Multiscale approach for InP etching simulation under high density
plasma of Cl2/Ar
R. Chanson1, A. Rhallabi1, C. Cardinaud1,M-C. Peignon-Fernandez1
1
Institut des matériaux Jean Rouxel (IMN), University of Nantes, CNRS, BP32229, F-44322 Nantes, France
Phone/FAX: +33 240373964/+33 240373959 E-mail:[email protected]
Abstract: Improvement of III-V devices strongly depend on a better control of
the dry etching process. In this way we developed a multiscale approach
combining a global model of plasma and a 2D Monte Carlo etching model. The
global model is based on the mass balance equations of reactive species diffusing
toward the surface. The kinetic constants of electron impact reactions are
established as a function of electron temperature assuming a maxwellian
distribution of electron energy. The additional equation of power balance in the
ICP reactor allows us to determine the electrons temperature evolution with the
plasma discharge parameters (Rf power, reactor pressure and the chlorine flow
rate). The etching model is based on the discretization of the computation domain
into a set of cells that are associated with different materials (substrate and
mask). Each cell includes a real number of atoms. Cellular method is combined
to the Monte-Carlo method. The latter allows to track the ion and neutral species
from the top of the etched surface until react with the surface or outgoes from the
etch pattern. The direct fluxes of the reactive species such as Ar+, Cl2+, Cl+ and Cl
are determined from the gas phase kinetic model and introduced as the input
parameters in the InP etching model. Good agreement between the simulations
and the experiments is shown.
Keywords: plasma, InP, dry etching, model
1. Introduction
Plasma processes are one of the keys for the topdown approach used in nanoelectronic and
nanotechnology. Indeed high density plasma etching
processes continue to contribute to the reduction of
pattern scales to the nanometer range [1-3].
InP and its alloys are good candidates for high speed
electronic devices such as HEMT and HBT
components [4] and for photonic devices such as
photonic crystal [5,6]. Improvement of the electrical
and optical performances of the majority of these
components is tributary of the improvement of
technology processes like lithography and dry
etching. For InP etching, either CH4/H2 [7] or Cl2based chemistries [8] have been proposed. CH4
provides sidewall passivation and prevents under
etching. Chlorine based plasma are commonly used
in the etching of InP based materials [9-14]. In order
to reach an anisotropic profile with a good etching
rate, N2 and H2 can be added [10, 12, 14, 15].
The good transfer of the patterns from the mask to
the InP substrate requires the control of the plasma
surface interactions. In this context, computer
simulation of plasma etching can contribute to the
optimization of the etching process.
In this study, we have developed a multi-scale
approach to simulate the InP etching process under
inductively coupled plasma (ICP) Cl2-Ar discharge.
Such model is composed of two modules permitting
to predict the 2D etched InP morphology versus the
operating conditions. The aim of this work is to
validate the set of simulation and show the influence
of different input parameters (Rf power, pressure,
bias voltage) in the etching process. In this goal,
experimental etching results taken from the literature
are used and compared with our model result.
2. Models description
2.1 kinetic model
The plasma is described by a global model,
which uses average plasma parameters. The model is
applied to a cylindrical un-anodized aluminum
chamber with R=160mm and L=120mm height,
ensuring both volume and surface equivalent to
those of our ICP reactor. The model adopts the same
assumption considered by Lieberman and Lee [16],
for the different profiles of different charged species.
(1) All species densities (ni) are assumed to be
volume averaged.
(2) The electron density profile ne(r,z) is taken as
uniform throughout the discharge, except near
the sheath edge. The profile of the negativeion total density is assumed to be parabolic,
dropping to zero at the sheath edge. The
profile of the positive-ion total density is also
assumed parabolic with a drop at the sheath
edge, such that it satisfies the charge neutrality
condition at the sheath edge.
(3) The ratio of wall density to bulk average
density of positive ion species i are taken from
the generalized form derived by Lichtenberg et
al [17].
(4) The transport of charged particles assumes
that both the electrons and the negative ion
species are in Boltzmann equilibrium. This,
together with the charge neutrality condition,
yields a modified Bohm velocity for positive
ion flow at the sheath edge in the presence of
negative ions [17].
Mass balance equations are established for each
species i with density ni [18] (Eq. (1)),
where kli
coefficient
species l;
coefficient
represents the electron impact rate
for the production of species i from
kim represents the electron impact rate
for loss of species i to species m; k rt' and
kij' represents the rate coefficient for the creation and
the loss of species i from the collision of heavy
species r, t and i, j, respectively; ks,i is the
production/loss rate of i onto the reactor surface; τr
is the residence time of species i.
∂ni
= ∑ k li ne nl −∑ k im ne nl + ∑ k rt' nr nt
∂t
n
− ∑ k ij' ni n j ±k s ,i ni − i
(1)
τR
The charge neutrality equation gives a closure
condition to the mass balance equation to selfconsistently determine the electron density (Eq. (2)).
n e + ∑ n − ,i = ∑ n + , j
(2)
The discharge power balance is given by equation
(3) [19], where Prf is the rf coupled power to the
reactor, VICP is the reactor volume, Pev represents the
electron power losses due to all electron-neural
collision processes, Pew and Piw represent
respectively the electron and the ion energy losses to
the walls. Pev is calculated considering the different
collisions process, the rate of theses process and
their threshold energies.
3

∂ Te ne 
2
 = prf − ( P + P + P )
ev
ew
iw
∂t
V ICP
(3)
2.2 Etching model
Surface etching model is based on the discretization
of the 2D etched surface on uniform cells [20]. The
latter are considered as the super-sites representing a
number of real indium and phosphorus surface sites.
Total particle flux, proportion of ions and neutrals,
ion angular distribution function (IADF) and ion
energy distribution function (IEDF) reaching the
surface are the output data from the global and
sheath models. Monte-Carlo technique is used to
follow the trajectory of a given plasma particle from
an upper plane close to the surface until it
encounters a full cell representing an indium site
InClx (x=0-3). If the particle is a neutral Cl atom, it
can adsorb on the InClx site (x=0-2) respecting
adsorption probability Pads to form InClx+1. If the
adsorption process does not occur the neutral
particle is reflected and moves to another InClx site
until it reacts or goes back into the plasma. If the
particle is an ion, sputtering mechanism may occur.
The adsorbed sites are ejected according to a
sputtering yield ysp which is given as a function of
ion energy. The energetic ion transport study in the
InP volume is very complex and requires
introduction of the linear cascade regime theory [20,
21]. It is not easy to combine our neutral kinetic
Monte-Carlo approach with linear cascade regime.
Nevertheless, a semi-empirical expression giving the
sputtering yield versus the ion energy is used [22,
23] (Eq. 5):
Ysx = A α ( x) α (θ )
(
Ei − Eth
)
(5)
where Ei is the incident ion energy and Eth is the
threshold energy, α(x) is the modulation coefficient
associated to the site InClx (x=0-3). α(θ) is the
Simulation
modulation coefficient due to the angle of incidence
between ion and the surface [22]. A is estimated
using TRIM code [23].
The cells size is 1nm2. This permits a good
compromise between calculation time and
resolution.
Experiment
3. Results
Experimental profile and modelling results are
compared in figure 1 for Prf=100Watt, VDC=-100V
which is the DC bias, p=1mTorr, Ts=180oC and
Q(Cl2:Ar)=2:6sccm. The simulation reveals a more
pronounced undercut and bowing than the
experiment. Furthermore, the simulated etch time is
not far from the experiment (7.6min instead of
7.5min). Figure 2 presents the etch profile evolution
with varying the adsorption probability from 0.2 to
1. The undercut is all the more pronounced that the
adsorption probability is high. Indeed, high
adsorption probability of Cl on InClx leads to the
acceleration of the chemical etching in the shallow
surface due to the chemical desorption of InCl and
InCl3. However, when adsorption probability of Cl is
low the atomic chlorine makes multiple reflections
inside the etch trench leading to a better uniformity
of the adsorbed sites InClx along the lateral surface
of trench. This allows decreasing the undercut.
Figure 3-b shows the temperature effect on the InP
etch profile for p=1mTorr, QCl2:Ar=2:6sccm,
Prf=100W and VDC=-100V. The simulation reveals
that the mask erosion products the faceting effect.
This could accentuate the undercut because the
faceting allows decreasing the shadowing effect of
the ions impinging on the InP surface located near
the mask. The undercut is all the more important as
the surface temperature is higher. Indeed, the
desorption percentage of InCl and InCl3 enhances
with the temperature leading to the increase of the
chemical etching especially near the mask. We note
in Figure 3-a that the etch profile is not sensitive to
the substrate temperature for the areas far from the
mask because of the shadowing effect of Cl flux.
The etching is clearly due to ion sputtering of In and
InClx and not to thermal desorption of InClx
products. At the bottom of the etched trench, InClx
are ejected by energetic ions directed through the
sheath toward the etched surface leading to the
anisotropic pattern transfer. So under ion
bombardment, only InCl and InCl2 sites were created
before sputtering, InCl3 sites are in negligible
quantity. This is due to a high ionic flux reaching the
surface in comparison with neutral flux (Figure 5).
Figure 1: Simulated profile and real etched profile with a
reflection coefficient of 0.8
(a)
273-390K
400, 450K
(b)
Figure 3: (a) evolution of etched profiles with temperature, (b)
evolution of undercut with temperature
0.2
1
Figure 2: Evolution of the undercut with various recombination
coefficients from 0.2 to 1 by step of 0.2
4. Conclusion
Multiscale approach has been developed to simulate
the pattern transfer from the mask to the InP
substrate under ICP Cl2-Ar plasma discharge. The
coupling of global kinetic model, sheath model and
etching model permits to predict the InP etch profile
as a function of the operating conditions of ICP
reactor. Influence of substrate temperature on the
undercut and bowing formation on the shallow
etched InP surface is presented. We show than the
bowing effect is only due to ionic bombardment.
Instead, because of the ion directionality undercut is
due to chemical etching and seems to occur only for
temperatures higher than 390K.
Acknowledgements
This work has been performed in the frame of
ANR project ANR-09-BLAN-0019 INCLINE. The
authors are grateful to Nantes-Metropole and
University of Nantes for its financial support.
References
[1] E. Pargon, M. Darnon, O. Joubert, T.
Chevolleau, L. Vallier and T. Lill, J. Vac. Sci.
Technol. B 23 (2005) 1913.
[2] J. Foucher, G. Cunge, L. Vallier and O. Joubert,
J. Vac. Sci. Technol. B 20 (2002) 2024.
[3] C. Welch, L. Goodyear, T. Wahkbrink, M.
Lemme and T. Mollenhaur, Microelectron. Eng.
83 (2006) 1170.
Y. Sakata and K. Asakawa, J. Vac. Sci. Technol.
B 14 (1996) 1764.
[10] P. Strasser, R. Wüest, F. Robin, K. Rausche, B.
Wild, D. Erni and H. Jackel, J. Vac. Sci. Technol.
B 25 (2007) 387.
[11] C. Constantine, C. Barratt, S.J. Pearton, F. Ren
and J.R. Lothian, Appl. Phys. Lett. 61 (1992)
1119.
[12] D.G. Lishan and E.L. Hu, Appl. Phys. Lett. 56
(1990) 1667.
[13] S. Miyakuni, R. Hattori, K. Sato, H. Takano
and O. lshihara, J. Appl. Phys. 78 (1995) 5734.
[14] L. Gatilova, S. Bouchoule, S. Guilet and P.
Chabert, J. Vac. Sci. Technol. A 27 (2009) 262.
[15] S. Vicknesh and A. Ramam, J. Electrochem.
Soc. 151 (2004) C772.
[16] C Lee, M.A Lieberman, J. Vac. Sci. Technol. A
13 (1995) 368.
[17] A.J. Lichtenberg, V. Vahedi, M.A. Lieberman
and T Rognlien, J. Appl. Phys. 75 (1994) 2339.
[18] A. Rhallabi and Y. Catherine, IEEE Trans.
Plasma Sci. 19 (1991) 4871.
[19] V.A. Godyak, in Soviet radio frequency
discharge research (Delphic Associates, Inc,
Falls Church, VA, 1986), chap 5.
[20] G. Marcos, A. Rhallabi, P. Ranson, J. Vac. Sci.
Technol. A 21 (2003) 87.
[4] Y. Nakasha et al, IEEE J. of solide state circuits,
37, (2002) 1703.
[21] A. J. Murrell, R.J. Price, R. B. Jackman and J.
S. Foord, Surface Science 227 (1990) 197.
[5] O. Painter, A. Husain, A. Scherer, P.T. Lee, I.
Kim, J.D. O’Brien, and P.D. Dapkus, IEEE
Photonics Technol. Lett. 12, (2000) 1126.
[22] Lionel Houlet, PhD thesis, University de Nantes
(1999)
[6] Kyoji Inoshita and Toshihiko Baba, IEEE J. of
selected Topics in Quantum electronics, 9 (2003)
1347.
[7] Y. Feurprier, Ch Cardinaud, B. Grolleau, G.
Turban, Plasma Source Sci. Technol. 6 (1997)
561.
[8] B.Liu, J-P.Landesman, J-L. Leclercq, A.
Rhallabi, S. Guillé, C. Cardinaud, F. Pommereau,
M. Avella, M.A. González, J. Jiménez, Materials
Science in Semiconductor Processing, 9, (2006)
225.
[9] T. Yoshikawa, Y. Sugimoto, Y. Sakata, T.
Takeuchi, M. Yamamoto, H. Hotta, S. Kohmoto,
[23] Ko-Hsin Lee, PhD thesis, University of Paris 11
(2008)