161504-2
Severin et al.
Appl. Phys. Lett. 88, 161504 ͑2006͒
N
N
O
N
N
O
poration of nitrogen into the growing film has been reported
for experiments in which the sum of both reactive gas flows
was held constant.
2
2
Q + F + F ͑1 − − ͒
c
c
c
c
c
c
N
O
7
,8
= ͑F + F ͒ balance of nitrogen coverage, ͑2a͒
c c
m
In this report we examine the effects of varying the oxy-
gen flow at a constant nitrogen gas flow. We have performed
a theoretical study based on the Berg’s model with an exten-
sion to two different reactive gases including different stick-
ing coefficients and sputter yields. The modified model takes
into account that metal-nitrogen bonds at the target surface
or chamber wall can be broken up and replaced by metal-
oxygen bonds. This is due to the higher reactivity of the
oxide since the heat of formation of metal nitrides is in most
cases lower than that of the corresponding oxide. This is
described by a replacement coefficient which has been intro-
duced in Ref. 7. As example for stabilizing the discharge
process we present the discharge voltage, deposition rate,
and stoichiometry during reactive sputtering at constant cur-
rent of zirconium oxide.
O
c
O
c
N
c
O
c
N
c
O
c
Q + F + F ͑1 − − ͒
O
N
=
͑F + F ͒ balance of oxygen coverage. ͑2b͒
c c
m
In order to calculate the gettered reactive gas flow we
take again into account the probability ␣ that a nitrogen
atom can be replaced by an oxygen atom at the chamber wall
and the target’s surface as well. Therefore the gettered reac-
tive gas flows at the target and at the chamber wall are
ON
N
t
N
N
N
t
O
t
O
ON
N
Q = ␣ F ͑1 − − ͒A − F ␣ A
t
t
t
gettered nitrogen on the target,
͑3a͒
͑3b͒
͑3c͒
͑3d͒
O
t
O
O
N
t
O
t
O
ON
N
Q = ␣ F ͑1 − − ͒A + F ␣ A
t
t
t
gettered oxygen on the target,
Starting point of the calculation is the target balance
equation which describes the balance between sputtered
compound molecules of the two species on the target surface
and the reaction of metal atoms with the corresponding re-
active gas. For simplification we assume simple stoichio-
metric compound Me O and Me N , respectively, but it can
N
c
N
N
N
c
O
c
O ON
N
Q = ␣ F ͑1 − − ͒A − F ␣ A
c
c
c
gettered nitrogen on the chamber wall,
O
c
O
O
N
c
O
c
O ON
N
1
1
1
1
Q = ␣ F ͑1 − − ͒A + F ␣ A
c
c
c
be easily scaled up to more complicated stoichiometric com-
pounds. The target balance equations are
gettered oxygen on the chamber wall,
O,N
where A is the effective chamber wall area and c the
c
j
fraction covered with the oxide or nitride. The corresponding
particle fluxes and the deposition rate are calculated in a
straightforward manner, as shown in Ref. 1. The solution of
these equation yields the partial pressures, the target, and the
chamber coverages as well as the deposition rate. Since no
analytic solution for this set of equation is available we have
performed numerical calculations using the Levenberg-
Marquardt algorithm.
Y = 2␣ F ͑1 − − ͒ − 2F ␣ON
N
N
N
N
N
O
O
N
c
t
t
t
t
q
balance of nitrogen coverage,
͑1a͒
j
Y = 2␣ F ͑1 − − ͒ + 2F ␣ON
O
O
t
O
O
N
t
O
t
O
N
t
c
q
Figures 1͑a͒–1͑c͒ depict the numerical solutions for the
same set of parameters, but using three different values of
fixed nitrogen flow ͑0, 0.75, and 1.5 SCCM͒. The fraction of
the target coverage with oxygen and nitrogen and the corre-
sponding sample stoichiometries are shown. It can be clearly
seen that with increasing nitrogen addition the hysteresis
gradually disappears. At the same time the nitrogen incorpo-
ration into the growing film can be small at sufficient oxygen
flow. The origin of the vanishing hysteresis is the higher
effective sputter yield due to a lower binding energy of the
nitride compared to that of the corresponding oxide. In gen-
eral, a higher sputter yield of the compound leads to a re-
duced hysteresis effect. The nitrogen addition into the oxy-
gen process yields a coexistence of a nitride and an oxide
compound system at the target surface. The higher the nitro-
gen addition the higher the effective sputtering yield and
therefore the lower is the hysteresis effect. The very low
nitrogen incorporation into the film is a result of the replace-
ment coefficient as also experimentally found by Refs. 7–9.
Simultaneously, the nitrogen coverage at the target is always
higher compared to that of the film since an already formed
metal nitrogen bond is more likely sputtered away before it
can be replaced by a metal oxygen bond. Figure 2͑a͒ shows
the corresponding calculated oxygen partial pressures and ͑b͒
the normalized mass deposition rates. The same behavior can
be found again. The hysteresis vanishes for higher nitrogen
flow. Note that slightly above 1.1 SCCM oxygen flow films
with the nominal stoichiometry are observed in the case of
balance of oxygen coverage,
͑1b͒
where j/q is the flux of the positive ions at the target surface,
the sputtering yield of the oxide compound, or the cor-
responding nitride compound, respectively. t are the frac-
O,N
Y
c
O,N
tions of the target which are covered by nitride or oxide and
O,N
ON
␣
the sticking coefficients of both reactive gases. ␣
describes the probability that a metal-nitrogen bond is re-
placed by a corresponding metal-oxygen bond since the
metal oxygen bond is energetically more favored than the
O,N
metal nitrogen bond. F
is the particle flux from the ambi-
ent gas atmosphere and proportional to the corresponding
partial pressure. Consequently, the left hand side of Eqs. ͑1a͒
and ͑1b͒ represents the number of compound molecules sput-
tered away from the target surface and the right hand side the
number of gettered species from the ambient reactive gas
atmosphere. The prefactor 2 has to be included since a reac-
tive gas molecule consists of two atoms. A similar balance
equation can be formed for the chamber wall coverage. Since
the sample is a part of the chamber wall, these equations are
balance equation for the sample stoichiometry as well. In
steady state the amount of metal atoms F plus the flux of
the other compound condensating on the covered fraction
m
O,N
c
of the chamber wall must be equal to the amount of the
O,N
gettered reactive gas molecules Q
plus flux of compound
c
O,N
molecules Fc increasing the compound fraction of the cor-
responding compound. Therefore the chamber wall balance
equations are
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Severin
