Molecular Dynamics of Sputtering Yield
as a Function of Ion Incident Angle in GaN Crystal
Kenji Harafuji1 and Katsuyuki Kawamura2
1
Department of Electrical and Electronic Engineering, Ritsumeikan University, Shiga, Japan
2
Department of Earth and Planetary Science, Tokyo Institute of Technology, Tokyo, Japan
Abstract: A molecular dynamics simulation has been performed for the physical
sputtering of a wurtzite-type GaN(0001) surface by an Ar ion with 250 eV.
Angular dependence of the sputtering yield is calculated for a wide range of very
oblique (10 degrees) to perpendicular (90 degrees) Ar incidence. The threshold
angle of the sputtering is approximately 30 degrees. Sputtering yields for Ga and
N atoms show maximum values of 0.33 and 0.60 at 50 degrees, respectively. A
sputtering of crystal atoms takes place within about 100 fs after the impact of an
incident ion due to a collision-cascade mechanism. After that, the kinetic energy
is distributed among many atoms in the crystal creating a hot spot. At
approximately 500 fs, the hot spot is maximized. At 3000 fs, the hot spot shrinks
and the original crystal structure is almost recovered. Nitrogen atoms are
preferably sputtered. Ga atoms are generally sputtered with N atoms in pairs.
Keywords: dry-etching, molecular dynamics, sputtering yield, GaN
1. Introduction
GaN is a promising material for power
devices and short-wavelength optoelectronic
devices such as light-emitting diodes (LEDs)
and laser diodes (LDs) [1,2]. Plasma dry
etching is a necessary step in device fabrication
since GaN is chemically inert in acids and bases
at room temperature [3]. Reactive ion etching is
thus conventionally used for mesa structure to
reach n-type material in LEDs and for ridge
structure to attain lateral optical confinement in
LDs [4].
Control of the incident angle of energetic ions
in sputtering process is an important item in
designing GaN-based power devices and
optoelectronic devices. This is because efficient
but damage-free dry-etching is strongly required
especially for atomic layers in active regions.
The dry etching mechanism is, however, least
well-understood.
Molecular dynamics (MD) simulation is a
powerful tool to investigate details of physical
and chemical mechanisms that would otherwise
be difficult or impossible to obtain [5]. Several
studies on silicon etching by MD simulation
have been reported [6-8].
In this article, MD simulation is made to
investigate the angular dependence of the
sputtering yield for a wide range of very oblique
(10 degrees) to perpendicular (90 degrees) Ar
incidence.
Preliminary results have been
presented elsewhere by the present authors
[9,10].
2. Simulation Model
2.1. Potential and Cell Parameters
Figure 1 shows the wurtzite-type GaN crystal
with P63mc symmetry identified by lattice
constants a, b, and c, the internal parameter u,
where a=b= 0.32003 nm, c=0.51574 nm, and u=
0.36989. Two kinds of unit cells are also
defined.
The functional form of a two-body
interatomic potential is modeled as follows:
uij 
 a  a j  rij
 f 0 (bi  b j ) exp i
 b b
4 0 rij
i
j

Zi Z je2
 D1ij exp(   1ij rij )  D 2ij exp(   2ij rij ) 




ci c j
Table 1.
(1)
rij6
where the first term is the Coulomb interaction,
the second term is the Gilbert-type short-range
repulsion, the third and fourth terms represent
the covalent bonding and covalent repulsion of
the modified Morse type, respectively, and the
last term is the van der Waals potential. The
variable rij is the interatomic distance between
the i-th and the j-th atoms, ε0 is the dielectric
constant of the vacuum, Zi is the effective
charge for each atom, f0 is the constant for unit
conversion [41.86 kJ/(nm ・ mol)], ai is the
repulsion radius, bi is the softness parameter, D1,
D2, β1 and β2 are covalent coefficients, and ci is
the van der Waals coefficient.


B 01 1 0 unit cell for constructing C 0001
MD basic cell
b’
b
a

c

C 0001
B
c×u
A
A 21 10
unit cell of
wurtzite-type GaN
Ga
N
Figure 1. Definitions of unit cell and lattice constants.
Unit cell parameters (a, b, c, and u) and
potential parameters are determined based on
the periodic restricted Hartree-Fock ab initio
method (CRYSTAL 98) [10,11]. The obtained
potential parameters are listed in Table 1. The
accuracy of the interatomic potential for Ga and
N atoms is checked with respect to elastic
constants, phonon spectrum, melting point and
phase transition [12-14]. The argon ion is
neutralized before impact and therefore the
potential is for neutral Ar.
atom
N
Ga
Ar
atomatom
N-Ga
Calculated potential parameters in eq.(1).
Z(e)
a (nm)
b (nm)
-1.150 0.1970 0.0123
1.150 0.0834 0.00911
0
0.1878 0.0117
c
(kJ/mol)1/2
(nm)3
0.0364
0.0
0.0788
D1
(kJ/mol)
β1
(nm-1)
D2
(kJ/mol)
β2
(nm-1)
-5250.5
20.0
6581.7
40.0
2.2. MD Model
As the unit cell for constructing the MD basic
cell, a rectangular parallelepiped is selected, as
shown by broken lines in Fig. 1. The lattice
constants a, b’, c in Cartesian coordinates are
shown there. In the figure, the definitions of the
crystal directions, A, B, and C are also depicted.
The MXDORTO code [15] is used for the
present MD simulation. The molecular motion
is solved by the Verlet method. The Coulomb
interaction is calculated by the Ewald sum
method. Details of the approach we took in the
simulation are similar to studies previously
reported [6-8].
Figure 2 shows the model configuration,
where Fig. 2(a) and Fig. 2(b) are the top view,
and the side view of the crystal part,
respectively. The small black and mediate white
circles denote Ga and N atoms, respectively, and
larger, gray one is Ar atom. An MD basic cell is
comprised of 10a×6b’×8c unit cells for a total
number of 1920 Ga atoms and 1920 N atoms.
The bottom one-pair layers for Ga and N atoms
of the MD basic cell, 240 atoms, are set to the
thermostat of 300 K. The surface area is 3.205
nm×3.330 nm. The height is 4.148 nm. The
vacuum region with its height of 12.44 nm is set
along the C direction of the cell. Periodic
boundary conditions are employed on the
boundary of the cell three dimensionally. MD
simulations are performed under the NVE
ensemble except for the bottom one-pair layers,
where N (number of atoms), V (volume) and E
(energy) are kept constant.
C 0001
N Ga Ar
Vacuum
Region
Ar
θ

(a)
2 1 1 0
0.7
A
300K thermostat
(b)
Figure 2. Simulation model. (a)Top view. (b)Side view.
First, relaxation calculation of 15 ps is made
to attain an equilibrium state. Second, an
energetic Ar atom with 250 eV is brought into
the surface with the angle from 10 to 90 degrees
with the increment of 10 degrees. The statistical
data of sputtering yield is obtained averaged
over 30 Ar ions for each incident angle. The
incident position is given by random number.
The time step of 0.6 fs is used. At each Ar
incidence, the motion of all atoms is followed at
least for 7 ps. It takes about 3 h CPU time for
each Ar impact to complete the simulation by
the use of a 2.4 GHz personal computer.
3. Calculation Result
A sputtering of crystal atoms takes place
within about 100 fs after the impact of an
incident Ar ion due to a collision-cascade
mechanism. After that, the kinetic energy is
distributed among many atoms in the crystal
creating a hot spot. At approximately 500 fs,
the hot spot is maximized. At 3000 fs, the hot
spot shrinks and the original crystal structure is
almost recovered.
0.6
Sputtering Yield

B 01 1 0
Angular dependence of the sputtering yield is
calculated for a wide range of very oblique (10
degrees) to perpendicular (90 degrees) Ar
incidence. Figure 3 shows the calculation result
of the sputtering yield as a function of Ar
incident angle with 250 eV averaged over 30
times. Sputtering yields for Ga and N atoms
show maximum values of 0.33 and 0.60 at 50
degrees, respectively. The threshold angle of the
sputtering is approximately 30 degrees. The
sputtering yield of N atom at perpendicular
incidence (90 degrees) is finite value of 0.2, but
that of Ga atom is zero.
0.5
● N atom
■ Ga atom
0.4
0.3
0.2
0.1
0
00 10
20 30 40
20
40 50 60
60 70 80
80 90
Incident Angle θ (deg)
Figure 3. Sputtering yield as a function of Ar incident angle.
For very oblique Ar incidence with the angle
less than 20 degrees, the Ar atom grazes over
the crystal surface, and does not generate
definite collision-cascade and hot-spot. At 30
degrees incidence, the Ar atom brings about
both the collision-cascade and hot-spot up to the
top three layers, but seldom generates the
sputtering.
At 40 degrees incidence, the sputtering rate
increases largely. The crystal randomization
takes place up to the top four or five layers.
For incident angles with 40-70 degrees, a
cooperation of the horizontal and vertical
momenta efficiently kicks atoms in the crystal,
and generates collision-cascade to a great deal.
This brings about the high sputtering rate.
Nitrogen atoms are preferably sputtered. The
reason is as follows. When an incident Ar atom
collides with a heavy Ga atom, Ar is reflected
upward, that is, backscattered. The heavy Ga
atom serves as a reflecting wall for the incident
Ar atom. The backscattered Ar atom gives the
upward momentum and energy of crystal atoms,
especially those of light N atoms. Ga atoms are
generally sputtered with N atoms in pairs.
The obliquely incident Ar atom efficiently
penetrates into the inner atomic layers through
the gap between atoms, reflected obliquely by
the Ga atom, and kicks upward both light N
atom and heavy Ga atom especially on the top
layer. This is the reason why obliquely incident
Ar atom brings about the large sputtering rate
not only of N atom but also of Ga atom. This
mechanism is shown in Fig.4.
Sputtering
Ar
Top Layer
Ga
N
Figure 4. The mechanism why the oblique incident Ar atom
efficiently sputters crystal atoms.
Figure 5 shows the snapshot of the side view
of the top five layers at 270 fs after the Ar
impact with 50 degrees incidence.
Reflected Ar
Sputtered Ga-N
Hot-Spot
Figure 5. Snapshot side view of near surface layers at 270 fs
after the impact of Ar atom with 50 degrees incidence.
A pair of Ga-N is sputtered from the surface,
and is going upward. Incident Ar is also
reflected from the surface. A hot spot is
growing at the Ar incident point.
4. Conclusion
MD simulation has been made to investigate
the angular dependence of the sputtering yield
for a wide range of very oblique (10 degrees) to
perpendicular (90 degrees) Ar incidence. The
threshold angle of the sputtering is
approximately 30 degrees. Sputtering yields for
Ga and N atoms show maximum values of 0.33
and 0.60 at 50 degrees, respectively.
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