The effect of noble metals in Si nanocrystals

Accepted Manuscript The effect of noble metals in Si nanocrystals Cedric L. Mayfield, Muhammad N. Huda PII: DOI: Reference:

S0009-2614(14)00376-5 http://dx.doi.org/10.1016/j.cplett.2014.05.010 CPLETT 32155

To appear in:

Chemical Physics Letters

Received Date: Accepted Date:

2 April 2014 5 May 2014

Please cite this article as: C.L. Mayfield, M.N. Huda, The effect of noble metals in Si nanocrystals, Chemical Physics Letters (2014), doi: http://dx.doi.org/10.1016/j.cplett.2014.05.010

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The effect of noble metals in Si nanocrystals

Cedric L. Mayfield and Muhammad N. Huda* Department of Physics, University of Texas Arlington, Arlington, Texas 76019, USA

In this letter, silicon nanocrystals doped with noble metal (Cu, Ag and Au) atoms have been studied by hybrid density functional theory. It is known that these metals play a significant role in Si nanowire growth, whereby Au is especially more favorable for this purpose. Our results show that the formation energies of noble metal impurities in Si nanocrystals are energetically high and hence less likely to be thermodynamically stable. In addition, our results show that Au atoms on the surfaces help promote the Si-Si covalent bonds in the nanostructures, whereas Cu and Ag induce some ionicity.

*[email protected]

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1

Introduction Silicon nanostructures are of increasing importance to photovoltaic technology because

of their size and dimension dependent physical properties[1–4]. Successive generations of photovoltaic (PV) devices are being developed by implementing silicon nanowires (SiNWs) and other Si nanostructures into their design[5–11]. The electronic, and optical properties of Si nanostructures can be modified by quantum confinement effects[1,12–14] which can help push the theoretical efficiency limit of silicon based PV devices to new heights. Lately much effort has been devoted to controlled synthesis of SiNWs by various methods with high scalability such as vapor-liquid-solid (VLS)[15–21], vapor-solid-solid (VSS) [22,23], chemical vapor deposition (CVD)[22,24,25], and chemical etching (CE) [26–31], whereby each can be mediated by Cu, Ag, or Au nanoparticles. These metal nanoparticles act as catalytic agents in the nucleation and growth of the SiNWs. Therefore it is well known that selection of the catalyst species, among other synthesis variables, can be used to control nanostructure size, crystallographic growth direction, and chemical composition. It is also well known that due to a relatively lower eutectic temperature of Au-Si composition [25] Au nanoparticles are preferred over Cu and Ag nanoparticles for vapor phase SiNW growth. Au-catalyzed SiNWs are mostly defect free, and apart from growth kinetics, requires an explanation from the electronic structure point of view as to why they are more crystalline-like and uniform than Cu and Ag-catalyzed SiNWs[22,29,32– 34]. In this letter two issues will be addressed with a simple model of noble metal doped Si nanocrystals (SiNCs): (i) the probability of noble atoms doping in SiNCs, and (ii) the effect of these doping on the electronic features of SiNCs. In our previous study [35] of pristine SiNCs we found the wurtzite structure was more stable than the diamond structure for particle sizes < 3 nm. The lower ‘surface area to volume’

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ratio of wurtzite translated to fewer dangling bonds than diamond structure and hence a reduced surface effect. Furthermore, this result can be related to the occurrence of wurtzite phase SiNWs grown by standard CVD methods [36]. Therefore hydrogen passivated wurtzite silicon nanocrystals (H-SiNCs) have been studied at three sizes (75, 150 and 300 Si atoms), with one Si atom at different sites replaced by a noble metal atom. These three representative sizes are selected with the intention to study the size effect on the metal atom dopants. With the systematics of the electronic properties, it can be argued that any Si nanocrystals of similar sizes would follow the same conclusions obtained in the letter. In addition, at the sizes considered here, the quantum confinement effect is not negligible since they are (for example, maximum distance between two furthest Si atoms in any directions) less than the Bohr exciton radius of Si which is about 4.9 nm [37]. To find the lowest energy configurations and probability of impurity incorporations, formation energies at different spin-multiplicities have been considered. In general our findings show that surface sites are the most probable doping sites. Also, Cu atoms show a higher probability of replacing Si atoms at these sites, but Au doping promotes the covalent nature of the host’s Si-Si bonding. Understanding noble metal related mechanisms that give rise to stabilized structural phases of SiNCs may be important to our plight of increasing photovoltaic efficiency. 2

Computational methods We performed geometry optimized calculations within the framework of density-

functional theory (DFT) as it is implemented by the Gaussian 03 software package [38] to acquire fully relaxed coordinates for both doped and undoped H-SiNCs at each size level. Treatment for the exchange and correlation was handled by Becke’s three parameter hybrid functional combined with the Lee-Yang-Parr correlation functional, denoted B3LYP [39–41].

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Hybrid functionals are known to provide better band gap and structural properties for semiconductors[42,43]. The electron orbitals were described by a double-ζ basis set with the effective core potential (ECP) of Hay and Wadt, known as the Los Alamos National Laboratory 2-Double Zeta basis set (LANL2DZ) [44]. Basis set superposition error (BSSE) was considered for Si orbital overlap with Cu, Ag and Au orbitals by using the Boys and Bernardi counterpoise correction method [45]. The BSSE correction energies were 102 meV, 42 meV and 1 meV for SiCu, SiAg, and SiAu respectively. To be assured of our treatment of Si with the noble metals we compared the calculated Si-Cu (since it has the highest BSSE energy) bond length (2.298 Ǻ) to the corresponding experimental value (2.280 Ǻ), and discovered they are in good agreement. The theoretical and experimental Si-Si bond lengths agree well too at 2.352 Å and 2.460 Å, respectively. Thus for the larger systems considered, this method is efficient, a compromise between the computing resources and accuracy. 3

Results and discussions 3.1 Dopants and structural distortions In Figure 1 substitutional positions for noble metal doping are illustrated. The first

substitutional position is a core site (1) which is defined as an interior site that has four-fold coordination. The second substitutional position is a trough site (2) which is defined as a site that is at most one atomic distance from the surface and is bonded to a core site. Four-fold coordination is preserved at the trough site but the nearest neighbors may be surface atoms that have dangling bonds. The third substitutional position is a crest site (3) which is defined as any surface atom having at least one dangling bond and is also bonded to a trough site. The structural distortions were similar because the ionic and covalent radii of Cu, Ag, and Au are similar being within tenths of an Angstrom to each other. For each of the core doped

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H66Si74X nanocrystals the calculated average bond length over all core bonds was just 2.381 Ǻ which is a 1.2% increase from the calculated Si-Si dimer bond length of 2.352 Ǻ. This was the largest deviation found among all instances of doping, therefore we have only presented the relaxed geometries of H66Si74X in Figure 2. It can be seen at the core the dopants gave rise to structural deformations at corners where surface atoms had a higher density of dangling bonds. In this case, which is similar for all of the dopants at this location, no reordering of the bonding takes place, just small expansions and contractions among the four-fold coordinated bond lengths. Trough site doping has a unique reordering of bonding based on the dopant. For Cu doping the reordering consisted of breaking bonds with the two crest atoms that are at least one atomic distance away from an edge or corner. The bonding to the crest atom on the corner (corners have more dangling bonds) and the bonding to the core atom were preserved with even fewer expansions and contractions of the four-fold coordinated bonds. For Ag doping all bonds were broken except for the bond with the crest atom on the corner of the structure. Au doping was done without reordering bonds however; bonds with crest atoms on the corners were appreciably elongated. For crest site doping, each dopant had a similar effect. In each case, the dopants broke the bond with H and a trough atom, leaving two-fold coordination but they sat there nicely without disturbing the Si structure beneath. For larger nanocrystals, both doped H100Si149X and H170Si299X nanocrystals exhibited more structurally stabilized doping. At the core the dopants relaxed into the substitutional position without noticeable distortions to the bonding. Furthermore for core doping, X atoms relaxed without any noticeable differences in bond lengths. For the trough and crest sites, structural changes and bond length changes occurred when X atoms relaxed into the structure,

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simply because of high surface state interactions with X atoms. In the following sections we will discuss in detail the energetic profile of each doped system. 3.2 Formation Energy Though each of the dopants has similar valence electron configuration, namely a filled d shell and half-filled s shell, they did not result in similar solubility in SiNCs. In Table 1 we present the formation energies (Ef) of the dopants which are formulated as: E f (Si n -1 M ) = [E (Si n -1 M ) − E (Si n ) ] + [µ (Si ) − µ (M )] ,

where E(…) represents the total energy of the system defined in the parenthesis, and µ(…) is the chemical potential of Si or noble metals which are determined from the solid phase reservoirs (at their respective ground state bulk configurations). The formation energy of a dopant in a H-SiNC determines that dopant’s relative solubility, i.e. high formation energy corresponds to low solubility. Also in Table 1, the formation energies are listed for each dopant with respect to dopant position and nanocrystal size. Overall, due to higher formation energies, we predict spontaneous formation of the dopants in the H-SiNCs is not likely at equilibrium conditions for the sizes considered. Clear trends in the formation energy associated with both dopant position and dopant concentration can be extrapolated from Table 1. For instance, at each SiNC size, as the dopant is moved from the core to the crest position the formation energy decreases showing a higher favorability for dopant atoms on the surfaces. Then holding the position static and decreasing the dopant concentration (by increasing SiNC size), we see a trend of decreasing formation energy as well. For example, Ag doping at the core at the 75 Si atom size level (the dopant concentration is its highest at 1.33 wt. %), dopant formation comes at an energy of 5.498 eV and decreases by 20 meV when the size is doubled to 150 Si atoms (0.66 wt. %). From 150 Si atoms to 300 (0.33

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wt. %), the further decrease in formation energy is approximately 10 meV. These trends indicate the formation energies converge to a bulk value as we approach the bulk regime or decrease dopant concentration. At the trough site this trend is interrupted when the system is in the doublet spin state. Here, relatively high formation energy is due to the interaction between the dopant and the monovalent passivant atom bonded to its nearest neighbor. This relative change in dopant formation energy with respect to a change in spin multiplicity indicates that formation of the dopants may also be facilitated by external field effects. For each dopant at each size the doublet spin state has the lower energy in terms of stability as will be seen by the binding energies to be discussed in the following section. In terms of formation energy the doublet spin state uniformly has values approximately 40 percent less than the formation energies calculated in the quartet spin state. The mechanism associated with quenching the magnetic moments upon passivation is thus affected by the presence of dopants and their ground state spin configuration. 3.3 Binding Energy The binding energy per atom (Eb) is calculated as:

Eb (Sin−1M ) = [ ETOT (Sin−1M ) − E(M ) − (n − 1)E(Si)] / n where, ETOT(Sin-1M) is the total energy of the M doped cluster of (n−1) Si atoms, E(M) and E(Si) are total energies of M and Si atoms, respectively, in their ground state spin multiplicity. We compared the Eb of each of the doped structures to the undoped structure of similar size and passivation. Then we studied the overall change in stability with increasing size. Finally we studied the binding as a function of dopant and note the E g . For H66Si74X we find a uniform reduction in stability upon doping by about 10meV per atom. For details of undoped SiNC please refer to reference 35. Reduction in stability is part of -7-

the cost for replacing a Si atom with a larger noble metal atom. Doping X at the core site has the largest cost for substitutional doping. The Cu and Au atom have similar Eb and are always more stable than Ag doping. As the X atom dopant is moved from the core to the surface, stability increases are on the order of meV per atom. For H100Si149X and H170Si299X we see a similar trend in stability as we saw in the previous case. The relative stability of Cu and Au at any of the dopant sites are of very small difference. 3.4 HOMO-LUMO Gaps The energy gap (Eg) was calculated as the gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of H66Si74X, H100Si149X and H170Si299X, where X = Cu, Ag, Au. Observing the HOMO LUMO gaps given in Table 1, we see for the doped H-SiNCs a trend associated with size. Having the dopant, position and magnetic moments fixed (with higher multiplicity 4) the HOMO LUMO gap decreases with size. This behavior is dictated by quantum confinement effect. In the doublet spin state, most of the Eg’s are less than 3 eV, while those in the quartet spin state are 3 eV and greater. The presence of mid gap states in doublet is responsible for not showing uniform quantum confinement effect. These mid gap states are charged defects and affect the electronic properties of the SiNC, which will manifest better when Mulliken charge distribution will be discussed. Note, even though the differences of binding energy per atoms for these doped nanostructures from Table 1 in doublet and quartet spin state are very small, it was the formation energy that determined the doping probability. The interplay of magnetic moments with noble metal atom doping is very important for particular properties. For instance, the Cu dopant at the core site we see a small E g at the 75 Si atom size level. However since the lowest energy state is almost degenerate with the quartet state -8-

(the energy differences are on the order of just a few meV) it is safe to say at the 75 Si atom size level the arrangement for magnetic moments favors the low spin state because the dopants behave as additional charge receptacles. The established quenching of magnetic moments associated with H passivation is complemented by the presence of the dopant in the core. At the trough site especially at the 150 Si atom size level the effect of the dopant having a nearest neighbor bonded to a passivant H atom is shown to decrease the gap below the value for bulk Si. For Ag atom doping at the trough, the low spin state contracts the gap; whereas the Au atom doping has small differences in gaps with respect to spin state. At the crest sites all dopants have E g greater than the bulk band gap regardless of spin state. At each dopant position the E g decreased with respect to dopant and the Au dopant had the smallest gap except at the crest site of the 300 size level SiNC, here Ag doping had a 0.018eV lower gap. 3.5 Density of States From the formation energies it was determined that the crest site was the more probable dopant site. In Figures 3 and 4 we show two representative DOS plots for Cu and Au dopants at the crest site for 75 and 300 Si atoms nanocrystals, respectively. The DOS plots are decomposed into atomic orbital contributions of the noble metal atom dopant. The overall shapes of the DOS plots do not change upon doping, therefore we have increased the resolution of the DOS plots to better visualize the mid-gap states. Mid-gap states are the focus because they have significant roles in charge transport and photoconductivity. For doping at the 75 and 150 Si atoms size level, the mid-gap states are similar for Cu and Ag, each dopant introduces an occupied level in both spin channels. In the majority spin (upspin) channel the mid-gap states are at the valence edge, in the minority spin channel (downspin) the mid-gap state is about 1.5 eV above the valence edge. As for Au doping, two mid-gap

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states are introduced, one occupied state and one unoccupied state for both spin channels. The two mid-gap states deriving from the Au atom are within 1 eV of each other which account for the small energy E g discussed in the HOMO LUMO gap section. For the 150 Si atoms nanocrystals, in the majority spin channel the separation of the mid-gap states is about 2 eV but in the minority spin channel the separation of mid gap states is approximately 1 eV. In the cases with Cu or Ag, the most significant contribution to the HOMO from the dopant atomic orbitals comes from the p orbitals, but the Au atom has contributions from both p- and d-orbitals. The dorbital contribution in HOMO implies that the Au on SiNC is more catalytically active than Cu and Ag on SiNC. In the LUMO we see that s orbitals comprise the contribution from all of the dopants. The HOMO and LUMO are free of H s-orbital contributions; however we see these sorbitals begin to hybridize near the HOMO and LUMO. For doping at the 300 Si atom size level the similarity between the mid-gap states of Cu and Ag doping is continued. The occupied state deriving from Cu or Ag doping is at the valence edge for the majority spin channel and in the minority spin channel the mid-gap state lays approximately 1.5 eV above the valence edge. For Au doping the mid-gap states are slightly different than any of the other cases (Figure 4). In both spin channels the occupied mid-gap state is at the valence edge and the unoccupied state is about 1.5 eV above the valence edge. At this size level the atomic contributions from dopant p-orbitals are the smallest ones seen in this study. Primarily it is Si atoms that make up the HOMO except in the case of Au doping, in which pand d-orbital contributions are prevalent. In the LUMO we see H atom contribution in the cases of Cu and Ag doping but no participation of H atoms occurs for the case of Au doping. The peculiarities associated with the doping scheme come from the ability of these atoms to behave

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as either a donor or acceptor. Au seems to be the most flexible because it has the most variation in its mid-gap states as well as in its orbital contributions. 3.6 Mulliken Charge Distributions In this section we discuss the Mulliken charge distributions to see how the ionic behaviors of dopants evolve in SiNCs (unpassivated) and H-SiNCs. The Pauling scale electronegativity of Si, Cu, and Ag are all around 1.9 and for H and Au the electronegativity is 2.54 and 2.20, respectively. Based on these differences in electronegativity it interesting to see how charge distributes upon relaxation of the doped SiNCs and H-SiNCs. To elucidate the charging based on passivation and species of dopant we will compare the Mulliken charge distributions of SiNCs and H-SiNCs for each of the dopants. For brevity we show in Figure 5 a schematic of the Mulliken charge distributions of wurtzite SiNCs and H-SiNCs at the 150 Si atom size level only, the 75 and 300 Si atom size levels are similar. Again we focus on the crest site since we obtained maximum solubility of the dopants for all structures at this site. For Cu and Ag doping at the crest site passivation does not change the charge on the dopant atoms significantly, and they remained mostly positively charged by donating electronic charges to the Si nanocrystals. On the other hand, for Au doping at the crest site passivation increased the intensity, shifting the negatively charged Au atom to even more negative by acquiring electronic charges from the nanocrystals. In addition, Au doped H-SiNC contains relatively neutral Si atoms which indicate the Au doping preserves the covalent bonding in the SiNC. This bonding behavior with Au doping explains the preference of Au catalyst in SiNW growth. Covalent bonding is necessary to maintain Si crystalline structure at the nanoscale. We can see that Cu and Ag give up charge to become more positive, however other Si atoms in the nanocrystals have similar charges as these dopant. Due to the smaller sizes

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and local distortions, some of the Si atoms also became slightly charged locally, and ionic contributions to some of the Si-Si bonds were enhanced by Cu and Ag doping. However, with Au doped Si-nanocrystals, Au atom becomes negatively charged, and the ionic contribution to the Si-Si bonds in Si-nanocrystals reduced significantly; the Si-Si bonds became mostly covalent. Experimental evidence [36,46] for the preference of Au catalyst is attributed to the solubility of Si in Au nanodroplets which corresponds to a higher degree of covalency when using Au catalyst. 4

Conclusions In this study we have found that the noble metal incorporations in Si nanostructures are

unlikely at thermodynamic equilibrium due to large formation energies at different dopant positions. Surface sites are relatively more preferable, with crest site having the lowest formation energy. Cu atom has lower formation energies at different sites except at the smallest 75 Si atoms nanocrystals, where Au is more favorable. However, the favorability of Au as doped on SiNC surface is due to the presence of d-orbital in HOMO which enhances its catalytic properties. From the density of states plot, even though Cu and Ag show traces of d-orbital contribution in the HOMO in one spin state or the other, Au uniformly has d-orbital influence to the HOMO and mid gap states in both spin states. Finally, Au demonstrates acceptor behavior that ultimately neutralizes charge of the host, promotes covalence bonding between Si atoms which results in a higher crystallinity.

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Acknowledgements: The computations were performed at the University of Texas at Arlington High Performance computing center. The research is partly supported by grants from National Renewable Energy Laboratory and National Science Foundation.

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Table1: Formation energies Ef, binding energies Eb (per atom) and HOMO-LUMO Gaps Eg, all in eV, of noble metal doped silicon nanocrystals at three different positions and two different spin states Species

position

Ef

Eb

Eg

H66Si74Cu

core trough crest

doublet 4.418 3.955 3.332

quartet 4.466 4.923 5.494

doublet -3.163 -3.167 -3.171

quartet -3.163 -3.160 -3.156

doublet 1.736 3.582 3.738

quartet 3.882 4.094 4.073

H66Si74 Ag

core trough crest

5.672 4.734 3.954

5.498 5.820 6.473

-3.154 -3.161 -3.167

-3.156 -3.153 -3.149

1.394 3.726 3.541

3.642 3.925 3.924

H66Si74 Au

core trough crest

4.414 4.152 3.102

4.441 4.805 5.403

-3.163 -3.165 -3.173

-3.163 -3.161 -3.156

1.610 2.285 3.449

3.590 3.853 3.835

H100Si149Cu

core trough crest

4.471 4.821 3.439

4.336 4.672 5.282

-3.278 -3.277 -3.282

-3.279 -3.278 -3.275

1.317 1.581 3.208

3.457 3.581 3.530

H100Si149Ag

core trough crest

5.624 5.833 4.506

5.471 5.726 6.426

-3.274 -3.273 -3.278

-3.274 -3.273 -3.271

1.355 0.909 2.805

3.283 3.480 3.358

H100Si149Au

core trough crest

4.419 4.573 4.203

4.384 4.640 5.325

-3.279 -3.278 -3.279

-3.279 -3.278 -3.275

1.422 1.577 2.131

3.220 1.050 3.303

H170Si299Cu

core trough crest

4.391 4.606 3.475

4.285 4.595 5.264

-3.344 -3.343 -3.346

-3.344 -3.343 -3.342

1.377 1.435 3.025

3.121 3.294 3.231

H170Si299Ag

core trough crest

5.585 5.729 4.486

5.458 5.666 6.370

-3.341 -3.341 -3.344

-3.342 -3.341 -3.340

1.377 1.468 2.643

2.954 3.180 3.063

H170Si299Au

core trough crest

4.391 4.482 3.796

4.365 4.590 5.257

-3.344 -3.344 -3.345

-3.344 -3.344 -3.342

1.286 1.481 2.665

2.903 3.091 3.012

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Crest (3)

Trough (2)

Core (1)

Figure 1: Passivated wurtzite silicon nanocrystal showing (1) core, (2) trough and (3) crest substitutional doping sites.

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a)

b)

c)

1)

2)

3)

Figure 2 : Relaxed geometry of a) H66Si74Cu, b) H66Si74Ag and c) H66Si74 Au at the 1) core, 2) trough and 3) crest doping sites.

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Figure 3: Density of states for H66Si74Cu crest doping.

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Figure 4: Density of states for H170Si299Au crest doping.

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a)

b)

c)

1)

2)

Figure 5: Mulliken Charge distribution of a) Cu, b) Ag, and c) Au doping of wurtzite silicon nanocrystals 1) unpassivated and 2) passivated at the 150 Si atom size level.

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Highlights: 1. 2. 3. 4. 5.

Noble metal impurities in Si nanocrystals are less likely to be thermodynamically stable. Surface sites are relatively more preferable for doping. Cu and Ag induce some iconicity in Si nanocrystals bonding. Au atoms on the surfaces help promote the Si-Si covalent bonds. Results provide justification why Au is a better catalyst to synthesize Si nanostructures.

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Graphical abstract:

H-passivated Si nanocrystal

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