Letter pubs.acs.org/NanoLett
Stability and Segregation of B and P Dopants in Si/SiO2 Core−Shell Nanowires Sunghyun Kim, Ji-Sang Park, and K. J. Chang* Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea S Supporting Information *
ABSTRACT: Using molecular dynamics simulations, we generate realistic atomic models for oxidized Si nanowires which consist of a crystalline Si core and an amorphous SiO2 shell. The amorphous characteristics of SiO2 are well reproduced, as compared to those for bulk amorphous silica. Based on first-principles density functional calculations, we investigate the stability and segregation of B and P dopants near the radial interface between Si and SiO2. Although substitutional B atoms are more stable in the core than in the oxide, B dopants can segregate to the oxide with the aid of Si self-interstitials which are generated during thermal oxidation. The segregation of B dopants occurs in the form of B interstitials in the oxide, leaving the self-interstitials in the Si core. In the case of P dopants, dopant segregation to the oxide is unfavorable even in the presence of self-interstitials. Instead, we find that P dopants tend to aggregate in the Si region near the interface and may form nearest-neighbor donor pairs, which are energetically more stable than isolated P dopants. KEYWORDS: Silicon nanowires, B and P dopants, doping, dopant segregation, density functional
S
and thereby causes the modification of both the structural and electronic properties of SiNWs. In metal oxide semiconductor field-effect transistors (MOSFETs) with planar Si/SiO 2 interfaces, it is well-known that dopant impurities, such as B and P, segregate at the interface.27 Especially, B diffusivity is greatly enhanced during ion implantation and subsequent thermal annealing or during thermal oxidation; this phenomenon is called transient or oxidation enhanced diffusion.28,29 The enhanced B diffusion is attributed to Si self-interstitials which are generated near the interface. In SiNWs, the enhanced B diffusion was also observed during thermal annealing.12 Previous theoretical calculations have been mostly focused on pristine or functionally terminated SiNWs with hydrogen (−H) or hydroxyl (−OH).30−32 Surface termination by functional groups has limitation in understanding the effect of oxide sheath on the electronic properties and segregation behavior of dopants in SiNWs. In recent theoretical studies, the Si/SiO2 core−shell structure was employed to study the structural, electronic, and optical properties of oxidized SiNWs.33,34 Although the segregation behavior of B and P dopants was theoretically investigated, previous studies were limited to the effect of dangling bonds on the site preference of dopants. Moreover, only substitutional dopants were considered to find energetically favorable sites, while Si self-interstitials are abundant during ion implantation or thermal oxidation. Thus, the mechanism for dopant segregation at the radial interface of
emiconductor nanowires have received much attention because of their unique electronic properties that are different from those of bulk materials due to the quantum confinement effect and the large surface to volume ratio. Among semiconductor nanowires, Si nanowires (SiNWs) have been extensively studied because of their promising building blocks of nanoscale devices and their compatibility with the matured Si technology. A variety of applications using SiNWs have been reported for devices such as field-effect transistors (FETs),1,2 solar cells,3 thermoelectric materials,4 and biological and chemical sensors.5 Impurity doping which controls the type of charge carriers and the carrier density is one of the critical issues in the device application of nanowires. SiNWs can be doped either p- or n-type with B and P impurities.6 However, it is generally difficult to dope nanocrystals and nanowires for several reasons, such as segregation of dopants to surfaces and/ or interfaces7−12 and high ionization energies caused by dielectric mismatch.11,13,14 When dopants are incorporated during the growth of SiNWs using a vapor−liquid−solid (VLS) method, vapor−solid deposition on the sides of nanowires causes unintentional surface doping and thereby nonuniform distribution of dopants.15−21 The trapping and depletion of charge carriers near nanowire surfaces and/or Si/SiO 2 interfaces also decreases the doping efficiency.14 Moreover, recent theoretical calculations suggested that donor-pair defects play a role in the low doping efficiency of P-doped SiNWs.22 Oxidized SiNWs can be synthesized by subsequent thermal oxidation of as-grown SiNWs. According to experimental and theoretical studies,23−26 oxidation induces compressive strain to the Si core, which results from the expansion of the oxide shell, © XXXX American Chemical Society
Received: April 13, 2012 Revised: July 11, 2012
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Figure 1. Atomic configurations in the generation process of a Si/SiO2 core−shell nanowire: (a) bulk amorphous SiO2 generated through MD simulations; (b) a circular hole in the oxide; (c) a crystalline Si core built in the circular hole; (d) a circular oxide shell by cutting the outer oxide; (e) a relaxed core−shell structure through additional MD simulations, with the oxide surface terminated by O atoms and the Si core atoms fixed; and (f) a fully relaxed configuration by using first-principles calculations. Blue and red balls denote Si and O atoms, respectively.
nanowires is small due to computational difficulty. Bulk amorphous SiO2 is generated through melt-and-quench classical molecular dynamics (MD) simulations, using the interatomic potentials of van Beest, Kramer, and van Santen,42 which are implemented in the GULP code.43 We start with an artificial oxide, where an O atom is inserted in each Si−Si bond of crystalline Si to satisfy the stoichiometry of SiO2. This oxide system is melted at a temperature of 4000 K for 100 ps and quenched with a rate of 100 K/ps down to 300 K, with keeping the mass density of 2.20 g/cm3. We dig a circular hole in the amorphous oxide and build a SiNW in it, as shown in Figure 1. When a Si core size is chosen, instead of removing all the oxide atoms within the core radius, we remove a certain number of atoms in the oxide, which is determined by the oxide mass at the core volume, with the use of the oxide mass density. With the Si core fixed, we relax all the oxide atoms by performing melt-and-quench MD simulations, prepare for a Si/SiO2 core− shell structure by cutting the oxide region outside the circular shell, and then optimize the oxide shell through MD simulations again. A small volume mismatch between the hole and the Si core is healed during MD simulations. The final configuration of the core−shell nanowire is obtained by performing additional first-principles calculations to optimize all the ionic coordinates and the lattice constant along the axis until the residual forces are less than 0.05 eV/Å. To exclude the effect of dangling bonds, we select the core−shell structure without dangling bonds at the interface and surface. We consider oxidized SiNWs under tensile and compressive strain to examine the strain effect on the band alignment and the doping characteristics. The strain can be controlled by changing the axial lattice constant of the Si core before the oxide shell is optimized. We finally obtain two oxidized core−shell NWs, which are denoted as SiO2−SiNW+ and SiO2−SiNW−. The average core diameters of SiO2−SiNW+ and SiO2−SiNW− are 13.10 and 13.48 Å, respectively, and the oxide shell consists of 4-fold coordinated Si and 2-fold coordinated O atoms, with the
oxidized SiNWs is not well studied yet. To better understand the effects of oxide sheath and Si self-interstitials on the site preference of dopants, realistic atomic models for Si/SiO2 core−shell nanowires are required. In this Letter, we use first-principles density functional calculations to investigate the stability and segregation of B and P dopants in oxidized SiNWs. We generate atomic models for oxidized SiNWs in which crystalline Si core is sheathed by amorphous SiO2. The electronic properties of oxidized SiNWs are compared with those for an H-terminated SiNW with the diameter similar to the Si core size. We examine the effect of Si self-interstitials on the segregation of dopants at the Si/SiO2 interface and find that B dopants in the presence of Si selfinterstitials easily diffuse toward the oxide in form of interstitials, leaving Si self-interstitials to the core side. On the other hand, P dopants prefer to subinterface sites and thereby tend to accumulate in form of donor-pair defects in the Si region near the interface. Our calculations are performed using the generalized gradient approximation35 (GGA) for the exchange−correlation potential within the density functional theory framework and the projector augmented wave (PAW) pseudopotentials,36,37 as implemented in the VASP code.38,39 The wave functions are expanded in plane waves up to a cutoff of 400 eV, and a set of k-points along the wire axis is generated by the 1 × 1 × 5 Monkhorst−Pack mesh.40 In supercell geometries, we chose the distance of about 10 Å between adjacent wires, which ensures for prohibiting wire−wire interactions. It is known that small-diameter SiNWs primarily grow along the ⟨110⟩ direction in a VLS growth process, whereas SiNWs with larger diameters favor the ⟨111⟩ orientation.41 We consider atomic structures for Si/SiO2 core−shell nanowires, in which crystalline Si is embedded in amorphous SiO2 with the O-terminated surface. We choose the ⟨111⟩ orientation for the Si core to compare with experiments which have been mostly done for large-diameter SiNWs, although the diameter of our B
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The band gaps of SiO2−SiNW+ and SiO2−SiNW− are calculated to be 1.47 and 1.55 eV, respectively, as compared to the value of 1.69 eV for the H-terminated SiNW. The reduction of the band gaps results from the interface and strain effects. In previous calculations,30−32 the band gaps of OH-terminated SiNWs were shown to be considerably reduced, relative to Hterminated SiNWs, and the red shift of the band gap was attributed to the hybridization between the surface Si 3p and O 2p states. In SiO2−SiNW+ and SiO2−SiNW−, we find that the charge densities of the valence band edge state are accumulated near the Si/SiO2 interface due to the hybridization with the interface O atoms, as shown in Figure 3. Thus, the
average thickness of about 6.1 Å. To compare the structural and electronic properties of oxidized SiNWs, we also construct an H-terminated SiNW which has the similar diameter of 13.37 Å. The Si core of SiO2−SiNW+ is slightly under tensile strain of 2.3%, with the periodicity of 9.70 Å along the axis, as compared to the H-terminated SiNW, while that of SiO2−SiNW− has the periodicity of 9.27 Å due to compressive strain of −2.2%. We calculate the radial distribution function in the oxide shell to examine the quality of the amorphous structure (Figure 2). The
Figure 2. Radial distribution functions of Si−O (red), O−O (green), and Si−Si (blue) pairs in the amorphous SiO2 shells of SiO2−SiNW+ (solid lines) and SiO2−SiNW− (dashed lines). A small peak at about 2.4 Å in the Si−Si radial distribution function comes from the O double bridge structure on the wire surface, in which a Si−Si pair is connected by two O atoms.
first and second peak positions of the Si−O, O−O, and Si−Si pairs are compared for SiO2−SiNW+ and SiO2−SiNW− in Table 1. The overall peak positions are in good agreement with Table 1. First and Second Peak Positions (in units of Å) of the Si−O, O−O, and Si−Si Pairs in the Radial Distribution Functions for SiO2−SiNW+ and SiO2−SiNW− Compared with the Experimental and Theoretical Results for Bulk Amorphous Silica Si−O
SiO2− SiNW+ SiO2− SiNW− calcd (ref 44) expt (ref 45)
O−O
Figure 3. (a) The local density of states of SiO2−SiNW+ along the radial direction. The distributions of charge densities for the (b) valence band maximum and (c) conduction band minimum states of SiO2−SiNW+.
Si−Si
first peak
second peak
first peak
second peak
first peak
second peak
1.64
4.15
2.63
4.99
3.01
4.86
1.63
4.12
2.62
4.89
3.06
4.70
1.595
4.12
2.590
5.01
3.155
5.05
1.62
4.15
2.65
4.95
3.12
5.18
characteristics of the valence band edge state are similar to those for OH-terminated SiNWs. To examine the interface effect on the band gap, we remove the H atoms in the Hterminated SiNW and then attach the oxide shells of SiO2− SiNW+ and SiO2−SiNW−. Without relaxations in the Si core, the band gaps are reduced by 0.21 and 0.07 eV, respectively, representing solely the interface effect. The oxidation of Si NWs not only reduces the diameter but also induces strain to the Si core due to expansion of the surrounding oxide.23−26 Recent experiments have reported that oxidation-induced strain leads to red-shifts of the band gap in oxidized SiNWs.23 According to theoretical calculations,46 the band gap of Hterminated SiNWs could be modulated by axial strain. In Hterminated SiNWs along the ⟨111⟩ direction, the band gap decreases as compressive strain applies, whereas the effect by tensile strain is less significant. In our study, we notice that the band gap of the H-terminated SiNW increases only by 0.01 eV under 2.3% tensile strain, whereas it decreases by 0.08 eV under −2.2% compressive strain. Thus, the combined effects of interface and strain well explain the reduction of the band gaps for SiO2−SiNW+ and SiO2−SiNW−. Figure 3a shows the local
experiments and theoretical calculations44,45 for bulk amorphous silica. Although the Si cores are under different strain, the oxide shells exhibit similar peak positions and amorphous characters. On the other hand, the crystalline structure of the Si core is well preserved even near the Si/SiO2 interface. The bond angles in the Si core are close to the tetrahedral bond angle of 109.47°, with a root mean square deviation of 2.5° at the core center and 4.7° in the subinterface region. Thus, our atomic models well reproduce experimentally synthesized SiNWs, which consist of crystalline Si core and amorphous oxide shell.12,18 C
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B−I complex, a substitutional B interacts with a nearby selfinterstitial at the tetrahedral site in both neutral and +1 charge states.50 In the core−shell NWs, we consider the +1 charge state of the B−I complex because this charge state is more stable for the p-type Fermi level. In the core region, we find that Bs forms the (B−I)+1 complex with a self-interstitial at the adjacent tetrahedral site (Figure 5a), similar to that in bulk Si.
density of states along the radial direction, which is obtained by averaging the charge densities over the angular and axial directions. In SiO2−SiNW+ and SiO2−SiNW−, the valence band offsets between the Si core and oxide shell are estimated to be about 2.1 and 2.2 eV, respectively, which are slightly smaller than the GGA results of 2.4−2.5 eV for planar Si/SiO2 interfaces due to the gap reduction. These offsets are severely underestimated relative to the measured value47 of 4.4 eV for Si/SiO2 films because the GGA calculations underestimate the band gaps of Si and SiO2. We next examine the effect of the oxide shell on the distribution of B and P dopants. For a substitutional B (Bs), we consider the −1 charge state which is energetically favorable in p-type Si. This charge state actually prevents the charge transfer from Si to SiO2 when B occupies a Si lattice site in the oxide. The site preference of Bs−1 is examined for various positions at different radial distances (Figure 1f). Because rotational and translational symmetries are broken due to the amorphous oxide, for a given radial distance, we take the average energy over several substitutional positions with similar radii. When Bs−1 resides in the Si core, the variation of energies with the site is quite small to within 0.16 eV, as shown in Figure 4a. At the
Figure 5. The atomic structures of (a) the B−I complex in the Si core and (b) the interstitial Bi in the oxide shell. Dark-blue, light-blue, red, and green balls denote the Si, self-interstitial, O, and B atoms, respectively.
Although the (B−I)+1 complex is more stable near the interface than at the core center, the energy variation within the core is small to within about 0.34 eV. When Bs diffuses toward the oxide, it turns into an interstitial B (Bi), leaving the selfinterstitial at the interface. In the +1 charge state, the interstitial B intervenes between the four-fold Si and two-fold O atoms and interacts with an adjacent two-fold O atom, making it a three-fold coordinated O (Figure 5b). The energies of Bi+ in the oxide shell are compared with that of the (B−I)+1 complex at the core center in Figure 4b. It is clear that the energy is significantly lowered by about 1.5 eV in the oxide region. This result indicates that B easily segregates to the oxide with the aid of a self-interstitial, being a stable interstitial form. This mechanism for B segregation is very similar to that proposed for planar Si/SiO2 interfaces48 and explains very successfully the experimental observation12 that B atoms segregate to the oxide shell during thermal oxidation of as-grown SiNWs. Due to the band offset at the Si/SiO2 interface, the interstitial B in the oxide donates an electron to the conduction band minimum of the Si core and thereby compensates for B acceptors, reducing the concentration of hole carriers. The compensation effect is actually more significant in oxidized SiNWs due to large surface to volume ratios, as compared to planar Si/SiO2 interfaces. Similarly, we examine the stability of a substitutional P (Ps) near the radial Si/SiO2 interface. In both SiO2−SiNW+ and SiO2−SiNW−, although the subinterface sites are energetically more favorable by about 0.03−0.11 eV than the core center, the variation of energies in the core region is in the range of 0.11 eV (Figure 4c). The preference of subinterface sites was also found for planar Si/SiO2 interfaces.27,51 In the H-terminated SiNW, the energy differences between different substitutional sites inside the wire are extremely small, less than 0.1 eV, similar to previous calculations.22 On the other hand, the energy of Ps increases significantly either at the interface or
Figure 4. The energies of (a) a substitutional B, (b) a B−I complex and an interstitial B, and (c) a substitutional P at different lattice sites in SiO2−SiNW+ and SiO2−SiNW−, with taking those of the core center labeled 1 as references. In (b), the energies of the interstitial B in the oxide are compared with those for the B−I complex in the Si core. In (c), filled red circles represent the energies of the substitutional P in the H-terminated SiNW.
interface site labeled 5, which is surrounded with the core Si and shell O atoms, the energy increases by about 0.65 eV. In the oxide region, the increase of energy becomes more significant, indicating that Bs is more stable in the Si core than in the oxide shell. The energy difference of about 1.3 eV between the core and the shell sites is very similar to that obtained for planar Si/SiO2 interfaces.48 In SiNWs, there is evidence from several experimental measurements that the concentrations of dopant impurities are generally higher at the surface than inside the nanowire.15−21 While high dopant concentrations observed in the surface region are mostly attributed to the surface doping effect, surface dangling bonds are partly responsible for dopant segregation to the surface.7−10 In SiO2−SiNW+ and SiO2−SiNW−, we find that Bs also prefers to occupy a dangling bond site at the interface, with the energy lower by about 0.6 eV than that at the core center. In MOSFET devices, B segregation to the Si/SiO2 interface commonly occurs under nonequilibrium conditions after ion implantation and subsequent thermal annealing, where Si selfinterstitials are abundant. In bulk Si, it is known that B easily diffuses via the formation of a B−I complex in the presence of a Si self-interstitial (I).49 In the most stable configuration of the D
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than at the core center. In the H-terminated SiNW, as the lattice relaxations around the d1 defect are ineffective, the difference between the binding energies at the subsurface and center sites is reduced to 0.25 eV. In conclusion, we have studied the structural and electronic properties of oxidized SiNWs and shown that oxidation of SiNWs reduces the band gap, as compared to H-terminated SiNWs. The band gap reduction is attributed to the effects of the chemical bonding between the interface Si and O atoms and the strain induced to the Si core. In NWs doped with B and P impurities, substitutional dopants are generally more stable in the Si core region rather than inside the oxide. We find that B dopants easily diffuse to the oxide with the aid of Si selfinterstitials. At the interface, the B diffusion proceeds in the form of an interstitial B, leaving the self-interstitial in the Si core. On the other hand, it is energetically unfavorable for the P dopants to segregate to the oxide even in the present of selfinterstitials. However, as P dopants aggregate in the Si region near the interface, the formation of nearest-neighbor donor pairs is very stable at the subinterface sites with respect to isolated substitutional P dopants. Our results for the distribution of B and P dopants are in good agreement with experiments. Finally we address that our proposed method can be used to generate realistic Si/SiO2 core−shell nanowires with any orientation. For the nanowire oriented along the ⟨110⟩ direction (see the Supporting Information), we find that overall the electronic structure is very similar to that of the ⟨111⟩oriented nanowire. Thus, the conclusions for the doping characteristics will not be altered by the different orientation of nanowires.
inside the oxide, in good agreement with recent calculations for oxidized SiNWs oriented along the ⟨100⟩ direction.34 The increase of energy is about 4 eV, which is much larger than that for a substitutional B. If dangling bonds exist at the interface, they become energetically favorable sites because of the neutralization by Ps. In the absence of interface dangling bonds, our results indicate that P segregation to the oxide is unlikely to occur in a substitutional form. To examine the effect of a Si self-interstitial on P segregation, we consider a defect complex which consists of P and I, similar to the B−I complex. In bulk Si, previous calculations52,53 showed that the P−I complex forms a bridge configuration in both neutral and −1 charge states, where P is bonded to two adjacent Si lattice atoms, occupying a bond-center site. Considering the −1 charge state in n-type Si, we compare the energy of the (P−I)−1 complex in the Si core with that of an interstitial P (Pi−1) in the oxide shell and find that the (P−I)−1 complex is energetically more stable by 0.49−0.82 eV for several lattice positions chosen. In contrast to the B−I complex, P dopants do not segregate to the oxide even with the aid of Si self-interstitials. During thermal oxidation of P-doped SiNWs, recent experiments12 reported that P dopants are accumulated in the Si region close to the interface, while B atoms segregate to the oxide shell. This different segregation behavior is well explained by our results for the energetics of B and P interstitials in the oxide, relative to defect complexes with selfinterstitial in the Si core. In as-grown SiNWs, a large pile of incorporated P dopants was observed in the surface region due to the surface doping effect.15−17,21 Subsequent annealing induces the diffusion of P dopants from the surface to the core and mitigates the gradient in dopant distribution.17 While some P dopants could be trapped by surface dangling bonds, it is more likely for the P dopants to diffuse inside the Si core due to the small variation of energies in the core region. When P atoms aggregate to the interface, they may form donor pair defects near the interface where dopant concentrations are high. In fact, at planar Si/SiO2 interfaces, theoretical calculation51 showed that it is energetically favorable for dopant segregation to occur in the form of nearest-neighbor donor pairs (denoted as d1), in which two substitutional Ps atoms are positioned at the nearest-neighbor distance. In SiNWs, the stability of nearest-neighbor donor pairs was also found for small diameters below a critical value.22 Similarly in SiO2− SiNW+ and SiO2−SiNW−, we find that the d1 defect is more stable than two isolated Ps atoms in the Si core. In the d1 defect, the two adjacent P atoms induce an antibonding defect level deep in the band gap. The stability of the d1 defect is attributed to the energy gain by lowering the defect level from shallow to deep, which overcomes the strain energy induced by relaxations around the d1 defect. For various lattice sites, we estimate the average binding energy of the d1 defect to be about 0.69 eV. The binding energy, which is defined as the energy difference between the d1 defect and two separated substitutional P dopants, is correlated to the P−P bond length (see figures in the Supporting Information for the details). The splitting of the bonding and antibonding levels tends to increase with decreasing of the P−P bond length. As the antibonding level moves toward the conduction band minimum, the energy gain is reduced. Near the interface, the strain induced by the d1 defect is properly released in the environment of the flexible amorphous network, increasing the P−P bond length. In fact, due to the larger P−P bond length, the d1 defect at the subinterface site is found to be lower in energy by about 0.5 eV
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ASSOCIATED CONTENT
S Supporting Information *
Antibonding defect levels of the nearest-neighbor donor pairs, their binding energies for different P−P bond lengths, and atomic and electronic structures of the ⟨110⟩-oriented nanowire. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (grant no. NRF-2011-0093845) and by the Converging Research Center Program through the Ministry of Education, Science and Technology (grant no. 2011K000626).
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