Growth kinetics of silicon dioxide on silicon in an inductively coupled rf
plasma at constant anodization currents
A. J. Choksi, R. Lal, and A. N. Chandorkar
Citation: J. Appl. Phys. 72, 1550 (1992); doi: 10.1063/1.351724
View online: http://dx.doi.org/10.1063/1.351724
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Published by the American Institute of Physics.
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Growth kinetics of silicon dioxide on silicon in an inductively
plasma at constant anodization currents
coupled
rf
A. J. Choksi, R. Lal, and A. N. Chandorkar
Department
of Electrical Engineering, Indian Institute of Technology, Powai, Bombay 400 076, India
(Received 17 June 1991; accepted for publication 30 April
1992)
The kinetics of plasma oxidation of silicon at constant anodization current have been
investigated. Oxidation was performed in an inductively coupled rf plasma anodization setup.
The oxidation model is based on the assumption that the oxidant from the plasma is neutral
atomic oxygen which captures an electron inside the oxide and forms a negative oxygen ion
(O-). The O- ion then hops through interstitial sites in the oxide due to the high drift field
during the anodization. A photon-assisted oxidation mechanism is assumed to occur at the
SiO,/Si interface in which the energy to break Si-Si bonds at the interface is supplied by UV
photons which are generated in the plasma. Based on these assumptions an analytical model was
developed that successfully explains the dependence of oxidation rate on the gas pressure in the
plasma, which was not explained by previous investigators. It has been shown that during
constant current anodization,, the space-charge effects inside the oxide are negligible. It was
found that the oxidation rate shows a weak temperature dependence with a thermal activation
energy of 0.04 eV. The data on oxide thickness versus the oxidation time were found to be in
good agreement with the theory.
I. INTRODUCTION
The process of thermal oxidation of silicon is associated with undesirable side effects such as oxidationinduced stacking faults,’ oxidation-enhanced diffusion, and
the formation of bird’s beak [lateral growth of oxide beneath silicon nitride film in the localized oxidation of silicon (LOCOS) process]. The redistribution of dopants
present in threshold adjusting layers and in shallow junctions is also disadvantageous. These problems become limiting factors for higher densities of integration as the linewidth in modern devices is scaled below 1 ,um. It is
therefore desirable to develop a low-temperature process
for the growth of high-quality insulators on silicon. Furthermore, the process must also be compatible with other
processing steps in modern integrated-circuit (IC) technology. As electron-beam- and ion-beam-based processes
are rapidly replacing conventional ones in the IC industry,
plasma oxidation is showing promise as a low-temperature
process for the future. Several studies have been carried out
on the electrical properties of plasma oxides and it was
found that high-quality oxide films could be grown with a
careful choice of plasma conditions.2Y3 Kimura et aL4 studied the performance of metal-oxide-semiconductor
fieldeffect transistors (MOSFETs) fabricated with plasma oxides by a complete
low-temperature
technology
( < 600 “C). They found the value of field-effect mobility to
be 650 cm’/V s, which is as good as that obtained by conventional technology. In spite of this, there do not exist
good models for growth kinetics and properties of plasma
oxides. This is because the conclusions of various investigators were not always comparable since their experimental configurations and oxide growth conditions were widely
different.
In order to investigate the effects of experimental parameters on the oxide growth kinetics and properties, a
1550
J. Appl. Phys. 72 (4), 15 August 1992
plasma oxidation system was designed and set up in which
several parameters such as gas pressure in the plasma, anodization current density, temperature of oxidation, and
the distance of the wafer from the plasma could be varied
and monitored. The design of this system is described in
brief and the basic growth phenomena is examined. Some
issues are: the identification of oxidant species, the role of
electron and photon fluxes, the transport of oxidants during plasma anodization, and the oxide-forming reaction at
the SiO,/Si interface. Based on these discussions, a quantitative model for the growth kinetics is constructed.
II. EXPERIMENT
A. System description
The experimental setup that was used for plasma oxidation experiments is shown in Fig. 1 (a). It consists of a
quartz reactor tube (1 m long, diameter=75 mm) fitted at
both ends with demountable vacuum seals. The evacuation
is carried out from one end by a diffusion pump backed by
a rotary pump, through a liquid nitrogen trap and a throttling valve. The gas inlet is at the other end, where a mixture of oxygen and argon is passed into the reactor tube
through a needle valve. The plasma is excited and sustained by an inductively coupled rf discharge at 13.56
MHz. An impedance matching network is used to adjust
the maximum power transfer to the discharge coil and also
to confine the plasma well within the discharge coil. The
forward rf power to the discharge coil is measured by a rf
power meter (Bird Electronic Corp. Thruline model 43 ) .
A dc power supply (O-100) V) isolated by radio-frequency
choke (RFC) is connected across a stainless-steel cathode
and the silicon wafer as the anode for anodization. The
silicon wafer is sandwiched between a stainless-steel disk
and a quartz stopper ring. A mica mask is placed on the
wafer so that only a limited area is exposed to the plasma.
0021-8979/92/161550-08$04.00
@ 1992 American Institute of Physics
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1550
for 40 min in Hz. High-frequency capacitance versus voltage (C-V) and quasistatic C-F’ measurements were performed to compare the oxide fixed charge and interfacestate densities of oxides grown by plasma anodization with
those of thermal oxides. The electrical properties of the
oxides grown under optimum anodization conditions were
as follows: midgap interface-state density Oit( midgap) =4-6 X 10”/eV/cm2:
fixed oxide charge IQ,, = 1 X 10’‘/cm2;
oxide breakdown field EBD= 8-10 MV/cm.
Ill. GROWTH MECHANISM
(a)
(b)
FTC+.1. (a) Block diagram of the rf plasma anodization setup. 1: Anodization bias supply; 2: cathode; 3: silicon wafer; 4: thermocouple; 5: furnace on wheels; 6: quartz reactor tube; 7: stainless-steel-demountable
vacuum seal 8: gas mixing chamber; 9: needlevalve; 10: rf generator; 11:
impedance matching network; 12: rf power meter; 13: discharge coil; 14:
pressure gauge; 15: line throttling valve; 16: liquid nitrogen trap; 17:
vacuum pumps (diffusion pumptrotary pump). (b) Cross-sectional
view of the quartz wafer holder. 1: quartz stopper ring; 2: quartz enclosure tube; 2: stainless-steeldisk, 4: silicon wafer.
The other side of the disk is in good electrical and thermal
contact with the thermocouple which is connected to the
“lead through” in the demountable vacuum seal. The anodization bias to the wafer is also applied through this
thermocouple. A furnace on wheels maintained at the temperature of oxidation can be rolled over the wafer region to
ramp up the wafer temperature to that required for anodization. The design of the wafer holder assembly is shown
in Fig. l(b).
B. Sample preparation
p-type (100) silicon wafers of resistivity 4-6 n cm
from Wacker were RCA cleaned’ and mounted one at a
time on the stainless-steel disk of the quartz wafer holder
which was subsequently loaded into the reactor tube. The
distance between the wafer and the load coil was kept constant (30 mm) throughout this series of experiments. The
system was then evacuated to high vacuum (5 x 10m5
Torr) and subsequently backfilled by a mixture of oxygen
and argon (95:5) to obtain a pressure of 1 mTorr. The
furnace was moved over to ramp up the temperature. The
throttling valve then closed so that the desired gas pressure
in the tube was obtained. The plasma was excited after
some time when the gas pressure and temperature stabilized. Anodization bias was applied after 10 min of plasma
excitation and the anodization current was slowly increased to the required value.
Postanodization anneals were performed at 800 “C in
NZ at atmospheric pressure for 20 min. The oxide thickness and refractive index were measured by an ellipsometer
(Rudolph auto EL). MOS capacitors (gate area=7.85
X lOA cm2) were fabricated by depositing aluminum in
an e-beam evaporation system through a molybdenum
mask. Postmetallization anneals were performed at 450 “C!
1551
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
A. Earlier models
It was observed by Perriere, Chang, and Siejka6 that
the contribution of purely thermal diffusion of the neutral
oxygen species inside the oxide is negligible compared to
the field-assisted drift component of ionic oxygen during
plasma anodization. Since the application of anodization
bias was found to enhance the rate of oxidation’ it was
conjectured that a negative oxygen ion is the oxidizing
species inside the oxide. Isotopic tracer experiments were
performed by various investigator&” to study ionic transport inside the oxide during plasma oxidation. Their results
indicate that the order of oxygen inside the oxide is largely
preserved and that the negatively charged oxygen species
migrates through the oxide to the SiO,/Si interface to oxidize silicon. However, identification of the source of negative ions is being debated. Some researchers”-15 have reported that negative oxygen ions are supplied by the
oxygen plasma. The yield of plasma oxidation for negative
oxygen ions was theoretically evaluated by Vinckier and
De Jaegere” from the experimental data of several researchers. They found that the role of neutral oxygen atoms from the plasma is negligible compared to negative
oxygen ions. It was also concluded that the yield due to Oions does not depend on experimental conditions such as
oxygen pressure or bias voltage or geometrical features of
the reactor system. This contradicts the experimental results of various experimenters’&” who performed anodization under different plasma conditions. For example,
Copeland and Papput observed for oxidation in a dc
plasma that the rate of oxidation in the positive column is
twice that in the negative glow region. It is to be noted that
the positive column contains O+ ions while the negative
glow is rich in O- ions. This means that OS ions from the
plasma are not the primary species to govern the oxide
growth rate. Similar inferences were drawn for oxidation in
a rf plasma by Olive and co-workers” and in a microwave
plasma by Kimura et al. I9 Hence it has been suggested that
a neutral oxygen species from the plasma must be playing
an active role in plasma oxidation. For the formation of
O- ions (to explain the transport of oxidant) an electronassisted surface mechanism has been invoked.m23 Two
possible mechanisms discussed in the literature2’ are given
below.
(a) Impact ionization or the dissociative attachment of
the electron by an adsorbed oxygen molecule:“‘23
0 2adsQ+e--+O&+O+0,
Chbksi, Lal, and Chandorkar
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(1)
1551
where @ represents an adsorption site on the oxide surface
and 0, is the mobile oxygen ion. The atomic oxygen is
then free to form either an O- ion further by electron
attachment or it could get liberated in the gas phase.
(b) Electron capture by the adsorbed oxygen
atom:“‘23
(2)
According to Anode and Matsumura22 the second
mechanism is more probable for it explained their experimental data for plasma anodization of aluminum. This
mechanism was also proposed by Ranke and Jacobi23 for
the plasma oxidation of GaAs. If this mechanism is operative then an increased oxidation rate is expected for an
increased gas pressure in the plasma. This, however, does
not match the experimental observation of several workers.14,24*25
We also observed an increased rate of growth
with the decrease of gas pressure (Sec. V A). Therefore,
the adsorbed oxygen model cannot be accepted for prediction of growth of Si02 on Si.
It was proposed by Kimura et al. l9 that a neutral oxygen atom from the plasma must be responsible for plasma
oxidation. This was substantiated by their oxidation experiments, when the wafer was moved across the boundary of
the plasma. We found this model to be promising, since it,
along with a model for.UV-enhanced oxidation26 successfully explained the dependence of electrical properties of
plasma-grown oxides on experimental conditions.” The assumptions of our model are described in the following subsection.
B. Our model
We propose the mechanism of plasma oxidation as follows:
(i) The oxidation is influenced by three fluxes from the
plasma: the electron flux, the UV photon flux, and the
oxidizing species flux.
(ii) The oxide growth is not dominated by the oxygen
ion directly supplied from plasma, but, neutral oxygen atoms from plasma must be responsible for the oxidation.”
(iii) The 0 atoms, after getting inside the oxide, lose
their excess energy via scattering. The temperature is too
low for any appreciable diffusion to occur, thus there exists
a thin layer of thickness 6 at the plasma/oxide interface
just inside the oxide surface which is rich in neutral oxygen
atoms. It is in this region that neutral oxygen atoms, which
are electronegative, trap electrons from the conduction
band of SiOE forming O- ions according to the following
mechanism:
O+eC-+O-.
(3)
We will call this region of thickness S the charging zone.
(iv) O- ions migrate toward the SiOz/Si interface by
hopping through interstitial sites in the oxide under the
action of an applied electric field. When close enough to
the interface, the ions lose their electrons to the silicon
possibly by tunneling.
1552
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
-I-=i
c
FIG. 2. Physical picture of plasma oxidation.
(v) The energy required for breaking Si-Si bonds at
the SiO,/Si interface is provided by UV photons from the
plasma. Free silicon bonds are then available for oxidation.
The processes in the last two steps can be described by
the equation
Si+20-1+YSi02+2e-.
(4)
A physical picture depicting this model is shown in
Fig. 2.
IV. GROWTH KINETICS
Based on our model, the process of plasma anodization
can be divided into three steps: (i) the formation of Oions inside the oxide; (ii) the migration of O- ions to the
SiO,/Si interface under the influence of a high drift field;
and (iii) the oxidation reaction and formation of SiOZ.
The analytical expression for each of these processes is
given below.
A. Formation
of O-
Various authors28-30 have assumed the current et%
ciency (the ratio of ionic component of the anodization
current to the total anodization current) of the anodization
process to be constant. However, this assumption is not
correct because the supply of ions would become limited as
the anodization current is increased. Further, we have
found that the ionic current density decreases with the
growing oxide (this is in spite of keeping the total anodization current density constant). Thus the assumption of
a constant current efficiency could lead to an inaccurate
value of the ionic component (the current due to O- ions)
of the anodization current.
A precise relation for the formation of an O- ion can
be obtained by writing the continuity equation in the
charging zone (assumed to be of 30-40 %, thickness) at the
plasma/oxide interface. As pointed out previously, neutral
oxygen is injected into the oxide in this region and forms
an O- ion via electron attachment.
It is assumed that the concentration of 0 atoms in this
region is constant (Co), as is shown in Fig. 3. Let Co (x)
be the concentration of O- ions inside the oxide at X. Then
one can write the continuity equation for CG (x) as
Choksi, Lal, and Chandorkar
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1552
P’asna
I--
Oxide
“_-._~-l.“l”-“.-
.._...................
- .._.-
-I Si’icon
F,(S)=Cou[
B. Transport
FIG. 3. Concentration profiles of the neutral (0) and ionic (O-) oxidant
speciesinside the oxide.
dC,(x)
Jo
-=-a[Co-CC,-(x)]
dt
q
dC,- (xl
vC,-(xl -D,- 7
-$
(5)
where v is the velocity of Do is the diffusivity of O- ions,
(T is the electron capture cross section of the 0 traps, J, is
the anodization current density, and q is the electronic
charge. The first term in this equation represents the generation of O- ions, while the second term represents the
rate with which they are swept away from the charging
zone. As discussed previously the diffusion term can be
neglected.
Under steady state dCG((x)/dt=O,
hence the above
equation reduces to
J,
-p-c,-(x)]-;
[UC,-(x)1=0-
Rearranging terms, we have
dC,-(xl
--jy+-&
J,
(TC(y(X) =;
CTco.
(6)
(7)
--$:)I.
(9)
of O- to SiOJSi interface
Models for growth kinetics were formulated by Taylor
and co-workers2’ and Roppe13’for constant voltage anodization in which it was assumed that the presence of space
charge reduces the field inside the oxide. However, this
assumption seems to be unreasonable for the case of constant current plasma anodization at low currents ( < 3
mA/cm2), because during plasma anodization the current
efficiency is usually very small. Moreover, it has been noted
by Fridel, Gourrier, and Dimitriou32 that the electrons
achieve a high velocity under the influence of high electric
field inside the oxide ( lo? cm/s). Hence the concentration
of electrons in the oxide conduction band must be very low
( lo9 cmB3>. They also found that the migration-coefficient
of the ions is several orders higher than their usual diffusion coefficient under a high field ( lo6 V/cm). Since the
experimentally deduced values of the current efficiencies of
the plasma anodization of silicon are .very small, it can be
concluded that the space-charge contribution must be negligible for low currents in the case of constant current anodization. This has been further substantiated in Sec. V D.
During plasma anodization the field inside the oxide
becomes so large ( lo6 V/cm) that the drift velocity of the
ions is no longer linearly proportional to it. To explain the
transport of ions under such a situation, a discrete hopping
model was proposed by Cabrera and Mott.33 According to
this -model the electric field inside the oxide, E,, lowers the
potential energy barrier W for the ionic point defects (interstitials or vacancies) in the forward direction and raises
it in the reverse direction by an amount q E,, a, where q is
the electronic charge and 2a is the distance between adjacent potential minima. Thus an ion will have to surmount
a potential barrier of W-qE,,, a and WfqE,, a in order
to hop in the forward and the reverse directions, respectively. During constant current anodization, the anodization potential is varied in order to keep a constant J, during the period of oxidation. It is assumed that the field
inside the oxide always remains constant (see Fig. 4).
Therefore, the net jump frequency of the ions is given by
The solution of this equation with the following boundary
condition at x =0, Co (x) =0, is given by
J,
pod
I-exp(
W--q-Q
kT
a
W+ @ox u
kT
)I
> (lo)
where Y is the frequency with which ions attempt to cross
the barrier. The velocity of the ions can then be written as
where A is the constant of integration. Solving the above
integral and substituting the .boundary condition for evaluating A, we obtain
W-q-G
kT
a
W+ q-G a
kT
)I,,4\
.
1111
CG(x)=Co[l-exp(
1
(8)
-.
Figure 3 depicts the concentration profile of O- ions and
the neutral 0 atoms inside the oxide represented by Eq.
(8). The flux of negative ions existing in the charging zone
at x=6 can now be written as
1553
-o$E)[
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
C. Formation
of oxide
It has been pointed’out above that the energy to break
Si-Si bonds is provided by UV photons. However, as the
oxide layer grows on the silicon, a significant fraction of
Choksi, Lal, and Chandorkar
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1553
Cathode
1 Plasma
I
I
tax= tax
No exp(~tox)dtox
s top0
I
I
I
= ~~~KC‘~v
[ 1-exp(
-o$“;)]
dt.
(17)
Solving this equation, an expression for tax is obtained
as follows:
NO
;
[exp(at,,)
- 1] = KC,vt [ l- exp( --*:$I.
(18)
It is shown in Sec. V that a= lo5 cm -l, v= lo2 cm/s,
and cr= 10m9 cm’. If S is assumed to be approximately
30-40 A, then
FIG. 4. Anodization potential distribution across the cathode (stainless
steel) and the anode (silicon wafer) during the plasma oxidation.
UV photons arriving at the SiO/Si interface gets absorbed
in the oxide. Therefore, the intensity of the UV photons
arriving at the SiO,/Si interface with growing oxide thickness can be written a?
I=lo
exp( --a: fox),
&x)9
(13)
where Fi, is a component of the ionic flux Fi which is
utilized for oxidation and K is a proportionality constant.
The oxidation rate can now be written as
4x
-=dt
Fio
(14)
N,,’
where to, is the oxide thickness and N, is the number of the
oxidant atoms incorporated into the unit volume of the
growing oxide network. As the oxidation reaction is governed by Eq. (4), it can be shown34 that N,=4.4~10~~
cme3.
Furthermore, we assume that the initial transient period occurs for a very short time and the onset of quasisteady state occurs at t=O. Substituting the values of FL,
from Q. (13),
dtox K
~=~Fi(Gx)exp(
0
-at,,).
Under steady state Fi( to,) = Fi( S). Substituting for Fi(i(s)
from Eq. (9), we obtain
dtox
dt=F
K
Cov [ 1-exp( -o:$]exp(-a&,,).
Cl
Integrating this equation for time t=O to t=t,
1554
NO
;
Eexp(at,,> - 11 =KCovtoq
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
(16)
J,S 1
J; [exp(cft,,)
=/? Jot
(12)
where I is the flux of UV photons arriving at the SiOJSi
interface, I0 is the incident photons flux, a is the absorption coefficient of the UV photons in the oxide, and tax is
the oxide thickness.
Statement (v) of the proposed model implies that the
oxidation rate is proportional to photon flux and the flux of
oxidants at the SiO,/Si interface. We can therefore write
Fio=KFi(tOx)eXp(-a
Expanding the exponential term on the right-hand side
(rhs) and neglecting second- and higher-order terms, we
obtain
-11
(19)
where /3= (KCoaS)/(Noq).
Typical thicknesses of the oxides in this study were in
the range of 100-1000 A. For toX(lp, o&(1.
Hence the
exponential term on the left-hand side (lhs) can also be
expanded neglecting the terms higher than second order.
We obtain
tax +;
& =/!? Jar.
(20)
It is to be noted that this expression is similar to the
linear parabolic relationship proposed by Deal and Grove34
for thermal oxidation. This kind of relationship has been
empirically assumed by various authors to explain plasma
oxidation; however, there is a great deal of difference in the
model and the substance of the derivation.
V. RESULTS AND DlSCUSSlON
A. Dependence
on gas pressure
The dependence of the oxide thickness on the gas pressure in the plasma is shown in Fig. 5. A uniform oxidation
was observed over the front side of the wafer. We observed
an inverse pressure dependence of the oxide thickness
which is in agreement with the results of other investigators. So far this phenomenon had been left unexplained but
is explained by our model. At higher gas pressures, the
average electron energy is reduced because of the reduced
mean free path. The formation of 0 in plasma is described
by a dissociative mechanism, as given by the reaction
02+ed +O+O+e-.
(21)
It is, therefore, at higher gas pressures, as the free electron
energy is reduced, that it will not be able to dissociate the
Choksi, Lal, and Chandorkar
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1554
0
0
I
I
20
40
Gas
I
pressure
8.
60
t
I
80
,
,
100
1.2
1.0
(mtorr)
FIG. 5. Dependenceof oxide thickness over the gas pressure in the
plasma. Oxidation conditions are anodization current density: 2.0 mA/
cm’; temperature: 500 ‘C!; time: 60 min.
1.4
1.6
1.8
lOOO/ T (OK-')
B. Dependence on temperature
There is good agreement between the theoretically derived exponential dependence on temperature and the experimental data. A strong dependence is anticipated in the
case of oxidation controlled by the diffusion and/or the
interface reaction. On the other hand, if field-assisted
transport is the rate governing step then a weak temperature dependence is expected. The Arrhenius plot between
the log of growth rate and 103/T is shown in Fig. 6. The
slope of the curve corresponds to a thermal activation energy of 0.045 eV, which is close to that reported by Fu et
aL21 (0.06 eV). However, for plasma oxidation without
anodization bias a value of 0.4 eV was reported by Kimura
et aL9 It should be noted that a small thermal activation
energy indicates a large migration coefficient which implies
a reduced ion concentration for a given ionic current.
1555
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
2.2
FIG. 6. Arrhenius plot of the plasmaoxidation rate. Oxidation conditions
are anodization current density: 2.0 mA/cm*; gas pressure:25 mTorr;
time: 60 min.
C. Ion velocity and space-charge
O2 molecule and generate larger concentrations of 0 atoms. A reduced oxidation rate at higher gas pressures thus
is in agreement with the hypothesis that the oxidant species
from the plasma is neutral oxygen and not an ionic oxygen.
It should be noted that at higher gas pressures the probability of formation of O- ions via an electron attachment
mechanism is greater.35
No appreciable oxidation on the backside of the wafer
was noticed. This is not in agreement with the results of
Ray and Reisman36 who reported that oxidation occurred
on the backside of the wafer for gas pressures above 10
mTorr; but, in this case sputtering of quartz from the walls
of the chamber could have occurred because of the large rf
power densities. used.
2.0
buildup
Knowing the activation energy W, the ion velocity v
can be calculated from Eq. ( 11). It has been shown by
various investigators that during plasma oxidation the field
inside the oxide is between 1.5 and 2.0 MV/cm. Substituting this for E,, and assuming Y= lO”/s, 2a= 1.8~ lo-*
cm, ,the velocity u is found to be 0.473 X lo2 cm/s.
The oxidizing. flux is of the order of 1013 cmW2 s- ‘,
which means that the O- ion concentration in the oxide
for the above velocity must be of the order of 10” cme3.
This clearly indicates that space charge due to O- would
not produce a dominating effect.
D. Dependence on the anodization
current
The oxidation was performed for 60 min varying the
anodization current density between 0.5 and 2.5 mA/cm2.
The oxidation data are shown in Fig. 7 (b). From these one
can calculate the oxidizing component of the ionic flux
F,, using electrochemical kinetics, as
F io=‘nF dt,,
qil4
(22)
dt ’
where p is the density of Si02 (2.2 g/cm’), M is the gram
molecular weight of the oxide formed by the electrochemical reaction as given by Rq. (4) and is equal to 60 for
Si02, F is Faraday’s constant (96 500 C), and n is the
number of electrons involved in the reaction; for Rq. (4),
n=2. The value of Fi,was then substituted into Eq. ( 13) to
compute K Fi(t”J or KF,(S). The value of (T and KC,
were obtained by regression analysis over the data points
using the relation given in Rq. (9). The following best-fit
values were obtained:
0=7.36x
10m9 cm2, KCo=3.48x
1012 cme3.
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1555
12
1OO(
2500r
cl
aoc
$a
ST;
;;
2
M^ 60(
6-
:
z
Ie 4oc
5
al
E
0”
200
a
E
2
.IL
4;
a
I
1.5
1.0
0.5
Anodization
current
2.0
2.5
0
In Table I some extracted model parameters are given.
In Fig. 7(a), the plot of J, vs KFi is shown. The extracted
cross section is high and requires further investigations.
From the oxide thickness versus atiodization current
data it is apparent that the oxide thickness does not increase linearly with the anodization current. This is in
agreement with our argument that current efficiency does
not remain constant with increase of the anodization current. A theoretical curve was generated for the oxide thickness versus the anodization current density using IQ. (20)
and substituting the values of constants from Table I. This
has been shown in Fig. 7 (b) .
In an investigation2’ on the dependence of electrical
properties of the oxide on experimental parameters, we
observed that for a given set of experimental conditions
there is an optimum anodization current density to yield a
high-quality oxide film. High defect densities were obTABLE I. Values of the constants used in this model.
Parameter
Unit
Value
NO
cm-’
4.4x 1o*s
1.8 x IO-*
cm
S--l
V/cm
/cm
eV
cm”
cm/s
cm-’
A
L”X
a
W
[T
k2
6
10’0
2x106
105
0.045
7.35 x lo-’
47.3
3.48 x 10”
40
25
Method
I
b
b
b
I:
by curve fitting
by curve fitting
calculated
by curve fitting
at 500 “C,
at 300 “C.
“See Ref. 34.
bSeeRef. 31.
“SeeRef. 37.
1556
60
(mA /cm*)
FIG. 7. (a) Theoretical plot of the oxide thickness vs the anodization
current density. (b) Theoretica fit of the ionic component of anodization
current vs the anodization current during plasma oxidation. Oxidation
conditions are gas pressure:25 mTorr; temperature: 500 ‘C; time: 60 min.
2a
30
J. Appl. Phys., Vol. 72, No. 4, 15 August 1992
90
I
4
120 150 180
Time (min)
210
240
270
300
FIG. 8. Theoretical plots of the oxide thicknessvs the oxidation time. 0:
300 ‘C; A: 500 “C. Oxidation conditions are anodization current density:
2.0 mA/cmL, gas pressure:25 mTorr; temperature: 500 OC.
served in the case where anodization current densities were
either very low or very high. This was explained as, in case
of low anodization currents (which is also a measure of
ionic current reaching the SiO,/Si interface), the proportion of UV photon flux is higher. Thus the probability of a
defect getting neutralized as the oxidation proceeds is low.
This results in an increased electron trap and interfacestate density. On the other hand, if the anodization current
is high, the damage due to ion bombardment over the oxide
surface is enhanced, which again leads to deterioration in
the oxide properties. This explanation is quite consistent
with the above-described model.
E. Time dependence
According to this theory, space-charge buildup is not
the reason for the reduction in oxidation rate with time but
it is the absorption of UV photons in the oxide which
results in reduced Si-Si bond breakage at the SiO,/Si
interface. The effective absorption coefficient of UV photons (which are in the range of 5-g eV from the oxygen
plasma) in amorphous SiO, is reported to be 10’ cm-‘.37
Using the values of constants shown in Table I, a theoretical plot of oxide thickness versus oxidation time is shown
in Fig. 8. It is to be noted that at 500 “C a value of 40 A was
assumed for 6, which gives good fits to the oxidation data;
however, at 300 “C, 6=25 A was found to give a better
theoretical fit..
VI. CONCLUSlONS
A model for growth kinetics is presented for plasma
anodic oxidation of silicon in an inductively coupled rf
plasma. This model consistently explains the dependence
of electrical properties and oxide growth on experimental
conditions. A neutral oxygen atom from the plasma is the
Choksi, Lal, and Chandorkar
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1556
oxidant species from the plasma entering the oxide. It undergoes an electron attachment inside the oxide in a thin
layer next to the plasma/oxide interface and forms an Oion, which subsequently hops through interstitial sites under the action of the large drift field created by the anodization bias. Oxidation occurs at the SiO,/Si interface and
a photon-assisted mechanism has been invoked. The dependence of oxide growth rate on various process parameters (gas pressure in the plasma, anodization current density, the temperature, and time of oxidation) was examined
and the values of several model parameters were obtained
by fitting the analytical solutions to the data. The values of
extracted parameters and fit to data are reasonable and
provide good support for the proposed model. The thermal
activation energy for migration of oxidants was found to be
0.04 eV, which implies that the thermal-assisted component is quite negligible. This model predicts a linear parabolic kind of relation between the oxide thickness and
growth time though the parameters of the model are quite
different from that of the Deal and Grove model. The
model was also found to explain successfully the dependence of electrical properties of plasma oxides on the experimental conditions.
ACKNOWLEDGMENTS
The authors are grateful to Professor J. Vasi for his
useful discussion and suggestions. They also wish to thank
Professor Raman Srinivasan for the critical evaluation of
this work. Thanks are also due to Mr. U. R. Kasbekar and
other members of the microelectronics group for their assistance during setting up the system and carrying out the
experiments.
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1557