Molecular dynamics simulation of icosahedral Si quantum dot formation from liquid droplets
Kengo Nishio,* Tetsuya Morishita, Wataru Shinoda, and Masuhiro Mikami
Research Institute for Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST),
Central 2, Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan
Received 31 August 2005; published 15 December 2005
The present paper reports on molecular dynamics simulations of the formation process of Si quantum dots
Si QDs. Icosahedral Si QDs are formed spontaneously by freezing 274-, 280-, and 323-atom Si droplets. We
find that the initialization of pentagonal channels leads into the overall icosahedral structure. We also study the
melting behavior of the 280-atom icosahedral Si QD. We find that the melting point is reduced more than 15%
compared with that of bulk Si. A possible approach to synthesize icosahedral Si QDs is discussed. The
formation of the icosahedral structure could be expected in other systems characterized by tetrahedral bonding
network.
DOI: 10.1103/PhysRevB.72.245321 PACS numbers: 78.67.Hc, 65.80.+n, 81.07.Ta
I. INTRODUCTION
Silicon quantum dots Si QDs are scientifically and tech-
nologically important semiconductor nanoparticles. Their op-
tical properties and electronic structures vary dramatically
with size and atomic arrangement.
1–7
For example, the peak
position of photoluminescence can be tuned by controlling
the size, and the intensity of photoluminescence is higher in
amorphous Si QDs than in crystalline Si QDs.
4,5
It has also
been suggested that the spin dephasing time and coherence in
optical excitations can be tuned by controlling the symmetry
of the atomic arrangement.
7
These facts stress the importance
of understanding and controlling the structure of Si QDs.
While the most stable structures are well understood in small
Si particles by theoretical calculations,
8,9
the determination
of the structures in the nanosize regime is a very hard
task.
7,10,11
The most stable morphology of rare gas, gold, and copper
nanoparticles changes from fcc to decahedral to icosahedral,
as the size decreases.
12–17
For Si, one can draw two analo-
gies. First, the space lattice of bulk crystalline Si is fcc. Sec-
ond, although the yield is quite low, decahedral Si QDs have
been observed in samples prepared by the gas evaporation
method.
18,19
It is then expected that small Si QDs can be
formed in the icosahedral structure.
From a geometrical viewpoint, the icosahedral structure,
which consists of 20 slightly distorted crystalline tetrahedra,
each exposing one of four 111 facets, can be built in the
framework of tetrahedral bonding.
20
The 111 facets have
the lowest area density of dangling bonds so that the surface
energy could be minimum. The stability of the icosahedral
structure at 0 K is determined by the competition of the
strain energy and the surface energy. Recent first-principles
calculations have shown that icosahedral Si QDs i-Si QDs
have lower structure energies than crystalline Si QDs c-Si
QDs at least for diameters smaller than 2.77 nm.
7
However
it is not clear whether such a structure really exists.
Previous theoretical and experimental studies in various
systems have suggested that the formation process actually
determines the morphology of a nanoparticle.
5,6,12–14,16,18,19,21
For example, by controlling experimental conditions, c-Si
QDs or amorphous Si QDs can be selectively synthesized.
5,6
Given the situation, molecular dynamics MD simulation is
a powerful technique to study the stable structure of Si
QDs
11,12,14,21
because it enables us to investigate the forma-
tion process of Si QDs directly by following up the motion
of Si atoms. In addition, the thermal stability of Si QDs can
be investigated.
In the present paper, we study the formation process of Si
QDs of diameters in the range of 2.17 to 2.31 nm by means
of MD simulations. Long-time simulations show that i-Si
QDs are formed spontaneously by freezing Si droplets. The
formation of pentagonal channels plays an important role in
the formation of i-Si QDs. We also find that the melting
point of the i-Si QD of 2.20 nm in diameter is reduced more
than 15% compared with that of bulk Si.
II. MODEL AND METHODS
As we shall show later, it takes more than 50 ns to pro-
duce i-Si QDs by freezing Si droplets. Phenomena of such a
long time-scale are intractable via first-principles or tight-
binding molecular dynamics TBMD simulations. A short
time-scale simulation by the TBMD method has shown that a
281-atom Si droplet freezes into an amorphous Si QD,
11
that
is, the system is trapped in some metastable state. In our MD
simulations, Si atoms are modeled by the empirical Tersoff
potential, which is known to reproduce structural properties
well, including tetrahedral bonding networks in both crystal-
line and amorphous phases.
22–24
By choosing the empirical
potential, we can perform simulations long enough to study
the formation process of i-Si QDs. When one uses empirical
potentials, it is necessary to consider the transferability of the
potentials. We consider that the Tersoff model captures the
essence for representing the structural properties of i-Si QDs
from the following two physical insights based on the results
of the first-principles calculations:
7
1 i-Si QDs are con-
structed by covalent bonding, or tetrahedral bonding not by
metallic bonding which is observed in very small clusters;
2 the poor description of the energetics of surface recon-
structions in the Tersoff model does not affect the overall
icosahedral structure, because i-Si QDs expose 111 facets
without surface reconstructions.
PHYSICAL REVIEW B 72, 245321 2005
1098-0121/2005/7224/2453214/$23.00 ©2005 The American Physical Society 245321-1