Journal of Modern Physics, 2013, 4, 1-26
Published Online November 2013 (
Open Access JMP
Ab Initio Molecular Orbital Calculation for Optical
and Electronic Properties Evaluation of Small and
Medium Size Silicon Nano-Clusters Found
in Silicon Rich Oxide Films
Néstor David Espinosa Torres1*, José Francisco Javier Flores Gracia1, José Alberto Luna López1,
Juan Carlos Ramírez García2, Alfredo Morales Sánchez3, José Luis Sosa Sánchez1,
David Hernández de la Luz1, Francisco Morales Morales1
1Research Center for Semiconductor Devices, CIDS-ICUAP-BUAP, Puebla, México
2The Faculty of Chemical Sciences, BUAP, Puebla, México
3Research Center for Advanced Materials S.C. Unit Monterrey-PIIT, Apodaca, México
Email: *
Received August 2, 2013; revised September 5, 2013; accepted October 3, 2013
Copyright © 2013 Néstor David Espinosa Torres et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In systems in atomic and nano scales such as clusters or agglomerates constituted of particles from a few to less than
one hundred of atoms, quantum confinement effects are very important. Their optical and electronic properties are often
dependent on the size of the systems and the way in which the atoms in these clusters are bonded. Generally, these
nano-structures display optical and electronic properties significantly different of those found in corresponding bulk
materials. Silicon agglomerates found in Silicon Rich Oxide (SRO) films have optical properties, which have reported
as depended directly on nano-crystal size. Furthermore, the room temperature photoluminescence (PL) of Silicon Rich
Oxides (SRO) has repeatedly generated a huge interest due to their possible applications in optoelectronic devices.
However, a plausible emission mechanism has not yet widespread acceptance of the scientific community. In this re-
search, we employed the Density Functional Theory with a functional B3LYP and a basis set 6 - 31G* to calculate the
optical and electronic properties of small (six to ten silicon atoms) and medium size clusters of silicon (constituted of
eleven to fourteen silicon atoms). With the theoretical calculation of the structural and optical properties of silicon clus-
ters, it is possible to evaluate the contribution of silicon agglomerates in the luminescent emission mechanism experi-
mentally found in thin SRO films.
Keywords: Nano-Crystals; Silicon Clusters; Silicon-Rich Oxide; Luminescence; Magic-Number
1. Introduction
Canham [1] reported visible light emission from porous
silicon at room temperature in 1990 and since then, sili-
con associated materials have received a huge interest
and have been studied intensively for their relevance to
the development of nano-electronics. In that sense, a ma-
terial which has generated great interest is SRO thin film
(Silicon Rich Oxide); this material exhibits optical prop-
erties in the same manner to porous silicon but is signifi-
cantly less assailable.
Si nanocrystals (Si-nCs) embedded in dielectric ma-
trices such as silicon dioxide exhibit unique optical and
electrical properties which are determined by quantum
size and Coulomb blockade effects [2]. Si-nCs can emit
and absorb light at energies which can be controlled by
their sizes. This fundamental property of Si-nCs is very
useful in 3rd generation solar cells [3].
Commonly, SRO is considered as a multi-phase mate-
rial constituted of a mixture of silica (SiO2), off-
stoichiometric oxides (SiOx, x < 2) and elemental silicon.
After thermal treatment at temperatures above 1000˚C,
the off-stoichiometric oxides, SiOx (x < 2), react to pro-
duce silicon nano-clusters, structures with different oxi-
dation states with or without defects and silica [4]. Sili-
con nano-crystals (Si-nCs) and silicon agglomerates have
been characterized in SRO films employing Transmis-
*Corresponding author.
sion Electron Microscopy (TEM) and Atomic Force Mi-
croscopy (AFM). The formation and the size of Si-nCs
depend on the excess silicon and annealing parameters
(time and temperature) and surely of type of carried gas
used. When the number of valence electrons in the clus-
ters is 8, 20, 40, or 58 etc., it is well known that silicon
clusters are “magic-number” [5]. The “magic-number”
behavior of small size silicon clusters is frequently cor-
related with the trend of binding energy per atom as a
function of cluster size [6].
The electronic configuration of an atom and the number
of atoms in the cluster are two factors that play the major
role in the cluster stability [7].
Over the past twenty years, medium-sized silicon
clusters Sin (n > 10) have attracted much attention both
experimentally [8] and theoretically [9]. Considerable
effort has been devoted to determine the ground-state
geometric structures, namely, the global minima as a
function of the cluster size n. For n 7, the global minima
are firmly established by both ab initio calculations and
Raman/infrared spectroscopy measurements; whereas for
n 12 the global minima based on ab initio calculations
[10-15] are well accepted.
For 13 n 20, unbiased search for the global minima
has been undertaken based on either the genetic algorithm
coupled with semi-empirical tight-binding (TB) technique
[16,17], or the single-parent evolution algorithm coupled
with density-functional (DF) TB and density-functional
theory (DFT) methods [18,19]. Set correctly the geometry
corresponding to the global minimum energy is critical for
a further evaluation, so reliable, of optical and structural
properties, and thereby contribute properly to the under-
standing of the underlying mechanisms of luminescence.
Crystalline silicon has an indirect band gap, which
means, every optical transition must be accompanied by
the creation or annihilation of a phonon. Another disad-
vantage is due to the low band gap value Eg,c-Si = 1.12 eV
(at Room Temperature) corresponding to a wavelength
λg,c-Si = 1107 nm: the radiation emitted by a light emitting
diode (LED) built of c-Si corresponds with infrared and
then is non-visible by the human eye.
By usage of nano-scaled silicon structures the last
mentioned disadvantage can be overcome. There are op-
tical transitions in quantum confined states of Si nano-
structures, which generate visible radiation. But the dis-
advantage of the indirect band gap still remains. Average
PL decay times for Si-nCs with diameters d ~ 3.4 nm are
reported to be τPL~(100 - 500) μs at RT [20]
The most intense light emission observed in SRO
films obtained by LPCVD technique has been reported in
films with approximately 5% excess silicon, but silicon
nanocrystals were not observed in those films [21]. It is
possible that silicon small size agglomerates (Sin, n < 20)
were presented in these particular films (R0 = 30) which
would hardly be detected due to atomic instead nano
scale. Size regimes in the evolution of semiconductor
spectroscopic properties were introduced by Efros [22].
Semiconductors sizes can be labeled with increasing size
as molecular (n < 50 atoms), quantum dot (50 n 105
atoms), polariton (105 n 109 atoms), and finally (n >
109 atoms) for bulk semiconductor species.
In this work, we calculated theoretically the IR, UV-
Vis and Raman spectra and a selected set of properties of
small and medium size silicon agglomerates (agglomer-
ates size less than 1.5 nm). The equilibrium energy cal-
culated of several propose d Si clusters at ground state
and the six first excitation states calculated result very
useful to evaluate the possible contribution to the PL
from different silicon structures present in SRO films.
2. Theory of Electronic States in
The excitation of nanocrystals with photons can only
happen from electronic states in the valence band to
electronic states in the conduction band. To obtain the
electronic states in a nano-crystal the assumption that
nanocrystals have a spherical shape is used. S. V. Gapo-
nenko [23] used spherical coordinates r, θ and ϕ and the
=−∇ +
where U(r) is the total potential energy of the electron
inside the quantum dot. In this Hamiltonian the Laplace
operator in spherical coordinates must be used:
sin sin
θθθ θ
=− 
∂∂ ∂
Due to the spherical symmetry of the potential a sepa-
ration of the wave function leads to the following wave
()() ()
,, ,, ,
is the spherical functions, n is the prin-
cipal quantum numbers, l is the orbital number and m the
magnetic number. The angular momentum L is deter-
mined by the orbital number l:
210,1,2,,Lll ln=−=1 (4)
The component parallel to the z axis is determined by
the magnetic quantum number m:1
() ()()
†Bessel function:l
jl l
ξξ ξ
=− 
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mml llll==−−+−+−
Inserting into the Schrödinger equation must
satisfy the equation:
() ()
22 2
uUrllu Eu
−++ +=
 (6)
In order to obtain a solution to this equation the poten-
tial is approximated as infinitely high which leads to the
following expression for the energy values of the elec-
tronic states in a spherical nano-crystal:
= (7)
where χnl are the roots of the spherical Bessel functions.
In the real space the electron and the hole are interact-
ing via coulomb attraction. This bound pair of electron
and hole is known as excitons. Quantum confinement
occurs if the Bohr radius, of the excitons is larger than the
size of the nano-crystal. Due to the high potential of the
silicon dioxide (approximately 9 eV) which surrounds the
silicon nanocrystals the excitons are confined within the
volume of the nano-crystal. This leads to further changes
of the band structure and the emissions spectrum.
Starting from the energy value already calculated
and applying perturbation theory it is possible to
obtain a correction factor due to the effective mass of the
electron and hole respectively.
Additionally, the Coulomb interaction between the
electron and the hole has to be considered. A combination
of both approaches leads to the Hamiltonian in the lowest
excited state:
olarization terms
ehe h
Hrrm m
=−−+ +
With the distance of electron and hole re rh, their ef-
fective masses me and mh respectively and the dielectrical
constant .
We assume in Equation (1) that the total potential en-
ergy U(r) to be of the following form:
()() ()
UrU rVr=+ (9)
The second part Vsp(r) describes an interaction between
the electron and its image, arising due to the charge po-
larization on the boundary between the silicon nano-
crystal and its dielectric surrounding. Vsp(r) is often re-
ferred to as a self-polarization term. It can be represented
sp l
Vr Rll R
and d are the static dielectric constants of
silicon and the dielectric matrix, respectively. The po-
larization terms enter because we must consider the cor-
rect form of the Coulomb interaction in the presence of the
crystallite surface. An analytical approximation for the
lowest eigenvalue (i.e., the first excited electronic state)
1.8 smaller terms
EE Rmm
≅− ++
where EG is the bulk band gap, R is the size of the nano-
crystal, the term to R1 is the coulomb term and the term
to R2 is the shift as a result of quantum localization of
electrons and holes (quantum confinement). This simple
formula is possible because the correlation between elec-
tron and hole positions, induced by the Coulomb interact-
tion, is not strong. The major effect is additive, inde-
pendent confinement energies for electron and hole.
Latest energy equation connects in a very simple way
the emitted wavelength of a nano-crystal to its size, by
means of:
=≈ (12)
In 1984 Brus [24] suggested the first theoretical calcu-
lation for semiconductor nanoparticles based on “effective
mass approximation” (EMA). This approximation as-
sumed that an exciton is confined to a spherical volume of
the crystallite and the mass of electron and hole is sup-
planted with effective masses ( and ) to define the
wave function.
g bulk
eh r
=+ −
 2
0 is the permittivity of vacuum and r is the relative
permittivity. Four year later, in 1988 Kayanuma [
ε ε
accounted for the electron-hole spatial correlation effect
and modified the Brus Equation, including a taking away
term proportional to Rydberg energy.
3. Analysis and Discussion of the Results
For many years, different methods have been used for
preparation of silicon nano-crystals, for instance, chemi-
cal vapor deposition [26], Si ion implantation [27], col-
loidal synthesis [28], magnetron sputtering [26], and
electron beam evaporation [29]. A high-temperature
thermal treatment at temperatures above 1000˚C is gen-
erally required in order to produce the crystallites. All
these techniques allow one to form silicon nCs with sizes
mainly ranging from 2 - 6 nm, and it is possible obtain
silicon nCs with sizes less than 2 nm in SRO films as de-
posited with Ro = 30 prepared using LPCVD technique.
Their electronic and optical properties depend on the
preparation conditions and method of fabrication. How-
ever, there are some common properties typical for silicon
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nCs, independent of the fabrication technique employed.
In particular, the nanocrystals’ surroundings, either vac-
uum or some host material like SRO, represent a high
potential barrier for carriers of both kinds. Such a barrier
is often referred to as a confining potential that mainly
defines the energy spectrum of the nano-crystal.
Figure 1 displays the optical band gap of silicon
nanocrystals obtained from optical absorption (unfilled
symbols) and PL data (filled symbols). Dashed and con-
tinuous lines are calculated values with and without ex-
citonic correction, respectively.
Silicon nCs are capable of emitting electromagnetic
energy in the visible spectrum. This is in contrast with
bulk silicon, in which energy of the interband transition
corresponds to the silicon band gap energy of 1.12 eV.
The variation of the photon frequency in nanocrystals
compared to the bulk material is a universal phenomenon
taking place in huge of semiconductor materials. The
energy of the emitted photon increases as the nano-crystal
size decreases. Such an increase is usually called a “blue-
shift” because the photon energy shifts toward the shorter-
wavelength side of the visible spectrum.
This blue-shift is illustrated for Si nCs in Figure 2.
Here, the mean nC size is controlled via the silicon excess
concentration, with the smallest nCs occurring in the most
silicon deficient samples. Reduction in intensity on the
silicon-poor side of the compositional map is due to the
lower number density of nCs, and on the silicon-rich side
it is due to the opening of non-radiative pathways in large
and highly interconnected nano-clusters.
There is a legitimately large uncertainly in the calcu-
lated values of the optical gaps as a function of nCs di-
ameter. Doubtless, several factors influencing the accu-
racy of the optical-gap measurements are as follows. First,
the nanocrystals studied by different research groups have
been prepared using different techniques. As a result, the
Figure 1. Optical band gap of silicon nano clusters. Theo-
retical calculus vs experimental data compilated by Delerue
Figure 2. PL spectra of silicon nCs in SiO2. The 200-nm-
thick samples were approximately identical except for the
amount of excess silicon [32].
nCs have different surroundings, surface bonds, and
shapes, all of which could lead to scatter in the experi-
mental data. Second, it is difficult to determine exactly the
dot sizes and the size distribution in luminescent ag-
glomerate of nCs. Finally, using the mean size in a cluster
of nCs in a plot like Figure 1 can be confusing, since it is
possible that the observed PL peak does not correspond
exactly to the mean size but instead to the largest PL rate.
Theoretically, the problem persists mainly due to the
difficulty to define an appropriate parameter for deter-
mining the diameter (equivalent). By simplicity a sphere
is used in most of the models suggested, since the actual
shape of the agglomerates formed is totally irregular.
Figure 3 shows the calculated Van Der Waal surfaces for
isomers Si7. In this case, only the isomer with lowest
energy is acceptably symmetric. And even then it is dif-
ficult to choose the appropriate size.
Thus, for example the greatest distance found in isomer
7A is which can be measured from either silicon atoms
placed in the vertex of a pentagon to its second nearest
neighbor obtaining values in range of 4.050 to 4.053 Å for
Si-Si not bonded in ten possible measures; of 2.506 to
2.508 Å in five measures corresponding to silicon atoms
contiguous around the pentagon (bond distance), the dis-
tance between silicon atoms in two pyramid corners or
vertex is 2.568 Å and the distance between a silicon atom
in pentagon to the silicon atom in pyramid corner is 2.486
to 2.488 Å (ten bond distance values).
Assuming for silicon a Van der Waals radii of 2.1 Å,
then the diameter for Si7 isomer 7A could be in range
0.4586 to 0.6153 nm. So, how can we set the most ap-
propriate diameter or crystallite size?
For solve this, we employ a space-filling model, also
known as a calotte model or CPK models, is a type of
three-dimensional molecular model where the atoms are
represented by spheres whose radii are proportional to the
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energy reported by Raghavachari and Rohlfing [6] No
qualitative change in the geometry of these isomers was
found except the capped trigonal prism. The lowest-en-
ergy isomer of Si7 corresponds with structure 7A, a pen-
tagonal bipyrimid with D5h symmetry, in accordance with
the experiment [34] and previous theoretical studies [6].
Note that the structures of small silicon clusters are dif-
ferent from the tetrahedral coordination characteristic of
bulk silicon. Table 2 contains specific bonds calculated
information for Si7 structures. Table 1 displays calculated
structural and geometric properties for Si7 nano-cluster.
The most stable structure (7A) presents the lowest Dipole,
CPK Area (Å2) CPK volume (Å3), ovality and polariza-
bility parameters and the highest symmetry and band gap.
Figure 6 shows ovality and polarizability calculated pa-
rameter for Si7 isomers. Ovality is a measure of how the
shape of the molecule approaches a sphere or cigar.
Ovality is described by the ratio of volume and area.
radii of the atoms and whose center-to-center distances are
proportional to the distances between the atomic nuclei,
all in the same scale. CPK models are distinguished from
other 3D representations, such as the ball-and-stick and
skeletal models, by the use of “full size” balls for the
atoms. They are useful for visualizing the effective shape
and relative dimensions of the molecule, in particular the
region of space occupied by it. Table 1 displays values for
CPK volume and CPK area for isomers Si7. For isomer 7A,
using CPK volume we obtain d1 = 6.987 Å (0.7 nm) and
d2 = 7.400 Å (0.74 nm) when we use CPK area. Finally,
we can co-relate CPK area and CPK volume, obtaining
the diameter [Å] with equation:
6CPK 32
CPK 42
Substitution of values gives D = 6.2295 Å, for isomer
7A 7B
Figure 4(a) corresponds with AFM image 3D. Adjunct
to coordinates (0, 3.5) it is possible to find thickness less
than 5 nm [33]. Whereas in Figure 4(b) adjacent to co-
ordinates (0, 2.8) it is possible to find thickness less than 1
In Figure 5(a) we can appreciate roughness less than 1
nm for SRO films as deposited with a Ro = 20 and less
than 5 nm for films deposited with Ro = 10 and Ro = 30.
Whereas Figure 5(b) is a 2D AFM image for SRO film
deposited by LPCVD, in blue line (Ro = 30) we are able to
find height less than 1 nm. For Ro = 20 (red line) is pos-
sible observe height less than 1 nm around χ 1.2 μm.
Finally, for Ro = 10 (black line) there is a small region
with altitudes less than1 nm everywhere χ 1.95 μm. The
highest agglomerates found correspond to Ro = 10 and it
is approximately 25 nm.
3.1. Structural and Optical Properties for N = 7
Figure 3. Calculated Van Der Waal surfaces for isomers Si7.
For Si7 we have evaluated four geometric isomers of low-
Table 1. Calculated Properties for Si7 nano-cluster.
Isomer E (au) E LUMO
band gap
Area (Ų)
Volume (ų)Ovality** Nsymop polarizability*
7A -2026.40489 3.17 6.35 3.177114890.01 172.06 178.60 1.12184512 4 55.1102671
7B 2026.34772 3.70 5.60 1.897523351.12 174.00 180.46 1.12674305 1 55.5653083
7C 2026.34325 3.25 5.61 2.363334240.25 183.44 185.93 1.16445201 1 55.8984076
7D 2026.34330 3.26 5.62 2.364984710.26 183.56 185.96 1.16504567 2 55.9003733
*; **
Polarizability0.08VDW _Volume13.0352hardness0.979920hardness41.3791=×− ×+×+
vality43 4AV=×π×××πO;
hardness 2EE=− −.
= 1005˚C
4.0 0.0
Y[μm] 2.0
(a) (b)
Figure 4. (a) AFM image 3D obtained of a SRO film deposited by HFCVD at 1005˚C; (b) AFM image 3D obtained of a SRO
film deposited by HFCVD on silicon substrate.
0510 15 20 25 30
Roughness (nm)
Ro = 10
Ro = 20
Ro = 30
0 12 3 4
X (μm)
Ro=10 Ro=20 Ro=30
As-Deposited Profile
Height (nm)
(a) (b)
Figure 5. (a) Histogram of roughness [nm] for SRO films as deposited; (b) 2D Image that shows the selection of the Rough-
ness and profile characteristics for statistical analysis of SRO10, 20 and 30 As-deposited films on Silicon for a scan size of 4 ×
4 μm2.
Table 2. Small nanoclusters Si7 exhibit a coordination different that found in bulk silicon (tetra coordinated).
Isomer Number of Silicon
atoms with 2 bonds
Number of Silicon
atoms with 3 bonds
Number of Silicon
atoms with 4 bonds
Number of Silicon
atoms with 5 bonds
Number of Silicon
atoms with six bonds
Total Number
of Si-Si bonds
7A 5 2 15
7B 3 1 2 1 15
7C 1 3 3 15
7D 1 4 2 14
In Raman spectroscopy a vibrational mode is active due
to a change in the polarizability during the vibration. On
the other hand, a vibrational mode is active in FTIR as
consequence of a change in the dipole moment during the
For isomer most stable (7A), FTIR spectra has a peak at
406 cm1. Due to poor symmetry or anti-symmetry of
isomers 7B, 7C and 7D there is a shift in frequency vi-
bration values (until 529 cm1) and appears additional
small peaks, see Figure 7.
The second most intense peak in isomer 7C has a fre-
quency of 436 cm1 (indicated with a small red circle on
Figure 7). Isomer 7D displays a similar peak in the fre-
quency 439 cm1. Luna et al. [33 ], have reported a peak at
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Figure 6. Ovality and polarizability plots for Si7 structures. Right side: Structure 7A (the lowest energy isomer).
Figure 7. FTIR spectra for isomer 7C.
440 cm1, in SRO films deposited at 873˚C by HFCVD,
but they associated this vibration frequency with Si-O
UV-Vis spectra calculated for isomers Si7 predict lu-
minescence in visible region, except for most stable
(isomer 7A) which results with emission in UV region.
This fact could be associated with the similarity with
tetrahedral coordination in bulk (there are five silicon
atoms with four bonds each one and only two with five
bonds). Figure 8 displays UV-Vis spectra for isomer 7D.
In Table 3 we collect luminescence calculated data for
isomers Si7.
The isomer Si7 with the highest stability (7A), results
with violet emission expected and other isomers with less
stability display a second expected peak in IR region.
3.2. Structural and Optical Properties for N = 12
Bahel and Ramakrishna [10,11] have examined 15 iso-
mers of Si12 and shown that the pentagonal and tetragonal
prismatic families are higher in energy than the trigonal
prismatic family. Zhu et al. [35] obtain similar conclusion
after examining several new low-energy isomers. For Si12
isomers found by Zhu [35], we have re-evaluated using
HF/6-31*, and we obtains some differences in results, see
Table 4. Whereas Zhu et al. results indicate that isomer
12A is the lowest-energy; our results give isomer 12E as
the most stable structure.
Dipole moment calculated for isomers Si12 varies in
range from 0.0 to 2.75 Debye’s, and band gap fluctuates
from 1.558 until 2.648 eV.
Table 5 contains the calculated properties for isomers
Si12 organized from low to high energy. Sorted in this way,
it is not possible correlate them with other parameter like
dipole moment, band gap, polarizability, ovality or the
size. The average size for isomers Si12, using CPK area
and CPK volume models results 0.8595 nm.Optical pro-
perties calculated for isomer Si12 are presented in right
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Figure 8. UV-Vis spectra for the isomer 7D.
Table 3. Calculated luminescence peaks for the isomers Si7.
Isomer The Most intense peak emission [nm] 2nd More intense peak emission [nm] 3rd peak emission [nm]
7A 382.41 (violet)
7B 660.93 (red) 930.99 (IR) 777.58 (IR)
7C 598.11 (orange) 807.37 (IR)
7D 591.98 (orange) 806.26 (IR)
Table 4. Comparation of energies calculated of Si12 isomers.
Isomer HF/6-31G* ref [ZZ] MP2/6-31G* ref [ZZ] OUR RESULTS USING HF/6-31G* Point Group
12a 3466.75512 3467.97520 3473.81817 (C2v)
12b 3466.72241 3467.96359 3473.84833 (Cs)
12c 3466.68583 3467.94708 3473.82730 (Cs)
12d 3466.72986 3467.94023 3473.829488 (C2v)
12e 3466.74850 3467.93946 3473.85018 (C1)
12f 3466.68104 3467.92139 3473.83045 (Cs)
12g 3466.71823 3467.91483 3473.82394 (Cs)
12h 3466.67983 3467.91127 3473.82681 (C3v)
12i 3466.56063 3467.90996 3473.80236 (D4h)
12j 3466.69196 3467.90872 3473.82995 (C2v)
12k 3466.63861 3467.90709 3473.81306 (C5v)
12l 3466.68552 3467.89061 3473.84834 (C2v)
ref [32] MP3/6-31G* MP4(SDQ)/6-316* CCSD/6-31G* CCSD(T)/6-31G*
12A 3467.87303 3467.96718 3467.92573 3468.03985
12B 3467.84017 3467.94730 3467.90060 3468.02069
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Table 5. Calculated properties for Si12 nano-clusters (sorted by energy value).
D [nm]
CPK Area
D [nm]
CPK Volume
FTIR frequency
of most
intense peak cm1
UV-Vis wavelength
of most intense
peak [nm]
12E 5.77 3.60 0.46 247.51 288.66 2.171419701.171786810.8876 0.8200 485 826.45 (IR)
12L 5.80 3.88 0.70 249.32 290.45 1.926875311.175504430.8908 0.8217 415 720.43 (red)
12B 5.80 3.88 0.70 249.26 290.36 1.924999911.175462730.8907 0.8216 415 720.22 (red)
12F 5.82 3.17 2.75 245.18 288.52 2.648491191.161119640.8834 0.8198 435 562.76 (green)
12J 5.59 3.79 0.31 249.86 291.95 1.801511561.174027280.8918 0.8231 442 830.71 (IR)
12C 5.69 3.77 1.19 250.22 291.07 1.918010371.178072380.8925 0.8222 408 635.2 (red)
12H 5.78 4.07 0.00 254.22 296.04 1.706528141.183472410.8996 0.8269 354 733.33 (red)
12G 5.43 3.37 0.98 251.45 292.34 2.062211741.180439490.8946 0.8234 427 576.75 (yellow)
12A 5.66 3.16 0.39 252.59 290.90 2.498778131.189702420.8967 0.8221 448 627.76 (red)
12K 5.54 3.99 0.44 259.84 294.83 1.558762481.212942700.9094 0.8258 492 772.49 (IR)
12I 5.67 3.51 0.01 264.24 297.70 2.160614891.225559310.9171 0.8284 445 641.76 (red)
12D Fails
side of Table 5. FTIR calculated vibrations frequencies of
442, 448 and 445 cm1 (highlight in yellow) for isomers 12J,
12A and 12I are in excellent agreement with experimental
results and they were reported in SRO films deposited by
HFCVD at temperatures in range of 750˚C to 873˚C).
Also UV-Vis calculations are in Table 5. All Si12 iso-
mers have an expected emission in visible range. We have
selected the most intense peaks for each isomers and we
plotted them in Figure 9. We can conclude that the likely
most intense emission of isomers Si12 will be in color red.
Chemical Function Descriptors CFD’s are descriptors
given to a molecule in order to characterize or anticipate
its chemical behavior or to identify commonality among
molecules with different structures. They parallel terms in
a chemist’s vocabulary such as lone pair (to suggest the
role of a hydrogen-bond acceptor) and sterically crowded
(to suggest that getting close may be difficult). Figure 10
displays VDW surfaces for isomers Si12 (12A, 12B, 12C
and 12E) and includes sketchs 12F to12 L to represent
CFD’s for isomers Si12 (12F to 12L). We can appreciate
silicon atoms with coordination different respect to found
in bulk. For instance, the isomer 12H has six silicon atoms
with only three bonds, three silicon atoms with five bonds,
two with six bond and one with seven bonds.That is, none
of the twelve silicon atoms present in the isomer 12H is
tetra coordinated.
Figure 11 includes FTIR spectra calculated for the
most stable isomer Si12. The most intense peak with a
frequency of 485 cm1, corresponds to silicon atoms vi-
bration that contains only three bonds. UV-Vis spectrum
for isomer 12E is shown in Figure 12.
In this case, luminescence is observed in a wide interval
of visible region and it extends to near IR, beginning in
574.67 nm and ending in 826.43 nm we can easily identify
six emission states.
3.3. Structural and Optical Properties for Si8
In 1988 Raghavachari and Rohlfing [6] reported seven
low-energy isomers Si8 on the basis of the HF/6-31G(d)
level of theory. Later, Xiaolei et al. [36] in 2003 reported
eight isomers Si8, after optimizing the geometry at the
MP2/6-31G(d) level followed by the total-energy cal-
culation at the CCSD(T)/6-31G(d) level. Among the
seven isomers originally cited, six geometric isomers,
have the same structure as Xiaolei [36] suggested despite
of some differences in energy ordering and geometric
parameters due to different levels of theory employed. We
evaluated full geometry optimizations followed by the
total-energy calculation at the HF/6-31G* level, for eight
structures suggested by Xiaolei [36], who reported isomer
8A as the lowest energy Si8. Our results indicate that
isomer 8E has the lowest energy. For isomers Si8, FTIR
spectra are displayed in Figure 13.
In this case, there are 18 degree freedoms and most of
them correspond with frequency vibrations of very low
intensity. In Table 6 we collect numerical data. For iso-
mers 8C, 8G and 8B, the highest vibration intensity cor-
responds with the maximum wavenumber.
In right column of Table 7 we include the wavelength
of the energy level with the highest emission. All results
obtained predict emission in visible region for isomers Si8.
A selected set of Si8 isomers UV-Vis spectra are shown in
Figure 14.
Figure 15 displays agglomerate’s shape and coordina-
tion isomers’s Si8. We can appreciate sub-coordinated (tri)
and supra-coordinated (penta and hexa) silicon atoms,
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400 500 600 700
Figure 9. Wavelengthmax for isomers Si12.
12A 12B 12C 12E
12F 12G 12H
12I 12J 12K 12L
Figure 10. Sketch 12A to 12E display VDW surfaces for isomers Si12 (A, B, C and E). 12F to12L represent CFD for isomers
Si12 (F to L).
Figure 11. IR spectra calculated for silicon isomer with the lowest-energy 12E.
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Figure 12. Luminescence spectra calculated for silicon isomer 12E.
Figure 13. FTIR calculated spectra for isomers Si8 (A to D).
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Table 6. Calculated properties for isomers Si8.
Isomer Energy
O [eV]
SIZE [nm],
using equation 14
of Si-Si
(Equation (15))
8A 2315.85400 5.48 3.81 1.66577122 0.00 190.10202.88 0.640326546 19 4.75
8B 2315.84487 5.40 3.90 1.49418089 0.94 189.68203.19 0.642714381 17 4.25
8C 2315.84982 5.66 3.40 2.25498620 0.99 190.19203.73 0.642716601 17 4.25
8D 2315.84767 5.10 3.33 1.76459166 0.80 193.41203.76 0.632105836 16 4.00
8E 2315.86794 5.80 3.21 2.58956912 0.00 191.09203.00 0.637395306 18 4.50
8F 2315.86179 6.06 3.86 2.19571567 0.46 191.99203.99 0.637486965 18 4.50
8G 2315.84487 5.40 3.90 1.49141814 0.94 189.69203.21 0.642738633 19 4.75
8H 2315.84642 5.65 3.57 2.07800261 0.85 192.08205.18 0.640911951 20 5.00
AVG 2315.85217 5.57 3.62 1.94177944 0.62 191.03203.62 0.639549527
MIN 2315.86794 6.06 3.90 1.49141814 0.00 189.68202.88 0.632105836
MAX 2315.84487 5.10 3.21 2.58956912 0.99 193.41205.18 0.642738633 0.00853663 0.29 0.28 0.39848214 0.42 1.36 0.74 0.00372214178
Table 7. Calculated numerical data in FTIR and UV-Vis spectra for isomers Si8.
Isomer Wavenumber of max vibration cm1 Wavenumber with max Intensity cm1 Wavelength of the highest emission nm
8E 508.432 507.490 535.14
8F 479.146 408.119 834.12*
8A 491.027 471.044 701.32
8C 470.320 470.320 510.90
8D 477.413 273.661 522.91
8H 485.637 372.866 643.56 and 662.48
8G 451.894 451.894 682.99
8B 452.367 452.367 595.57
*There are other three energy levels in isomer 8F with emissions closely respect the highest emission (593.17, 711.70 and 753.90 nm).
Using this definition, we can calculate for isomer Si8
CAN values in the range of 4 to 5 (refer to Table 6)
besides tetra-coordinated. In silicon bulk there is only
tetra-coordinated silicon atoms. It’s possible to suggest
growing mechanisms for silicon nano-crystals based on
coordination number. Isomers Si8 have been cited as a
magic number. The “magic-number” behavior of small
silicon clusters has been correlated with the trend of
binding energy per atom as a function of cluster size [6].
Luo, Zhao, and Wang [7] pointed out that two factors can
play major role in the cluster stability, one is the electronic
configuration of an atom and another is the number of
atoms in the cluster. We define the useful relationship
“Coordination Average Number (CAN)” as:
The energies calculated for isomers Si8 are included in
Table 6. The energy differences regarding the isomers
with lowest energy are in range from 0.16746 to 0.62787
eV. Band Gap calculated varies between 1.49141814 and
2.58956912 eV. In this case, the isomer 8E shows the
global minimum energy and the maximum band gap.
Dipole moments are in range 0.0 to 0.99 Debye.
2number of SiSi bonds
umber of Silicon Atoms
= (15)
Statistical values for optical and geometrical parame-
ters are listed in bottom of Table 6. In 1999 Luo et al.
thought that isomer 8H to be the global minimum based
on a semi-empirical method. The isomer 8 G, a singly-
capped pentagonal bi-pyramid, was also previously thought
o be the global minimum based on the tight-binding t
Figure 14. Calculated luminescence spectra for isomers Si8 (E to H).
Figure 15. Agglomerate’s shape and coordination isomers’s Si8, using ball and wire model.
molecular dynamics calculation [37].
3.4. Structural and Optical Properties for Si9
For isomers Si9, the global-minimum isomer appears to be
the stacked distorted rhombi (9A) with an additional atom
capped on top [38,39]. This lowest-energy structure was
predicted by Vasiliev, Ogut, and Chelikowsky [40] and
confirmed later by other groups [39,41]. It can be also
viewed as a bi-capped pentagonal bi-pyramid. The isomer
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9B, also a bi-capped pentagonal bi-pyramid (but the two
caps are on the same side of the pyramid), is a local
minimum. In this case, we evaluated five isomers (9A to
9E) the first four as Xiaolei Zhu and X. C. Zeng [36]
suggested, and additionally we evaluated the isomer 9E,
and the results obtained indicate that the global-minimum
energy isomer could be the isomer 9A with an energy
almost equal than 9C (difference of 6.7*10 - 6 au), in
accordance with most of results previously reported.
The structures and FTIR spectra calculated for isomers
Si9 are displayed on Figure 16. Spectra for isomers 9A
and 9C are closely similar as expected, numerically the
maximum wavenumber calculated are 480.892 and
479.594 cm1 respectively. In a similar way, FTIR spectra
for isomers 9B and 9E are comparable with the highest
vibration intensity at 392.101 and 386.835 cm1, accord-
ingly. Isomer 9D displays two intense peaks, at wave-
numbers of 485.265 and 450.588 cm1. Isomers Si9 have
21 freedom degree and the number of basis functions
employed was 171 in a basis set 6-31G(d).
UV-Vis spectra calculated for isomers Si9 are displayed
on Figure 17. Similarities discussed in FTIR spectra
about isomers 9A and 9C are found again in UV-Vis
spectra. Isomers Si9 show a blue-shift respect to isomer Si8,
but most of them present a maximum expected emission
in green. Specifically isomer 9D displays a very wide
emission since green to IR.
Quantitative information for isomers Si9 is collected in
Table 8. We can say that isomers 9A and 9C are nearly
iso-energetic, they share the global minimum (relative
Figure 16. Structures and FTIR spectra calculated for isomers Si9.
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Figure 17. UV-Vis spectra calculated for isomers Si9.
Table 8. Calculated properties for isomers Si9.
Isomer E
rel. E
[nm] ovality polarizability BandGap
max [nm]
9C 2605.37750 0.0000 0.30 0.6584718 1.14282787 58.7832223 2.92214238 495.9544 green
9A 2605.37749 0.0002 0.30 0.6584469 1.14286446 58.7831785 2.92100793 497.0215 green
9B 2605.35171 0.7016 0.56 0.6599471 1.14308208 58.9760305 2.67515482 552.6431 green
9E 2605.35158 0.7051 0.70 0.6599086 1.14304081 58.9624295 2.71063434 457.2400 blue
9D 2605.3406964 1.0013 0.82 0.650300676 1.16259063 59.2340282 2.09779370 794.863530
energy has a difference less than 102 eV).
3.5. Structural and Optical Properties for Silicon
Isomers Si10
Our calculation confirms that the isomer 10A, a tetra-
capped trigonal prism, is the global minimum, as already
predicted by other groups [12,13], and we obtain energies
differences of only 0.35 eV in respect of the global
minimum for isomers 10B, 10C and10D, whereas that
Xiaolei et al. reported differences of 1.99 and 1.27 eV
using MP2/6-31G(d) level theory and 0.75 and 0.81 eV
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for isomers 10B and 10C when they apply CCSD(T)/
6-31G(d). The isomer 10B corresponds with a tetra-capped
octahedron, and is a low-energy local minimum as shown
by Raghavachari and Rohlfing [6].
The isomer 10C, was obtained by B. X. Li et al. [19],
via a full geometry optimization from the geometric iso-
mer Cs.
Additionally to isomers previously reported, we include
the isomer 10D. This isomer has a local minimum and its
FTIR and UV-Vis spectra displayed on Figures 18 and 19
are quite closely than other similar isomers with local
minimum. Quantitative differences are detailed in Table 9
where we have sorted isomers by energy column.
The band gap calculated for global minimum isomer
Si10 (3.03117115 eV) is greater than obtained for smaller
isomers (7 n 9), and even for greater isomers like Si12.
This fact attracts our attention. We should remember that
Si10 is a magic-number cluster which has been extensively
studied theoretically.
Maximum emission for global minimum (isomer 10A)
is predicted in green region, but emission extends to blue
color. Whereas, for local minimum isomers (10D, 10C
and 10B) the maximum expected emission includes yel-
low and extends until red.
Figure 18. Structures and FTIR spectra calculated for isomers Si10.
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Figure 19. UV-Vis spectra calculated for isomers Si10.
Table 9. Optical and structural parameters calculated for isomers Si10.
Isomer E
rel. E
[nm] ovality Band Gap
[eV] PolarizabilityEmission max
10A 2894.89078 0.00 0.683933275 1.131522503.03117115 60.3433322 544.828431 (green) 0.849136022
10D 2894.87788 0.35 0.672424038 1.155210412.4694636460.6994128 573.646862 (yellow) 0.542605980
10C 2894.87788 0.35 0.672457582 1.155102892.4725120060.6961078 572.438798 (yellow) 0.543559417
10B 2894.87787 0.35 0.672419970 1.155191782.4685791660.6982988 574.066039 (yellow) 0.546128917
3.6. Structural and Optical Properties for Silicon
Isomers Si11
Isomer 11A is a distorted tri-capped tetragonal anti-prism
or a distorted penta-capped trigonal prism, isomer 11B is a
tri-capped trigonal prism with two additional caps on side
trigonal faces, and the isomer 11C a bi-capped tetragonal
anti-prism with an additional cap on one upper trigonal
face. Among the three isomers, Lee, Chang, and Lee [37]
and also later Sieck et al. [39] suggested isomer 11A as
global minimum. Whereas isomers11B and 11C were
predicted by Rohlfing and Raghavachari [12,13] based on
the HF/6-31G(d) and MP4SDQ/6-31G(d) calculations.
The isomer 11B was also predicted to be a possible global
minimum by Ho and co-workers [16,17] using a density-
functional pseudo-potential theory within both local den-
sity and generalized gradient approximations; 11A in Ref.
[42,43] was predicted to be a local minimum. Ho and
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co-workers [16,17] recently used Car-Parrinello molecu-
lar dynamics combined with the simulated annealing
method to search for the global-minimumstructure of Si11.
They found again that 11B is most likely the global
minimum. At the MP2/6-31G(d) and CCSD(T)/6-31G(d)
levels, Zhu et al. [35] found that both isomers 11A and
11B are the possible global minimum while 11C is only
about 0.2 eV higher in energy than 11A and 11B.
The isomer 11D, another capped trigonal prism, is a
new low-energy isomer whose energy is 0.52 eV higher
than that of 11E. The newly optimized starting from 11C
is hereafter called 11E, which is also a capped trigonal
prism. Our calculus, disclose that isomer 11E is the global
minimum, sharing this possibility with isomer 11B with
an energy difference less than 103 eV and near closely
with isomer 11A with only a difference of 0.23 eV. Refer
to Table 10 for numerical details.
Zhu et al. found isomer 11E should be the global
minimum using extended levels of theory MP2/6-311(2d)
and CCSD(T)/6 - 311(2d). Structures for isomers Si11, are
displayed on inset of plots on Figure 20 (11A to 11E).
Green planes are only a guide to improve view. FTIR
spectra for Si11 isomers display two or three intense peaks
located in intervals 470.2 - 498.4, 415.1 - 447.8 and 394.6
- 397.1 cm1 (refer to Figure 20). One imaginary (nega-
tive) frequency for rotation was found in isomers 11A and
11C. One imaginary frequency indicates that you are at a
saddle point (transition state), which is a potential energy
maximum rather than a Potential Energy Surface (PES)
minimum.Negative frequencies indicate instability in the
molecule or, in other words, saddle points on the potential
energy surface. A stable molecule should have no
imaginary frequencies, a transition state should have one
(1st order saddle point), and while more than one imagi-
nary frequency means that there is a problem with mole-
cule’s geometry.
Figure 21 displays UV-Vis spectra for isomers Si11.
Calculated luminescence for isomers 11A, 11C and 11D
indicates emission in visible and the most intense emis-
sion in IR region (details on Table 10). Isomer 11B will
not show IR emission, only in part of visible region, with
the most intense wavelength at 482.9 nm. Whereas the
global minimum (11E) displays a little bite different
spectra, with partial emission in high energy levels visible
region, around 523.2 nm and additionally emission in NIR.
3.7. Structural and Optical Properties for Silicon
Isomers Si13
The Jahn-Teller effect (JTE), sometimes also known as
Jahn-Teller distortion, describes the geometrical distor-
tion of molecules associated with certain electron con-
figurations. JTE proved, using group theory, that orbital
nonlinear spatially degenerate molecules cannot be stable
[44]. The effect essentially states that any nonlinear
molecule with a spatially degenerate electronic ground
state will undergo a geometrical distortion that removes
that degeneracy, because the distortion lowers the overall
energy of the species. Another type of geometrical dis-
tortion occurs in crystals with substitutional impurities
(off-center ions). The Jahn-Teller effect is manifested in
the UV-VIS absorbance spectra of some compounds,
where it often causes splitting of bands. Many theoretical
studies have been devoted to the Si13 cluster because of the
possibility of finding a high-symmetry (Ih) core-based
icosahedral structure [40]. It was later shown that the
high-symmetry icosahedral cluster is unstable due to the
Jahn-Teller distortion [45].
Using a quantum Monte Carlo method, Grossman and
Mitas [46] investigated several isomers of Si13 and found
that the C3v trigonal anti-prism isomer 13B is more stable
than the core-based icosahedral Si13(Ih). Here, we confirm
that isomer 13A has the global minimum and there are two
isomers (13B and 13D) near iso-energetic with only a
difference of 0.20 eV.
FTIR spectra calculated for isomers Si13 are displayed
on Figure 22. Note that we increase scale of intensity (0 -
40 U.A.) mainly due to that isomer 13C results with rela-
tive high intensity at frequencies of 360.282, 471.024 and
499.159 cm1. Isomers Si13 exhibit 33 freedom degrees
and employ 247 basis functions.
All isomers Si13 are supra-coordinated (CAN in range
from 56/13 for isomer 13B to 66/13 for isomer 13E).
Calculated zero point vibration energy (ZPVE) resulted
near of 0.5 eV (see Table 11).
Except for isomer 13E, most of Si13 isomers have high
Table 10. Optical and structural parameters calculated for isomers Si11.
Isomer Energy
rel. E
[eV] Ovality PolarizabilityUV-Vis_ lambda
11E 3184.35805 0.693056173 0.00 2.195093151.1515003262.4448440 523.201425 0.45 1.24
11B 3184.35756 0.677192371 0.00 2.800855811.1580547562.1385317 482.900429 0.46 1.42
11A 3184.34961 0.695816933 0.23 2.100331431.1450689962.3623936 845.486195 0.44 0.85
11C 3184.34615 0.698294535 0.32 2.219353061.1433426462.4663103 743.763218 0.43 1.58
11D 3184.3373902 0.678075916 0.52 1.934149271.1587676162.4122287 959.659273 0.44 0.70
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Figure 20. Structures and FTIR spectra calculated for isomers Si11.
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Figure 21. UV-Vis spectra calculated for isomers Si11.
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Figure 22. Structures and FTIR spectra calculated for isomers Si13 (13A to 13E).
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Table 11. Optical and structural parameters calculated for isomers Si13.
Isomer Energy
rel. E
[eV] Ovality PolarizabilityUV-Vis_ lambda
13A 3763.34 0.7171138350.00 1.85408440 1.1686782665.9397550 1040.06464 0.552653862 1.75427983
13B 3763.33 0.7063466620.20 2.04189784 1.1929823966.3075238 831.133765 0.526377920 1.33654866
13D 3763.33 0.7062923530.20 2.04096395 1.1930290066.3048626 832.318003 0.526413642 1.34921474
13E 3763.32 0.7153297810.37 1.76424755 1.1774625366.3388454 676.653707 0.514426303 0.637141338
13C 3763.32 0.7116603330.39 2.23694992 1.1813224666.0842505 563.351931 0.545898936 1.78208642
dipole moment values (greater than 1.3 Debye). Average
size of isomers Si13 is 0.71134 nm. Band gap average
calculated over five isomers is 1.9876 eV. We can appre-
ciate structural shapes in left inset 13A to 13E of Figure
Calculated luminescence for isomers Si13 is shown on
Figure 23. For isomer 13A, the spectra calculated include
two main peaks, one with emission in visible region (red)
and another with the highest emission intensity in NIR
(1040.064 cm1).
On both sides of the peaks there are shoulders with
similar intensities, at 670.75nm and 1098.66nm, respec-
tively. Isomers 13B and 13D are iso-energetic, and for this
reason their UV-Vis spectra are quite similar. To appre-
ciate numerical differences see Table 11.
As we have said already, isomer 13C has the highest
vibrations intensity and its luminescence spectra content
two symmetric peaks. The highest local minimum corre-
sponds to isomer 13C. Also, isomer 13C results with the
highest band gap (2.237 eV) and dipole moment calcu-
lated (1.782 Debye). Whereas that, the isomer 13E has the
lowest band gap, ZPVE and dipole moment, and the
emission in IR trends to disappear.
3.8. Structural and Optical Properties for Silicon
Isomers Si14
For Si14 clusters, a number of low-lying isomers have been
cited in the literature [16,17,37,39,47-50]. Isomer 14A (Cs)
has two stacked rhombi with distortion and one five-fold
ring capped with an atom. The vibrational frequency
analysis done by Zhu et al. [15] indicates isomer 14A has
one imaginary frequency. Ours results to not contain a
transition state for this isomer. A structural perturbation
followed by geometry relaxation gives isomer 14A bis (C1)
which is very close in structure to 14A. 14A bis also ex-
hibits a stacking sequence of two distorted rhombi, one
five-fold ring, and an atom on top. General agreement is
that the isomer 14A (Cs) found by Sieck et al. [39] is pos-
sibly the global minimum. Ours calculus confirm isomer
14A as global minimum (see Table 12) sharing the pos-
sibility to be global minimum with isomer 14A bis with an
energy difference of only 0.00009 eV.
Isomers 14B, 14C, and 14D all exhibit a stacking se-
quence of three (distorted) rhombi with one atom at the
top and another at the bottom. The vibrational frequency
analysis indicates that isomer 14D has one imaginary
frequency, it means that, this isomer is a transition state.
Isomer 14E has a capped trigonal-prism unit and we ob-
tain two imaginary frequencies for this isomer. Structures
for isomers Si14 are included on insets Figures 24 and 25.
Energy differences calculated for isomers 14A bis to 14E,
respect to isomer 14A, are much higher than 0.4 eV.
There are 36 freedom degrees for isomers Si14. Isomers
with global minimum (14A and 14A bis) have the lowest
vibration intensities, whereas isomer 14D which results to
be a transition state, has the highest vibration intensity
which corresponds to 393.601 cm1.
The highest emission expected for isomer 14A corre-
sponds with green color (509.249 nm) and is quite similar
to expected for isomer 14A bis (509.263 nm). Most of
their properties are similar except may be the size. This
pair of isomers will emit in a wide band from violet to
green. Isomers 14B and 14C show a redshift and extend
covering a great part of visible region, isomer 14D does
not display detectable emission and isomer 14E will emit
preferably in NIR.
4. Conclusions
We have calculated low-energy nano-structures of Si7 -
Si14 at the HF/6-31G(d) level of theory. The vibrational
frequency analysis has been used to confirm the stability
of the lowest-energy structures of Si7 - Si14 isomers. We
employed FTIR calculated spectra in order to identify
silicon agglomerates found in SRO film deposited by
LPCVD. We evaluated different local energy isomers and
we obtained the global isomers Si7 - Si14 (lowest-energy),
and found energy differences less than 0.5 eV for most of
isomers evaluated, except for Si14 in which the differences
in energy are bigger. By plotting the binding energy per
atom as a function of n1/3 where n is the cluster size, for
small agglomerates (Si7 - Si11), the binding energy per
atom has an n1/3 dependence, suggesting that small sili-
con clusters trends spherical-like cluster growth. Haber-
land proposed that the deviaon from the linear behavior ti
Figure 23. UV-Vis spectra calculated for isomers Si13 (13A to 13E).
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Table 12. Optical and structural parameters calculated for isomers Si14.
Isomer E (au) rel. E (eV) Size[nm] BandGap eVOvality PolarizabilityDipole (debye) UVVIS_ LAMDAMAX
14A 4052.84522 0.00000 0.7266395 2.749521 1.18227167.65458 1.434 509.249
14A BIS 4052.84522 0.00009 0.7184460 2.749496 1.18227167.65463 1.434 509.263
14B 4052.81350 0.86313 0.7223203 2.172161 1.18951767.80396 3.119 669.498
14C 4052.83006 0.41248 0.7125147 2.330958 1.21238468.20395 0.647 565.667
14D 4052.77424 1.93145 0.7382580 1.792246 1.16491967.96963 0.002 Non detectable emission
14E 4052.75299 2.50957 0.7145326 1.112898 1.20549568.25954 1.436 958.566
Figure 24. Structures and FTIR spectra calculated for isomers Si14. Isomer 14D with the highest frequency intensity, scale 0 -
50 (u.a.) for isomers 14D and 14E.
Figure 25. UV-Vis spectra calculated for isomers Si14. Isomer 14D has not detectable emission.
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for the binding energy versus n1/3 curve suggests the
growth pattern of the low-lying medium-sized (Si12 - Si14)
clusters deviates from the spherical growth pattern [50].
This fact indicates that the low-lying Si7 - Si14 clusters
follow a non-spherical growth pattern. Also, we note that
the lowest-energy structures of Si12 - Si14 all contain the
TTP Si9 unit. Although the TTP Si9 unit is not a stand-
alone local minimum, it appears to be a favorable building
block [38] for medium-sized clusters Si12 - Si14.
We calculated UV-Vis spectra for isomers Si7 - Si14.
We found that most of the silicon agglomerates with small
and medium size (less than 1.0 nm) could emit in visible
region and this is a transcendental fact; because up to now,
it is not possible to detect experimentally nanoagglomer-
ates with size less than 1.0 nm and could be an explantion
for finding luminescence in SRO thin films with Ro = 30.
5. Acknowledgements
This work has been partially supported by CONA-
CyT-154725, PIFI-2013 and VIEP-BUAP-2013. N.D.
Espinosa-Torres acknowledges the financial support of
CONACYT by the scholarship given to carry out PhD
studies, to VIEP and ICUAP-CIDS for support through
PIFI 2012 projects and gives a special acknowledgment to
the Academic Team: “Organic and Nano-structured Semi-
conductors” for their invaluable support.
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