Molecular Dynamics of Sputtering Yield as a Function of Ion Incident Angle
in Chlorine-Adsorbed GaN Crystal
K. Harafuji1 and K. Kawamura2
1
Department of Electrical and Electronic Engineering, Ritsumeikan University, Shiga, Japan
2
Graduate School of Environmental and Life Science, Okayama University, Okayama, Japan
Abstract: A molecular dynamics simulation has been made to study the dependence
of sputtering yield on the ion incident angle in the wurtzite-type GaN(0001) surface
with the Cl-adsorbed layer. Angular dependence of the sputtering yield is calculated
for a wide range of very oblique (10 degrees) to perpendicular (90 degrees) 250 eV
Ar incidence. Sputtering yields for Ga and N atoms show maximum values of 0.63
and 0.20 at 50 degrees, respectively.
Keywords: dry-etching, molecular dynamics, sputtering yield, GaN
1. Introduction
GaN is a suitable material for power devices and
short-wavelength optoelectronic devices such as lightemitting diodes (LEDs) and laser diodes (LDs) [1,2].
Since GaN is chemically inert in acids and bases at
room temperature, plasma dry etching is a necessary
step in device fabrication [3]. Reactive ion etching is
thus conventionally used for mesa structure to reach ntype material in LEDs and for ridge structure to attain
lateral optical confinement in LDs [4]. A gas mixture
of Cl-based chemicals is usually used for etching
discharge [5, 6].
Control of the incident angle of energetic ions in
sputtering process is an important item in achieving
efficient but damage-free dry-etching 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 [7]. Several studies on silicon
etching by MD simulation have been reported [8-10].
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. Two cases
are simulated, one with a clean surface and the other
with a Cl-adsorbed surface. Preliminary results have
been presented elsewhere by the present authors [1113].
2. Simulation Model
2.1. Potential and Cell Parameters
The functional form of a two-body interatomic
potential is modeled as follows:
uij
Zi Z j e2
4
r
f 0 (bi
b j ) exp
r )
D2ij exp(
0 ij
D1ij exp(
1ij ij
ai
aj
bi
rij
bj
r )
2ij ij
ci c j (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.
Potential parameters are determined based on the
periodic restricted Hartree-Fock ab initio method
(CRYSTAL 98) [12,14]. 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 [15-17]. The argon
ion is neutralized before impact and therefore the
potential is for neutral Ar.
Table 1. Calculated potential parameters in eq.(1).
atom
N
Ga
Ar
Cl
Na
atomatom
N-Ga
Z(e)
a (nm)
b (nm)
-1.150
1.150
0
-0.48
0.48
0.1970
0.0834
0.1878
0.2061
0.1493
0.0123
0.00911
0.0117
0.0190
0.0120
D1
(kJ/mol)
-5250.5
β1
(nm-1)
20.0
c (kJ/mol)1/2
(nm)3
0.0364
0.0
0.0788
0.0573
0.0184
D2
(kJ/mol)
6581.7
β2
(nm-1)
40.0
2.2. MD Model
The MXDORTO code developed by Kawamura is
used for the present MD simulation [18]. 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 those in previously reported studies [1113]. All atomic pairs among gallium, nitrogen,
chlorine, sodium, and argon are taken into account
using the potential of eq. (1). Figure 1 shows the
model configuration, where Figs. 1(a) and 1(b) are the
top view and the side view of the crystal part,
respectively. The small blue and intermediate green
circles denote Ga and N atoms, respectively. The
small yellow and orange circles are the Cl and Na
atoms, respectively. The large pink circle is the Ar
atom.
An MD basic cell consists of 1920 Ga atoms and
1920 N atoms. The top surface has half-monolayer Cl
coverage (60 Cl atoms with －0.48e charge). Counter
60 Na atoms with +0.48e charge are set on the bottom
surface to satisfy the charge neutrality condition for
the Ewald sum method. In Fig. 1(a), Na atoms on the
bottom surface are omitted to clearly show the
distribution of Cl atoms. Potential parameters of Cl
and Na are determined on the basis of the rock-salt
crystal of NaCl. The charge of Cl atoms is estimated
by the ab initio method (Gaussian 03) with MP2/321G for GaCl2 and GaCl3 molecules [19].
The bottom one-pair layer of Ga and N atoms of the
MD basic cell, 240 atoms, and 60 Na atoms are set to
the thermostat of 300 K. The surface area of the MD
basic cell is 3.21×3.33 nm2. The height is 4.31 nm. A
vacuum region with a height of 12.28 nm is set along
the C direction of the cell. Periodic boundary
conditions are employed three dimensionally on the
boundary of the cell. MD simulations are performed
under the NVE ensemble except for the bottom
thermostat layers, where N (number of atoms), V
(volume), and E (energy) are kept constant.
First, the relaxation calculation of 15 ps without Cl
and Na atoms and that of 14 ps with Cl and Na atoms
are carried out to attain an equilibrium state. Second,
an energetic Ar atom with 250 eV is brought into the
surface with the angle θ 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. A time step of 0.6-0.7 fs is used
depending on the Ar energy. At each Ar incidence, the
motion of all atoms is followed at least for 6 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.
C 0001
Ar
NG C N
a l a
θ
01 1 0
21 10
(a)
Vacuum
Region
300K thermostat
(b)
Fig. 1. Simulation model. (a)Top view. (b)Side view.
3. Calculation Result
Figure 2 shows the result of Ga and N sputtering
yields for a wide range of very oblique (10 degrees) to
perpendicular (90 degrees) Ar incidence. Circle and
triangle denotes Ga and N sputtering yields,
respectively.
Blue line denotes the case of clean surface without
Cl-adsorbed layer. Sputtering yields for Ga and N
atoms show maximum values of 0.33 and 0.60 at 50
degrees, respectively. On the other hand, red line
denotes the case with the Cl-adsorbed layer.
Sputtering yields for Ga and N atoms show maximum
values of 0.63 and 0.20 at 50 degrees, respectively.
In the case with the clean surface, 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
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.
In the case with the Cl-adsorbed layer, chemical
sputtering of Ga is promoted, whereas N sputtering is
much suppressed due to the Coulomb repulsive force
between N and Cl atoms. Ga atom is chemically
sputtered mostly in the form of Ga-Cl2 or Ga-Cl.
These products escape from the surface in the time
range of mainly 200-500 fs after the impact of the
incident Ar ion. There are small amounts of products
escaping in the time range of 500-2000 fs. N atom is
mostly sputtered in the form of Ga-N in the time range
less than 200 fs. It is to be noted that there is a finite
sputtering rate even at 20 degrees for both Ga and N
atoms.
For both cases with and without Cl-adsorbed layer,
sputtering rate is peaked at 50 degrees. 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.
Figure 3 shows the snapshot of the side view of the
top five layers after the Ar impact to the Cl-adsorbed
surface. The incident angle is 20 degrees. Ar atom
reaches the surface at 93 fs.
Figure 3(a) shows the snapshot at 643 fs. The
incident Ar atom collides with a Cl atom, and is
reflected from the surface.
The Cl atom itself
subsequently collides with Ga-N atoms on the first
layer shown by dashed line. A very thin hot spot on
the adsorbed Cl and the first Ga-N layers is generated
around the collided Cl incident point. The original
hexagonal crystal structure is disordered there. The Cl
atom is also reflected from the surface.
Reflected Ar
643 fs
Sputtered Cl
Hot-Spot
0.7
S puttering Yield
0.6
0.5
N
Ga
N (C l)
G a(C l)
0.4
(a)
0.3
1755 fs
0.2
GaCl2 product is leaving.
0.1
0
0 10 20 30 40 50 60 70 80 90
Incident A ngle (deg)
Fig.2 Angular dependence of the sputtering yield for
Ar ion incidence with 250 eV, where 90-degrees
denotes the normal incidence.
(b)
Fig.3 Snapshot side view of near surface layers after
the impact of Ar atom with 20 degrees incidence.
(a)643 fs, (b)1755 fs.
.
Figure 3(b) shows the snapshot at 1755 fs. The hot
spot shrinks, and then disappears. The original
hexagonal crystal structure is almost recovered. That
is, recrystallization takes place. A volatile product of
a GaCl2 molecule is generated, and this molecule
begins to leave the surface.
4. Conclusion
A molecular dynamics simulation has been made to
study the dependence of sputtering yield on the ion
incident angle in the wurtzite-type GaN(0001) surface
with and without a Cl-adsorbed layer. Angular
dependence of the sputtering yield is calculated for a
wide range of very oblique (10 degrees) to
perpendicular (90 degrees) 250eV Ar incidence. In
the case with the Cl-adsorbed layer, chemical
sputtering of Ga is promoted, whereas N sputtering is
much suppressed due to the Coulomb repulsive force
between N and Cl atoms. Ga atom is chemically
sputtered mostly in the form of Ga-Cl2 or Ga-Cl.
Sputtering yields for Ga and N atoms show maximum
values of 0.63 and 0.20 at 50 degrees, respectively.
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