Molecular dynamics simulation of low energy boron and arsenic implant into silicon Page: 4 of 6
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
a = aB (Z.23 20Z.23)-1 (5)
128) a
where aB is the Bohr radius.
The ZBL B-Si and As-Si potentials are smoothly
truncated at a distance comparable to that used in the
Tersoff Si-Si potential, i.e. at around 1.5 x the sum of the
covalent radii of the atoms involved.
The repulsive pair term in Tersoff-type potentials is not
sufficiently strong for small atomic separations. To
overcome this deficiency, the repulsive term is splined to
a shifted ZBL potential, by joining the two functions at the
point where they are cotangent. In the case of Si-Si
interactions, the join is at an atomic separation of 0.69 A,
and requires the ZBL function to be shifted by 148.7 eV.
The increase in the value of the short-range repulsive
potential compensates for the attractive part of the Tersoff
potential, which is present even at short-range.
III. ELECTRONIC STOPPING MODEL
A new model that involves both global and local
contributions to the electronic stopping is used for the
electronic energy loss [1]. The model contains only one
fitted parameter that has the same value for B and As ions,
for all energies and incident directions.
The model was developed for use in a modified UT-
Marlowe BC code. One small modification to the model is
required to allow its use in MD, due to the fact that an
atom is usually interacting with more than one other atom
at a time. This modification takes account of multiple
contributions to the local electron density, whilst ensuring
that the background electron density is only counted once.
This is achieved by calculating the one electron radius as;
rs = p where p = 0 + Ors.1oc - ( 19x
ri <1.441
where rslloc is the one electron radius calculated from the
charge density of a single atom, and the constant term is
the contribution from the background charge density. This
ensures that the damping force is a continuous function of
atomic position.
IV. INTEGRATION SCHEME
The paths of the atoms are integrated using Verlet's
algorithm [4];
rn+ = rn + vnAt + anAt2/2
vn+ = Vn + [a + an ]At/2 (7)As the velocity of the particles varies considerably
during a trajectory, a variable timestep scheme is used for
the integration. For high energy simulations the potential
energy as well as the velocity of atoms is important, as
atoms may be moving slowly but have high potential
energies during impacts. The timestep is selected using;(8)
At
Sm[2C (
max 2 x [KE, + max(0, PE )
i=1,NI MJwhere KEI , PEZ and M are the kinetic energy, potential
energy and mass respectively of atom i, and CDIS is a
constant with a value of 0.05 A. When the timestep is
increasing a weighted sum of the previous and predicted
timestep of the form;At =4 At,_1 +4 At0
(9)
is used, to prevent rapid oscillations in the size of the
timestep. During a typical trajectory, the timestep
averages about 0.8 fs, with the total energy of the system
conserved to 0.03 %.
V. SIMULATION DETAILS
The atomic masses were set to that of the most
abundant isotope in each case. The target was 28 A on a
side, and up to 450 A deep. This required around 24,000
atoms for the largest simulations and resulted in around
95% of incoming ions becoming trapped within the lattice,
with 5% passing through the base. At the start of each
trajectory an undamaged silicon target was heated to
300 K by giving all atoms appropriate velocities and
displacements from their lattice sites. Periodic boundary
conditions were applied to the sides of the target, with free
boundaries in the vertical direction.
Ions were always incident at random positions over the
smallest possible representative area of the surface. The
incident direction of the ions was either normal to the
surface (channeling case), or at 100 to the surface normal
(non-channeling). For the non-channeling case, half the
ions had an azimuthal angle of 22* to the surface dimer
rows, and half were at an angle of 680 to the dimer rows.
Simulations were run until the total energy of the ion
was below 5 eV, at which point it was assumed to be
trapped. Around 1000 trajectories were run to generate
statistics for each case considered. The simulations were
run on 25 SUN & 30 SGI workstations over a period of two
months.
VI. RESULTS
Fig 1. to Fig 6. show the calculated concentration
profile of the B and As ions for various incident energies
and directions. Also shown are the profiles calculated
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Beardmore, K.; Cai, D. & Gronbech-Jensen, N. Molecular dynamics simulation of low energy boron and arsenic implant into silicon, article, July 1, 1996; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc665077/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.