pubs.acs.org/NanoLett
Defects Responsible for the Hole Gas in Ge/Si Core-Shell Nanowires Ji-Sang Park,† Byungki Ryu,† Chang-Youn Moon,‡ and K. J. Chang*,† †
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea, and ‡ Department of Physics and IPAP, Yonsei University, Seoul 120-749, Republic of Korea ABSTRACT The origin of the ballistic hole gas recently observed in Ge/Si core-shell nanowires has not been clearly resolved yet, although it is thought to be the result of the band offset at the radial interface. Here we perform spin-polarized density-functional calculations to investigate the defect levels of surface dangling bonds and Au impurities in the Si shell. Without any doping strategy, we find that Si dangling bond and substitutional Au defects behave as charge traps, generating hole carriers in the Ge core, while their defect levels are very deep in one-component Si nanowires. The defect levels lie to within 10 meV from or below the valence band edge for nanowires with diameters larger than 33 Å and the Ge fractions above 30%. As carriers are spatially separated from charge traps, scattering is greatly suppressed, leading to the ballistic conduction, in good agreement with experiments. KEYWORDS Core-shell nanowires, dangling bond defect, Au impurity, electronic structure
S
dopants to generate carriers in a different region. Indeed, recent calculations showed that in Ge/Si core-shell NWs the valence band edge is confined in the core region, and neargap electronic states are spatially separated within the core or the shell region.14,15 Despite the experimental observation of a ballistic hole gas and the theoretical understanding of the band offset, the origin of hole carriers has not been clearly understood yet. As both the Ge core and the Si shell were undoped, the p-type doping is likely to be caused by intrinsic and/or extrinsic defects. In Si NWs, electron spin resonance (ESR) experiments showed that dangling bond (DB) defects are abundant at the radial interface between Si and gate oxide, as the core region is pure crystalline.16,17 The DB defect (identical to the Pb center) is a major charge trap at the Si/SiO2 interface of MOS devices, with the defect levels deep in the band gap.18 In Ge/Si core-shell NWs, despite the lattice mismatch between two different materials, DB defects are expected to be absent at the Ge/Si interface because of the epitaxial core-shell structure.12,13 Considering the band offset of about 0.5 eV between Si and Ge, it is likely that Si DB defects will be shallow charge traps in Ge/Si core-shell NWs. In recent theoretical studies, the charge transition levels of surface DB defects relative to vacuum were shown to behave as a common energy reference in Si, Ge, and Ge/Si core-shell NWs.19 This study further showed that due to the confinement potential DB defect levels relative to the valence band edge are shallower in Ge NWs than those of Si NWs. However, in Ge/Si NWs, the minimum defect level of 0.13 eV obtained for the diameter of about 20 Å was still too high to generate free carriers at room temperature. Furthermore, as the calculations relied on the nonspin-polarized density functional scheme, the effects of spin-polarized electrons and spin-orbit interactions, which are significant for Ge, were not considered.
ilicon nanowires (Si NWs) have attracted much attention because of their unique electronic properties, for instance, control of the band gap by the low-dimensional confinement effect,1,2 superiority as building blocks of devices, and compatibility with the existing Si technology.3 Several applications of Si NWs to nanoscale devices have been demonstrated, including field-effect transistors (FETs),4–6 sensors,7 solar cells,8,9 and switches.10 As the operation of devices relies on the density of free carriers, doping is critical to achieve high-performance devices based on nanowires. However, it is generally difficult to dope lowdimensional nanocrystals and nanowires due to segregation of dopants to surfaces and/or interfaces, high ionization energies caused by reduced screening, and compensation by charge traps.11 In doped nanowires, scattering by charged impurities usually reduces the intrinsic mobility of devices and hence limits the device performance. Recently, without any doping strategy, high-performance FETs have been realized based on Ge/Si core-shell NWs.12,13 The key structure of this device is a core-shell heterostructure in which hole carriers are confined in the narrow Ge core.13 Because scattering of carriers by impurity centers is suppressed, the mobility is greatly improved, leading to a ballistic transport regime even at room temperature, in which on-current values are three to four times greater than those for conventional metal-oxide-semiconductor (MOS) devices. The existence of a hole gas was thought to be the result of the band offset at the radial heterojunction between the core and shell bands.13 The band offset generates a confinement potential for carriers, making it possible for
* To whom correspondence should be addressed. E-mail:
[email protected]. Telephone number: 82-42-350-2531. Fax: 82-42-350-2510.. Received for review: 09/9/2009 Published on Web: 12/17/2009 © 2010 American Chemical Society
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Among extrinsic impurities, Au is commonly used as a catalytic material without any intentional dopants during vapor-liquid-solid growth of nanowires. In Si NWs, surface migration of Au from the droplet to the sidewall was reported, suggesting that Au wets the sidewall.20 Although the Au solubility is extremely low in bulk Si, a large concentration of Au was observed near the wire surfaces.21,22 In bulk Si, Au introduces deep donor and acceptor levels of 0.35 and 0.62 eV, respectively, above the valence band edge, while these levels are much shallower in Ge, located at 0.05 and 0.15 eV.23,24 In Ge/Si NWs, which are grown using the Au catalyst, the defect levels of Au are also expected to be shallow due to the band offset, similar to surface DB defects. In this communication, we report the results of spin density functional calculations for the defect levels of surface dangling bonds and substitutional Au impurities in Si, Ge, and Ge/Si core-shell NWs. The defect levels relative to the valence band edge have a tendency to decrease with increasing of the wire diameter. Thus, both dangling bond and Au defects give rise to shallow defect levels near the valence band edges in Ge and Ge/Si NWs, while the defect levels lie deep in the band gap in Si NWs. The shallowness of the defect levels is more significant in Ge/Si NWs, suggesting that surface dangling bond and Au defects are likely to behave as charge trap centers. Because of the spatial separation of hole carriers confined in the Ge core from charge traps in the Si shell, scattering by charge traps are greatly suppressed in the core-shell structure, as compared to Ge NWs, where accumulated hole carriers are close to the charged surface. Our calculations provide a clue for understanding the observation of the hole gas in Ge/Si NWs and the suppression of carriers at zero gate voltage in one-component Si and Ge NWs. The electronic properties of defects in NWs are calculated using the local spin density functional approximation25 for the exchange-correlation potential and ultrasoft pseudopotentials,26 as implemented in the VASP code.27 The wave functions are expanded in plane waves up to a cutoff of 188 eV for DB defects, whereas a higher cutoff of 225 eV is used for Au impurities. We employ supercells containing one and two unit cells along the wire axis for DB and Au defects, respectively, with a vacuum region of about 10 Å, which prohibit interactions between adjacent wires, and use the special k-points generated by the 1 × 1 × 4 Monkhorst-Pack mesh.28 We fully relax the wire lattice constants and the ionic coordinates until the residual forces are less than 0.01 eV/Å. We also examine the effect of spin-orbit interactions on the valence band edge by using the projector augmented wave (PAW) potentials.29 We consider Si, Ge, and Ge/Si NWs oriented along the [111] axis with the surfaces passivated by hydrogen. In Ge/ Si NWs, the wire diameters (dNW) are in the range of 17.42-33.60 Å whereas the Ge cores with the diameters (dGe) of 10.30, 14.52, and 18.57 Å are chosen, which represent the Ge fractions of 10-50%. In pure Si and Ge © 2010 American Chemical Society
FIGURE 1. Top views of H-passivated Si and Ge/Si core-shell NWs oriented along the [111] direction with the diameters of 21.28 and 21.40 Å, respectively. In the Ge/Si NW, the diameter of the Ge core is 10.30 Å and numbers denote possible positions of a substitutional Au impurity.
NWs, a surface DB defect is obtained by simply removing a hydrogen atom on the surface. Similarly, a surface DB in the Si shell is considered for Ge/Si core-shell NWs, as DB defects are unlikely to exist at the interface between Ge and Si. In [111] NWs with hexagonal cross sections, there are two types of surface atoms that are bonded to one or two H atoms on the facets (Figure 1a). As the energy of a surface DB on the facet is lower by 0.2-0.3 eV than that at the hexagon apex, a surface DB defect on the facet is chosen for all the NWs considered. For each nanowire, we optimize the wire structure to find the effect of relaxations on the defect levels. For Au impurities, we consider a substitutional Au (see sites in Figure 1b) because this defect gives rise to acceptor levels whereas only a donor level appears for an interstitial Au in bulk Si and Ge.23,24,30 In Ge/Si NWs, due to the valence band offset (VBO) between Ge and Si at the heterostructure interface, the Ge core serves as a confinement potential for hole carriers, when the Fermi level lies below the valence band maximum (VBM) of the Ge core. Figure 2 shows the band structure of 117
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FIGURE 3. Spin-polarized band structures are compared for (a) Si, (b) Ge/Si, and (c) Ge NWs, which have a surface dangling bond defect per unit cell and the similar diameters of 25.27, 25.38, and 26.28 Å, respectively. In (b), the diameter of the Ge core is 10.30 Å. Black solid lines denote the Fermi levels with the VBM set to zero, and red dots represent the occupied (εDB,v) and unoccupied (εDB,V) levels of the Si or Ge dangling bond.
FIGURE 2. (a) The band structure and (b) the local density of states (LDOS) of Ge/Si NW with dNW ) 17.42 Å and dGe ) 10.30 Å. In (b), white line represents the interface between the Ge core and the Si shell.
TABLE 1. The Lowest Unoccupied Defect Levels of the Surface Dangling Bond (εDB,V) and the Substitutional Au (εAu,V) with Respect to the VBM Are Compared for Fully Relaxed Si, Ge, and Ge/Si NWs with Different Diametersa
a Ge/Si NW with dNW ) 17.42 Å and dGe ) 10.30 Å and the local density of states (LDOS), which is defined as
Σn,kδ(ε - εnk)Fnk(r)
dNW (Å) 17.25(17.94) 21.28(22.06) 25.27(26.28) 17.42 21.40 25.38 25.53 25.74
(1)
where Fnk(r) is the radial charge density averaged over the angular and axial directions, and n and k denote the band index and k-point, respectively. It is clear that the VBM state is derived from the Ge core, while the second VBM state is extended into the Si shell. The energy difference (∆) between these two states represents the confinement energy in the core-shell structure.14 For several Si and Ge/Si NWs with similar diameters, ∆ is found to be very close to the difference of the VBM states with respect to the vacuum level. As dNW increases from 17.42 to 33.36 Å in Ge/Si NWs with the same dGe, ∆ decreases from 0.45 to 0.34 eV, in good agreement with previous calculations.14 For dNW ) 33.36 Å, ∆ further decreases to 0.27 eV as dGe increases to 18.57 Å due to the reduced confinement effect of the Ge core. We examine the defect levels of a surface DB by performing spin-polarized calculations. Figure 3 shows the band structures and the surface DB levels for Si, Ge/Si, and Ge NWs with the diameters of dNW ) 25.27, 25.38, and 26.28 Å, respectively, and the Ge core of dGe ) 10.30 Å. The DB levels split into spin-up (εDB,v) and spin-down (εDB,V) states with the similar exchange splitting of about 0.4 eV for Si and Ge/Si NWs. In the Ge NW, as the εDB,v and εDB,V levels lying close to the VBM are associated with a Ge surface DB, the exchange splitting is found to be much smaller, being about 0.1 eV. In Ge/Si NWs, the exchange splitting for a given wire diameter tends to decrease with increasing of the Ge core size. Note that there is a distinctive difference in the defect levels between Si and Ge/Si NWs. For a neutral DB defect in the Si NW, the εDB,v level is fully occupied near the valence band edge, whereas the empty εDB,V level is located at about 0.49 © 2010 American Chemical Society
a
dGe (Å)
εAu,V (eV)
10.30 10.30 10.30 14.52 18.57
0.44 (0.21) 0.38(0.13) 0.33 (0.08) 0.24 0.09 0.02 -0.18 -0.18
εDB,V (eV) 0.64 (0.18) 0.54 (0.14) 0.49 (0.05) 0.26 0.15 0.11 0.05 0.05
Numbers in parentheses represent the results for Ge NWs.
eV above the VBM, being a deep level defect. In the Ge/Si NW, the εDB,v level is significantly lowered to 0.11 eV, while the εDB,V level moves into the valence band. For both Si and Ge/Si NWs with large diameters above 25 Å, the DB defect levels relative to the vacuum level are found to be almost constant to within 0.03 eV with increasing of dNW, consistent with other calculations.19 These defect levels are less sensitive to the variation of the Ge core. On the other hand, as dNW and dGe increase, the VBM state relative to the vacuum level increases more rapidly. Thus, the relative position of εDB,V is lowered, and the surface DB becomes a shallow acceptor. For various Si and Ge/Si NWs, the empty εDB,V levels relative to the VBM are summarized in Table 1 and plotted as a function of the wire diameter in Figure 4a. In Ge/Si NWs, we consider three different Ge cores with dGe ) 10.30, 14.52, and 18.57 Å. The εDB,V levels of Ge/Si NWs are generally lower by 0.38-0.44 eV which are close to the difference of the valence band edges relative to the vacuum level, as compared to Si NWs. Both Si and Ge/Si NWs exhibit the decreasing behavior of the εDB,V level with increasing of dNW, with similar decay rates. However, in Si NWs, as εDB,V is higher than 436 meV, the surface DB acts as a deep level defect, similar to that of bulk Si. In a Ge/Si NW, with dNW ) 33.60 Å and dGe ) 10.30 Å, εDB,V is positioned at 52 meV and further 118
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FIGURE 4. (a) The lowest unoccupied levels (εDB,V) of the surface DB defect with respect to the VBM and the change of εDB,V (∆εDB,V) by relaxations are plotted for Si NWs (black circles) and Ge/Si NWs with different diameters. Green circles, red boxes, and blue boxes represent Ge/Si NWs with the Ge core diameters of 10.30, 14.52, and 18.57 Å, respectively.
decreases to 4 meV as dGe increases to 18.57 Å. Thus, it is expected that the εDB,V level will be below the valence band edge in Ge/Si NWs with large diameters above 30 Å and the Ge factions above 30%, considering the fact that the VBM increases more rapidly than the εDB,V level. We check the sensitivity of the εDB,V level to relaxations around a DB defect. When the bond angles of the defect atom increase, the DB defect level usually increases with a rate of about 50 meV per degree.31 In Si NWs, structural relaxations increase the bond angles by about 1.3-1.6° and then raise the εDB,V level by 50-90 meV (Figure 4b). In defectfree Ge/Si NWs, as the Si shell is under tensile strain, the initial bond angles in the Si shell are larger than the tetrahedral bond angle32 and have a tendency to increase with increasing of dGe. When a surface DB defect is formed in large-diameter NWs, the bond angles are little affected, leading to very small changes in εDB,V, which are less than 10 meV for diameters larger than 29 Å. However, as the Ge core becomes thicker, relaxations actually decrease the bond angles, making the εDB,V level shallower. Thus, the shallowness of the surface DB defect is not much affected by relaxations in Ge/Si NWs. Recent experiments reported the existence of both interstitial and substitutional Au atoms in Si NWs.21 Theoretical calculations showed that a substitutional Au is energetically more favorable than interstitial configurations at tetrahedral and hexagonal sites.21 In Ge/Si NWs, we compare the formation energies of an Au atom for various substitutional positions, which are defined as
Ef ) Etot(AuX) - Etot(0) + µX
FIGURE 5. Spin-polarized band structures are compared for (a) Si and (b) Ge/Si NWs, which have a substitutional AuSi in the Si shell and similar diameters of 21.28 and 21.40 Å, respectively. In (b), the diameter of the Ge core is 10.30 Å. Black solid lines denote the Fermi levels with the VBM set to zero, and red dots represent the occupied and unoccupied t2 levels of AuSi. In (c), the total density of states (black lines) and the projected densities of states (PDOS) onto the AuSi and four surrounding Si atoms are drawn for the Ge/Si NW. Blue, green, and red lines represent the defect states associated with the Au 5d, Si 3s, and Si 3p orbitals, respectively. Three red peaks near the VBM correspond to the t2 levels of AuSi.
is obtained from bulk Si and Ge. For a nanowire dNW ) 21.40 Å and dGe ) 10.30 Å (Figure 1b), the most stable site is found to be the surface Si site labeled 4. The formation energies of AuX at the sites 1, 2, and 3 relative to the lowest energy site 4 are 0.07, 0.11, and 0.17 eV, respectively. As the energy differences between the Ge core and the Si shell are very small, Au impurities which would be initially located in the Ge core are likely to diffuse into the wire surface as the Si shell subsequently grows. This result is consistent with the experimental observation of abundant Au atoms near the surfaces in Si NWs.21 At the surface site, the Au defect levels are severely disturbed by the presence of H (also see figures in the Supporting Information for the details). To remove the artifact of interactions on the hydrogenated surface, we consider a subsurface site labeled 3 in the Si shell, as shown in Figure 1b. By employing a supercell that is twice larger than that used for the surface DB, we obtain the dispersion of the Au defect levels less than 0.1 eV. Figure 5a,b shows the band structures and the defect levels of a substitutional AuSi in Si and Ge/Si NWs with similar diameters of 21.28 and 21.40 Å, respectively. The defect levels of AuSi can be understood in terms of the vacancy
(2)
where Etot(AuX) and Etot(0) are the total energies of supercells with and without a substitutional AuX at the site X (X ) Si or Ge), respectively, and µX is the chemical potential of X, which © 2010 American Chemical Society
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model,33 in which the Au 5d levels lie deep in the valence band and do not form the defect levels. In this model, the defect levels are mainly determined by the dangling bond orbitals around a Si vacancy (VSi). In bulk Si, the singlet a1 level of VSi lies in the valence band, whereas the triplet t2 levels are deep in the band gap. From the projected density of states (PDOS) onto the Au and Si atoms (Figure 5c), it is clear that the Au 5d levels are located well below the VBM. Because of the symmetry breaking into C2v, the AuSi-related t2 levels split into three levels, one fully occupied level in the valence band, one partially occupied level near the VBM, and one unoccupied level in the band gap. The PDOS further shows that the t2 levels are mainly characterized by the Si 3p orbitals, consistent with the Si-vacancy model. As one Au 6s electron behaves as a donor electron, the AuSi defect resembles the 1- charge state of VSi. In spin-polarized calculations, the t2 levels near the VBM, which are partially occupied unless the spin polarization effect is included, split into spin-up (εAu,v) and spin-down (εAu,V) states. The exchange splitting between the εAu,v and εAu,V levels is estimated to be 0.14 and 0.06 eV for the Si and Ge/Si NWs, respectively, and these energy separations are much smaller than that those for the surface DB. The εAu,V levels relative to the VBM are compared for Si, Ge, and Ge/Si NWs in Table 1. In Si NWs, the εAu,V levels are generally lower by 0.16-0.20 eV than the εDB,V levels and tend to decrease with increasing of dNW. However, the AuSi defect appears as a deep level center with the εAu,V levels above 0.33 eV. In Ge and Ge/Si NWs, the εAu,V levels are significantly lowered. Especially in Ge/Si NWs, the εAu,V level is calculated to be about 20 meV for dNW ) 25.38 Å and dGe ) 10.30 Å. In this wire, as dGe increases, εDB,V further decreases, lying at -0.18 eV below the valence band edge for dGe ) 14.52 and 18.57 Å, while this level is located at 0.08 eV in the Ge NW with the similar diameter. Because of the shallowness of the εAu,V level, it is also expected that AuSi behaves as a charge trap in large-diameter Ge/Si NWs. We examine the effect of spin-orbit (SO) interactions on the valence band edge in Ge/Si NWs. In bulk Ge, it is known that the SO coupling splits the degenerate VBM states by about 0.29 eV.34 In Ge/Si NWs, as the VBM is derived from the Ge core, the SO effect is also expected to be large. For two NWs with similar diameters of about 13.5 Å but different Ge cores of dGe ) 6.14 and 10.30 Å, the SO coupling increases the valence band edge by about 6 and 11 meV, respectively. For dNW ) 25.74 Å, as dGe increases to 18.57 Å, the VBM increases by 22 meV. Thus, if the Ge core becomes thicker, the SO coupling actually enhances the shallowness of the εAu,V and εDB,V levels. To determine whether surface DBs and Au impurities behave as shallow acceptors in Ge/Si NWs, we need to estimate the charge transition levels. However, at this point it is difficult to calculate accurate total energies for charged defects in nanowires.35 In addition, there remains an issue in the energy levels of the DB defect, especially in Ge, © 2010 American Chemical Society
because the band gap vanishes in the local density functional approximation (LDA) calculations. In hybrid density functional calculations in which the band gap is improved, the charge transition levels of the DB were shown to lie at 0.05-0.11 eV just above the VBM, while they were located below the VBM in the LDA.36 In Ge/Si NWs, as the LDA band gaps are underestimated, our calculated εAu,V and εDB,V levels relative to the VBM would be similarly underestimated. However, we point out that the NW diameters considered here are much smaller than those of experimentally grown NWs. In NWs with diameters in the range of about 20 nm,12,13 the increase of the valence band edge may compensate for the LDA error of the defect levels, which are much less sensitive to the wire diameter. Thus, the surface DB and Au defects are still considered as a candidate for the origin of the hole gas observed in Ge/Si NWs. According to transport measurements, both Si and Ge NWs were found to be nonconducting at zero gate voltage, although they exhibited p-type FET behavior under negative gate bias.13 In pure Ge NWs, the electron trap level, which is known as the surface state, was suggested to be located near the valence band edge.37 The appearance of p-type FETs was attributed to the surface charge which promotes hole accumulation and upward surface band bending. In Ge NWs, we find that the εDB,V levels of the Ge DB lie at 0.05-0.18 eV for diameters of 17.94-26.28 Å, whereas the εAu,V levels are located at 0.08-0.21 eV for the AuGe defect (Figure 3c and Table 1). As these defect levels are somewhat higher than those for Ge/Si NWs, it will be difficult for hole carriers to be activated. Moreover, even if hole carriers are accumulated near the surface due to the surface band bending, they will be significantly scattered by charge traps. Thus, the mobility will be greatly suppressed in contrast to Ge/Si NWs, which exhibit a nearly ballistic transport due to the spatial separation of hole carriers from the charge traps in the Si shell. In conclusion, we have studied the defect levels of Si dangling bonds and AuSi impurities in Ge/Si NWs. As the valence band edge is mainly derived from the Ge core, it increases with increasing of the wire diameter and of the Ge core due to the reduced confinement effect, whereas the defect levels of Si DBs and AuSi impurities are less sensitive. Thus, the lowest unoccupied defect levels of the Si DB and AuSi defects with respect to the valence band edge have a tendency to decrease as the wire diameter and the Ge core increase. Although the Si DB level slightly increases when tensile strains by the Ge core are induced to the Si shell, it does not alter the general trend. While the lowest unoccupied defect levels of the Si DB and AuSi defects are deep in Si NWs, they become sufficiently shallow even at room temperature in large-diameter Ge/Si NWs, leading to the p-type conduction. As hole carriers are confined in the Ge core region and well separated from the charged defects, the carrier mobility is greatly enhanced, in good agreement with experiments. 120
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Acknowledgment. This work was supported by the Korea Research Foundation Grant (KRF-2005-084-C00007) and Samsung Electronics Co., Ltd.
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Supporting Information Available Defects responsible for the hole gas in Ge/Si core-shell nanowires
Ji-Sang Park†, Byungki Ryu†, Chang-Youn Moon‡, and K. J. Chang†* †
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
‡
Department of Physics and IPAP, Yonsei University, Seoul 120-749, Korea
*Corresponding author. E-mail:
[email protected]. Telephone number: 82-42-350-2531. Fax number: 82-42-350-2510.
Figure 1. (a) Top and (b) side views of a Ge/Si core-shell nanowire with a substitutional Au at the site 4 on the surface. (c) Unrelaxed and (b) relaxed structures around the substitutional Au at the site 4. The nanowire diameter is 21.40 Å and the Ge core size is 10.30 Å. Numbers in (a) represent possible positions of a substitutional Au, which are indicated in Figure 1 of the manuscript. 1
Figure 2. (a)-(d) The band structures of Ge/Si core-shell nanowires with dNW = 21.40 Å and dGe = 10.30 Å are compared for different sites of a substitutional Au, which are labeled 1, 2, 3, and 4 in Figure 1a. Red dots denote the Au defect levels and black solid lines represent the Fermi level, with the valence band edge set to zero. The defect levels of AuGe at the site 1 in the Ge core are higher than those for AuSi at the site 3 in the Si shell (in Figure 5b of the manuscript). At the site 4, the defect levels disappear from the band gap, moving into the valence and conductions bands due to large relaxations around the Au atom (as shown in Figure 1d).
Figure 3. (a)-(c) Plots of the charge densities for the Au defect levels and the valence band maximum (VBM) in Figure 2c. 2
Figure 4. (a)-(d) The total density of states (DOS) and the projected density of states (PDOS) onto the Au and the neighboring Si atoms are plotted for different sites of a substitutional Au, which are labeled 1, 2, 3, and 4 in Figure 1a. Blue, green, and red lines represent the defect states associated with the Au 5d, Si(Ge) 3s(4s), and Si(Ge) 3p(4p) orbitals, respectively. 3
