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Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học
Effects of simultaneous doping with boron and phosphorous on the structural, electronic and optical properties of silicon nanostructures F. Iori a , S. Ossicini b, Ã a CNR-INFM-S 3 and Dipartimento di Fisica, Universita’ di Modena e Reggio Emilia, via Campi 213/A, I-41100 Modena, Italy b CNR-INFM-S 3 and Dipartimento di Scienze e Metodi dell’Ingegneria, Universita’ di Modena e Reggio Emilia, via Amendola 2 Padiglione Morselli, I-42100 Reggio Emilia, Italy article info Available online 14 August 2008 PACS: 73.22.Àf 71 .1 5.Àm 78.55.Àm 78.20.Àe Keywords: Silicon nanocrystals Silicon nanowires Multidoping Formation energy Optical properties Electronic structures Doping abstract We show, by means of ab-initio calculations, that by properly controlling the doping a significant modification of both the absorption and the emission of light of silicon nanocrystals can be achieved. We have considered impur ities, boron and phosphorous (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 to 1.8 nm in diameter. We have found that the codoped nanocrystals have the lowest impurity formation energies when the two impurities occupy nearest neighbour sites near the surface. In addition, such systems present band-edge states localized on the impurities giving rise to a red-shift of the absorption thresholds with respect to that of undoped nanocrystals. Our detailed theoretical analysis shows that the creation of an electron–hole pair due to light absorption determines a geometry distortion that in turn results in a Stokes shift between absorption and emission spectra. In order to give a deeper insight in this effect, in one case, we have calculated the absorption and emission spectra going beyond the single-particle approach showing the important role played by many-body effects. Moreover, we also investigate how the properties of the codoped nanoclusters are influenced by the insertion of more impurities (multidoping). Finally, we have studied the effect of B and P codoping on the electronic and optical properties of Si nanowires, thus investigating the role of dimensionality. The entire set of results we have collected in this work give a strong indicati on that with the doping it is possible to tune the optical properties of silicon nanostructures. & 2008 Elsevier B.V. All rights reserved. 1. Introduction and computational methods During the last decade, several breakthroughs have boosted the hopes that silicon (Si) could be used as an optical active material when it is nanostructured [1,2]. The basic idea is to take advantage of the reduced dimensionality of the nanocrystalline phase (1–5 nm in size) where quantum confinement, band folding and surface effects play a crucial role [3–6]. Indeed, it has been found that Si nanocrystals (Si-nc) band-gap moves to the visible region with decreasing size, moreover, optical gain has been demonstrated [7,8]. Nevertheless, Si-nc still have a memory of the indirect band-gap of the bulk phase. This drawback can be circumvented by introducing isoelectronic impurities or by the simultaneous doping with n- and p-type impurities. In this last case, it has been established that a codoped (B and P) Si-nc shows always a higher photoluminescence intensity than a single-doped (B or P) Si-nc and than a pure undoped Si-nc [9]. Besides the codoped samples did not exhibit structures related to momentum- conserving phonons suggesting that, in this case, the quasi-direct optical transitions are predominant [9–11]. From theoretical point of view, a handful number of first- principle studies have been devoted to quantum confinement effects in single-doped Si-nc [12–16]. The outcomes point out that the ionization energy for the Si-nc is virtually size independent that the impurity formation energy (FE) is greater for smaller nanocrystals and that impurity segregation strongly affects the conductance properties of the nanostructures. In these last years, we have performed several theoretical studies that also consider the simultaneous doping of Si-nc with n- and p-type impurities [17–25] showing that the codoped Si-nc undergo a minor structural distortion around the impurities and that the formation energies are always smaller than those for the corresponding single-doped cases. Moreover, we have found that the band-gap of the codoped Si-nc is reduced with respect to the gap of the pure ones showing the possibility of an impurity-based engineering of the optical properties of Si-nc. Here, we report on a comprehen- sive investigation of the structural, electronic and optical proper- ties of B and P simultaneously doped Si-nc and Si nanowires using ab-initio density functional theory. Our results are obtained in a plane-wave pseudopotential DFT scheme, using the ESPRESSO package [26]. Full relaxation with respect to the atomic positions ARTICLE IN P RESS Contents lists available at ScienceDirect journal h omepage: www.elsevier.com/locate/physe Physica E 1386-9477/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2008.08.010 Ã Corresponding author. E-mail address: ossicini@unimore.it (S. Ossicini). Physica E 41 (2009) 939–946 is performed for all systems. All the DFT calculations are performed within the generalized gradient approximation using Vanderbilt ultrasoft pseudopotentials [27] for both the determination of the structural and electronic properties and norm-conserving pseudopotential within the local density approximation (LDA) at the relaxed geometry to evaluate the optical properties. All the considered Si nanostructures are embedded in large supercells in order to prevent interactions between the periodic replicas. A careful analysis has been performed in order to test the convergence of the structural and electronic properties with respect to both the supercell side and plane-wave basis set cut-off. 2. Doped Si nanocrystals 2.1. Single-doped Si nanocrystals We resume, here, the effects of size and shape of Si-nc on the incorporation of group-III (B and Al), group-IV (C and Ge) and group-V (N and P) impurities. Single-doping has been investigated both in spherical and faceted-like Si-nc [13,16]. The spherical Si-nc are built taking all the bulk Si atoms contained within a sphere of a given radius and terminating the surface dangling bonds with H; whereas the faceted Si-nc are resulting from a shell-by-shell construction procedure, which starts from a central atom and adds shells of atoms successively. We consider spherical Si-nc with radius ranging from 0.52 nm (Si 29 H 36 ) to 1.12 nm (Si 293 H 172 ) and the impurity is located in a substitutional site. As for impurities in bulk Si, Jahn–Teller distortions occur in the neighbourhood of the impurity sites and the bond lengths show a dependence with respect to size and shape of the Si-nc. Starting from the Si n H m nanocluster [28], the FE for the neutral X impurity can be defined as the energy needed to insert the X atom with chemical potential m X within the cluster after removing a Si atom (transferred to the chemical reservoir, assumed to be bulk Si) [29] E F ¼ EðSi nÀ1 XH m ÞÀEðSi n H m Þþ m Si À m X (1) where E is the total energy of the system, m Si the total energy per atom of bulk Si, m H the total energy per atom of the impurity. The results show that for smaller. Si-nc a larger energy is needed for the formation of the impurity. We have also calculated how the FE changes as a function of the impurity position within the Si-nc [13] (see Fig. 1). For the B neutral impurity in the large Si 146 BH 100 cluster, we have moved the impurity from the cluster centre towards the surface along different paths still considering substitutional sites. It comes out that as far as the internal core is concerned, variations not higher than 0.06 eV are found. On the contrary, an energy drop between 0.25 and 0.35 eV is found as the B impurity is moved to the Si layer just below the surface. This is explained by considering that such positions are the only ones which 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 towards the surface the FE decreases, making the subsurface positions more stable. The situation is different for the P atom [16]. Concerning the electronic properties, the acceptor (group-III) and donor (group-V) levels become deeper as the Si-nc become smaller and their level positions are influenced by the position of the impurity site. Significant changes on the onset of the absorption spectra are present due to the doping. Moreover, the radiative lifetimes are sensibly influenced by the shape, especially for the small Si-nc, whereas these influences disappear when the size of the nanoparticles increase. 2.2. B and P codoped Si nanocrystals Since Fujii et al. [9] have shown that B and P impurities occupy substitutional sites of the Si-nc, we always locate the B and P impurity atoms substitutionally in the Si layer just below the nanocrystal surface, since we have previously demonstrated [22] (in accordance with other theoretical predictions [31] and experimental outcomes [32] that in the case of codoping, these are the most stable positions. Initially, we consider impurities located at the largest possible distance on opposite sides of the Si-nc of different size, and then we explore different configuration by varying the distance between the dopants. 2.2.1. Structural properties and formations energies First we fix out attention on the structural changes induced by the impurities, comparing the B and P codoped cases with the single-doped ones (for the structure of a codoped Si-nc see Fig. 2). If we compare the impurity-Si bond lengths with those of the corresponding Si atoms in the pure Si-nc, it is clear that some significant relaxation occurs around the impurities. The amount of the relaxation around the impurity is directly related to the ARTICLE IN PRESS Fig. 1. Formation energies for neutral impurities as a function of the impurity position in the nc (b). The impurity is moved along two different paths toward the surface, as shown in (a). The lines are guides for eyes. Fig. 2. Calculated atomic structure of the Si 85 BPH 76 codoped nc. B ((magenta), grey) and P (black) impurities have been located at sub-surface position in substitutional sites on opposite sides of the Si-nc. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946940 impurity valence, actually, the more significant distortion is found for the trivalent atom (B) than for the pentavalent one (P). Beside that, it is interesting to note that in the codoped case the differences among the four impurity-Si bond lengths are always smaller with respect to the single-doped case. Thus, if carriers in the Si-nc are perfectly compensated by simultaneous n- and p-type impurities doping, an almost T d configuration is recovered in which the four impurity-Si bonds are practically the same. In order to clarify which are the parameters that play an important role in the determination of the FE, we have performed a series of total energy calculations considering: (i) single-doped and codoped nanocrystals, (ii) nanocrystals of different sizes, (iii) impurities located in different sites and (iv) variable impurity–impurity distance in a nanocrystal. In Fig. 3, we report the calculated formation energies of Si 35 H 36 (diameter d ¼ 1.10 nm), Si 87 H 76 (d ¼ 1.50 nm) and Si 147 H 100 (d ¼ 1.79 nm) nc compared, as reference, with the single-doped Si-nc FE values. For the codoped case, B and P impurities have been placed as second neighbours. From Fig. 3, it is clear that the simultaneous B- and P-doping strongly reduces (of about 1 eV) the FE with respect to both B and P single-doped cases and that this reduction is similar for Si-nc of different sizes. Thus, while B or P single- doping is very costly, the codoping is much easier and, as a good approximation, independent of the nanocrystal size. The impor- tant point here is that Si-nc can be more easily, simultaneously doped than single-doped; this is due to both the charge compensation and to the minor structural deformation. Also the distance between impurities plays a fundamental role on the decrease of the FE. For each nanocrystal, the FE takes on negative values below a given distance. Moreover, the FE have a minimum value when the impurities are located at the minimum possible distance. Indeed, the impurity–impurity distance seems to play a major role with respect to the nanocrystals size, since the FE for similar impurity configurations are quite independent of the nanocrystal dimension. 2.2.2. Electronic properties Concerning the electronic properties, in the single-doped cases, we have already shown that the presence of donor or acceptor states can considerably lower the energy gap E g of the undoped Si-nc [13]. Actually for single-doped Si-nc, the highest occupied state (HOMO) level contains only one electron and is strongly localized either on B or P impurity. Now, what is important is that the electronic properties of B- and P-codoped Si-nc are qualitatively and quantitatively different from those of either B- or P- single-doped Si-nc. The presence of both a n and a p impurity leads to a HOMO level that contains two electron and to a HOMO-LUMO (lower unoccupied state) gap strongly lowered with respect to that of the corresponding undoped nanocrystals. As an example, Fig. 4 reports the calculated energy levels at G point for the Si 33 BPH 36 system at the optimized geometries, where only the levels corresponding to the HOMO, LUMO, HOMO-1 and LUMO+1 states are depicted. Calculated square modulus contour plots related to HOMO and LUMO states reveal their localization within the Si-nc, in particular the HOMO state is localized on the B impurity, while the LUMO is localized on the P one [17]. The presence of these donor and acceptor states lowers the energy gap from 3.51 eV for the pure cluster to 2.86 eV for the codoped one. The possibility of modulating the Si-nc energy gap E g , it is evident if we keep the distance between the impurities constant and look at the dependence of E g on the Si-nc size. Fig. 5 shows, for three different Si-nc where the impurities are placed as second neighbours, how the undoped Si-nc E g is reduced in the presence of codoping. The same quantum confinement effect trend (i.e. larger gap for smaller nanocrystals) is observed for both the undoped and codoped cases. The E g of the codoped Si-nc is shifted towards lower energies with respect to that of the undoped E g ; this shift is stronger for smaller nanocrystals. Moreover, our results show that the mutual impurity distance affects not only the FE, but also the electronic structure. We observe that, within the same Si-nc, E g decreases almost linearly with the increase of the impurity distance [22]. In principle, it is possible to tune E g as a function of both the Si-nc size and the impurity–impurity distance. It is easy to predict that for Si-nc larger than those considered here it would be possible by codoping to obtain a E g even smaller than that of bulk Si. Playing with both the nanocrystal size and the distance between the impurities, may open new interesting routes for optoelectronic applications. 2.2.3. Absorption and emission spectra Now, we discuss the results for the absorption and emission spectra. The Si-nc excitation has been studied considering the excited state as the electronic configuration in which the HOMO contains a hole h, while the LUMO contains the corresponding electron e, thus simulating the creation of an electron–hole pair [30]. Initially the system is in its ground state and the electronic excitation occurs with the atomic positions fixed in this config- uration. After the excitation, due to the change in the charge density, relaxation occurs until the atoms reach a new minimum energy due to the presence of the e–h pair. The new atomic positions modify the electronic spectrum, implying that the levels involved in the emission process change. This model assumes that the relaxation under excitation is faster than the e–h recombination. The difference between the absorption and emission energies due to the different atomic positions represents the nanocrystal Stokes shift (SS). The calculations have been performed for two Si-nc of different sizes taking, in the larger Si-nc, the impurities located at different distances. As shown in Table 1, both the absorption and emission HOMO–LUMO energies are affected by these two parameters. With regard to the first parameter, we note that the SS strongly depends on the size showing a strong decrease on increasing the diameter of the Si-nc. This is due to the fact that for larger nanocrystals the excitation determines a minor distortion of the geometry. Concerning the second parameter, we see that the SS tends to slightly increase ARTICLE IN P RESS Si:B -0.25 0 0.25 0.5 0.75 1 1.25 1.5 Formation Energy (eV) Si:B:P Si:P Si 87 H 76 clusters Si 35 H 36 clusters Si 147 H 100 clusters Fig. 3. Formation energy for single-doped and codoped Si-nc. In the codoped nanocrystals, the impurities are placed as second neighbours in the first subsurface shell (see text). (Green) Triangles are related to Si 35 H 36 , (blue) diamonds to Si 87 H 76 and (red) circles to Si 147 H 100 based nanocrystals. The lines are a guide for eyes. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 941 with B–P distance, although this effect is small if compared with the lowering due to the increase of the Si-nc dimensions. The comparison between these results and the ones previously obtained for undoped clusters (0.92 eV for the Si 35 H 36 -nc [28] and 0.22 eV for the Si 87 H 76 -nc [30] confirm that the SS is mainly determined by the Si-nc size, but that nevertheless it depends slightly on the presence of the impurities and also on their mutual distance. Looking at the single-particle optical spectra in Fig. 6, we note that the HOMO-LUMO transition in Si 85 BPH 76 (1.75 eV, bottom panel) is almost dark when the two impurities are far apart and becomes instead allowed (2.32 eV, top panel) when their distance decreases. The emission ((red) dashed lines in Fig. 6) spectra is red-shifted with respect to the absorption ((black) solid lines in Fig. 6). This shift is a consequence of the geometry relaxation in the excited ARTICLE IN PRESS Fig. 4. Calculated energy levels at G point for the Si 33 BPH 36 -nc. Alignment has been performed locating at the same energy the fully occupied levels with the same type of localization. 5 7 7.5 8 8.5 9 9.5 Radius (Å) 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 Energy Gap (eV) Undoped Codoped 5.5 6 6.5 Fig. 5. Comparison between E g of the undoped ((black) triangles) and the codoped ((red) circles) Si-nc as a function of the Si-nc radius. Impurities are located in the first shell below the surface, as second neighbours. The lines are a guide for the eye. Table 1 Absorption and emission energy gaps (and their difference, 5th row) calculated as HOMO-LUMO differences in the ground and the excited relaxed geometries configuration, respectively Si 33 BPH 36 Si 85 BPH 76 d (nm) 1.10 1.50 1.50 D BP (A ˚ ) 3.56 2.00 10.60 Abs. (eV) 2.77 2.32 1.75 Ems. (eV) 1.78 2.20 1.36 D (eV) 0.99 0.12 0.39 The results are obtained within the DFT single-particle approach. d is the nanocrystal diameter, D BP is the distance between impurities, and D the calculated Stokes shift between absorption and emission energy gaps. 1 1.5 2 2.5 Energy(eV) ε 2 (ω) (arb.units) 1 1.5 2 2.5 Ener gy (eV) 0 ε 2 (ω) (arb.units) Excitedgeometry Groundgeometry Groundgeometry Excitedgeometry Fig. 6. Single-particle imaginary part of the dielectric function for the codoped Si 85 BPH 76 -nc in the ground ((black) solid line) and in the excited ((red) dashed line) geometries. B and P atoms are at the smallest possible distance (2.00 A ˚ , top panel) or at the largest possible distance (10.60 A ˚ , bottom panel) for this nanocrystal. A Gaussian broadening of 0.1 eV has been applied. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946942 state due to the excess energy necessary for promoting an electron in the LUMO level. The dependence of the emission spectra both on the nanocrystals size and on the impurities positions reveals once more the possibility of tuning the optical response of Si-nc. 3. Many-body results In order to give a complete description, within the many-body framework, of the codoped Si-nc response to an optical excitation, we consider both the self-energy corrections by means of the GW method [33] to obtain the quasiparticle energies and the excitonic effects through the solution of the Bethe-Salpeter equation (BSE) [34]. The effect of local fields is also included, to take into account the inhomogeneity of the systems. To carry out emission spectra calculations, we have used the excited state geometry and the ground state electronic configuration, as already described. The choice of studying the small Si 35 BPH 36 -nc is due to the fact that the GW-BSE calculations, necessary to obtain the many- body optical spectra, are very computing demanding. Thus, the electron–hole interaction is considered here also in the emission geometry [22]. Fig. 7 (right panel) shows the calculated absorption and emission spectra fully including the many-body effects. The e–h interaction yields significant variations with respect to the single-particle spectra (shown in the left panel), with an important transfer of the oscillator strength to the low-energy side. Moreover, in the emission spectrum, the rich structure of states characterized, in the low-energy side, by the presence of excitons with largely different oscillator strengths, determines excitonic gaps well below the optical absorption onset. Thus, the calculated emission spectrum results to be red-shifted to lower energy with respect to the absorption one. This energy difference between emission and absorption, the SS, can be lead back to the relaxation of the Si-nc after the excitation process. The new important features that appear in the emission many-body spectra are related to the presence of both B and P impurities as showed by Fig. 8, which gives the real-space probability distribu- tion | C exc (r e , r h )| 2 , for the bound exciton as a function of the electron position r e , when the hole is fixed in a given r h position. In this case, the hole is fixed on the boron atom and we see that the bound exciton is mainly localized around the phosphorous atom. From Table 2, it can be seen that the single-particle DFT results strongly underestimate the absorption and emission edge with respect to the GW+BSE calculation, in which the excitonic effect are taken exactly into account. This means that, in this case, the cancellation between GW gap opening (which gives the electronic gap) and BSE gap shrinking (which originates the excitonic gap) is only partial [35]. The difference between the GW electronic gap and the GW+BSE optical excitonic gap gives the exciton binding energy E b . We note the presence of exciton binding energies as big as 2.2 eV, which are very large if compared with bulk Si (15 meV) or with carbon nanotubes [36,37] where E b $1 eV, but similar to those calculated for undoped Si-nc [38] of similar size and for Si and Ge small nanowires [39,40]. It is interesting to note that the HOMO-LUMO transition in the emission spectrum at 2.20 eV is almost dark, while an important ARTICLE IN P RESS ε 2 (ω) (arb.units) 1 1.5 2 2.5 3 3.5 4 4.5 Energy (eV) ε 2 (ω) (arb.units) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Energy (eV) Fig. 7. Single-particle imaginary part of the dielectric function for the codoped Si 33 BPH 36 -nc in the ground (dashed line) and excited (solid line) geometries. Right panel: absorption (dashed line) and emission (solid line) many-body spectra of Si 33 BPH 36. Fig. 8. Excitonic wave function of Si 33 BPH 36 (atom colors as in Fig. 1). The gray isosurface represents the probability distribution of the electron, with the hole fixed on the B impurity. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 943 excitonic peak is evident at about 2.75 eV (see Fig. 7), red-shifted with respect to the first absorption peak. 4. Multidoping In this section, we will study how the FE and the electronic properties of the Si-nc are influenced by the insertion of more and more impurities. We call this insertion of several impurities multidoping. Fig. 9 shows how the FE of a large Si 147 H 100 -nc varies as function of the impurity numbers. We note that the presence of an odd number of dopants (1 or 3) already brings the FE to higher values. Instead, the presence of an even, compensated number of B and P impurities strongly lowers the FE that drop down to a negative value, indicating that as in the case of simple codoping, multidoping is much easier to realize when one has the same number of donor and acceptor dopant atoms. In fact the Si 145 BPH 100 -nc, Si 143 BBPPH 100 -nc and Si 141 BBBPPPH 100 -nc (not showed in the figure) show a FE of À0.32, À0.42 and À0.97 eV, respectively. Next, we investigate how the electronic levels are influenced by adding one or t w o mor e impurities to the c odoped Si 145 BPH 100 -nc. We consider the Si 145 BPH 100 -nc where the starting B and P pair is located in a particular site, which is the more stable configuration. Thus we add first one single impurity in order to obtain either the Si 144 BBPH 100 (with an excess of B: 2 B atoms and 1 P) or the Si 144 BPPH 100 -nc (with an excess of P: 1 B and 2 P) and finally, adding simultaneously two B and two P atoms, we obtain the Si 143 BBPPH 100 -nc. Looking at the electronic structure in Fig. 10, the two Si-nc with 3 impurities present a similar behaviour to those corresponding to B or P single-doped Si-nc (Si 146 BH 100 -nc, or Si 146 PH 100 -nc). Every new dopant inserted gives raise to a new impurity level, which is half occupied. Thus looking at the figure, we see that the HOMO- LUMO energy difference for the nanoclusters with an odd number of impurity atoms are very similar: 2.02 eV for the Si 144 BBPH 100 -nc with respect to 2.08 eV for the B single-doped case (Si 146 BH 100 ), and 0.15 eV for the Si 144 BPPH 100 -nc, with respect to 0.13 eV for the P single-doped case (Si 146 PH 100 ), respectively. Besides, another time, when the impurities are compensated, as in the case of the Si 143 BBPPH 100 -nc Si, the system becomes a semiconductor, now the HOMO contains again two electrons, and the value of the energy gap (1.97 eV) is an intermediate one between the two corresponding extrema E g of the codoped Si 145 BPH 100 -nc with impurities located at different distance (2.03 eV for impurities closer to each other and 1.59 eV for impurities at the opposite side of the Si-nc). The single-particle absorption spectra reflect the results for the electronic properties. For what concern all the compensated codoped Si-nc, we observe a shift of the absorption onset toward lower energy on increasing the distance between impurities. It is worth pointing out that when impurities are at a larger distance, the transition intensities near the band edges become weaker due to small oscillator strengths. When, instead, impurities are closer to each other due to the strong localization of HOMO and LUMO ARTICLE IN PRESS Table 2 Absorption and Emission energies calculated as HOMO-LUMO energy difference within the singleparticle DFT, the many-body GW and the GW+BSE approaches Si 33 BPH 36 DFT GW GW+BSE Abs. (eV) 2.80 5.52 3.35 Ems. (eV) 1.79 4.37 2.20 D (eV) 1.01 1.15 1.15 D is the calculated Stokes shift between absorption and emission energy gaps. Fig. 9. Formation energies for single, codoped and multidoped Si 147 H 100 based nanocrystals. Fig. 10. Calculated energy levels at the G point for the Si 145 BPH 100 -nc, the Si 144 BBPH 100 -nc, the Si 144 BPPH 100 -nc and the Si 143 BBPPH 100 -nc. Alignment has been performed, locating at the same energy, the fully occupied levels with the same type of localization. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946944 on the impurity sites, the transitions near the band edge are more intense. 5. Codoped silicon nanowires Among one-dimensional semiconducting nanostructures, silicon nanowires (Si-nw) have attracted in the last years an increasing interest since it has been shown that they are, together with carbon nanotubes, potential candidates to build up future nanoelectronic and nanophotonic devices [41–43]. In fact, they offer the advantage to be compatible with the existing silicon- based microelectronics. Moreover, the possibility to tailor their electronic properties by changing thickness, orientation, surface morphology and doping is another important point in their favour [44,45]. Obtain a systematic relation between structure, surface morphology and electronic properties is from an experimental point of view, a very difficult task. For this reason, theoretical/ computational investigations, based on reliable ab-initio DFT approaches, can be of great help to the experimentalists to grow Si-nw suitable for a particular application. Several ab-initio studies on Si-nw are present in the literature. They are mainly concentrated on H-passivated or pristine Si-nw and demonstrate the dependence of the energy band-gap from the wire diameter and from the surface morphology [4,40,46–51]. Instead, few investigations have been dedicated to the influence of the electronic and transport properties from doping [52,53]. In particular, due to the application in electronic devices, the main efforts have been devoted to the study of B and P single- doped Si-nw, while only one ab-initio study has investigated the B and P codoping [53]. For this reason, in complete analogy with the Si-nc, we have recently performed a systematic analysis of the effect of the B and P codoping in Si-nw, concentrating not only on the structural properties but also on how doping influences the electronic and optical properties. Here, we aim to resume the main outcome of this work and illustrate specific results only for one single-doped and codoped H-passivated Si-nw (with a linear cross section of about 1 nm) grown in the [110] direction, while a more complete discussion will be found elsewhere [54].In particular, we have considered different positions for the impurities in the Si-nw; moreover, we have varied the unit cell in our calculations. Augmenting the unit cell, correspond to an increase of the overall number of atoms within the cell and thus to a decrease in the dopant concentration. Fig. 11 shows how the FE for the B and P codoped Si-nw changes as function of the position of the dopants within the nanowire. In the figure, the inset show the single Si-nc unit cell used in this case. We note that the minimum is reached when the P atom moves to a surface position. Moreover, also in the corresponding case (not shown in the figure) where the P impurity is located in a subsurface position and the B atom is in a surface site, the FE becomes negative. Indeed it is worthwhile to note that in all cases of single-doped Si-nw, the FE shows high positive value (1.13 and 0.66 eV for the single B- and P-doped nanowire, respectively), thus confirming the stabilizing role of compensated doping. Concerning the electronic properties, the band structure show a direct energy gap behaviour at G , whose values depends on the impurity position. For the positions labelled 1, 2 and 3 in Fig. 11, these values are 0.63, 0.08 and 0.97 eV, respectively. If we concentrate on the dependence of the doped Si-nw properties on the dopant concentration, we note first that on augmenting the number of atoms in the cell (thus lowering the dopant concentration), the FE lowers. For the smallest unit cell (28 atoms in total) the FE shows a value of 0.41 eV, where using a two-time (56 atoms), three-time (84 atoms) and fourth-time (112 atoms) larger unit cell brings this value to À0.15, À0.60 and À0.64 eV, respectively. This demonstrates that a lowering of the impurity concentration results in a gain of the stability for the nanowire. The impurity concentration plays a role also re- garding the electronic properties. From Fig. 12, we see that the direct band-gap increases as the impurity concentration lowers (the impurities here are located in the position 2 of Fig. 11), approaching asymptotically the value of the band-gap of the undoped Si-nw. This is another indication of how doping can modify the electronic and optical properties of the Si nanostructures. 6. Conclusions The structural, electronic and optical properties of Si nanos- tructures doped with different numbers of B and P impurities have been studied from first-principles. We have considered Si-nc with the impurities located at different distances and in different combinations. Besides also doped Si nanowires have been investigated. We show, in all systems, that compensated codoping ARTICLE IN P RESS 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 Impurity distance (Å) Formation Energy (eV) 1 3 B 2 P in 1 B at I shell P in 3 B at I shell P in 2 B at I shell Fig. 11. Formation energy for the codoped Si-nw (shown in the inset) as function of the related position between the two dopants. The B impurity is frozen in a subsurface site, while the P occupies different sites labelled 1, 2 and 3. The lines are guide for the eye. Fig. 12. DFT-GGA direct band-gap calculated at G point for the codoped Si-nw with respect to the number of atoms in the unit cell. A larger number corresponds to a decrease in impurity concentration. The dotted line is a guide for the eye. The dashed line corresponds to the band-gap for the undoped Si-nw. F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 945 is always energetically favoured with respect to a not compen- sated number of B- or P-doping. Our results demonstrate that the codoped nanostructures present valence and conduction band- edge states which are localized on the two impurities, respec- tively, and energy band gaps always lower in energy with respect to that of pure undoped Si nanostructures. On going from nanocrystals to nanowires, the reduced quantum confinement results in a reduced energy band-gap that is direct at the G point, elucidating the role of dimensionality. Indeed the impurity located band-edge states originate absorption and emission thresholds in the visible region which are shifted lower in energy with respect to that of corresponding pure undoped Si structures. 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Effects of simultaneous doping with boron and phosphorous on the structural, electronic and optical properties of silicon nanostructures F another indication of how doping can modify the electronic and optical properties of the Si nanostructures. 6. Conclusions The structural, electronic and