (triangles in Figure 25). The model describes the experimental data both for por-Si in vacuum (curve 1) and after oxygen adsorption, which leads to the superlinear dependence I PL on I ex (curves 2,3). The fitting parameters correspond to the product of (β·n 0 ) −1 = 200 µs, which is close to the experimentally determined τ ET (see Figure 25). The fitting parameter β can be calculated by considering the microscopic mechanism of the energy transfer [78].
the radiative lifetime of a free O2 molecule. The shortening of  can be explained by the interaction of the 1  state of (1) O2 with nc-Si surface. The same interaction should also influence the radiative lifetime r of adsorbed (1) O2 molecules. Firstly, the quantum yield r710 -5 of the radiative decay of the 1  state is estimated from the comparison from the integral intensity of the exciton PL band. The radiative lifetime of (1) O2 r7 s is obtained by using the simple relation r=/r. On the one hand, the obtained r is much shorter than the intrinsic radiative lifetime ~50 min. On the other hand, r7 s is close to the 1  radiative lifetimes of (1) O2 in different liquids. Therefore, the photoexcited Si nanocrystals contribute simultaneously to the photosensitization process and to the quenching of (1) O2 in por-Si layers and MPs.

Phenomenological Model of the Photosensitization by Si Nanocrystals
The photosensitized generation of (1) O2 in nc-Si ensembles is quantitatively explained by using a model based on the rate equations for excitons and oxygen molecules [65,79]. In brief, the number of excitons in the nc-Si ensemble at low temperatures is limited due to the long radiative lifetime of excitons and efficient nonradiative Auger recombination in nc-Si [80]. According to the experimental data the PL intensity of por-Si in vacuum increases linearly with the excitation intensity up to 0.01 W/cm 2 as shown in Figure 25 [65]. At higher excitation intensities an occupation of each nc-Si by two electron-hole pairs can be achieved and the nonradiative Auger recombination results in a saturation behavior of the emission intensity (triangles in Figure 25). The model describes the experimental data both for por-Si in vacuum (curve 1) and after oxygen adsorption, which leads to the superlinear dependence IPL on Iex (curves 2,3). The fitting parameters correspond to the product of (βn0) −1 = 200 µs, which is close to the experimentally determined ET (see Figure 25). The fitting parameter β can be calculated by considering the microscopic mechanism of the energy transfer [78].   (16) and (17) with the following parameters: N = 10 19 cm −3 , σ = 10 −15 cm 2 , τ ex = 0.8 ms, τ ∆ = 4 ms, β = 5·10 −16 cm 3 /s and n = 0 (curve 1) and oxygen concentrations are taken as n = 10 19 sm −3 (curve 2), n = 3·10 19 cm −3 (curve 3). Excitation photon energy E exc = 2.41 eV, T = 5 K. (The experimental data are taken from Reference [65]. Reprinted from Reference [79] by permission from Springer Nature Customer Service Centre GmbH. Springer © 2007).
A coupled system, which consists of nc-Si and O 2 molecules, under optical excitation can be described by a simple set of the rate equations [79]: where N 0 and N 1 are the numbers of nc-Si containing 0 and 1 exciton, respectively, n 0 and n 1 are the numbers of O 2 molecules being in the ground 3 Σ and singlet 1 ∆ states, respectively, τ ex is the exciton lifetime, τ ∆ is the lifetime of the 1 ∆ state, σ is the cross section of optical absorption of nc-Si, Φ is the photon flux density of exciting light, β is the coupling coefficient. The latter value describes the energy transfer probability of in nc-Si/O 2 system and the reciprocal product (βn 0 ) −1 corresponds to the experimentally accessible energy-transfer time τ ET .
To solve Equation (16) the following expressions for the total numbers of interacting species can be used: where N and n are the total numbers of nc-Si and O 2 molecules, respectively. The discussed phenomenological model does not account contributions of the upper excited states of nc-Si and O 2 molecules, the nonradiative recombination of excitons in nc-Si and the reverse energy transfer from (1) O 2 to nc-Si.
The exciton PL intensity of nc-Si is obtained from the steady state solution of Equations (16) and (17) and from the relation I PL = N 1 /τ ex . The time constants used in the model are obtained from the experimental data discussed above whereas σ is known from Reference [61]. Solutions of Equation (16) fit the experimental dependences of the PL intensity of por-Si on excitation intensity I ex (solid lines in Figure 25).
The described model assumes that the larger number of adsorbed O 2 molecules results in shorter τ ET at the same conditions of the energy transfer. The energy transfer efficiency is described by β and it is obviously dependent on nc-Si size and surface conditions [79]. Hydrogen terminated nc-Si assembles with lowest number of nonradiative surface defects as Si DBs are preferable for the (1) O 2 photosensitization [81]. For por-Si aged in air at room temperature, the photosensitization process is additionally complicated by the thermally activated desorption of O 2 molecules as well as by the thermally activated exciton migration and nonradiative recombination. Besides, it should be analyzed both the generation rate and the quenching process of (1) O 2 via the interaction with internal surface of por-Si and ambient molecules. The quenching processes are especially important for por-Si suspended in different solvents. The theoretical description of the photosensitized generation of (1) O 2 by real systems based on por-Si needs rather sophisticate analysis. The experimental results presented in the next sections of this chapter can be used as experimental basis for future complete theory of the photosensitized generation of (1) O 2 by nc-Si.
Contrary to cryogenic temperatures, the conditions of efficient interaction between excitons in nc-Si and O 2 molecules adsorbed on the surfaces of nc-Si are not fulfilled at elevated temperatures. First of all, because of the thermally activated desorption, a small spatial separation between excitons and O 2 molecules is realized only during a short time of collisions [65]. Furthermore, the exciton lifetime and spin-triplet state occupation drop down with rising temperature [59][60][61]. It results in a weaker PL quenching, which scales with the collision rate, that is, the gas pressure and in a broad spectral resonance of the energy transfer to the 1 Σ state [64]. Spectra of the photosensitization efficiency of nc-Si in por-Si at different temperatures are shown in Figure 26 [65]. At intermediate temperatures (T = 110 K) the second quenching band in the spectral region of 1.75-1.95 eV is observed and it becomes better pronounced with increasing oxygen concentration (Figure 26a). This quenching band is attributed to the energy transfer from excitons confined in nc-Si to (1) O 2 dimers, that is, to the 2( 1 ∆) state formation [65]. The energy transfer to the 2( 1 ∆) states is enhanced at higher pressures due to increasing the probability of dimer formation. A decrease of the dimer-related quenching band is observed at higher temperature because the dimer formation is less probable. For temperatures above 250 K the energy transfer to the (1) O 2 dimers cannot be resolved spectroscopically (see Figure 26b). This fact agrees with results of the spectroscopic investigation of (1) O 2 [67]. Appl. Sci. 2020, 10, x FOR PEER REVIEW 28 of 47 Dependence of the exciton PL quenching detected at 1.63 eV on the O2 ambient pressure at different temperatures are shown in Figure 27 [65]. The pressure dependence is well described by using the Langmuir approach for molecular adsorption on a surface [82], that considers the dynamic equilibrium between the rates of adsorption and desorption by the following Equation: Figure 27. Dependences of the exciton PL quenching strength at 1.63 eV on oxygen pressure at different temperatures: T = 120 K (squares), T=200 K (circles), T=300 K (triangles). Solid lines are fits by Equation (18). (From Reference [65]).
where K is the equilibrium constant, Pox is the oxygen gas pressure and A is the part of exciton energy transferred to adsorbed O2 molecules [65]. The experimental pressure dependence of the photosensitization efficiency is well described by theoretical predictions (solid lines in Figure 27). As expected, in the entire pressure range a decrease of the temperature increases the mean number of adsorbed molecules and enhances the efficiency of energy transfer to O2 molecules. The steady state concentration of (1) O2 is a product of its generation rate and the collision-related deactivation one. Because both quantities are rising with oxygen ambient pressure [67], there is an optimal Pox for the maximal steady state concentration of (1) O2 [65].
Additional information about the (1) O2 photosensitization at room temperature is obtained from the PL transient measurements. Figure 28 presents several transients of the exciton PL of por-Si MPs Dependence of the exciton PL quenching detected at 1.63 eV on the O 2 ambient pressure at different temperatures are shown in Figure 27 [65]. The pressure dependence is well described by using the Langmuir approach for molecular adsorption on a surface [82], that considers the dynamic equilibrium between the rates of adsorption and desorption by the following Equation: where K is the equilibrium constant, P ox is the oxygen gas pressure and A is the part of exciton energy transferred to adsorbed O 2 molecules [65]. Dependence of the exciton PL quenching detected at 1.63 eV on the O2 ambient pressure at different temperatures are shown in Figure 27 [65]. The pressure dependence is well described by using the Langmuir approach for molecular adsorption on a surface [82], that considers the dynamic equilibrium between the rates of adsorption and desorption by the following Equation: Figure 27. Dependences of the exciton PL quenching strength at 1.63 eV on oxygen pressure at different temperatures: T = 120 K (squares), T=200 K (circles), T=300 K (triangles). Solid lines are fits by Equation (18). (From Reference [65]).
where K is the equilibrium constant, Pox is the oxygen gas pressure and A is the part of exciton energy transferred to adsorbed O2 molecules [65]. The experimental pressure dependence of the photosensitization efficiency is well described by theoretical predictions (solid lines in Figure 27). As expected, in the entire pressure range a decrease of the temperature increases the mean number of adsorbed molecules and enhances the efficiency of energy transfer to O2 molecules. The steady state concentration of (1) O2 is a product of its generation rate and the collision-related deactivation one. Because both quantities are rising with oxygen ambient pressure [67], there is an optimal Pox for the maximal steady state concentration of (1) O2 [65]. The experimental pressure dependence of the photosensitization efficiency is well described by theoretical predictions (solid lines in Figure 27). As expected, in the entire pressure range a decrease of the temperature increases the mean number of adsorbed molecules and enhances the efficiency of energy transfer to O 2 molecules. The steady state concentration of (1) O 2 is a product of its generation rate and the collision-related deactivation one. Because both quantities are rising with oxygen ambient pressure [67], there is an optimal P ox for the maximal steady state concentration of (1) O 2 [65].
Additional information about the (1) O 2 photosensitization at room temperature is obtained from the PL transient measurements. Figure 28 presents several transients of the exciton PL of por-Si MPs in gaseous oxygen ambient. The inset of Figure 28 shows the transients after the pumping of oxygen molecules. The PL transients are not actually single exponential. However, they can be well fitted by single exponential decays for times about 50-70 µs after the excitation laser pulse [83]: where τ PL is the PL lifetime and I PL (0) is the PL intensity just after excitation. The values of τ PL for the samples in vacuum are found to be within a microsecond time scale that is in good agreement with the singlet lifetimes of excitons in nc-Si [60,61].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 29 of 47 in gaseous oxygen ambient. The inset of Figure 28 shows the transients after the pumping of oxygen molecules. The PL transients are not actually single exponential. However, they can be well fitted by single exponential decays for times about 50-70 s after the excitation laser pulse [83]: where is the PL lifetime and ) 0 ( PL I is the PL intensity just after excitation. The values of for the samples in vacuum are found to be within a microsecond time scale that is in good agreement with the singlet lifetimes of excitons in nc-Si [60,61]. The admission of O2 causes a decrease of and this effect is stronger at higher oxygen pressure (curve 3 in Figure 28). The PL lifetime shortening after oxygen adsorption with Pox > 10 Torr is partially reversible (inset of Figure 28). The strongest lifetime shortening occurs at the PL energy of 1.6 eV, which correlates with the spectral maximum of the PL intensity quenching.
While the energy transfer time at room temperature can be obtained from the PL decay times by applying Equation (13), in which has to be substituted by in vacuum, the energy transfer efficiency is estimated by using the following expression [83]: It is obvious that 1-Q -1 where Q is described by Equation (14). If the PL quenching is not completely reversible due to the oxidation of nc-Si by photosensitized (1) O2 [81], Equations (15) and (20) will give the lower and upper limits of the corresponding energy transfer time and photosensitization efficiency, respectively [83]. It was found that the photosensitization efficiency in por-Si layers and powder is strongly dependent on the porosity of nc-Si assemblies ( Figure 29). The minimal value of ET and maximal value of are supposed for highly porous layers and powder of MPs, which consist of smallest nc-Si. The porosity dependence of  and ET can be explained by considering the following reasons. The admission of O 2 causes a decrease of τ PL and this effect is stronger at higher oxygen pressure (curve 3 in Figure 28). The PL lifetime shortening after oxygen adsorption with P ox > 10 Torr is partially reversible (inset of Figure 28). The strongest lifetime shortening occurs at the PL energy of 1.6 eV, which correlates with the spectral maximum of the PL intensity quenching.
While the energy transfer time at room temperature can be obtained from the PL decay times by applying Equation (13), in which τ ex has to be substituted by τ PL in vacuum, the energy transfer efficiency is estimated by using the following expression [83]: It is obvious that η ≈ 1-Q −1 where Q is described by Equation (14). If the PL quenching is not completely reversible due to the oxidation of nc-Si by photosensitized (1) O 2 [81], Equations (15) and (20) will give the lower and upper limits of the corresponding energy transfer time and photosensitization efficiency, respectively [83].
It was found that the photosensitization efficiency in por-Si layers and powder is strongly dependent on the porosity of nc-Si assemblies ( Figure 29). The minimal value of τ ET and maximal value of η are supposed for highly porous layers and powder of MPs, which consist of smallest nc-Si. The porosity dependence of η and τ ET can be explained by considering the following reasons. The first one is a growth of the specific surface area of nc-Si with porosity increasing that promotes the O 2 adsorption and then the total rate of (1) O 2 photosensitization. The second reason is related to a decrease of the nonradiative recombination with increasing the porosity that results in an increase of the exciton concentration. In fact, the PL quantum yield increases in por-Si with high porosity that indicates the second reason impact [83]. esides the characteristic energy of about 1.63 eV (the 1   3  transition energy in O2 molec ectrally selective quenching of the exciton PL intensity in por-Si at room tempera strate an additional maximum at photon energy of 2-2.2 eV, which is related to the forma eroxide radicals, that is, O  2 [76]. The PL quenching at 2-2.2 eV can be also explained by ng of nc-Si due to the O  2 radical formation on the nc-Si surface [83] because the positi d Si nanocrystals exhibit an enhanced rate of the nonradiative Auger recombination [61,8 he infrared PL of nc-Si in por-Si MPs at room temperature was investigated to get informa photosensitized generation of (1) O2 [70]. Since the radiative transitions in (1) O2 molecules terized by extremely low probability, the experimental observation of the horescence at 0.98 eV required very sensitive detection system and was possible only for h rather efficient generation of (1) O2. Figure 30 shows typical infrared PL spectra of po er obtained by mechanical milling of por-Si films [73]. While the PL spectrum of por-Si pow uum shows a featureless emission band related to defects states in nc-Si [61], the PL line o hosphorescence at 0.98 eV appears just after the admission of O2 to por-Si powder. For sev es after the O2 admission the (1) O2 phosphorescence intensity decreases, while the intensit fect-related band increases. The relative intensity of the (1) O2 phosphorescence intensity to decrease in por-Si subjected to mechanical grinding, which resulted in increasing the de Besides the characteristic energy of about 1.63 eV (the 1 Σ → 3 Σ transition energy in O 2 molecule), the spectrally selective quenching of the exciton PL intensity in por-Si at room temperature demonstrate an additional maximum at photon energy of 2-2.2 eV, which is related to the formation of superoxide radicals, that is, O − 2 [76]. The PL quenching at 2-2.2 eV can be also explained by the charging of nc-Si due to the O − 2 radical formation on the nc-Si surface [83] because the positively charged Si nanocrystals exhibit an enhanced rate of the nonradiative Auger recombination [61,80].
The infrared PL of nc-Si in por-Si MPs at room temperature was investigated to get information on the photosensitized generation of (1) O 2 [70]. Since the radiative transitions in (1) O 2 molecules are characterized by extremely low probability, the experimental observation of the (1) O 2 phosphorescence at 0.98 eV required very sensitive detection system and was possible only for por-Si with rather efficient generation of (1) O 2 . Figure 30 shows typical infrared PL spectra of por-Si powder obtained by mechanical milling of por-Si films [73]. While the PL spectrum of por-Si powder in vacuum shows a featureless emission band related to defects states in nc-Si [61], the PL line of the (1) O 2 phosphorescence at 0.98 eV appears just after the admission of O 2 to por-Si powder. For several minutes after the O 2 admission the (1) O 2 phosphorescence intensity decreases, while the intensity of the defect-related band increases. The relative intensity of the (1) O 2 phosphorescence intensity was found to decrease in por-Si subjected to mechanical grinding, which resulted in increasing the defect-related PL [73].
in vacuum shows a featureless emission band related to defects states in nc-Si [61], the PL line of the (1) O2 phosphorescence at 0.98 eV appears just after the admission of O2 to por-Si powder. For several minutes after the O2 admission the (1) O2 phosphorescence intensity decreases, while the intensity of the defect-related band increases. The relative intensity of the (1) O2 phosphorescence intensity was found to decrease in por-Si subjected to mechanical grinding, which resulted in increasing the defectrelated PL [73]. Dependences of the intensity of (1) O2 luminescence at 0.98 eV and defect-related PL at 0.94-0.95 eV for por-Si photoexcited at room temperature indicate formation of new defect states on the nc-Si surfaces due to the photosensitized generation of (1) O2 [73]. Most probable reason of the defect Dependences of the intensity of (1) O 2 luminescence at 0.98 eV and defect-related PL at 0.94-0.95 eV for por-Si photoexcited at room temperature indicate formation of new defect states on the nc-Si surfaces due to the photosensitized generation of (1) O 2 [73]. Most probable reason of the defect formation is the photo-induced oxidation of nc-Si by (1) O 2 , which is accompanied by irreversible quenching of the exciton PL [81]. The latter process induces decreasing the (1) O 2 photosensitization efficiency and then the (1) O 2 luminescence intensity drops down (see Figure 31). Therefore por-Si acts both as the photosensitizer and quencher of (1) O 2 . The lifetime τ ∆ ≈ 15 ms was estimated from the comparison of (1) O 2 luminescence and exciton PL of nc-Si at room temperature at P ox = 1 bar [73]. On the one hand, the estimated lifetime is significantly shorter than the radiative lifetime of (1) O 2 [67]. On the other hand, τ ∆ ≈ 15 ms is larger than the (1) O 2 lifetime in water (3 µs) or biosystems (<1 µs) [69]. This fact implies that nc-Si can be considered as a potential photosensitizer of (1) O 2 in liquids, including aqueous media [70,71].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 31 of 47 formation is the photo-induced oxidation of nc-Si by (1) O2, which is accompanied by irreversible quenching of the exciton PL [81]. The latter process induces decreasing the (1) O2 photosensitization efficiency and then the (1) O2 luminescence intensity drops down (see Figure 31). Therefore por-Si acts both as the photosensitizer and quencher of (1) O2. The lifetime τ  15 ms was estimated from the comparison of (1) O2 luminescence and exciton PL of nc-Si at room temperature at Pox = 1 bar [73]. On the one hand, the estimated lifetime is significantly shorter than the radiative lifetime of (1) O2 [67]. On the other hand, τ  15 ms is larger than the (1) O2 lifetime in water (3 µs) or biosystems (<1 µs) [69]. This fact implies that nc-Si can be considered as a potential photosensitizer of (1) O2 in liquids, including aqueous media [70,71]. Beside the PL diagnostics of the nc-Si-induced photosensitization the EPR technique was shown to be efficient for the quantitative analysis of the (1) O2 photosensitization [84]. It is known that por-Si possesses intrinsic defects as Si DBs, which can act as spin labels for (1) O2. Typical EPR spectra of por- Beside the PL diagnostics of the nc-Si-induced photosensitization the EPR technique was shown to be efficient for the quantitative analysis of the (1) O 2 photosensitization [84]. It is known that por-Si possesses intrinsic defects as Si DBs, which can act as spin labels for (1) O 2 . Typical EPR spectra of por-Si are shown in Figure 32. The EPR signal is characterized by the effective g-factor of 2.0055 ± 0.0005. The corresponding paramagnetic defects are usually attributed to so-called P b -like centers, which are Si DBs at Si/SiO 2 interface [85]. The EPR signal intensity (I EPR ) of por-Si in vacuum is the weakest at high microwave power because of the saturation effect of the microwave power absorbance by Si DBs [74]. The 1 O 2 can be also detected by monitoring a decrease of the concentration of paramagnetic (3) O 2 [75]. It was found that por-Si in O2 atmosphere was characterized by larger IEPR in darkness than under illumination. Furthermore, IEPR for the sample under short time illumination in O2 atmosphere decreased almost reversibly [74]. Note, that prolonged intensive illumination led to an irreversible increase of IEPR due to the defect formation under photo-oxidation [81]. The saturation effect of the EPR signal of por-Si results from relatively long time of the spin relaxation of Pb-centers [85]. In general, IEPR depends on the number of paramagnetic centers (Si DBs in the case of nc-Si) and their relaxation time, which can be expressed in the following way [75]: where is the longitudinal relaxation time (spin-lattice relaxation) and is the transverse relaxation time, associated with spin-spin relaxation. For nc-Si systems with low defect density-<< and then T2T1. While the value of T1 for bulk c-Si at the room temperature lies typically in the range of several microseconds [85], this time can be longer in small nc-Si because of a low density of phonon modes. Indeed, IEPR for the sample in vacuum exhibits the strong saturation even at relatively low microwave power ( Figure 33). The spectral shape of the EPR signal of the sample in vacuum does not change significantly under illumination [75]. Note, the factor of phonon mode depletion in nc-Si can also influence the longitudinal relaxation time of nuclear spin as 29 Si what is essential for the hyperpolarization method (see Section 2). It was found that por-Si in O 2 atmosphere was characterized by larger I EPR in darkness than under illumination. Furthermore, I EPR for the sample under short time illumination in O 2 atmosphere decreased almost reversibly [74]. Note, that prolonged intensive illumination led to an irreversible increase of I EPR due to the defect formation under photo-oxidation [81]. The saturation effect of the EPR signal of por-Si results from relatively long time of the spin relaxation of P b -centers [85]. In general, I EPR depends on the number of paramagnetic centers (Si DBs in the case of nc-Si) and their relaxation time, which can be expressed in the following way [75]: where T DB 1 is the longitudinal relaxation time (spin-lattice relaxation) and T DB 2 is the transverse relaxation time, associated with spin-spin relaxation. For nc-Si systems with low defect density-T DB 1 << T DB 2 and then T ≈ 2T 1 . While the value of T 1 for bulk c-Si at the room temperature lies typically in the range of several microseconds [85], this time can be longer in small nc-Si because of a low density of phonon modes. Indeed, I EPR for the sample in vacuum exhibits the strong saturation even at relatively low microwave power ( Figure 33). The spectral shape of the EPR signal of the sample in vacuum does not change significantly under illumination [75]. Note, the factor of phonon mode depletion in nc-Si can also influence the longitudinal relaxation time of nuclear spin as 29 Si what is essential for the hyperpolarization method (see Section 2).
in the range of several microseconds [85], this time can be longer in small nc-Si because of a low density of phonon modes. Indeed, IEPR for the sample in vacuum exhibits the strong saturation even at relatively low microwave power (Figure 33). The spectral shape of the EPR signal of the sample in vacuum does not change significantly under illumination [75]. Note, the factor of phonon mode depletion in nc-Si can also influence the longitudinal relaxation time of nuclear spin as 29 Si what is essential for the hyperpolarization method (see Section 2). The T2 value is reciprocal to the paramagnetic center concentration, which depends on the number of adsorbed triplet O2 molecules on nc-Si surface. The saturation of IEPR at high microwave The T 2 value is reciprocal to the paramagnetic center concentration, which depends on the number of adsorbed triplet O 2 molecules on nc-Si surface. The saturation of I EPR at high microwave power can be absent when T 2 decreases due to the spin-spin relaxation. Indeed, there is no saturation of the I EPR signal on microwave power for por-Si in oxygen atmosphere ( Figure 33). Since I EPR for the samples at P ox = 760 Torr decreases by 40% under illumination with photon flux of about 10 20 cm −2 , the concentration of triplet O 2 molecules decreases by ∆n ≈ 0.4n 0 , where n 0 is the initial O 2 concentration. The latter number at P ox = 760 Torr is about 10 19 cm −3 (the Avogadro number divided by the molar volume). From the comparison of I EPR in the O 2 atmosphere in darkness and under illumination, one can estimate the (1) O 2 molecular concentration to be ∆n ≈ 4·10 18 cm −3 . The latter value is comparable with the number of nc-Si and it is by 2 orders of magnitude larger than the Si DBs concentration. This fact demonstrates that Si DBs are only probes to monitor the (1) O 2 photosensitization. The observed features of I EPR for por-Si in oxygen atmosphere in darkness and under illumination were confirmed by means of the pulsed EPR technique and similar concentration of photosensitized (1) O 2~1 0 18 cm −3 was detected by using the Q-band EPR [75].
While por-Si looks rather efficient photosensitizer of the (1) O 2 generation in gaseous atmosphere, the photosensitization by por-Si in liquids and, especially, in aqueous solutions is required for biomedical applications [86][87][88][89][90]. Unfortunately, the fast nonradiative relaxation of (1) O 2 in water complicates detection of the (1) O 2 luminescence. In this case the (1) O 2 photosensitization can be indirectly probed by monitoring the intensity and lifetime of the exciton PL of por-Si. Although the exciton PL quenching for nc-Si dispersed in water is weaker, its spectral shape is similar to that measured in gaseous ambient. Note, the relative contribution of the high-energy quenching at 2-2.2 eV is stronger in water because of more efficient charging of the nc-Si surfaces followed with formation of O − 2 radicals [76]. The lifetime of the exciton PL of por-Si MPs dispersed in water decreases after saturation of the solution by oxygen as shown in Figure 34 [91]. The energy transfer times determined from transients of the exciton PL by using Equation (13) are plotted in inset of Figure 34. The spectral dependence of the energy transfer time is similar to that observed for por-Si in gaseous oxygen ambient (see Figure 26). A slightly longer energy transfer time correlates with weaker quenching of the PL intensity of por-Si in water than that in gaseous O 2 . This fact indicates an influence of water molecules on the exciton recombination and/or energy transfer from the excitons to O 2 molecules. Indeed, the energy transfer is mostly efficient for nc-Si with S-H surface bonds, which are hydrophobic [77]. Therefore nc-Si dispersed in water should be partially oxidized that results in decreasing the (1) O 2 photosensitization efficiency [65]. The oxidation of nc-Si dispersed in water or aqueous solutions can be a limiting factor to achieve the stable and efficient (1) O 2 photosensitization. The oxidation process can be also stimulated during the photosensitization [81].
For biomedical applications of nc-Si in PDT it is obviously necessary to stabilize nc-Si surface against the (1) O 2 induced photooxidation. It can be done, for example, by using rapid thermal annealing or laser irradiation. For example, nearly spherical colloidal nc-Si obtained by femtosecond laser ablation of c-Si wafer in deuterated water (D 2 O) water were found to photosensitize the (1) O 2 generation with a yield estimated at 10% of that of the standard molecular sensitizer a photofrin [86].

Si Nanocrystals as Photosensitizers of Singlet Oxygen Generation for Biomedical Applications
The (1) O2 photosensitization efficiency by nc-Si dispersed in water was confirmed by measurements of the exciton PL of por-Si MPs excited by laser pulses. The relaxation time of the exponential part of the PL transients in the solution without O2 was τex≈85 µs, which is close to the natural radiative lifetime of excitons confined in nc-Si. The saturation of the solution with gaseous O2 at a pressure of 760 Torr leads to a decrease in the PL decay time to τD≈50 µs. The ratio τex/τD≈1.6 is close to the measured PL quenching. These observations indicate that the decrease of the PL lifetime of nc-Si in oxygen-saturated suspensions is caused by the photosensitized generation of (1) O2 [87].
The photosensitized generation of (1) O2 was confirmed by experiments in vitro, which showed that number of living cells with added por-Si MPs decreased strongly after photoexcitation as compared to the reference group (see Figure 35). At the same time, the effect of por-Si MPs was almost absent over the entire concentration range in darkness. This fact is concerned with the (1) O2 generation process under the illumination in the active solution with dispersed nc-Si, because (1) O2 being strong oxidizing substance results in both killing of cells and the inhibitions of cell proliferation [87]. An analysis of the DNA content of the cells incubated with photoexcited por-Si MPs indicates smaller DNA content is typical for the cell death due to the apoptosis mechanism [88].

Si Nanocrystals as Photosensitizers of Singlet Oxygen Generation for Biomedical Applications
The (1) O 2 photosensitization efficiency by nc-Si dispersed in water was confirmed by measurements of the exciton PL of por-Si MPs excited by laser pulses. The relaxation time of the exponential part of the PL transients in the solution without O 2 was τ ex ≈ 85 µs, which is close to the natural radiative lifetime of excitons confined in nc-Si. The saturation of the solution with gaseous O 2 at a pressure of 760 Torr leads to a decrease in the PL decay time to τ D ≈ 50 µs. The ratio τ ex /τ D ≈ 1.6 is close to the measured PL quenching. These observations indicate that the decrease of the PL lifetime of nc-Si in oxygen-saturated suspensions is caused by the photosensitized generation of (1) O 2 [87].
The photosensitized generation of (1) O 2 was confirmed by experiments in vitro, which showed that number of living cells with added por-Si MPs decreased strongly after photoexcitation as compared to the reference group (see Figure 35). At the same time, the effect of por-Si MPs was almost absent over the entire concentration range in darkness. This fact is concerned with the (1) O 2 generation process under the illumination in the active solution with dispersed nc-Si, because (1) O 2 being strong oxidizing substance results in both killing of cells and the inhibitions of cell proliferation [87]. An analysis of the DNA content of the cells incubated with photoexcited por-Si MPs indicates smaller DNA content is typical for the cell death due to the apoptosis mechanism [88].

Si Nanocrystals as Photosensitizers of Singlet Oxygen Generation for Biomedical Applications
The (1) O2 photosensitization efficiency by nc-Si dispersed in water was confirmed by measurements of the exciton PL of por-Si MPs excited by laser pulses. The relaxation time of the exponential part of the PL transients in the solution without O2 was τex≈85 µs, which is close to the natural radiative lifetime of excitons confined in nc-Si. The saturation of the solution with gaseous O2 at a pressure of 760 Torr leads to a decrease in the PL decay time to τD≈50 µs. The ratio τex/τD≈1.6 is close to the measured PL quenching. These observations indicate that the decrease of the PL lifetime of nc-Si in oxygen-saturated suspensions is caused by the photosensitized generation of (1) O2 [87].
The photosensitized generation of (1) O2 was confirmed by experiments in vitro, which showed that number of living cells with added por-Si MPs decreased strongly after photoexcitation as compared to the reference group (see Figure 35). At the same time, the effect of por-Si MPs was almost absent over the entire concentration range in darkness. This fact is concerned with the (1) O2 generation process under the illumination in the active solution with dispersed nc-Si, because (1) O2 being strong oxidizing substance results in both killing of cells and the inhibitions of cell proliferation [87]. An analysis of the DNA content of the cells incubated with photoexcited por-Si MPs indicates smaller DNA content is typical for the cell death due to the apoptosis mechanism [88].  Mesoporous Si NPs with mean sizes of the order of 100 nm and pore size of 12 nm were used to enhance the photosensitized generation of (1) O 2 with quantum yield~10% in ethanol and 17% in aqueous medium [89]. Such NPs with concentration of 0.1 g/L were added to cancer cell cultures followed with white light illumination that resulted in 45% decrease of cell number [89]. A stronger effect for the cancer cell suppression was observed for microporous Si NPs, which could enter cancer cells by endocytosis mechanism, resulting in~70% cell death [90]. Photoluminescent NPs prepared from meso-and microporous Si were shown to be efficient both as the photosensitizers of (1) O 2 generation and photoluminescent labels in bioimaging in vitro. The photosensitization ability combined with the PL bioimaging property allow us to consider por-Si NPs as a potential agent for application in as-called cancer theranostics, that is, simultaneously therapy and diagnostics [89,90]. Note, the biological effect of photoexcited nc-Si can be related with both the photosensitized (1) O 2 other active forms of oxygen, for example, superoxide (O − 2 ion), whose signature was observed as spectral features of the exciton PL quenching at 2.0-2.2 eV [91].
While the results of fundamental studies and in vitro experiments on the (1) O 2 photosensitization by nc-Si seem to be promising, there is a lack of in vivo tests to assess the real potential of nc-Si for PDT applications. Note, the biocompatibility and biodegradability of nc-Si and por-Si NPs [92,93] together with the photosensitization ability are well satisfied to the modern requirements for PDT application [94]. Besides nc-Si prepared from por-Si [87][88][89][90] the photosensitizing property was also reported for nc-Si prepared by laser ablation of bulk Si in water [86]. This finding indicates a possible way to obtain nc-Si, which can at as stable and efficient photosensitizers for the cancer theranostics [3].

Si NPs with Electron Spin Centers as Potential Contrast Agents for 1 H MRI
Si NPs with a high number of the electron spin centers can act as contrast agents (CAs) for the conventional biomedical MRI at the proton ( 1 H) frequency [95]. The MRI contrast property of Si NPs was explained by considering the magnetic dipole-dipole interaction between electron spins on the Si NP's surfaces and those of surrounding protons [96] as schematically shown in Figure 36. While a solid NP itself can increase the proton spin relaxation (Figure 36a), Si NPs especially prepared from por-Si provide additional opportunities to increase the spin center density due to huge specific surface area of small nc-Si [62]. While por-Si usually contains numerous paramagnetic centers as Si dangling bonds (Si DBs) and their number can be significantly increased by physical and chemical treatments [77]. It was shown that Si NPs prepared from por-Si subjected to thermal annealing (TA) in vacuum could contain a lot of paramagnetic centers, which strongly enhanced the proton spin relaxation of water molecules surrounding those NPs (Figure 36b). It is well known that surface of electrochemically prepared por-Si is passivated by hydrogen atoms [77]. Because the TA treatment induces the hydrogen desorption from the NP's surface followed by creation of new Si DBs, which can be quantitatively detected by EPR technique [77]. Tailoring of the paramagnetic center number in Si NPs is a possible way to improve their CA properties for MRI applications [96].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 35 of 47 Mesoporous Si NPs with mean sizes of the order of 100 nm and pore size of 12 nm were used to enhance the photosensitized generation of (1) O2 with quantum yield ~10% in ethanol and 17% in aqueous medium [89]. Such NPs with concentration of 0.1 g/L were added to cancer cell cultures followed with white light illumination that resulted in 45% decrease of cell number [89]. A stronger effect for the cancer cell suppression was observed for microporous Si NPs, which could enter cancer cells by endocytosis mechanism, resulting in ~70% cell death [90]. Photoluminescent NPs prepared from meso-and microporous Si were shown to be efficient both as the photosensitizers of (1) O2 generation and photoluminescent labels in bioimaging in vitro. The photosensitization ability combined with the PL bioimaging property allow us to consider por-Si NPs as a potential agent for application in as-called cancer theranostics, that is, simultaneously therapy and diagnostics [89,90]. Note, the biological effect of photoexcited nc-Si can be related with both the photosensitized (1) O2 other active forms of oxygen, for example, superoxide (O  2 ion), whose signature was observed as spectral features of the exciton PL quenching at 2.0-2.2 eV [91].
While the results of fundamental studies and in vitro experiments on the (1) O2 photosensitization by nc-Si seem to be promising, there is a lack of in vivo tests to assess the real potential of nc-Si for PDT applications. Note, the biocompatibility and biodegradability of nc-Si and por-Si NPs [92,93] together with the photosensitization ability are well satisfied to the modern requirements for PDT application [94]. Besides nc-Si prepared from por-Si [87][88][89][90] the photosensitizing property was also reported for nc-Si prepared by laser ablation of bulk Si in water [86]. This finding indicates a possible way to obtain nc-Si, which can at as stable and efficient photosensitizers for the cancer theranostics [3].

Si NPs with Electron Spin Centers as Potential Contrast Agents for 1 H MRI
Si NPs with a high number of the electron spin centers can act as contrast agents (CAs) for the conventional biomedical MRI at the proton ( 1 H) frequency [95]. The MRI contrast property of Si NPs was explained by considering the magnetic dipole-dipole interaction between electron spins on the Si NP's surfaces and those of surrounding protons [96] as schematically shown in Figure 36. While a solid NP itself can increase the proton spin relaxation (Figure 36a), Si NPs especially prepared from por-Si provide additional opportunities to increase the spin center density due to huge specific surface area of small nc-Si [62]. While por-Si usually contains numerous paramagnetic centers as Si dangling bonds (Si DBs) and their number can be significantly increased by physical and chemical treatments [77]. It was shown that Si NPs prepared from por-Si subjected to thermal annealing (TA) in vacuum could contain a lot of paramagnetic centers, which strongly enhanced the proton spin relaxation of water molecules surrounding those NPs (Figure 36b). It is well known that surface of electrochemically prepared por-Si is passivated by hydrogen atoms [77]. Because the TA treatment induces the hydrogen desorption from the NP's surface followed by creation of new Si DBs, which can be quantitatively detected by EPR technique [77]. Tailoring of the paramagnetic center number in Si NPs is a possible way to improve their CA properties for MRI applications [96].   Figure 37 shows typical transients of the longitudinal (left) and transverse (right) proton magnetizations in aqueous suspensions of NPs (mean size~100 nm) prepared from mesoporous (MPSi), microporous (µPSi) and from c-Si wafers by using high-energy ball milling of the corresponding bulk samples [96]. The MRI contrasting is caused by shortening of the relaxation times of protons in surrounding water molecules (see Figure 38). Table 1 presents data on the Si DB density and proton relaxation times for several types of Si NPs. The sample of c-Si NPs does not cause significant proton relaxation despite they have high paramagnetic centers concentration. Indeed, the surface area c-Si NPs is rather low and most of the centers are located deeply inside the NPs. NPs prepared from both MPSi and ∝PSi demonstrate significant T 2 shortening. Pore sizes are different in µPSi (≤2 nm) and MPSi (2 nm to 50 nm) that means a bigger surface area for µPSi and a stronger interaction of water molecules with the surface of NPs.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 36 of 47 Figure 37 shows typical transients of the longitudinal (left) and transverse (right) proton magnetizations in aqueous suspensions of NPs ( mean size ~100 nm) prepared from mesoporous (MPSi), microporous (µPSi) and from c-Si wafers by using high-energy ball milling of the corresponding bulk samples [96]. The MRI contrasting is caused by shortening of the relaxation times of protons in surrounding water molecules (see Figure 38). Table 1 presents data on the Si DB density and proton relaxation times for several types of Si NPs. The sample of c-Si NPs does not cause significant proton relaxation despite they have high paramagnetic centers concentration. Indeed, the surface area c-Si NPs is rather low and most of the centers are located deeply inside the NPs. NPs prepared from both MPSi and PSi demonstrate significant T2 shortening. Pore sizes are different in µPSi (≤ 2nm) and MPSi (2 nm to50 nm) that means a bigger surface area for PSi and a stronger interaction of water molecules with the surface of NPs.   Appl. Sci. 2020, 10, x FOR PEER REVIEW 36 of 47 Figure 37 shows typical transients of the longitudinal (left) and transverse (right) proton magnetizations in aqueous suspensions of NPs ( mean size ~100 nm) prepared from mesoporous (MPSi), microporous (µPSi) and from c-Si wafers by using high-energy ball milling of the corresponding bulk samples [96]. The MRI contrasting is caused by shortening of the relaxation times of protons in surrounding water molecules (see Figure 38). Table 1 presents data on the Si DB density and proton relaxation times for several types of Si NPs. The sample of c-Si NPs does not cause significant proton relaxation despite they have high paramagnetic centers concentration. Indeed, the surface area c-Si NPs is rather low and most of the centers are located deeply inside the NPs. NPs prepared from both MPSi and PSi demonstrate significant T2 shortening. Pore sizes are different in µPSi (≤ 2nm) and MPSi (2 nm to50 nm) that means a bigger surface area for PSi and a stronger interaction of water molecules with the surface of NPs.    The EPR spectroscopy can be used to clarify both the origin of electron spin centers and to measure their concentration in Si NPs after TA. Figure 38a shows EPR spectra of µPSi NPs before and after TA. The both spectra have the effective g-factor of about 2.005, which can be explained by superposition of several types of Si DBs [96], for example, P b -centers with differently coordinated Si and O atoms [97,98]. The number of Si DBs after TA increases due to thermally induced desorption of hydrogen from the internal surface of µPsi. Despite the concentration of DBs after TA increased by a factor of 10, the T 2 relaxation time decreases only by 3 times (Figure 38b). This discrepancy can be explained by a partial passivation of Si DBs by water molecules [96]. While TA in vacuum can induce a lot of new DBs in por-Si [77], the DB concentration decreases strongly in MPSi after thermal oxidation (TO) in air at 900 • C. This effect is explained by passivation of Si DBs due to formation of a thin layer of the thermal oxide [96].
The transverse proton relaxation rate induced by Si NPs can be defined as follows [96]: where T NP 2 is the time of transverse relaxation due to the presence of NPs, T 2 is the measured transverse relaxation time and T W 2 is the transverse relaxation time in pure water. Figure 39 shows that R 2 depends almost linearly on concentration of as-prepared MPSi NPs and those after TO. The latter NPs are characterized by nearly 3 times lower concentration of paramagnetic centers in comparison to the as-prepared ones (see Table 1), what causes 3 times lower R 2 in the whole range of the NP concentration (see Figure 39). This fact indicates that both types of NPs do not aggregate in highly concentrated suspensions and the pores are still open to ensure access of water molecules.
Si NP based CAs can be characterized by their specific relaxation efficiency, that is, relaxivity, which is defined as the change in relaxation rate after addition of CAs, divided to the concentration of NPs [95,96]. The transverse proton relaxivity can be given by the following expression: where R 2 is the proton relaxation rate governed by Si NPs, C NP is the concentration of NPs in suspensions.
those after TO. The latter NPs are characterized by nearly 3 times lower concentration of paramagnetic centers in comparison to the as-prepared ones (see Table 1), what causes 3 times lower R2 in the whole range of the NP concentration (see Figure 39).This fact indicates that both types of NPs do not aggregate in highly concentrated suspensions and the pores are still open to ensure access of water molecules  The transverse relaxivity r 2 ≈ 0.5 L/(gs) was determined for µPSi NPs after TA that resulted in the large number of electron spin centers~10 17 g −1 [96]. The corresponding maximal relaxivity normalized on the number of Si atoms in NPs is about 0.01 L/(mMs) that is smaller than for the standard CAs based on Gd 3+ ions, which is about 4-6 L/(mMs) [99]. Note, the relaxivity of superparamagnetic iron oxide NPs is reported to be up to 10 2 -10 3 L/(mMs) [100]. However, specially designed porous Si NPs with required number of electron spin centers seem to be considered as potential CAs for biomedical application in MRI [96].
In order to improve the 1 H MRI contrasting property of Si NPs, one can use nanocomposite NPs with iron oxide [101]. Such composite Si NPs are prepared by arc-discharge plasma-assisted method in a closed-cycle inert gas (Ar or N 2 ) ambient at atmospheric pressure. The process consists of evaporation of high purity polycrystalline Si powder with addition of metallic iron powder at temperature of about 5500 • C followed with condensation of the vapor mixture in a cooling gas stream to form polycrystalline powder with mean size of nc-Si of about 20-30 nm confirmed by XRD measurements. Despite the relatively small nanocrystal size the prepared NPs after dispersing them in aqueous media exhibit several times larger hydrodynamic sizes detected by using a DLS method (see Table 2) that indicates either polycrystalline structure of these NPs or/and their aggregation in aqueous medium [101]. EPR spectra of Si NPs with iron oxide impurities (see Figure 40) consist of a broad band with effective g-factor ≈ 2.1 related to strongly interacting Fe 3+ ions in γ-Fe 2 O 3 [102] and a narrow line with g-factor of 2.0055, which can be assigned to Si DBs as P b -centers [97]. The larger iron concentration in the samples the stronger broadening of the corresponding EPR band due to increasing the spatially inhomogeneous interactions between Fe 3+ ions. As for the second line of intrinsic Si DBs they are supposed to be localized in SiO 2 surface coating of the NP surfaces, which was confirmed by X-ray photoelectron spectroscopy and FTIR measurements [101]. Furthermore, HR-TEM images of iron doped Si NPs reveal numerous defects of the crystalline structure as twins and grain boundaries related to the fast cooling rate during their formation in argon flow [103]. Both the iron impurities and intrinsic defects as Si DBs are responsible for the large number of electron spin centers in such NPs [101,103]. The total concentration of electron spin centers in Si NPs approaches 10 18 spin/g [101] that makes this type of NPs to be efficient for shortening the proton spin relaxation in aqueous media as it was already demonstrated for porous Si NPs (see Figure 36). In fact, both the longitudinal and transverse relaxation times of protons in aqueous suspensions of plasma-ablated Si NPs were found to be dependent on iron content [101]. The stronger decrease of the transverse proton relaxation was detected for the samples with higher iron content up to 0.2 at%. MRI experiments with phantoms showed that the latter NPs exhibited properties of efficient CAs for the 1 H MRI. The maximal transverse relaxivity accounted 7.3 L/(gs). The latter value corresponds to the molar relaxivity of about 200 L/(mMs) [101], which is close to that reported for CAs based on superparamagnetic iron oxide NPs [100].
The CA property of plasma-ablated Si NPs with iron oxide impurity was confirmed by experiments in vivo [101]. The experiments were carried out with grafted cancer tumor (lung carcinoma 3LL). In vivo MRI visualization of mice with tumor was carried out by using a protocol, which included the following steps: (i) obtaining whole body PD-weighted MRI before injection the NP suspension; (ii) obtaining whole body PD-weighted MRI 20 min after intratumorally injection of 0.5 mL suspension of Si NPs with concentration of 0.5 mg/mL. It was found that tumor area with injected NPs became darker and have more clear boundaries (see Figure 41). The MRI study of the mice for the time period of 24 h after injection of Si NPs showed a decrease of the MRI contrast. This fact can be explained by biodegradation of Si NPs similarly to that of pure Si NPs [101]. The total concentration of electron spin centers in Si NPs approaches 10 18 spin/g [101] that makes this type of NPs to be efficient for shortening the proton spin relaxation in aqueous media as it was already demonstrated for porous Si NPs (see Figure 36). In fact, both the longitudinal and transverse relaxation times of protons in aqueous suspensions of plasma-ablated Si NPs were found to be dependent on iron content [101]. The stronger decrease of the transverse proton relaxation was detected for the samples with higher iron content up to 0.2 at%. MRI experiments with phantoms showed that the latter NPs exhibited properties of efficient CAs for the 1 H MRI. The maximal transverse relaxivity accounted 7.3 L/(gs). The latter value corresponds to the molar relaxivity of about 200 L/(mMs) [101], which is close to that reported for CAs based on superparamagnetic iron oxide NPs [100].
The CA property of plasma-ablated Si NPs with iron oxide impurity was confirmed by experiments in vivo [101]. The experiments were carried out with grafted cancer tumor (lung carcinoma 3LL). In vivo MRI visualization of mice with tumor was carried out by using a protocol, which included the following steps: (i) obtaining whole body PD-weighted MRI before injection the NP suspension; (ii) obtaining whole body PD-weighted MRI 20 min after intratumorally injection of 0.5 mL suspension of Si NPs with concentration of 0.5 mg/mL. It was found that tumor area with injected NPs became darker and have more clear boundaries (see Figure 41). The MRI study of the mice for the time period of 24 h after injection of Si NPs showed a decrease of the MRI contrast. This fact can be explained by biodegradation of Si NPs similarly to that of pure Si NPs [101].
Moreover, aqueous suspensions of Si NPs were explored as efficient sensitizers of electromagnetic radiofrequency (RF) hyperthermia, which is a prospective approach for mild cancer therapy with non-magnetic Si NPs. In Reference [101] the stronger heating rate was reported for iron-doped Si NPs with hydrodynamic size~50 nm (see Table 2). The obtained results indicate possible ways for applications of Si-based NPs in the MRI diagnostics and RF therapy of cancer, that is, theranostics. Additional promises in biomedical applications of Si NPs can arise from multinuclear MRI diagnostics by using both the standard 1 H mode and hyperpolarized 29 Si NPs/MPs (see Section 2) as well as other NPs with conventional biomedical nuclei, for example, 13 C, 19 F and so forth (see, for example, Reference [104]).
Besides the MRI diagnostic modality, it was recently demonstrated the possibility to use Si NPs with iron impurities to suppress the cancer tumor growth in vivo [103]. The intratumoral injection and intravenous administration of iron-doped Si NPs resulted in a decrease of the tumor volume by 32% and 23%, respectively. While the intratumoral injection induces the stronger antitumor effect, the observed decrease in tumor volume after intravenous administration confirms accumulation of Si NPs in the tumor due to as-called enhanced permeability and retention effect, which is well known for various NPs [105]. It was found that the antitumor effect of iron-doped Si NPs correlate with lifetime of laboratory animals [103]. Figure 42 shows temporal dependences of the number of mice with cancer tumor after intravenous and intratumoral administration of NPs. The average lifetime of laboratory animals of the experimental group was about 30% longer than for the control one. The observed antitumor effect of iron-doped Si NPs can be related to dissolution of Si NPs accumulated in tumor followed with release of iron ions, which induce reactive oxygen species with high toxicity for cancer cells [103]. Moreover, aqueous suspensions of Si NPs were explored as efficient sensitizers of electromagnetic radiofrequency (RF) hyperthermia, which is a prospective approach for mild cancer therapy with non-magnetic Si NPs. In Reference [101] the stronger heating rate was reported for irondoped Si NPs with hydrodynamic size~50 nm (see Table 2). The obtained results indicate possible ways for applications of Si-based NPs in the MRI diagnostics and RF therapy of cancer, that is, theranostics. Additional promises in biomedical applications of Si NPs can arise from multinuclear MRI diagnostics by using both the standard 1 H mode and hyperpolarized 29 Si NPs/MPs (see Section 2) as well as other NPs with conventional biomedical nuclei, for example, 13 C, 19 F and so forth (see, for example, Reference [104]).
Besides the MRI diagnostic modality, it was recently demonstrated the possibility to use Si NPs with iron impurities to suppress the cancer tumor growth in vivo [103]. The intratumoral injection and intravenous administration of iron-doped Si NPs resulted in a decrease of the tumor volume by 32% and 23%, respectively. While the intratumoral injection induces the stronger antitumor effect, the observed decrease in tumor volume after intravenous administration confirms accumulation of Si NPs in the tumor due to as-called enhanced permeability and retention effect, which is well known for various NPs [105]. It was found that the antitumor effect of iron-doped Si NPs correlate with lifetime of laboratory animals [103]. Figure 42 shows temporal dependences of the number of mice with cancer tumor after intravenous and intratumoral administration of NPs. The average lifetime of laboratory animals of the experimental group was about 30% longer than for the control one. The observed antitumor effect of iron-doped Si NPs can be related to dissolution of Si NPs accumulated in tumor followed with release of iron ions, which induce reactive oxygen species with high toxicity for cancer cells [103].

Summary and Outlook
Spin-dependent phenomena in semiconductor NPs are overviewed starting from the basic properties of solid-state semiconductor systems, which depend on preferential orientation of electron and nuclear spins therein, to the recent advances in the development and characterization of semiconductor (mainly, silicon) NPs with spin-dependent properties that are promising for versatile biomedical applications.
A challenging task to control the nuclear-spin polarization in solids has been successfully

Summary and Outlook
Spin-dependent phenomena in semiconductor NPs are overviewed starting from the basic properties of solid-state semiconductor systems, which depend on preferential orientation of electron and nuclear spins therein, to the recent advances in the development and characterization of semiconductor (mainly, silicon) NPs with spin-dependent properties that are promising for versatile biomedical applications.
A challenging task to control the nuclear-spin polarization in solids has been successfully accomplished in the pioneering work by G. Lampel on the DNP by optical pumping in c-Si. The hyperfine dipolar interaction between the electron and nuclear spins caused an appreciable polarization of the nuclear spins due to the optically induced saturation of the electron spins. Starting from then, the role of the hyperfine interaction was carefully explored to realize the hyperpolarized nuclear states in semiconductor NPs and compound MPs. The hyperpolarization efficiency of 29 Si was found to depend on the nuclear relaxation time controlled by the density of electron spins. The nuclear longitudinal relaxation time was shown to shorten with increasing the charge-carrier concentration in semiconductor. The nuclear-spin relaxation in Si NPs underwent a strong shortening with decreasing the mean size of NPs, while surface-passivated Si NPs exhibited the relaxation time from 10 2 s to 10 3 s. In contrast to the nuclear relaxation, the spatial confinement of charge carriers (electrons and holes) in nanostructures significantly increased the electron spin-lattice relaxation time. A transition from itinerant to fully-localized electrons, while inducing hyperfine dephasing, was beneficial in quenching the electron spin-lattice relaxation. The phenomenon of DNP of 29 Si in Si NPs and compound MPs was shown to open fascinating prospects for creation of new efficient contrast agents for MRI. The most efficient DNP was achieved for Si MPs, which consisted of hundreds of nanometer-size NPs, what ensured the optimal ratio between nuclear polarization/depolarization as it was confirmed by experiments in vivo.
Besides the nuclear polarization, the electron-spin related phenomena were shown to be very promising for MRI applications. The experimental results confirmed a key role of unpaired electron spins as Si DBs in porous Si MPs and NPs for the enhancement of the proton spin relaxation in aqueous suspensions. The samples of nonporous crystalline Si NPs exhibited a relatively weak decrease of both longitudinal and transverse relaxation times because of low efficiency of the interaction of their unpaired electron spins with proton spins in surrounding water molecules. On the one hand, the thermally oxidized mesoporous Si NPs did not induce a valuable rate of the proton-spin relaxation due to the low density of Si DBs. On the other hand, the vacuum annealed microporous Si NPs exhibited a strong decrease of the relaxation times, especially the transverse one by 2 to 3 times for the NP concentration of the order of 1 mg/mL. The transverse relaxation rate was found to depend nearly linearly on the concentration of porous Si NPs in suspensions ranging from 0.1 to 20 g/L. The relaxation rate induced by porous Si NPs was approximately proportional to the number of Si DBs on their surfaces, what indicated a way to enhance the proton relaxation via the interaction with unpaired localized electron spins of Si NPs. The transverse specific relaxation rate (relaxivity) of thermally annealed microporous Si NPs is estimated to be 0.5 L/(gs) and for plasma-ablated Si NPs with 0.2 at% of iron oxide the corresponding relaxivity is of the order of 10 L/(gs), which is already promising for MRI applications. The relaxivity of Si NPs can be further improved by using physical and chemical treatments, which will lead to increasing the number of paramagnetic centers in Si NPs that ensures further progress in the design and validation of those NPs as contrast agents for MRI. It is worth noting that both the 1 H MRI contrast properties of Si NPs and their hyperpolarizing properties allow us to consider such NPs as binuclear CAs, which are simultaneously detected at the proton and 29 Si frequencies, what is a promising direction in MRI.
In addition to the diagnostic modality of the spin-dependent properties of Si NPs, it was found that the triplet excitons confined in Si NPs of sizes below 10 nm could transfer their energy to molecular oxygen that resulted in generation of highly chemically reactive singlet oxygen promising for the photodynamic therapy of cancer. The energy-transfer process depended on the magnetic field that indicated the spin-related origin of the singlet-oxygen photosensitization. The photosensitizing properties of NPs made from porous Si were tested in experiments with photoinduced destruction of cancer cells in vitro. Further experiments are ongoing to advance Si-NP-based contrast agents for clinical applications in both the MRI diagnostics and the mild therapy of cancer.