Doped and Codoped Silicon Nanocrystals: the Role of Surfaces and Interfaces

Si nanocrystals have been extensively studied because of their novel properties and their potential applications in electronic, optoelectronic, photovoltaic, thermoelectric and biological devices. These new properties are achieved through the combination of the quantum confinement of carriers and the strong influence of surface chemistry. As in the case of bulk Si the tuning of the electronic, optical and transport properties is related to the possibility of doping, in a controlled way, the nanocrystals. This is a big challenge since several studies have revealed that doping in Si nanocrystals differs from the one of the bulk. Theory and experiments have underlined that doping and codoping are influenced by a large number of parameters such as size, shape, passivation and chemical environment of the silicon nanocrystals. However, the connection between these parameters and dopant localization as well as the occurrence of self-purification effects are still not clear. In this review we summarize the latest progress in this fascinating research field considering free-standing and matrix-embedded Si nanocrystals both from the theoretical and experimental point of view, with special attention given to the results obtained by ab-initio calculations and to size-, surface- and interface-induced effects.


Introduction
Silicon has become the most studied material in the past decades owing to its unique characteristics: Si is the second most abundant element (after oxygen) in the Earths crust, making up 25.7% of its mass; it can be produced with impurity levels of less than 10 −9 ; it remains a semiconductor at higher temperatures than germanium; its native oxide is easily grown in a furnace and forms a better semiconductor/insulator interface than any other material. Silicon is not only easy to handle and fairly simple to manufacture but it is also cheap. Moreover it shows excellent electrical properties, high stability, optimal thermal characteristics and high mechanical strength. For these motives, this environmental friendly material is the most used element in semiconductor industry and, today, it represents the electronic material per excellence. It is also commonly used for solar or photovoltaic applications and its role in the optoelectronic industry is becoming more and more important.
However, the rapid evolution in the electronic, optoelectronic and photovoltaic sectors is facing severe constrictions due to the actual physical limits of Si-based technologies [1,2,3]. Some examples are: i) the limitations in the operating speed of microelectronic devices due to interconnects, ii) bulk Si is an indirect band-gap material which emits in the infrared region with very low efficiency, iii) radiative recombination times in Si are very large, so the de-excitation dynamics are strongly affected by the occurrence of fast non-radiative recombinations mechanisms, iv) bulk Si shows a significant free carrier absorption and Auger recombination rates which impede population inversion and, hence, optical gain, v) its band gap impedes fully exploitation of solar radiation in photovoltaic applications, vi) the absence of a bulk second-order dipolar nonlinear optical susceptibility due to the bulk crystal centrosymmetry, that do not permit to use bulk Si in order to produce a wide variety of wavelengths from an optical pump.
The increasing demand for new, innovative and more efficient devices has driven scientists to explore new functionalities in Si-based materials. In photonics the main interest lies in the possibility to merge electronics and photonics on the same chip and therefore to render Si a good light emitter. Moreover the introduction of second-order nonlinearity by proper material engineering would be highly desirable, because the all-optical data management requires nonlinear silicon photonics [4]. Finally, for photovoltaic applications we have to add to Si new features in order to maximize solar radiation harvesting and to minimize loss by thermalization processes. It has been suggested that the problems related to the indirect band-gap of bulk-Si might be overcome in highly confined systems. For example, in lowdimensional Si-based nanostructures such as porous-Si, a quantum sponge made up of Si nanostructures, nanowires (Si-NWs) and nanocrystals (Si-NCs), the possibility to achieve efficient visible photoluminescence (PL) has been demonstrated [5,6,7,8]. In these nanostructures the low-dimensionality causes the zone folding of the conduction band minimum of bulk Si, that is located near the X-point, thus introducing a quasi-direct band gap. Moreover the quantum confinement (QC) effect associated with the reduced size of the nanosystems enlarges the energy band gap enabling light emission in the visible range [9]. This effect can also enhance the spatial localization of electron (e) and hole (h) wave functions and their overlap, and therefore the probability of e-h recombination (see Fig. 1).
Among the different Si-based nanostructures, Si-NCs have attracted, from the beginning, much interest because they exhibit very bright visible PL (see Fig. 1), which is tunable with respect to the dimension of the Si-NCs [10], and sample dependent high quantum yields, ranging from 1% up to 60%. The quantum yields can be enhanced by careful surface passivation and by avoiding oxygen contamination during all stages of the Si-NC preparation [11]. Moreover optical gain in Si-NCs has been successfully observed and discussed [12,13,14,15,16,17,18,19] as well as giant Raman gain [20,21]. Finally carrier multiplication effects in excited carrier dynamics after the absorption of a single high-energy photon have been observed in ensemble of Si-NCs, proving thus the possibility of better exploiting processes of photo-generated carriers to increase solar cell performances [22,23,24,25,26,27,28,29]. Reprinted with permission from Ref. [9]. Left: PL spectra of Si-NCs embedded in SiO 2 thin films at room temperature. The average diameters are changed from about 9 to 2.5 nm.
Visible PL in Si nanostructures has been attributed to transition between states localized inside the Si-NC [51,52,53,54], or between defects and/or interface states [55,56,57,58,59,60]. Despite the discussion on which of the above mechanisms primarily determines the emission energy is still open, recent results seem to indicate the coexistence of both the effects, whose relevance depends on the structural properties of the sample [55,56,61,62,63,64,65,66,67,68,69,70,71]. In particular, it was suggested that for diameters above a certain threshold (from about 3 nm up to diameters of the order of two times the bulk Si exciton Bohr radius, about 9 nm) the emission peak of the Si-NCs simply follows the QC model, while interface states assume a crucial role only for small-sized Si-NCs (less than 3 nm) [69,72,73,74].
It is well known that an additional degree of freedom in semiconductor materials design is given by the introduction of impurities. Controlled doping is at the heart of the modern Si-based semiconductor industry. The best known example is the p-n junction. Here elements of the column III and V, like the B and P atoms, are used to electrically dope the Si by introducing positive holes or negative electrons. The presence of the doping atoms changes remarkably the optical and electronic properties of the hosting material. B and P impurities introduce very shallow levels in the band gap of bulk Si, above the valence band and below the conduction band, than can be efficently ionized at room temperature increasing dramatically the conductivity of bulk Si.
Doping in Si-NCs, as in bulk semiconductor devices, can be used to alter in a controllable way the electronic, optical and transport properties of nanomaterials. As a consequence, intentional doping with n-and p-type impurities can be exploited to design and realize novel devices based on Si-NCs. 6 The possibility of enhancing the electrical conductivity of nanosized systems has been attempted, for instance, by obtaining porous Si from n-or p-doped bulk Si by means of an electrochemical etching [75]. Nevertheless, even for the larger mesoporous samples, a very low conductivity was measured, despite the fact that the etching process does not remove the impurities from the system [76]. This suggests that the ionization of the impurities at room temperature may be strongly quenched with respect to the bulk. Therefore the possibility of generating free charge carriers from impurity states can be limited by size effects.
Regarding the optical properties, the introduction in the Si-NC of an isoelectronic impurity can circumvent the indirect gap behavior of bulk Si. However Si does not possess proper isoelectronic impurities that can strongly localize excitons at room temperature and enhance the PL intensity. An alternative approach is given by codoping. i.e. the formation of Si nanocrystals with the same number of n-and p-type impurities [77]. The first attempts to dope Si-NCs started about 20 years ago. The results obtained revealed that doped Si-NCs showed different properties with respect to the doped Si-bulk [78,79]. For example a shallow impurity level in bulk may become a deep level at the nanoscale. In bulk Si the level of doping lies in the interval 10 13 -10 18 cm −3 . In a Si-NC of about 2 nm in diameter, which possess more than 200 Si atoms, the introduction of a single impurity atom corresponds to a doping level of about 10 20 cm −3 , that is a quite different situation. Despite the large number of works dedicated to the study of doped and codoped Si-NCs, important issues still exist.
The effective dopant location (within the nanocrystals, at their surface-interface, or in the surrounding matrix?), the occurrence of self-purifications effects (that is the tendency of the Si-NC to expel the dopant atoms to its surface) as well as the role played by the chemical environmental of the Si-NC are issues not yet solved by the scientific community [76,78,79,80,81,82,83,84,85,86,87].
Experimentally, several factors contribute to make the interpretation of the measurements on these systems a difficult task. First of all, independently on the fabrication technique, in experimental samples there aren't two identical Si-NCs. For instance, samples show a strong dispersion in the Si-NC size, that is difficult to determine. In this case it is possible that the observed quantity does not correspond exactly to the mean size but instead to the most responsive Si-NCs [88]. Moreover, Si-NCs synthesized by different techniques often show different properties in size, shape and in the interface structure. Finally, in solid nanocrystal arrays some collective effects caused by electron, photon, and phonon transfer between Si-NCs can render more complicated the interpretation of the experimental results.
The aim of this review is to summarize the latest progress in the fascinating research field related to the understanding of the doping in Si-NCs with n-and p-type impurities. It should be pointed out that in these last few years some review articles on this topic have been published [41,78,79,89,90]. At variance with these reviews, since the role of theoretical modelings and simulations has becomed more an more important, we will give particular attention to the theoretical outcomes. Moreover we will focus our attention not only on single doped Si-NCs but also on compensated codoped Si-NCs, a very interesting and rapidly growing field. Mainly, we will consider B and P as dopant atoms due to their high solid solubility in silicon and because they are the most commonly used impurities in experiments.
In this work we will use the notation "doped Si-NCs" to indicate systems where B and/or P atoms are incorporated in Si-NCs. However, in principle, it would be better to speak about impurity atoms in the case of simple incorporation and of dopants in the case of activated impurities. Nevertheless in line with the use in the literature we will adopt the term dopant; it will be clear from the discussion the real meaning of this term.
The review is organized as follows. First, in section 2 we will sketch the abinitio models used for the calculations of the structural, electronic and optical properties of the nanostructures. In section 3 we will review the experimental results regarding doped free-standing Si-NCs, with particular focus on the theoretical outcomes (see subsections 3.1 and 3.2). Section 4 is instead devoted to the discussion of the properties of matrix-embedded doped Si-NCs; a subsection 8 Figure 2: (Color online) Scheme of the three processes described in the text: (a) ground state, described by DFT,(b) photoemission experiment (charged excitation) described by GW, (c) absorption experiment (neutral excitation) described by Bethe-Salpeter equation and/or by Time Dependent DFT. Reprinted with permission from Ref. [19] . is dedicated to the theoretical results (subsection 4.1). Transport is discussed in section 5, whereas section 6 is entirely devoted to the study of codoped compensated Si-NCs. Conclusions are presented in section 7.

Theoretical Modelling
The structural, electronic and optical properties of complex systems are nowadays accessible, thanks to the impressive development of theoretical approaches and to the availability of High-Performance Computing platforms. Surfaces, nanostructures, and even biological systems can now be studied within ab-initio methods [19,87]. In principle, within the Born-Oppenheimer approximation to decouple the ionic and electronic dynamic, the equation that governs systems of strongly interacting particles is the Many-Body (MB) equation whose solution is a formidable task. Among all, the single-particle Density Functional Theory (DFT) is one of the most popular methods to study ground state properties of systems of interacting particles. This approach allows to map an interacting quantum MB system into a fictitious system of non-interacting particles.
The Green function approach, instead, permits to calculate the excitations of a system of interacting particles by mapping the MB electronic problem into a problem of weakly interacting quasi-particles, where the quasi-particle describes the particle plus its screened interaction with the rest of the system. Fig. 2 shows some schemes used to calculate ground state properties, band structures, and optical spectra: DFT for ground state properties, GW for band structure calculations (charged excitations), and the Bethe-Salpeter equation (BSE) and the time dependent (TD) DFT approaches for optical spectra (neutral excitations).
Concerning DFT, it is worth noting that the Kohn-Sham (KS) equations, on which the method is based, represent a fictitious auxiliary system with no physical meaning. Nevertheless, their eigenvalues are often interpreted as oneelectron excitation energies corresponding to the excitation spectra of the system upon removal or addition of an electron, and DFT is in this way used to calculate band structures. The qualitative agreement with experiments is often remarkable. The quantitative agreement, instead, depends on the approximations used to describe the exchange-correlation energy in the KS equations. The most used approximations, named local density approximation (LDA) and generalised gradient approximation (GGA), lead to a systematic underestimation of the semiconductor energy gap. This fact can be overcomed by computing quasiparticle energies within the GW scheme. This approach represents the most refined method for the band structure calculation of solids, surfaces, nanostructures and for the determination of the energy levels of molecules and atoms.
GW well describes direct and inverse photoemission spectroscopies (see panel b of Fig. 2), where the final state is a charged system since one electron have been removed or add to the system, but fails to describe optical excitations. A correct description of optical spectra (see panel c of Fig. 2) for both free-standing and embedded Si-NCs requires an appropriate treatment of the local field effects [72,73] and an exhaustive calculation of the electron-hole interaction, that can be obtained by solving the BSE within the Many-Body Perturbation Theory (MBPT) [91].
In the DFT+MBPT approach, therefore, a detailed estimation of the optoelectronic properties of a system requires: (i) the optimization of the atomic positions obtained by minimizing the interatomic forces on each atom without any symmetry constraint, (ii) the calculation of the Kohn-Sham states and energies, (iii) the inclusion of quasiparticle corrections withing the GW approximation and (iv) the resolution of the excitonic Hamiltonian, for instance using the BSE approach.
It is now a widespread belief among the nanoscience research community that ab-initio approaches constitute a unique and very powerful instrument to control and design the properties of novel materials and devices with an accuracy that complements experimental observations [91].
In the next sections we will review, together with experimental outcomes, theoretical results regarding both free-standing (Section 3) and matrix-embedded doped Si-NCs (Section 4) with particular attention to the determination of formation energies and self-purification effects, the electronic and optical properties, the role of the Si-NC surfaces and interface terminations. Most of the presented results habe been obtained within the DFT using the LDA for the exchange-correlation energy. As previously pointed out, this approximation leads to an underestimation of semiconductor energy gaps. Nevertheless the results obtained through LDA are interesting for several reasons: i) the inclusion of MB effects is very computationally demanding and thus limited to very small nanocrystals [92], ii) an almost complete compensation of self-energy and excitonic effects [68,93,94] has been observed in silicon based nanostructures, thus rendering the LDA based optoelectronic outcomes useful, iii) often scientists are interested in trends and trends will remain similar on going from the independent-particle approximation to the many-body approach. Reprinted with permission from Ref. [30].

Free-standing Nanocrystals
Free-standing Si-NCs are attractive due to the possible fabrication of large area optoelectronic devices by vacuum-free printable processes and for their use in biological applications. Researchers have employed several methods to obtain free-standing Si-NCs, among these we note laser pirolysis [95] and thermal dissociation [96,97,98], laser ablation [99], plasma synthesis [100], liquid [101] and solid phase synthesis [102]. Several excellent reviews about different routes utilized to synthetize free-standing Si-NCs are appeared [41,103,104,105,106]. Figure 3 shows an overview of the steps usually followed for the generation of free-standing Si-NCs. Through these techniques is possible to have a good control of the Si-NCs size and shape [104] and to synthetize high quality Si-NCs [107] with PL peaks spanning the entire visible spectrum [108,109] and with a high quantum yield up to 60% [11]. The surface of the Si-NCs can be covered by different species and functional groups [30,104]. Dasog et al. [109], for instance, have synthetized colloidal Si-NCs of 3-4 nm in diameter functionalized with alkyl, amine, phosphine, and acetal functional groups. They proved that the PL of the Si-NCs can be effectively tuned across the entire visible spectral region without changing particle size, thus elucidating the role of surface termination. Doped Si-NCs with diameter down to 3 nm have been synthetized using different strategies [89,90,110,111,112,113]. Among all, Fujii and coworkers developed an efficient procedure [114,115,116,117,118,119,120] where Si, SiO 2 , P 2 O 5 or B 2 O 3 were simultaneously sputter-deposited and then annealed in N 2 gas atmosphere. During annealing the B-or P-doped Si-NCs were grown in borosilicate (BSG) or phosphosilicate (PSG), i. e. B-or P-doped silica, glass matrices. Then the Si-rich BSG or PSG films were peeled from the plates and annealed in a N 2 gas atmosphere to obtain Si-NCs embedded in BSG or PSG matrices. To isolate Si-NCs from the matrices, these films were dissolved in HF solution in ultrasonic bath. This process led to a HF solution containing isolated Si-NCs, that were separated from the solution by centrifugation obtaining in the concentrator a Si-NC powder. Methanol was then added to disperse the Si-NCs.
Resuming the experimental information (see Fig. 4 and   Si-NCs that have been exposed to air for 5 days. Solid lines result from linear fits to the data. Reprinted with permission from Ref. [110]. Bottom Left Panel: PL spectra from assynthesized intrinsic B-doped Si-NCs (solid lines) and the same Si-NCs after five-days exposure to air at room temperature (dashed lines). The B-doped Si-NCs are labeled according to the B atomic concentrations. The intensity of PL from as-synthetised Si-NCs with B concentrations of 0.25 % and 0.34 % is magnified by a factor 15. Reprinted with permission from Ref. [110].
Bottom Right Panel: PL spectra from as-synthesized intrinsic P-doped Si-NCs (solid lines) and the same Si-NCs after five-days exposure to air at room temperature (dashed lines). The P-doped Si-NCs are labeled according to the P atomic concentrations. The intensity of PL from as-synthetised Si-NCs with P concentrations of 1.9 % and 5.6 % is magnified by a factor 3. Reprinted with permission from Ref. [110]  atoms are green balls and P atoms red balls. Reprinted with permission from Ref. [129]. 123,133,135] even if only a small part of the dopants are activated [135,136,137]. Moreover doping efficiency depends both on Si-NCs size and on Si-NCs environment [120]. For a review on the experimental results regarding doping efficiency and electrical activity of doped Si-NCs the reader is referred to Refs: [89,90]. The doped Si-NCs have a good crystallinity, showing that the lattice spacing with respect to undoped Si-NCs is not affected for P-doped Si-NCs, whereas it is slightly reduced for B-doped ones, owing to the smaller size of the B atom [114,123]  Experiments pointed out that the hyperfine splitting (HFS) shows a clear size dependence [130] and that impurities are mainly incorporated in substitutional sites [114,120,131,132,134]. Still regarding the dopant location, several studied pointed out that B atoms prefer to stay in the Si-NC core, whereas P atoms prefer to reside at the Si-NC surface [110,122,135]    From a theoretical point of view, DFT-based ab-initio calculations for freestanding Si-NCs have been performed in real space [87] or in reciprocal space [138]. The first approach doesn't show problems connected with spurious interaction between replicas of NCs. The second one, implementing a supercell approach, requires large cells (thus large vacuum regions) to prevent interactions between a NC and its image. Moreover in the case of charged systems, the reciprocal space approach requires a procedure to neutralise the background Si-NC (one follows this procedure because both EPR [134] and EDMR [131] have demonstrated that impurities are not interstitials). By taking into account only one impurity per Si-NC one can simulate a wide range of high doping concentrations, which vary approximately from 2x10 20 cm 3 (1 mol%) to 7x10 21 cm 3 (20 mol%).
Starting from a Si n H m -NC the formation energy for a neutral X impurity can be defined as the energy needed to insert the X atom with chemical potential µ X within the Si-NC after removing a Si atom, that is: where E is the total energy of the system, µ Si is the total energy per atom of bulk Si, and µ X is the total energy per atom of the impurity.  Reprinted with permission from Ref. [81]. 20 are always higher in Si-NCs than in Si bulk. Moreover, for similar radius, calculations pointed out that B incorporation cost more than P segregation, in agreement with experimental outcomes [110]. Similar results have been obtained by other authors, confirming that the effect of size is much more evident for B-doping that for P-doping. [80,84,144,145,146,147,148,149].
It was also possible to bring out the role of the relaxation with respect to that of Si-NC size (see Fig. 7). Three different sets of data were presented and discussed [81]. In the first situation (filled squares) the total energies were  with permission from Ref. [150] only ones that allow a significant atomic relaxation around the impurity, because in the other cases the surrounding Si cage is quite stable. Thus, as the B atom is moved toward the surface the formation energy decreases, making subsurface positions more stable. The preference of B to be incorporated subsurface has been experimentaly established in the case of B-doped Si-NCs passivated by deuterium [121]. The bottom of Figure (8) shows the corresponding results for a P impurity [151]. It is clear that, in this case, for Si-NCs, whose diameter is smaller than about 2 nm, P tends to substitute Si near the surface. Otherwise, the Si-NC center is the energetically most favorable position. Similar results for B and P dopants are shown in the right panel of Fig. 8 [150].
These results have been interpreted in term of a self-purification effect for the smaller Si-NCs: below a diameter of about 2 nm the impurity atoms will be energetically expelled toward the surface and will be hardly incorporated [80,83,81,144,150,152].
In particular, Chan et al. [84,152] showed that this effect can be related to However, the self-purification effects can be strongly influenced by the presence of defects, vacancies or different capping species used to saturate the dangling bonds at the interface; this fact explains the efficient incorporation of dopant atoms in small Si-NCs with diameter less than 2 nm [129,153,154,155,156].
In this context, for example, Chelikosky's group [157] showed that the mech-  VBM and CBM strongly depends on the Si-NC size [150]. Moreover, differently from the bulk, the extra hole or electron tends to remain localized near the impurity [80,82].
A more precise definition of the BE at the nanoscale is given by the impurity activation energy E act [80,81,143,167] where I and A give the Si-NC ionization energy and electron affinity, respectively, while the subscripts u and d refer to the pure (undoped) and doped system, respectively. The activation energy represents the energy required to ionize the P-doped Si-NC by removing an electron minus the energy gained by adding the electron to a pure Si-NC. Therefore, the ionization energy is given by where n is the number of electrons in a neutral P-doped Si-NC and E(n) and E(n − 1) are the total energies of the ground state for the neutral and positively charged P-doped Si-NC. The electron affinity of undoped Si-NCs is given by where E(n − 1) and E(n) are the ground state total energies of a neutral and negatively charged Si-NC, respectively. Similar equations can be derived for the B impurity.
Calculated E act for B-and P-doped Si-NCs, with dopants located at the nanocrystal center, as a function of the Si-NC size are shown in the top panel of Fig. 10. The figure shows that E act scales almost linearly with the inverse of the Si-NC radius [81], indicating that the main contribution to E act is mainly due to the almost unscreened Coulomb interaction. This is a consequence of the reduction of the screening that is observable moving to the nanoscale [168] and that also leads to a strong localization of the impurity states [80]. The calculated activation energies for P-doped Si-NCs [81] are in fair agreement with those calculated in Ref. [80] and showed in the bottom panel of Fig. 10.
Here it is interesting to note that the behavior of the activation energy is mainly due to the decrease with size of the Si-NC electronic affinity, whereas the ionization energy depends weakly on Si-NC size. It is worthwhile to note that investigations by magnetic resonance of the P hyperfine splitting in doped Si-NCs [130] showed that the donor localization is dominated by a reduction in dielectric screening for Si-NCs with radii above 6 nm, whereas for radii below 2  which means a decrease of the Si-NC size, leads to the formation of deeper impurity levels [142,150]. Moreover, differently from the bulk, the extra hole, or electron, tends to remain localized near the impurity [80,92]. The impurity level with the lower energy (spin-up or spin-down) is occupied, while the level with higher energy is not occupied. Besides, the increase of the QC induced by size reduction leads to an enhancement of the differences in energy between the spin-up and spin-down impurity-related levels.

Matrix-embedded Nanocrystals
Matrix-embedded Si-NCs offer advantages in terms of stability and low-cost manufacturability. Moreover they can be exploited to develop CMOS compatible devices and novel third-generation photovoltaic systems. Methods for the fabrication of matrix-embedded Si-NCs are the plasma enhanced chemical vapor deposition (PECVD) [179], the reactive magnetron sputtering [180], the ion implantation [181] and the formation of superlattices of alternating SiO x and SiO 2 layers (see Fig. 3, for scheme of the different techniques used) [67,182,183].
Unfortunately, the high resistivity of the embedding matrix reduces the possibility to employ such materials in applications that require a high carrier mobility.
For this reason, the possibility to introduce dopants has been explored in order to improve transport and other fundamental characteristics [78,79]. The first report of B and P doping performed during Si-NCs synthesis was due to the group of Fujii [186]. Si, SiO 2 , P 2 O 5 or B 2 O 3 were simultaneosuly sputter-deposited and then annealed in N 2 gas atmosphere. During the annealing the B-or P-doped Si-NCs were grown in BSG or PSG, i e. Bor P-doped silica, glass matrices [35,77,120,129,155,174,175,184,185,187,188,189,190,191]. The doped Si-NCs were investigated by HRTEM [185,186,189,191], Raman [186], ESR [120,174,175,192] absorption and PL spectroscopies [35,77,174,175,184,185,189,191,192], ATP and proximity histograms, that enable the visualization of the Si-NCs structure as well as of the dopant distribution with subnanometer resolution [129].
The obtained results pointed out that the presence of impurities during the synthesis affects the growth kinetics of the Si-NCs, resulting in a wide size distribution that depends on the annealing temperature and on the nature and concentration of dopants. Doped Si-NCs with a diameter ranging from 2.7 to 3.8 nm, slightly larger than the corresponding undoped Si-NCs grown using the same annealing temperature, were prepared [79]. The doped Si-NCs showed good crystallinity and were well separated from each other in the matrix. The PL spectra showed a quenching in the intensity (top center panel of Fig 12). For B doping, the quenching was found to increase with the NC size. This behavior was explained by assuming that B impurities were localized in substitutional sites in the Si-NCs and that they were responsible to promote non-radiative recombination mechanisms (Auger recombination) of trions formed by the photogenerated e-h pairs and the B-induced hole. Concerning the PL activity in P-doped systems, two opposite trends were recorded. Initially an increase in the PL intensity was detected, then, on increasing the P concentration, a decrease of the PL intensity was recorded. Also in this case this PL quenching was explained in term of Auger recombination, whereas the initial PL intensity increase was assigned to P passivation of the dangling bonds at the interface between the Si-NCs and the matrix.
In both cases, the PL spectra became broader, indicating the development of low energy features with respect to the undoped case (left panel of Fig. 12).
Optical absorption in the infrared region, was observed for P-doped Si-NCs. In this region of frequencies, absorption increases when the P concentration increase and seems to be not affected by the presence of the PSG matrix. This effect was interpreted as the consequence of intra-conduction band transitions (bottom center panel of Fig 12) induced by the presence of the impurities.
Quantum confinement of P donors in Si-NCs was evidenced through the clear dependence of the hyperfine splitting on the Si-NC size (left panel of Fig 12).
Regarding the impurity location, APT and proximity histogram [129] revealed incorporation of B and P into the Si-NCs with clear differences. The B concentration sligthly decreased on going from the matrix to the Si-NC interfaces and from the Si-NC interfaces to the NC core. The P concentration started 36 to increase about 1 nm far from the Si-NC interface, reaching a maximum in Si-NC core (see bottom panel of Fig 5).
The behavior of the PL spectra was found to be similar to those of the doped Si-NCs embedded in BSG and PSG. SIMS data suggested that the dopants were located in the silicon layer and not in the silica layer [66,193] (see Fig.   13, bottom left panel), while XPS data pointed out that B is either inside or at the surface of the Si-NCs, with a concentration equilibrium distribution of B between the Si and the SiO 2 [198] (see Fig. 13, top panel). In the case of P, the XPS spectra suggested that most of the P atoms were located in the Si layer and at the Si/SiO 2 interface [205] (see Fig. 13, bottom right panel). Even after high temperature annealing, P atoms did not tend to move into the SiO 2 layer and were better incorporated in the Si-NCs [154, 209,210]. APT and proxigram analysis were used to determine the dopants localization. Gnaser et al. [202] founded that the concentration of P was enhanced in the region of Si-NCs with a maximum at the Si/SiO 2 interface; their results seemed to indicate the occurrence of self-purifications effects. Nevertheless the incorporation of P B40 (middle curve) and B120 (bottom curve). Reprinted with permission from Ref. [198].
Bottom left panel: SIMS data of B-doped Si-NCs and SIMS data of P-doped Si-NCs, reprinted with permission from [196] and [197].

39
atoms in very small Si-NCs with diameter as small as 2 nm was demonstrated by the same group [156] (see Fig. 14). This result was confirmed by Perego et al. [153,154] that, using a combination of TEM, ToF-SIMS and XPS, showed that P atoms are definitevely incorporated within Si-NCs of diameter of the order of 2 nm. These results have been interpreted as a consequence of the favored P diffusion towards the Si-rich region (see Fig. 15).
Indeed it has been demonstrated that ion beam synthesis, which is a well known approach to grow undoped Si-NCs embedded in SiO 2 , is also an efficient technique to grow doped Si-NCs with diameters of few nanometers, if the dopants are co-implanted with Si [213,214,215]. Combining the results obtained by APT, Raman, PL and PLE analysis, the authors concluded that P impurities tend to be efficiently incorporated in the Si-NC core whereas B atoms are mainly localized at the Si-NC/SiO 2 interface (see Fig. 14, top left panel) [213,214,215].
The electrical activity of matrix-embedded doped Si-NCs, monitored by current voltage measurements, demonstrated that majority carriers, originated from substitutional P-donors, must be generated to overcome significant Pionization energies between 110 and 260 meV. In the absence of electrical fields at room temperature, however, no significant free carrier densities were detected [208].
As a consequence, it has been concluded that only a small fraction of P-atoms are in substitutional sites within the Si-NCs, while the majority of them, reside in interstitial sites. These atoms are considered to be at the origin of the PL quenching that was previoulsy assigned to the occurance of Auger recombination mechanisms [203,204,208]. Interestingly Almeida et al. [120] have studied both free and SiO 2 embedded P-doped Si-NCs using EPR spectroscopy. Their results showed that P dopant atoms are prevalently incorporated at substitutional sites and act as donors. Moreover the donor electron density decreased by several order of magnitude when matrix-embedded Si-NCs were etched by HF to remove the SiO 2 matrix and were subsequently exposed to air. Once more, these results pointed out that doping efficiency depends not only on the dopant location 40 but also on the Si-NCs environment and on the doping strategies. A marked difference in effective mobility for B-doped Si-NCs has been evidentiated in sample obtained by diffusion or by in-situ doping methods, respectively [200].
Doping after synthesis is usually made by ion implantation in Si-NCs formed in SiO 2 matrices [216,217,218,219] or delivering a controlled amount of dopant atoms from a spatially separated diffusion source [209,210,211] (see Fig. 14).
The first strategy suffers of implantation damages. The second, instead, make possible to decouple equilibrium properties from kinetics effects, thus providing, for the first time, results that can be compared directly with the theoretical predictions. These experiments show that high levels of P impurities can be introduced in the Si-NC core, trapped with a binding energy of 0.9 eV.  A different encapsulated Si-NC was obtained by Ni et al. [220,221]. Starting from the H-terminated Si 71 H 84 , they replaced H atoms with oxygens, which were then outwardly bonded by adding Si atoms. Finally, they passivated the system with H atoms to restore a fourfold coordination for all the Si atoms.

Ab-initio calculations. Formation energies and electronic properties
The final system, that is the Si 123 O 96 H 100 , represented a Si-NC covered by a 0.25-nm-thick SiO 2 shell. Effects induced by the presence of dangling bonds at the Si-SiO 2 interface were also investigated. The obtained results for the formation energies were in agreement with those of Carvalho et al. [164,165] for the fully passivated Si-SiO 2 systems: B showed a small preference for the subinterface region, whereas P clearly preferred to stay in the Si-NC core. In contrast, when dangling bonds are induced in the system, B preferred to stay at the Si/SiO 2 interface. It is important to note that the impurity formation energies are reduced on going from the H-saturated Si-NCs to the embedded ones. Moreover, electronic and optical properties still revealed the presence of deep levels in the band gap and light emission at energies smaller than the energy gap of the undoped system [220] (see Fig. 16 left panel).
Realistic calculations for Si-NCs embedded in a solid matrix were performed by Guerra et al. [166,222]. SiO 2 -embedded Si-NCs were generated starting from a 3x3x3 β-cristobalite-SiO 2 matrix (for a total of 648 atoms), by removing all the O atoms inside a sphere whose radius determines the Si-NC size. The soobtained Si-NC, embedded in the SiO 2 , presented perfectly coordinated atoms and the same Si-Si distance of β-cristobalite, corresponding to about 3.2Å.
After the relaxation, the Si/SiO 2 interface formed strongly stressed bonds, while far from the interface the bulk atomic densities were recovered [68]. Dopant impurities were introduced in a substitutional Si-site located in the Si-NC center, at the Si/SiO 2 interface, or in the SiO 2 matrix far from the Si-NC. Since the Si atoms at tn interface can be bonded to one, two or three O atoms (i.e., Si1+, Si2+, Si3+), for each structure all the possible oxidation types for the interfacial doping were considered. Each structure was fully relaxed after doping in order to include effects induced by structural rearrangements around the dopant atom.
In Fig. 16  Instead, B atoms tend to form, when placed at the interface with two O atoms, a strong antibonding with one of the neighbors, causing repulsion to a large distance [166].
Several experimental results based on atom probe tomography and proximity histograms support these tendencies. APT demonstrated that n-type dopants (P and As) are efficiently introduced in the Si-NC core, whereas p-type dopants As pointed out before, in recent works [204,208] it has been suggested, based on electronic transport measurements in P-doped Si-NCs, that the impurity atoms are located preferentially in interstitial sites. DFT calculations have been performed for P impurities in SiO 2 , in SiO 0.9 and in Si-NC/SiO 2 systems, where the SiO 0.9 and SiO 2 were simulated through transition Si-O shells capped by hydrogen. The results showed that P-atoms located in interstitial sites generate states in the fundamental gap of Si-NCs (see Fig. 17). In order to explain the observed quenching of the PL in P-doped Si-NCs, authors hypothesized the occurrence of new non-radiative recombination dynamics generated by these interstitial-P induced states, as an alternative procedure with respect the Auger recombination processes. No calculations were made about the formation energies for the P impurity in this interstitial position. It is worthwhile to note that in a recent study devoted to energetic and carrier transport properties of doped Si-NCs embedded in SiO 2 [222] it was found that P prefers to stay in the Si-NC and B at the interface, bonded to three oxygen atoms and that, in this last case, the formation energy is even lower with respect to the undoped case. Reprinted with permission from Ref. [222].

Carrier transport
In this section we will briefly analyze carrier transport in doped Si-NCs, and we will discuss how electric mobility can be used to discern the role played by the impurities.
In order to prove that impurities located in Si-NCs effectively act as dopant, it is necessary to assess their electrical activity. This can be done using, for instance, conductivity and resistivity data [40,133,134,207], current density versus electric field measurements [40,200,208,212,224], Hall mobility experiments [225] and field effect transistor analysis [136].

Codoping
The main limitation to high PL efficiency in Si-NCs is due to radiationless Auger recombination. This drawback can be circumvented by simultaneous ptype (B) and n-type (P) compensated doping of the Si-NCs [82,184,227]. In this section we will discuss the concept of impurity compensation in Si-NCs. We will show that B and P codoped compensated Si-NCs exhibit properties that strongly differ from the ones of the undoped and single doped Si-NCs. Moreover  we will prove that codoping can be exploited to tune the electronic and optical properties of Si-NCs, in a highly controllable way.
Codoped Si-NCs were firstly grown by Fujii and coworkers [184,227] using a co-sputtering method. During the annealing, the Si-NCs were grown in borophosphosilicate glass (BPSG) matrices. The evidence that impurities were located into substitutional sites of the Si-NCs was obtained through infrared absorption spectra [189] and by electron spin resonance (ESR) [184,190].
The PL spectra of the B and P codoped Si-NCs strongly differ from the ones recorded for both the single doped (B or P) and the undoped Si-NCs [184,188,191]. The codoped Si-NCs, for instance, exhibit PL energies redshifted with respect to those of the corresponding undoped Si-NCs; in particular PL peaks, originated by optical transitions between donor and acceptor states, extend from the visible range to energies below the energy gap of the bulk Si [77,184,228].
More recently the same group reported a new method to obtain B and P codoped colloidal Si-NCs, where NCs were dispersed in methanol without a surface functionalization process [115,116,117,119]. To isolate Si-NCs from BPSG matrices, the BPSG films were dissolved in HF solution in ultrasonic bath. This process produced isolated Si-NCs dispersed in solution, that were separated from the HF by centrifugation obtaining in the concentrator a Si-NC powder. Methanol was then added to disperse the Si-NCs. Even if the majority of Si-NCs were dispersed in methanol, a fraction of Si-NCs were precipitated.
These precipitates were removed by centrifugation and a supernatant liquid was obtained [116]. High resolution transmission electron microscopy (HRTEM) images showed the presence of lattice fringes corresponding to the {111} planes of a Si crystal. Moreover it proved the presence of a large number of defectedfree Si-NCs with an average diameter of about 3 nm (see Fig. 19).
An advantage of this method concerns the possibility of producing highly dispersive Si-NCs in polar solvents or water solutions of different PH, without employing organic ligands, thus permitting the use of these Si-NCs for biomedical applications [49]. Figure 20 shows a picture of a methanol solution in which  (c) PL spectra of codoped Si-NCs with different size, that is, grown at different temperatures.
The solution is very clear and light scattering by agglomerates is not seen.
The average diameter of the codoped Si-NCs can be varied from 1 to 9 nm controlling the growth temperature and the resulting PL energy peaks range from 1.85 to 0.90 eV. Since after dispersion of the Si-NCs in methanol, the position of the PL peak shifted to slightly higher energy with increasing storage time and then is stabilized, the authors concluded that the surface dangling bonds were terminated by O molecules [117].
Codoping of Si-NCs has been recently obtained also for silica embedded Si-NCs using ion implantation [228], co-sputtering [230] or using B 2 H 6 and PH 3 gases in PECVD [231]. In all these cases donor-acceptor pair recombination emission has been clearly observed. Moreover evidence of carrier multiplication were detected [230].  [82,92]. Moreover a reduction of the distance between the two impurities results in a reduction of the formation energy; its minimum is obtained when the impurities are located at the nearest neighbors positions at the surface of the Si-NCs. In these cases the formation energy assumes negative values. It is interesting to note that Nomoto et al. [129] have observed that codoping is an effective means of promoting segregation and stability of the   that differs from the one predicted by tight binding for hydrogen-type impurities in H-terminated Si-NCs [239], whereas they are in the same energy range of those calculated by ab-initio methods [82,92,240].
The reduction of Si-NC energy gap as a consequence of the simultaneous presence of B and P impurities is also confirmed by DFT calculations of the density of states (DOS) and of the absorption spectra (see Fig. 24) [177]. By comparing the calculated DOS obtained for the undoped and the codoped cases, we observe the presence of states localized in the forbidden energy region of the undoped NC, states that are originated by the presence of B and P impurities.
The energy localization of these new states (that can be experimentally detected by scanning tunneling microscopy or other techniques [241]), and therefore the resulting energy gap, depend on the NC size.
Indeed, a free-standing codoped Si-NC, the Si 85 BP(OH) 76 , was generated and studied by Guerra et al. [166]. As a first step, impurities were located by considering their preferred position in the single doped Si-NCs, that is by placing P in the centre of the Si-NC and B at the Si-NC surface. Then structural and electronic properties were investigated as a function of the impurities separation and first principle calculations (open triangle) [240]. Broken curves are acceptor and donor levels calculated by tight binding approximations [239]. Reprinted with permission from Ref. [229]. Due to the polar nature of the P-B bond, the above condition implies the formation of a static electric dipole radially directed and preferentially located at the Si-NC surface, which points toward the Si-NC center. Similar results have been obtained by Ni et al. [221]. The high stability of the dipole direction is evidenced by considering a configuration in which the codopants are switched, a B-P pair, named 1i (see Fig. 25). Quite interestingly, such configuration produces a total energy higher than all the other cases. The formation of stable dipoles at the Si-NCs surfaces radially directed inward the Si-NCs can provide an explanation of the production of stable colloidal codoped Si-NCs without surface functionalization processes [115,116,117,242]. Moreover, since in the codoped case the minimum energy formation is found for the strong and stable P-B bond, also the intensity of the transition between HOMO (acceptor) and LUMO (donor) states in the codoped Si-NCs is affected by the impurity distance. Stronger transitions arise when the impurities are closer, whereas the intensity gets lower when the impurities are at larger distances, as shown by the calculated absorption spectra [92]. These results were confirmed by the experimental determination of strong PL intensities in colloidal and matrix-embedded codoped Si-NCs [117]. Similar theoretical outcomes have been obtained also for codoped Si-NWs [236,237,243,244].
All these results found a confirmation in the atom probe tomography analysis of the B and the P distribution in codoped Si-NCs [129]. In Fig. 26 the proxigram analysis of codoped Si-NCs in BPSG matrix annealed at 1150 • C is reported. The distance at 0 nm represents the interface between the Si-NC and the matrix. Going to positive (negative) distance means moving towards the center of the Si-NC (inside the matrix). Clearly in the codoped Si-NCs the P concentration increases on going into the Si-NC, i.e. the P atom prefers to stay inside the Si region, whereas the B concentration does not show abrupt changes and reaches its maximum exactly at the Si-NC/matrix interface. Moreover a cluster analysis found that a large fraction of the B and P atoms present in the codoped samples were consumed to form B-P clusters in the Si-NCs, in good agreement with the theoretical results shown in Fig. 25.

Conclusions
We presented a review of the recent activities concerning doping in silicon nanocrystals. Particular attention has been devoted to the theoretical outcomes it has been demonstrated that this activation is possible, the efficiency is very low for both p-and n-impurities, with a clear preference for phosphorus with respect to boron. There is then space for new ideas aiming at the development of innovative strategies to realize doping in Si-NCs.

Acknowledgements
We are grateful to M. Amato, F. Iori and R. Guerra for useful discussions.