ARTICLE IN PRESS Journal of Luminescence 121 (2006) 335–339 www.elsevier.com/locate/jlumin Doping in silicon nanocrystals: An ab initio study of the structural, electronic and optical properties Federico Ioria, Elena Degolib,, Eleonora Luppia, Rita Magria, Ivan Marrib, G. Cantelec, D. Ninnoc, F. Tranic, Stefano Ossicinib a CNR-INFM-S3 and Dipartimento di Fisica, Università di Modena e Reggio Emilia, via Campi 213/A, I-41100 Modena, Italy CNR-INFM-S3 and Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, via Amendola, I-42100 Reggio Emilia, Italy c CNR-INFM-Coherentia and Università di Napoli ‘‘Federico II’’, Dipartimento di Scienze Fisiche, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy b Available online 26 September 2006 Abstract There are experimental evidences that doping control at the nanoscale can significantly modify the optical properties with respect to the pure systems. This is the case of silicon nanocrystals (Si-nc), for which it has been shown that the photoluminescence (PL) peak can be tuned also below the bulk Si band gap by properly controlling the impurities, for example by boron (B) and phosphorus (P) codoping. In this work, we report on an ab initio study of impurity states in Si-nc. We consider B and P substitutional impurities for Si-nc with a diameter up to 2.2 nm. Formation energies (FEs), electronic, optical and structural properties have been determined as a function of the cluster dimension. For both B-doped and P-doped Si-nc the FE increases on decreasing the dimension, showing that the substitutional doping gets progressively more difficult for the smaller nanocrystals. Moreover, subsurface impurity positions result to be the most stable ones. The codoping reduces the FE strongly favoring this process with respect to the simple n-doping or p-doping. Such an effect can be attributed to charge compensation between the donor and the acceptor atoms. Moreover, smaller structural deformations, with respect to n-doped and p-doped cases, localized only around the impurity sites are observed. The band gap and the optical threshold are largely reduced with respect to the undoped Si-nc showing the possibility of an impurity-based engineering of the Si-nc PL properties. r 2006 Elsevier B.V. All rights reserved. PACS: 73.22
f; 71.15.m Keywords: Nanocrystals; Doping; Luminescence 1. Introduction During the last 10 years, various experimental and theoretical results have raised hopes for a real employment of nanostructured silicon as an optical active material [1]. The idea stems from the possibility of confining carriers into tiny silicon nanocrystals (Si-nc) (1–4 nm in size) and to use quantum confinement effects to change the physical properties of bulk silicon. In particular, it has been observed that Si-nc band gap increases with decreasing size and visible luminescence external efficiency in excess of 10% has been obtained [1,2]. Moreover, optical gain in SiCorresponding author. Tel.: +39 059 2055289; fax: +39 059 374794. E-mail address: degoli.elena@unimore.it (E. Degoli). 0022-2313/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2006.08.062 nc has been demonstrated in a variety of situations [3]. Nevertheless, Si-nc still remain indirect band gap materials where structures related to momentum-conserving phonons were clearly observed. This drawback can be circumvented by introducing in the Si-nc isoelectronic impurities [1,2] or by codoping with n- and p-type impurities [4]. In a series of intriguing papers, Fujii and collaborators [4–6] have shown the possibility of controlling the photoluminescence (PL) properties of Si-nc by nand p-type codoping, proving not only that the PL intensity of codoped (boron (B) and phosphorus (P)) Si-nc is always higher than that of either P-doped or Bdoped Si-nc, but also that it is even higher with respect to the pure Si-nc. Besides, under resonant excitation conditions, the codoped samples did not exhibit structures ARTICLE IN PRESS 336 F. Iori et al. / Journal of Luminescence 121 (2006) 335–339 related to momentum-conserving phonons suggesting that in this case the quasidirect optical transitions are predominant. Theoretical studies of impurities in silicon quantum dots have lagged relative to calculations for pure, undoped systems. Only few first-principle studies are present in the literature, devoted to quantum confinement effects in Si-nc doped with the introduction of only one impurity atom [7–9]. The results point out that the ionization energy for the Si-nc is virtually size-independent while donor and acceptor binding energies are substantially enhanced. Recently, we have performed a preliminary theoretical study considering the codoping of Si-nc with n- and p-type impurities [10]. In the present paper, we will present our recent results concerning the structural, electronic and optical properties of n-doped, p-doped and codoped Si-nc. The paper is organized as follows: in Section 2, we briefly elucidate the theoretical framework used, Section 3 is devoted to the discussion of the results and Section 4 presents our conclusions. 2. Computational methods Our results have been obtained by using a plane-wave, pseudopotential density functional calculation of impurity states in spherical Si-nc, with diameter ranging from 1.04 nm (Si29H36) to 2.24 nm (Si293H172). The Si-nc have been built taking all the bulk Si atoms contained within a sphere of a given radius and terminating the surface dangling bonds with hydrogen. Each cluster has been centered on an Si atom. As in the experiments, we consider B and P impurities in substitutional sites. Full relaxation with respect to the atomic positions has been performed for both doped and undoped systems. All the calculations have been done using the Quantum-Espresso package [11], within the GGA approximation using Vanderbilt ultrasoft [12] pseudopotentials. The Si-nc have been embedded in a large supercell in order to prevent interactions between the periodic replicas (about 6 Å of vacuum separates neighbor clusters in all the considered systems). A careful analysis has been performed on the convergence of both the electronic and structural properties with respect to both the supercell side and plane-wave basis set cut-off. Both the structural and electronic properties have been investigated as a function of the size and of the impurity position within the Si-nc. The impurity formation energy (FE) has been calculated as a function of the Si-nc dimension and of the impurity position within the nanocluster. Absorption properties of the Si-nc have been calculated through the imaginary part of the dielectric function. 3. Results: structural, electronic and optical properties The structural changes of the doped Si-nc have been investigated as a function of the size of the impurity position and of the number of dopant species present within the Si-nc. The first important point is that the amount of the relaxation around the impurity is directly related to the impurity valence. A more significant distortion is obtained doping with trivalent atoms (e.g. B), in which an electron that could be used to form a bond with the surrounding Si atoms is missing. Actually, in the B-doped clusters, while the Si–Si bond lengths keep almost unchanged, some reconstruction occurs around the impurity. The overall structure has C3v symmetry, with an impurity displacement along the /1 1 1S direction when it is placed at the nanocluster center. Such a displacement leads to one longer and three shorter (and equal) Siimpurity distances. While the longer bond is ‘‘almost’’ independent of the Si-nc size, the shorter one decreases with the size. It is interesting to note that the relaxation of the bulk Si supercell containing the B impurity leads to an ‘‘almost’’ Td configuration, in which the four B–Si bonds are practically the same. On the contrary, for pentavalent atoms, such as the P-doped Si-nc, the relaxation leads to a nearly Td symmetry, in which the differences between the four P–Si bonds are negligible, less than 0.7% [13]. Starting from the SinHm nanocluster [14], the FE for the neutral X impurity can be defined as the energy needed to insert the X atom with chemical potential mX within the cluster after removing a Si atom (transferred to the chemical reservoir, assumed to be bulk Si) E f ¼ EðSin
1 XHm Þ
EðSin Hm Þ þ mSi
mX , (1) where E is the total energy of the system, mSi the total energy per atom in bulk Si, mX the total energy per atom of the impurity [15]. Our calculations clearly show that for smaller Si-nc, a larger energy is needed for the formation of the impurity. For B-doped Si-nc, a decreasing behavior of Ef vs. R is observed, that can be described by the linear formula E f ¼ 0:796 þ 4:63971=R, (2) where R is expressed in Å and Ef in eV, and the value Ef ¼ 0.796 eV corresponds to doped Si bulk. For P-doped Si-nc, the same decreasing behavior is observed and the linear formula is now: E f ¼ 0:21008 þ 4:98131=R. (3) The fact that the calculated FE is lower for larger Si-nc is in qualitative agreement with the observed suppression of the PL in doped Si-nc. The increase of the Si-nc size and the stronger PL suppression observed by Fujii et al. [6] when the annealing temperature is augmented (this effect is a signature of a higher impurity concentration) show that larger Si-nc can more easily sustain the doping. The FE changes also as a function of the impurity position within the Si-nc. An energy drop of about 0.30 eV is found as the B impurity is moved from the cluster center to the Si layer just below the surface. Thus as the impurity atoms are moved toward the surface, the FE decreases, making the subsurface positions more stable. The local structure has now a C2v symmetry, with two shorter and ARTICLE IN PRESS 337 F. Iori et al. / Journal of Luminescence 121 (2006) 335–339 Bond Si87H76 (Å) Bond Si86BH76 (Å) Si86PH76 (Å) Si85BPH76 (Å) Si–Sis Si–Sis Si–Sii Si–Sii 2.355 2.355 2.363 2.363 B–Sis B–Sis B–Sii B–Sii Si–Sis Si–Sis Si–Sii Si–Sii 2.355 2.355 2.363 2.363 P–Sis P–Sis P–Sii P–Sii 2.036 2.036 2.014 2.014 2.021 2.021 2.034 2.034 2.294 2.294 2.380 2.380 2.295 2.295 2.331 2.331 1.2 1 Formation Energy (eV) Table 1 Bond lengths at the subsurface substitutional site where the impurities are located for the undoped Si87H76 cluster, the B-doped, the P-doped and codoped ones 0.8 0.6 0.4 0.2 0 -0.2 -0.4 Si:B Sis and Sii refer to surface and inner Si atoms around this site, respectively. two longer Si-impurity distances with respect to the surface and inner Si atoms (see Table 1). Table 1 gives the optimized bond lengths around the impurity in subsurface positions for the Si87H76-nc (the results are quite similar for Si147H100). Both n-doped or pdoped and codoped cases have been considered. It is interesting to note that in the codoped case, the differences among the four impurity-Si bond lengths are clearly smaller with respect to the n-doped or p-doped case. Thus, when carriers in the Si-nc are perfectly compensated by codoping with n- and p-type impurities, an almost Td configuration is recovered in which the four impurity-Si bonds are practically the same. This fact is reflected in the FE results reported in Fig. 1, for B-doped, P-doped and B–P-codoped Si-nc for two, different in size, nanocrystals. In all cases the impurities are located in subsurface positions. In the figure, dashed lines connect the FE values obtained when neutral impurities are located at the largest possible distance in the codoped clusters, while solid lines are used for the cases in which the impurities are nearest neighbors. From Fig. 1, it is clear that codoping strongly reduces (of about 1 eV) Ef with respect to the doping with only one type of impurity atom. This reduction is similar for Si-nc of different size. The important point here is that Si-nc can be more easily codoped than doped with the introduction of only one impurity atom; this is a consequence of both the charge compensation and the minor structural deformation. Moreover, the FE is lower when the impurities are nearest neighbors. The presence of a single donor or acceptor state (ndoping or p-doping) gives rise to a reduction of the energy gap EG, inducing the formation of a highest occupied molecular orbital (HOMO) level strongly localized on B or P impurity. Nevertheless, whereas the EG reduction in Bdoped Si-nc is due to the formation of a defect level just above the valence edge (see for instance the case of the Si86BH76-doped Si-nc [10], where EG reduces to 2.59–2.31 eV), in P-doped Si-nc the effect is caused by the formation of a single level localized just below the Si:BP Si:P Fig. 1. Formation energy of the neutral impurities located at subsurface positions as a function of the doping: B-doped, P-doped and B–P codoped nanoclusters are considered. The lines are a guide for the eyes. Dashed lines (green and blue): neutral impurities located at largest possible distance, and solid lines (black and red): neutral impurities located at nearest-neighbor distances in the codoped clusters. Squares (green and black) are related to the Si87H76 nanoclusters, circles (red and blue) to the Si147H100 ones. conduction band (see for instance the case of the Si86PH76 nanocrystal [10], where EG is 0.28 eV). Changes in EG have been evaluated also for various B- and P-codoped Si-nc; e.g. we have observed a reduction of EG from 2.59 (for the pure Si-nc Si87H76 ) to 1.82 eV for the codoped Si85BPH76 and similarly a reduction from 2.30 (for the pure Si-nc Si147H100 ) to 1.56 for the codoped Si145BPH100. Obviously, for pure Si-nc larger than those considered here, having a smaller EG, it would be possible by codoping to obtain an EG even smaller than the bulk Si band gap in agreement with the experimental outcomes [4,6]. Besides, on going from the pure, to the B-doped or P-doped case, to the codoped Si-nc, the HOMO and lowest occupied molecular orbital (LUMO) states progressively localize on the impurities. In the codoped case, the HOMO is strongly localized on the B impurity and the LUMO on the P impurity. These facts have a profound influence on the optical properties of the Si-nc. The optical properties have been calculated through the imaginary part e2 of the dielectric function: a2 ðoÞ ¼ 4p2 e2 X 2 m2 o2 v;c;k V cc;k pa cv;k d½E c ðkÞ
E v ðkÞ
_o, 2 ð4Þ where a ¼ ðx; y; zÞ, Ev and Ec denote the energies of the valence cv,k and conduction cc,k band states at a k point (G in our case), and V is the supercell volume. The optical absorption coefficient aðoÞ ¼ o 2 ðoÞ nc (5) is directly related to e2; thus the imaginary part of the dielectric function contains all the necessary information ARTICLE IN PRESS 338 ε2 (a.u.) F. Iori et al. / Journal of Luminescence 121 (2006) 335–339 0 0.5 1 1.5 2 Energy (eV) 2.5 3 3.5 Fig. 2. Top panel: calculated imaginary part of the dielectric function (e2) for the Si86BH76 cluster (solid-red line). Center panel: the same for the Si86PH76 cluster (solid-red line). Bottom panels: the same for the Si85BPH76 codoped cluster (solid-red line). In all panels, the result for the e2 of the undoped Si87H76 cluster is reported for comparison (dashedblack line). A Gaussian broadening of 0.1 eV has been used. electronic and optical properties as a function of size and impurity position within the cluster. We have shown that in n-doped and p-doped Si-nc, the structural deformation around the impurity depends on both the impurity valence and impurity position. The impurity subsurface positions are always the most stable ones. As a consequence of charge compensation, it is easier codoping the nanocrystal than doping it with only one type of impurity atom. The study of the electronic properties shows that for B-doped and P-doped Si-nc, the HOMO is located around the impurity, whereas the LUMO is delocalized in the nanocrystals and that the energy gap strongly depends on the impurity valence. For the B- and P-codoped Si-nc, both HOMO and LUMO are localized around the impurity sites thus strongly lowering the energy gap with respect to that of the pure silicon nanostructures. The optical properties reflect the electronic ones, thus for B-doped and P-doped nanocrystals absorption features are present in the infrared region, whereas for the case of B–P-codoping electronic transitions between donor and acceptor states in the optical region are allowed, making it possible to engineer the PL spectrum of the nanocrystals that will depend on the nanocrystal size. Acknowledgements about the absorption properties of the nanocrystals. Owing to the strong confinement effects present in nanoclusters, only transitions at the G point have been considered. Fig. 2 reports the calculated imaginary parts of the dielectric function (e2) for the Si87H76 clusters, considering B-doped (top panel) and P-doped (center panel) nanocrystals and the B–P codoped (bottom panel) nanocrystal. For all cases, the result is compared with the corresponding one for the undoped Si87H76 clusters. Concerning both the B-doped and P-doped cases, we see that several new peaks appear in the low-energy region between 0 and 2 eV. These peaks are due to the interband and intraband transitions that involve the impurity state located in the band energy gap. These new features could be important for applications in the infrared region and in Raman lasers technology. For the codoped Si85BPH76 cluster, as shown at the bottom of Fig. 2, we note the shift of the optical gap to lower energies and the rise of new features not present for the undoped Si87H76 cluster. The enhancement of the intensity in this region is a direct consequence of the localization process of the HOMO and LUMO states on the impurities described above. These outcomes can explain the experimental data [4,6] that show a PL intensity for codoped Si-nc even higher than that of pure Si-nc and prove that by codoping it is possible to shift the PL peak even below the Si bulk band gap. 4. Conclusions A detailed first-principle study of B- and/or P-doping in Si-nc has been performed analyzing their structural, We acknowledge the support of the MIUR PRIN (2005) Italy and of the CRUI Vigoni Project (2005) Italy–Germany. All the calculations were performed at CINECABologna (‘‘Iniziativa Calcolo Parallelo del CNR- INFM’’), CICAIA-Modena and ‘‘Campus Computational Grid’’Università di Napoli ‘‘Federico II’’. References [1] S. Ossicini, L. Pavesi, F. Priolo, Light Emitting Silicon for Microphotonics, STMP 194, Springer, Berlin, 2003. [2] O. Bisi, S. Ossicini, L. Pavesi, Surf. Sci. Rep. 38 (2000) 5. [3] L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franzò, F. Priolo, Appl. Phys. Lett. 82 (2003) 4636; J. Ruan, P.M. Fauchet, L. Dal Negro, M. Cazzanelli, L. Pavesi, Appl. Phys. Lett. 83 (2003) 5479; M. Cazzanelli, D. Kovalev, L. Dal Negro, Z. Gaburro, L. Pavesi, Phys. Rev. Lett. 93 (2004) 207042. [4] M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, S. Hayashi, Appl. Phys. Lett. 87 (2005) 211919. [5] M. Fujii, K. Toshikiyo, Y. Takase, Y. Yamaguchi, S. Hayashi, J. Appl. Phys. 94 (2003) 1990. [6] M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, S. Hayashi, Appl. Phys. Lett. 85 (2004) 1158. [7] D.V. Melnikov, J.R. Chelikowsky, Phys. Rev. Lett. 92 (2004) 046802. [8] G. Cantele, E. Degoli, E. Luppi, R. Magri, D. Ninno, G. Iadonisi, S. Ossicini, Phys. Rev. B 72 (2005) 113303. [9] Z. Zhou, M.L. Steigerwald, R.A. Friesner, L. Brus, M.S. Hybertsen, Phys. Rev. B 71 (2005) 245308. [10] S. Ossicini, E. Degoli, F. Iori, E. Luppi, R. Magri, G. Cantele, F. Trani, D. Ninno, Appl. Phys. Lett. 87 (2005) 173120. [11] S. Baroni et al. /www.quantum-espresso.orgS. [12] D. Vanderbilt, Phys. Rev. B 41 (1990) R7892. ARTICLE IN PRESS F. Iori et al. / Journal of Luminescence 121 (2006) 335–339 [13] Calculations have been done also for isovalent impurity (C and Ge) and other group III (Al) and group V (N) impurities; in general, trivalent impurity tends to lower the symmetry down to a C3v one while an almost Td symmetry is preserved for isovalent and pentavalent impurities. A role seems to be played also by the impurity dimension: in B-doped, C-doped and N-doped clusters, the Si-impurity bond lengths are shorter with respect to typical Si–Si bond-length in the undoped cluster 339 while the Si–P, Si–Al and Si–Ge distances are slightly larger. An extensive study can be found in L.E. Ramos, E. Degoli, G. Cantele, S. Ossicini, D. Ninno, J. Furthmuller, F. Bechstedt Phys. Rev. B, submitted. [14] E. Degoli, G. Cantele, E. Luppi, R. Magri, D. Ninno, O. Bisi, S. Ossicini, Phys. Rev. B 69 (2004) 155411. [15] We consider the total energy per atom in the tetragonal B50 crystal for B, and the orthorhombic black phosphorus for P.