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Supplemental Information
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Dynamics of Charge Transfer at Au/Si Metal-semiconductor Nano-
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interface
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Yulun Han1, Sergei Tretiak2, Dmitri Kilin1*
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Department of Chemistry, University of South Dakota, Vermillion, SD 57069
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2
Los Alamos National Laboratory, Center for Integrated Nanotechnology, NM 87545
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Discussion of placements of dopings
As shown in Figure S1, contributions of Al and P to the Kohn-Sham orbitals
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depend on the dopant positioning. It is found that Al mainly contributes to the states in
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VB, and P mainly contributes to the states in CB. It should be noted that the states in VB
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are mainly attributed to Au, and the states in CB are attributed to both Au and Si. Thus,
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contributions of dopants are not obvious. The following trend can be found: as dopants
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interface Au, their contributions would become even smaller. And the smallest dopant
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contribution is found for the model (-Al-Si-Si-P-), where both Al and P interface Au.
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The largest dopants contributions are found in panel (f) and (j) in Figure S1 where both
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dopants are placed into the middle layers of silicon.
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Table S1. Total energies of various placement of dopings
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Configuration
Etot, eV
Panel in Fig. S1
-Al-Si-Si-P-
-421.2989
(c)
-Al-Si-P-Si-
-421.2595
(b)
-Si-Al-P-Si-, original, bulk
-420.3610
(a)
-Si-Al-Si-P-
-419.8360
(d)
-Si-Al-P-Si-, surface
-418.9964
(e)
states
Densityofof
Density
states
(a)
(f)
0.4
0.15
0.3
states
Densityofofstates
Density
0.10
0.2
0.05
0.1
0.0
-5
-4
-3
-2
-1
0
(g)
0.4
0.15
0.3
states
Density
Density
of of
states
-4
-3
-2
-1
0
-5
-4
-3
-2
-1
0
-5
-4
-3
-2
-1
0
-5
-4
-3
-2
-1
0
-5
-4
-3
-2
-1
0
0.10
0.05
0.1
-5
-4
-3
-2
-1
0
0.00
(h)
0.4
0.15
0.3
0.10
0.2
0.05
0.1
0.0
states
Density
Density
of of
states
-5
0.2
(c)
-5
-4
-3
-2
-1
0
0.00
(d)
(i)
0.4
0.15
0.3
0.10
0.2
0.05
0.1
0.0
states
Density
Density
of of
states
0.00
(b)
0.0
-5
-4
-3
-2
-1
0
0.00
(e)
(j)
0.4
0.15
0.3
0.10
0.2
0.05
0.1
0.00
0.0
-5
1
Al
Au
H
P
Si
-4
-3
-2
-1
Orbital
energy,
Orbital
energy,
eV eV
0
Orbital energy, eV
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Figure S1. (a)-(e) DOS and (f)-(j) PDOS of periodic array of Au/Si nanostructure with
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different positions of dopants. Atomic structures are shown as insets in panels (a)-(e)
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with blue and red circle pointing at Al and P atoms, respectively. For panel (f)-(j), red,
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blue, orange, purple, green represent Al, Au, H, P, and Si, respectively.
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Discussion of Au-Si chemical bond
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Silicon part of the periodic array of Au/Si nanostructure and co-doped Si QD
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differ by the (111) facet treatment. In co-doped Si QD, there are hydrogen termination
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atoms, while in the periodic array of Au/Si nanostructure, the (111) facet silicon atoms
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are interfacing Au atoms. Removing hydrogen termination and offering gold atoms at
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similar sites may lead to Si-Au chemical bond formation and noticeable changes in the
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electronic structure. A quantitative analysis of Au-Si bond formation is based on
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comparison of Radial Distribution Functions (RDF) of periodic array of Au/Si
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nanostructure, Au38 cluster, and Al and P co-doped Si QD. RDF is defined as
𝑔𝑎𝑏
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1
𝑟 =
𝑁𝑎 𝑁𝑏
𝑁𝑎 𝑁𝑏
< 𝛿( 𝑟𝑖𝑗 − 𝑟) >
𝑖=1 𝑗 =1
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Here g(r) is the probability of finding two ions at distance r from each other. According
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to Figure S2, the RDF of periodic array of Au/Si nanostructure exhibits an additional
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feature around 2.5 Å, not seen neither in Al and P co-doped Si QD nor in Au38 model.
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This peak is witnessing formation of Au-Si bonds. Au-Si distances have been also
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directly measured for Au-Si pairs of ions. Those in the range below 3 Å are listed as
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follows: 2.5296, 2.4829, 2.5323, 2.4535, 2.4446, 2.4908, 2.4479, 2.4985, 2.4851, 2.4149,
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2.4791, 2.5200, 2.5489 with the average of <dAu-Si>=2.4868 Å, which are consistent
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with literature data 2.47 Å.[1]
1.0
Au/Si nanostructure
Au38
Al/P co-doped Si QD
g(r)
0.8
0.6
0.4
0.2
0.0
1.0
1
1.5
2.0
2.5
3.0
Distance, angstrom
3.5
4.0
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Figure S2. Radial Distribution functions of three original models. Solid red, dashed
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blue, and dashed green represent periodic array of Au/Si nanostructure, Au38 cluster, and
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Al and P co-doped Si QD, respectively. RDF of periodic array of Au/Si nanostructure
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exhibits an additional feature around 2.5 Å, not seen in Al and P co-doped Si QD. This
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peak is witnessing formation of Au-Si bonds. It should be noted that in the figure of
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RDF, normalized g(r) (g(r)/maximum g(r)) is plotted as a function of distance, since we
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are only interested in the peak positions.
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Discussion of the relaxation for charge carriers
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Figures S3-S8, panel (a)-(c) represent relaxation dynamics of periodic array of
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Au/Si nanostructure upon initial excitations according to Table 1. Panels arrangement
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and color code of each panel is identical to those of Figure 5. Panel (a) shows
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distribution of charge as a function of energy and time, with color code red, green, blue
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representing electron, equilibrium distribution, and hole. Panel (b) provides details on
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electron dynamics in space. Panel (c) shows hole dynamics in space.
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Figures S3-S8, panel (d)-(f) Pairs of occupied and unoccupied KSOs
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contributing to low-energy optical transitions according to Table 1, for the atomic model
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of periodic array of Au/Si nanostructure. Red, green, blue, yellow, dark blue stand for Si,
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H, Au, P and Al, respectively. Black dashed circles pointing at Al and P atoms. Gray
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clouds represent isosurfaces of KSO. Panels (d),(e) show partial charge density of a
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given KSO. Panels (f) show partial charge density integrated over the x,y direction, as a
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function of z.
E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
Z, (Å)
60
0
50
5
0
40
10
5
30
10
4
20
15
10
3
(e)
20
20 (d)
15
0
2
(f)
5
6
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Figure S3. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (a) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-36. Panel (e) shows partial charge density of orbital LU+42.
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Red and green in panel (f) represents 1D projection of orbital HO-36 and LU+42 on Z
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direction, respectively.
E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
0
Z, (Å)
60
5
0
50
10
5
40
15
10
30
15
20
20
2
(e)
10
0
20 (d)
(f)
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Figure S4. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (b) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-8. Panel (e) shows partial charge density of orbital LU+45.
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Red and green in panel (f) represents 1D projection of orbital HO-8 and LU+45 on Z
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direction, respectively.
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E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
0
Z, (Å)
60
5
0
50
10
5
40
15
10
30
15
20
20
2
(e)
10
0
20 (d)
(f)
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Figure S5. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (d) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-19. Panel (e) shows partial charge density of orbital LU+23.
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Red and green in panel (f) represents 1D projection of orbital HO-19 and LU+23 on Z
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direction, respectively.
E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
0
Z, (Å)
60
5
0
50
10
5
40
15
10
30
15
20
20
2
(e)
10
0
20 (d)
(f)
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Figure S6. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (e) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-3. Panel (e) shows partial charge density of orbital LU+41.
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Red and green in panel (f) represents 1D projection of orbital HO-3 and LU+41 on Z
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direction, respectively.
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E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
0
Z, (Å)
60
5
0
50
10
5
40
15
10
30
15
20
20
2
(e)
10
0
20 (d)
(f)
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Figure S7. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (f) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-1. Panel (e) shows partial charge density of orbital LU+26.
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Red and green in panel (f) represents 1D projection of orbital HO-1 and LU+26 on Z
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direction, respectively.
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E-Efermi , eV
(a)
Z, Å
(b)
Z, Å
(c)
log10(time/1ps)
1
3
x10
0
Z, (Å)
60
5
0
50
10
5
40
15
10
30
15
20
20
2
(e)
10
0
20 (d)
(f)
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Figure S8. Panels (a)-(c) show relaxation dynamics of periodic array of Au/Si
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nanostructure upon the initial excitation (g) according to Table 1. Panel (d) shows partial
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charge density of orbital HO-5. Panel (e) shows partial charge density of orbital LU+6.
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Red and green in panel (f) represents 1D projection of orbital HO-5 and LU+6 on Z
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direction, respectively.
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Additional possible hypothetic reaction pathways:
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In addition, simulated results show for selected photo-excitations, the electron is
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promoted from aluminum to phosphorus in the photon-mediated process and then
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recombines to the ground state through golden bridge. This simulation illustrates the
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basic effect of a photovoltaic cell in the limit of short current circuit.
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Discussion of future research
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Various placements of co-dopants may alter relaxation pathways and relaxation
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rates. This exploration is left for future works, due to numerically expensive procedure
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of computing nonadiabatic couplings.
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References
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[1]I. K. Robinson, P. A. Bennett, and F. J. Himpsel, Phys. Rev. Lett. 88 (9), 096104 (2002).
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