LETTER pubs.acs.org/NanoLett
Confinement Effects and Hyperfine Structure in Se Doped Silicon Nanowires Guido Petretto,*,†,‡ Alberto Debernardi,*,† and Marco Fanciulli†,‡ † ‡
Laboratorio MDM-IMM-CNR via C. Olivetti, 2 I-20041 Agrate Brianza (MB), Italy Dipartimento di Scienza dei Materiali, Universita degli Studi di Milano-Bicocca, via Cozzi 53, I-20125 Milano, Italy ABSTRACT: We report a density functional study of the electronic properties and hyperfine structure of substitutional selenium in silicon nanowires using plane-wave pseudopotential techniques. We simulated hydrogen passivated [001] oriented nanowires with a diameter up to 2 nm, analyzing the effect of quantum confinement on the defect formation energy and on the hyperfine parameters as a function of the diameter and of the defect position. We show that substitutional Se in silicon has favorable configurations for positions near the surface with possible formation of chalcogenhydrogen complexes. We also show that hyperfine interactions increase at small diameters, as long as the nanowire is large enough to prevent surface distortion which modifies the symmetry of the donor wave function. Moreover, surface effects lead to strong differences in the hyperfine parameters depending on the Se location inside the nanowire, allowing the identification of an impurity site on the basis of electron paramagnetic resonance spectra. KEYWORDS: DFT, silicon nanowires, chalcogen, hyperfine structure, doping, nanoelectronics
I
n the last few years one-dimensional nanostructures and in particular silicon nanowires (SiNWs) have received growing attention since they are considered promising building blocks for many possible applications, such as electronic devices,13 lasers,4 nanosensors,5,6 and photovoltaic cells.7,8 Along with the availability of experimental SiNWs with small diameter, a considerable effort has been devoted to the theoretical investigation of electronic properties of pristine and doped SiNWs.9 In particular, since the doping efficiency is of paramount importance to control the carrier density, several investigations, from both theoretical and experimental points of view, have addressed the problem of the distribution of dopant atoms inside the nanowire and of the change in ionization energy due to confinement effect. Theoretical studies have predicted a tendency to surface segregation for various kind of donors and acceptors10,11 and the dielectric mismatch between the nanowire and its environment has been demonstrated to play an important role in deepening defect levels (dielectric confinement).12 Experimental results seem to support the predictions of dielectric confinement,13 while for surface segregation the comparison between simulation and experiment is more difficult, since the experimental nanowires actually available have a diameter which is at least 1 order of magnitude larger than the simulated ones. Various electrical transport,14 atom-probe tomography15 and Kelvin probe force microscopy (KPFM)16 measurements have shown a higher dopant concentration on the surface of SiNWs, but this has been attributed to vaporsolid deposition on the surface during vaporliquidsolid (VLS) growth. Nonetheless, recently Koren et al.17 have obtained uniform dopant distribution by annealing after VLS growth, but with a residual higher density near the surface, suggesting that a segregation mechanism could be at work. r 2011 American Chemical Society
Another important aspect related to the doping of semiconductor nanostructure is the hyperfine structure of the defect, given the possible development of electron and/or nuclear spin qubits based on donors with large hyperfine contact term.1820 For group V elements this problem has already been addressed in nanocrystals with theoretical simulations2123 and electron paramagnetic resonance spectroscopy (EPR) measurements,24 while for nanowires hyperfine parameters have been calculated by Rurali et al.25 for P donors. A deeper analysis of the hyperfine properties based on other kinds of donors can thus provide further insight. In this work we studied SiNWs with different diameters doped with Se impurities.26 We show that (1), like other dopants, substitutional Se in SiNWs has favorable configurations for positions near the surface in nanowires with small diameter, (2) there are stable states with charge +1 that enable measurement of hyperfine parameters, (3) hyperfine interactions for core dopant increase with decreasing diameter if the effects of surface relaxation do not alter the symmetry of the defect wave function but they quickly approach the bulk values if the diameter is increased above a few nanometers and (4) hyperfine structure exhibits strong changes between core and surface dopant positions, allowing, at least in principle, the identification of the impurity site on the basis of EPR data. All of our calculations are based on plane-wave pseudopotential density functional theory (DFT) as implemented in the QUANTUM ESPRESSO package.27 The exchange correlation functional Received: August 14, 2011 Published: September 27, 2011 4509
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Figure 2. Section view of silicon nanowires obtained without surface reconstruction. NW4 has a diameter of about 0.8 nm, while NW5 and NW6 have a size similar to NW1 and NW2, respectively. All these SiNWs have been passivated preserving the tetrahedral symmetry of the surface Si atoms.
Figure 1. Section view of the silicon nanowires obtained after surface reconstruction and H passivation. NW1 has a diameter of about 1.2 nm, NW2 of about 1.5 nm, and NW3 of about 2 nm. The yellow atoms indicate the position of the substitutional Se atom considered for each nanowire.
has been approximated by generalized gradient approximation (GGA) as proposed by Perdew, Burke, and Ernzerhof28 both for spin-polarized and spin-unpolarized cases. The surface Brillouin zone integration was performed with a 1 1 11 Monkhorst Pack grid29 along the nanowire axis. We have made use of ultrasoft pseudopotentials30 with an energy cutoff of 25 Ry for all the energy calculations and norm-conserving TroullierMartins31 pseudopotentials with a cutoff of 40 Ry for the hyperfine parameters. About 10 Å vacuum space is used in lateral directions in order to reduce interactions between the replicas of the nanowire. The calculations of Se in bulk Si have been performed in a cubic supercell of side 1.64 nm with a 3 3 3 k-point grid. For the doped nanowires, the distance between fictitious replicas of the defect is about 1.6 nm. However, since this distance is not sufficient to fully reduce their interactions,32 in the case of a charged defect we have introduced a correction to the total energy, based on the expression for the Madelung constant that has been proposed by Rurali and Cartoixa.33 In our case the dielectric tensor ε̅ has been calculated for each nanowire as a linear response to an external electric field.34 The evaluation of the hyperfine parameters is based on the projector augmented wave (PAW) method,35,36 with a scalar-relativistic correction for the Fermi contact term,37 since we are dealing with a heavy atom. The nanowire structure has been obtained by cutting from bulk silicon a cylinder with axis oriented along the [001] direction. In this work we have focused mainly on an approach to the surface passivation that considers the surface reconstruction of SiNW, since we think this could better resemble the nanowires with the smallest diameter obtained by growth or lithography/etching processes. This approach consists in relaxing the atomic positions until all the forces are lower than 0.02 eV/Å1, passivating the dangling bonds with hydrogen atoms, and then performing a further relaxation. However, in order to determine the effects of surface relaxation on the hyperfine parameters, we have also considered SiNWs obtained through a different procedure which consists of passivating the initial structure with hydrogen atoms and relaxing the system just once. In both cases the supercell size
of the pristine nanowire has been relaxed along the direction of the nanowire, until the stress was lower than 1 kbar along the z axis. We have studied three different nanowires with surface reconstruction with diameter d = 1.18, d = 1.52, d = 1.99, referred to as NW1, NW2 and NW3, respectively, and whose cross sections are depicted in Figure 1. The three nanowires without surface reconstruction used as a comparison have diameters of d = 0.84 (NW4), d = 1.21 (NW5), and d = 1.61 (NW6) and are shown in Figure 2. The value of the nanowire radius is given by an average of the radial positions of the external silicon atoms. The relaxation processes in SiNWs previous to the hydrogen passivation lead to surface reconstruction, a mechanism extensively investigated in literature.38 In the passivated SiNWs under examination we observe that, while for the bigger ones the reconstruction does not alter significantly their symmetry, NW1 loses its symmetry near the surface, as can be seen in Figure 1. This will result in a modification of the wave function associated with the defect and subsequently of the electronic properties related to it. We should point out that in the case of NW1 we have found two possible reconstructions which, after H passivation, are almost equivalent in energy, but here we consider only the one with the highest symmetry. In the case of a subsurface defect the initial tetrahedral geometry could be altered during the relaxation, depending on the nanowire diameter and on the defect position. In the final structure the external SiH couple has moved apart from the Se donor, and the defect wave function is localized mostly around these atoms. This is probably due to the formation of chalcogen hydrogen complexes, whose existence in bulk Si has been already proved both experimentally and theoretically.39 The formation energy of Se inside the SiNWs has been studied as a function of the Se position and of the nanowire diameter. In this calculation we have considered only SiNWs with surface reconstruction. The formation energy of a charged Se defect is given by Ef ¼ ED Epristine þ μSi μSe þ qðεV þ μe Þ
ð1Þ
where ED and Epristine are the total energies of the defective and pristine SiNW, respectively, μSi and μSe are the chemical potentials of the Si and Se atoms, q is the charge state of the defect, εV is the top of the valence band, and μe is the chemical potential for electrons. We did not consider corrections to μSi due to the absence of a bulk reservoir,33 because this contribution was found to be negligible compared to the results. Since we are only interested in the differences between formation energies, all the values will be expressed as differences from a reference value, which is chosen to be the formation energy of the 4510
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Figure 3. Relative formation energy (eq 2) for (a) NW1, (b) NW2, (c) NW3 depending on defect position. The subsurface position is the most stable configuration for all the nanowires.
Se defect in bulk Si obtained from our calculation ΔEf ¼ Ef ðSiNWÞ Ef ðbulkÞ
ð2Þ
The results obtained from our simulations can be seen in Figure 3, where ΔEf is represented as a function of the defect position for the three nanowires NW1, NW2, and NW3 . From these values we can see that there is a tendency to surface segregation and in particular the subsurface position is energetically the most favorable, in agreement with calculations performed on other impurities (P, B).10,11 Still, this tendency depends strongly on the nanowire radius and especially on the deformations near the surface. In fact, in NW1 the relaxation of the surface and the consequent reduction of the symmetry are probably responsible for a reduction of the formation energy even for the defect in the central position. The highest value of the segregation energy is found instead in NW2 (0.48 eV) and can be ascribed to what we have recognized to be related to the formation of a SeH complex, whereas in NW3 the central position is no more the least favorable. In fact, as the nanowire diameter becomes larger, the formation energy of central defect tends to the bulk value (the reference value in Figure 3). It is also worth mentioning that for nanowires with small diameter, alteration of the tetrahedral symmetry brings the formation energy of the defect with Se close to the surface below the value that we have obtained for the defect in the bulk. This suggests that the contribution to the energy originating from the deformation overcomes the one coming from confinement inside the SiNW. However, one needs to be careful in drawing conclusions, since, if the formation of complexes is important in determining the segregation behavior, the choice of different passivation mechanisms could change these results significantly. Since the aim of this work is the inspection of the hyperfine parameters, which are different from zero only for the Se+ defect, the study of the formation energies for the charged states can provide useful information. This has been done only for the defects on the axis of the SiNW, in order to isolate as much as possible these values from the influences of the surface deformations. As expected from the confinement effect the ionization energy increases noticeably from 0.31 eV in NW3 to 0.88 eV in NW2, while it decreases to 0.49 eV in NW1. Again, this should be ascribed to
Figure 4. Relative formation energy (eq 2) for NW1, NW2, and NW3 depending on the electron chemical potential μe. μe ranges in the band gap of the nanowire. Different charge states correspond to different slopes.
the high influence of the surface deformations occurring during relaxation in NW1. In Figure 4 the formation energies ΔEf for the charged defect are shown as a function of the electron chemical potential μe. Only the charge state that gives the lowest formation energy with respect to the Fermi energy is shown. Change in the slope therefore indicates transitions to a different charge state. As can be seen, for all the nanowires there is a wide interval in the values of μe for which the defect in the singly ionized charge state is the most stable. This is important since it establishes that it is possible to measure experimentally the hyperfine parameters for Se in this kind of nanowires. The hyperfine structure originates from the interaction between nuclear spin and electron spin distributions. The coupling constant A is given by the sum of two terms A ¼ Aiso 1 þ A dip
ð3Þ
where Aiso ¼
4πge μe gN μN 3ÆSz æ
Z d3 rns ðrÞδðrÞ
ð4Þ
is the scalar Fermi-contact term and is determined by the electron spin density near the nucleus and Z 3ri rj δi, j r 2 ge μe gN μN ij d3 rns ðrÞ ð5Þ A dip ¼ 2ÆSz æ r5 is the dipolar tensor, which depends on the anisotropic part of the electronic spin density. Here, ns(r) = nv(r) nV(r) is the electron spin density, ge is the electron g factor, μe is the Bohr magneton, gN is the nuclear gyromagnetic ratio of the nucleus, μN is the nuclear magneton, and ÆSzæ is the expectation value of the z component of the total electronic spin. The dipolar term Adip is a traceless tensor and, in its principal axis system, is usually described by two independent parameters, uniaxiality b and asymmetry b0 , such that 1 0 b þ b0 C B C b b0 ð6Þ A dip ¼ B A @ 2b 4511
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Table 1. Hyperfine Contact Term Aiso, and the Two Dipolar Interaction Parameters b and b0 with Se Defect on the Axis of the Nanowirea d (nm)
Aiso (MHz)
b (MHz)
b0 (MHz)
NW1*
1.18
1519
6.34
18.34
NW2†
1.52
1640
0.77
0.21
NW3
1.99
1489
0.44
0.01
NW4
0.84
2019
0.46
0.15
NW5* NW6†
1.21 1.61
1822 1621
0.42 0.63
0.09 0.03
a
NW1, NW2, NW3 (NW4, NW5, NW6) refer to nanowires with (without) surface reconstruction. Nanowires marked with the same symbol (* or †) denote nanowires with similar diameters.
Figure 5. Hyperfine contact term Aiso of Se defect on the nanowire axis as a function of the diameter. The bulk value (green) is the one obtained from our calculations. For nanowires with surface reconstruction (blue), Aiso has a maximum at 1.5 nm, while for nanowires without surface reconstruction (red), Aiso monotonically increases with decreasing diameter.
These parameters vanish for systems with tetrahedral symmetry, like bulk Si, and b0 describes the deviation of the system from axial symmetry. We are interested in establishing the changes in the hyperfine structure depending on both nanowire diameter and position of the defect. In order to test the reliability of the PAW method for the case under consideration, we compared our results for the defect in the bulk with experimental data of hyperfine40 and superhyperfine41 parameters. Our value of the hyperfine contact term is 1327 MHz against an experimental value of 1658 MHz. Similar or even better accuracy has been achieved for superhyperfine parameters, at least for the shells closer to the defect. Comparing these results with others obtained for shallower dopants, we concluded that the good agreement depends on the fact that Se in the bulk is deep enough to reduce interaction with defect replicas, even inside a supercell having a side of 1.64 nm. The use of scalar relativistic correction deserves further comments. Although this correction is suitable when working with an heavy atom, like Se, we found that neglecting it leads to an overestimation of about 20% for the contact term in the bulk Si compared to the experimental value, while taking it into account causes an underestimation of approximately the same amount. In the following all the results will include this relativistic correction and we will consider as a term of reference the calculated value of Aiso in bulk Si and not the experimental one. First, we investigated the dependence of the hyperfine structure on the nanowire diameter. In doing that, we have limited ourselves to the case of Se atoms placed on the axis of the nanowire, in order to highlight the effects of confinement. In Figure 5 we have reported the change in the contact term as a function of the diameter for nanowires both with and without surface reconstruction. As a consequence of the squeezing of the defect level wave function, Aiso is always higher in nanowires than in bulk Si and its value tends to increase as the diameter is reduced. However, while nanowires without the initial surface reconstruction respect this trend, for nanowire with surface reconstruction the value of Aiso at diameter of about 1.2 nm is lower than that at 1.5 nm. Comparing the values of Aiso for nanowires with same diameter but different surface structure we can deduce that surface relaxation is
responsible for the small value in NW1 . Thus, we can conclude that even for a deep donor as Se, the effects of surface cannot be neglected for nanowires with diameter comparable or smaller than 1 nm in the determination of the hyperfine structure. Apart from this case, the contact term follows an almost linear relationship between Aiso and the diameter, in the range we have covered. Noticing that at a diameter of 2 nm the difference between the contact term in the bulk and in the nanowire is only about 10%, we do not expect to have sizable differences at diameters above a few nanometers. In Table 1 we display our results of the calculations of parameters b and b0 , defined in eq 2, for all the nanowires here considered. In this case, since we are dealing with Se on the axis of nanowires oriented along the z direction, the values Aizdip (i = x, y) xx yy 0 are zero or negligible, so we set 2b = Azz dip and b = |Adip Adip| after tensor diagonalization. As can be seen, the values of b and b0 are quite small (less than 1 MHz) except for the case of NW1, where the stronger anisotropic interaction highlights again the effects of surface relaxations for nanowires of this size. Notably, the values of b have a different sign depending on the surface structure: positive in the presence of surface reconstruction and negative for nanowire passivated from the beginning. This can be due to the small differences in the local structure near the defect caused by the different surface structures. However, we performed some tests on NW4 subject to compressive and tensile strain and we have observed that, while Aiso and b0 are quite stable, b undergoes dramatic fluctuations, even for a departure of less than 1% of the nanowire lattice constant from our relaxed value. Since b0 is a measure of the nonaxial symmetry of the donor wave function, its values for surface reconstructed nanowires are considerably larger than those of nanowires with similar diameter but without surface reconstruction. These results about the scaling of the hyperfine parameters of Se donor with the size of the nanowires are in agreement with what have been found by tight-binding calculations for chalcogen donors in Si quantum dots.42 Having established that at diameters greater than 1.5 nm the effects of surface relaxation for defect on the axis of the SiNW are sufficiently small, we now move on to the analysis of the dependence of the hyperfine parameters on the position of the defect, focusing on the nanowire NW2, because it has the maximum Aiso among the relaxed nanowires with Se at the central site. The results for Aiso are summarized in Table 2. It is evident from these values that, for defects located near the axis of the nanowire, the contact terms are quite similar among them and greater than in the bulk. Conversely, near the surface of the 4512
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Table 2. Hyperfine Contact Term Aiso for NW2 with the Se Defect in Different Positions (see Figure 1)a
Aiso (MHz)
defect
defect
defect
defect
position 1
position 2
position 3
position 4
1641
1548
856
928
a
The values can be divided in two groups, one with Se being in the core and the other with Se in the surface region.
[001] SiNWs. The formation energy of the defect is found to depend strongly on the size of the nanowire and on the position of the defect itself. In particular, a tendency to surface segregation has been recognized with the possible formation of the SeH complex. The conditions for the existence of the stable Se+ have been identified, depending on the electron chemical potential. Hyperfine parameters have been determined with PAW method in order to exploit their dependence on nanowire diameter and defect position. It is found that the contact term increases at smaller diameter, but with limitations for SiNW smaller than 1.2 nm, and approaches the bulk value quickly as the size of the nanowire is increased. Moreover the hyperfine structure shows significant differences between central and peripheral defect positions. This suggests the possibility to use EPR to identify the position of the impurities. These calculations demonstrate the usefulness of Se doped SiNW for application in which large hyperfine interactions are required and suggest a possible way to determine the distribution of the defect inside the nanowire.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]; alberto.debernardi@ mdm.imm.cnr.it.
Figure 6. Section and side view of the defect wave function modulus in NW2. With the defect in position 1 (top), the four lobes of the wave function point toward the four tetrahedral directions and this structure is quite similar to that obtained in bulk as well as in other nanowires with defect in central positions. This symmetric structure is lost for defects located near the surface, as in position 3 (bottom). In this case the wave function is mainly localized near the external Si atom. The isosurface of the two wave functions have been evaluated at approximately the same isovalue.
nanowire, the deformations lead to a steep decrease of Aiso, bringing it well below the bulk value. This should be due to the interaction with the surface and to the possible formation of complexes with H atoms. In the case of a subsurface position the contact term of the superhyperfine interaction gives some insight about this possibility: the contact term of the superficial Si close to the Se is greater than that of the other impurity nearest neighbors and also the superficial H atom has non-negligible Aiso. This supports the previous hypothesis of a wave function delocalized over the SeSiH atoms (see Figure 6). For defects located off the axis of the nanowire, the tensor Adip is not oriented along the z axis and the parameters b and b0 are about 1 order of magnitude bigger than the values reported in Table 1 and strongly dependent on the defect position. This is a further confirmation of the changes in the hyperfine structure between different regions of the nanowire, but contrary to the Fermi contact term, it seems hard that the dipolar term can be used to localize the position of the defect, due to large fluctuations of the component of the Adip tensor. Given these different properties of the hyperfine structure for the defect near the axis of the nanowire with respect to the defect close to the surface, we suggest that this could be a way to determine the distribution of the dopants inside the SiNW. In conclusion, we have used first principles DFT calculations to investigate the electronic properties of Se double donor in
’ ACKNOWLEDGMENT The research activity here presented is performed in the framework of the ELIOS research project, which is supported by Fondazione Cariplo. We acknowledge CASPUR consortium for providing computational resources for the project “Chalcogen Impurities in Si-NAnowires (CISNA)”. ’ REFERENCES (1) Cui, Y.; Lieber, C. M. Science 2001, 291, 851–853. (2) Gudiksen, M. S.; Lauhon, L. J.; Wang, J.; Smith, D. C.; Lieber, C. M. Nature 2002, 415, 617–620. (3) Cui, Y.; Zhong, Z.; Wang, D.; Wang, W. U.; Lieber, C. M. Nano Lett. 2003, 3, 149–152. (4) Duan, X.; Huang, Y.; Agarwal, R.; Lieber, C. M. Nature 2003, 421, 241–245. (5) Cui, Y.; Wei, Q.; Park, H.; Lieber, C. M. Science 2001, 293, 1289–1292. (6) Yang, C.; Barrelet, C. J.; Capasso, F.; Lieber, C. M. Nano Lett. 2006, 6, 2929–2934. (7) Tian, B.; Zheng, X.; Kempa, T. J.; Fang, Y.; Yu, N.; Yu, G.; Huang, J.; Lieber, C. M. Nature 2007, 449, 885–889. (8) Kempa, T. J.; Tian, B.; Kim, D. R.; Hu, J.; Zheng, X.; Lieber, C. M. Nano Lett. 2008, 8, 3456–3460. (9) Rurali, R. Rev. Mod. Phys. 2010, 82, 427–449. (10) Peelaers, H.; Partoens, B.; Peeters, F. M. Nano Lett. 2006, 6, 2781–2784. (11) Leao, C. R.; Fazzio, A.; da Silva, A. J. R. Nano Lett. 2008, 8, 1866–1871. (12) Diarra, M.; Niquet, Y.-M.; Delerue, C.; Allan, G. Phys. Rev. B 2007, 75, 045301. (13) Bjork, M. T.; Schmid, H.; Knoch, J.; Riel, H.; Riess, W. Nat. Nanotechnol. 2009, 4, 103–107. (14) Xie, P.; Hu, Y.; Fang, Y.; Huang, J.; Lieber, C. M. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 15254–15258. (15) Perea, D. E.; Hemesath, E. R.; Schwalbach, E. J.; Lensch-Falk, J. L.; Voorhees, P. W.; Lauhon, L. J. Nat. Nanotechnol. 2009, 4, 315–319. 4513
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