Review
Fundamental understanding and modeling of reactive
sputtering processes
S. Berg*, T. Nyberg
The Angstrom Laboratory, Uppsala University, Box 534, 751 21 Uppsala, Sweden
Accepted 21 October 2004
Available online 7 January 2005
Abstract
Reactive sputtering is a commonly used process to fabricate compound thin film coatings on a wide variety of different substrates. The
industrial applications request high rate deposition processes. To meet this demand, it is necessary to have very good process control of such
processes. The deposition rate is extremely sensitive to the supply of the reactive gas. A too low supply of the reactive gas will cause high rate
metallic sputtering, but may give rise to an understoichiometric composition of the deposited film. A too high supply of the reactive gas will
allow for stoichiometric composition of the deposited film, but will cause poisoning of the target surface, which may reduce the deposition
rate significantly. This behaviour points out that there may exist optimum processing conditions where both high rate and stoichiometric film
composition may be obtained.
The purpose of this article is to explain how different parameters affect the reactive sputtering process. A simple model for the reactive
sputtering process is described. Based on this model, it is possible to predict the processing behaviour for many different ways of carrying out
this process. It is also possible to use the results of the modeling work to scale processes from laboratory size to large industrial processes.
The focus will be to obtain as simple a model that will still quite correctly describe most experimental findings. Despite some quite crude
approximations, we believe that the model presented satisfies this criterion.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Reactive sputtering; Thin film coatings; Reactive gas
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
2. Definition of conditions for the reactive sputtering model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
2.1. Flux of reactive gas in processing chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
2.2. Conditions at the target surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
2.3. Conditions at collecting area (substrate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
2.3.1. Flux of material approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
2.3.2. Sputtered elemental target atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
2.3.3. Material conservation approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
2.4. Deposition rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
2.5. Modeling as a function of reactive gas partial pressure P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
2.6. Kinetics of the reactive gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
2.7. Modeling as a function of the total reactive gas supply rate Qtot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2004.10.051
* Corresponding author.
E-mail addresses: soren.berg@angstrom.uu.se (S. Berg)8 tomas.nyberg@angstrom.uu.se (T. Nyberg).
Thin Solid Films 476 (2005) 215–230
www.elsevier.com/locate/tsf
3. Parameters influencing the hysteresis effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
3.1. Influence of target material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
3.2. Influence of reactive gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
3.3. Influence of system pumping speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
3.4. Target to substrate distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
3.5. Target ion current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
3.6. Target area: hysteresis-free operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
4. Dissociation of sputtered compound molecules: effect on modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5. Reactive co-sputtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6. Reactive sputtering from an alloy target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7. Processing with several reactive gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
8. Transient behaviour: pulsed DC reactive sputtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
9. Ion implantation: reactive gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
10. Effect of secondary electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
11. Non-uniform target current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
12. Modelling conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
1. Introduction
Reactive sputtering for thin film coatings is used in
numerous industrial applications. By simply adding a gas
that reacts with the sputtered material, it is possible to form
a wide variety of useful compound thin film coatings. At
first sight, this may seem very simple. However, the reaction
mechanisms between the sputtered material and the reactive
gas may cause some processing stability problems. Combining
a high deposition rate and true compound stoichiometry
of the deposited film turn out to appear as contradicting
desires. In many cases, the main reason for this complication
is that as well as forming a compound of the deposited
film, compound formation will also take place at the surface
of the sputtering target (target poisoning). Normally, the
sputtering yield of the compound material is substantial
lower than the sputtering yield of the elemental target
material. This causes the deposition rate to decrease as the
supply of the reactive gas increases. The relationship
between the film composition and supply of reactive gas
is very non-linear. This is also the case for the deposition
rate vs. the supply of the reactive gas. Therefore, reactive
sputtering processes controlled by the supply of the reactive
gas exhibit quite complex processing behaviour [1,2].
Fig. 1 shows a typical experimental processing curve for
the sputter erosion rate vs. the supply of the reactive gas for
a reactive sputtering process (carried out with constant
target current during processing). The characteristic feature
of this curve is that it exhibits a hysteresis effect. The
deposition rate does not decrease and increase at the same
value with the supply of the reactive gas. The separation
width between the decrease and increase denotes the width
of the hysteresis region.
A corresponding hysteresis effect is observed for the
relationship between the partial pressure and the supply rate
of reactive gas. This is shown in Fig. 2. This figure clearly
illustrates a difference in increasing and decreasing the
supply of the reactive gas. During the increase sequence of
the reactive gas supply, the partial pressure of the reactive
gas remains at a very low level until reaching the upper
limiting value of the hysteresis width. During a decrease of
the supply of the reactive gas, the partial pressure remains
significantly higher in the hysteresis region than during the
increase of the gas. This points out that more gas is
consumed for compound formation during the increase
sequence. This may be understood by comparing the sputter
erosion rate curve for the corresponding sequences. A
higher sputter erosion rate needs more reactive gas to form
compound coatings.
The hysteresis effect is one of the key problems in
experimental reactive sputtering systems. In the following
treatment, we will therefore demonstrate how the hysteresis
is affected by different processing parameters. The goal is to
better understand the influence of processing parameters on
the overall behaviour of this process.
Fig. 1. Typical experimental curve for a reactive sputtering process. The
optical emission (OES) from sputtered metal atoms represents the sputter
erosion rate. Qtot is expressed in standard cubic centimeters per minute
(sccm).
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230216
In order to be able to predict the outcome of reactive
sputtering processes, there is a need for a reliable model. In
the following paragraphs, we will outline a simple model for
reactive sputtering processes. The core idea of this model
has been published earlier [3]. It has become the commonly
accepted treatment and is frequently referred to as bBerg’s
modelQ. However, the results should be considered as first
order approximations. Despite the simplicity, however, the
results have proved to fit surprisingly well to most
experimentally found results. There exist process conditions,
however, where a more sophisticated treatment must
be considered. Even in these cases, the treatment can be
based on a similar balance philosophy as suggested in the
basic simple bBerg’s modelQ [3–8].
2. Definition of conditions for the reactive sputtering
model
In order to understand the influence of different processing
parameters for the reactive sputtering process, we will
try to keep the number of parameters as low as possible. To
satisfy this goal, we have as a first order approximation
neglected some effects that may influence the overall
processing behaviour. We will comment on this later in
the article.
A schematic of a simple sputtering equipment is shown
in Fig. 3. The mathematical model describing this system is
shown in Fig. 4a–b. We assume a target (area At) in front of
a collecting surface (area Ac) in a vacuum chamber. There is
a pump connected to the vacuum chamber having a constant
pumping speed S for the gases involved. A reactive gas
supply is connected to the vacuum chamber. We assume that
the following conditions exist in the chamber:
The total supply rate of the reactive gas is denoted Qtot.
There is a uniform partial pressure P of the reactive gas in
the chamber. Since there is reactive gas present, the
reactions between elemental target atoms and the reactive
gas will cause a fraction ht of the target to consist of
compound molecules. This compound formation is of
course uniformly distributed over the whole target surface.
To clearly illustrate that a fraction ht of the target has a
different composition than the remaining (1Àht) fraction,
we treat the ht fraction as a separate continuous area. The
remaining part (1Àht) of the target surface consists of
elemental non-reacted target atoms.
The same situation exists at the receiving area Ac where
all sputtered material is assumed to be uniformly collected.
The compound fraction at this surface area (deposited film)
is denoted hc. Notice that, with this definition, hc is also a
Fig. 2. The partial pressure, P, of the reactive gas corresponding to the
curve in Fig. 1.
Fig. 3. Schematic of a simple reactive sputtering system.
Fig. 4. (a) Theoretical equivalent for the system shown in Fig. 3. The
notations are referred to and explained in the text. (b) Illustration of flux of
sputtered material to the substrate area Ac. The notations are referred to and
explained in the text.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 217
measure of the composition of the deposited film. We also
assume that the ratio between the electron and ion currents
does not change during processing. The ion current density
J (Amps/unit area) is assumed to be uniformly distributed
over the target surface At. The sputtering contribution by
ionized reactive gas is neglected, which is valid when the
partial pressure of the reactive gas is significantly lower than
the partial pressure of the argon gas. We also assume that
sputtering of a compound molecule from the target surface
results in exposing the original non-reacted surface at that
target position. This corresponds to forming only one
monolayer of the compound by chemisorption.
2.1. Flux of reactive gas in processing chamber
A uniform partial pressure P of the reactive gas will
cause a uniform bombardment of neutral reactive molecules
F (molecules/unit area and time) to all surfaces in the
processing chamber. From gas kinetics [9], the relationship
between F and P is
F ¼
P
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2kTpm
p ; ð1Þ
where k is the Boltzmann constant, T is the temperature and
m is the mass of the gas molecule. In the following, we will
derive steady-state values for some representative parameters
during different processing conditions. The definition
for steady state is that there be no time variations in the
processing parameters. The consequences will be discussed
in the following sections.
2.2. Conditions at the target surface
For simplicity, we assume the compound molecules at
the target and substrate to consist of one reactive gas atom
and one metal atom. Proper correction factors should be
added for other stoichiometries. In the following description,
we refer to Fig. 4a. During processing, the target will
be sputter eroded. Elemental metal atoms are sputtered from
the surface fraction (1Àht) and, for simplicity, the sputtered
material from the surface fraction ht is assumed to be
sputtered as molecules, irrespective of whether the material
is ejected in atomic or molecular form. The only way
sputtered compound molecules may be replaced is by
reactions between neutral reactive gas molecules and the
elemental non-reacted target material. We assume that no
reactions between underlying elemental target atoms and the
reactive gas can take place on the compound fraction ht of
the target area At. A steady-state equation for the target may
therefore be defined as
J
q
Ycht ¼ a2F 1 À htð Þ; ð2Þ
where Yc is the sputtering yield of compound molecules
from the compound-covered fraction ht of the target, a is the
probability (sticking coefficient) for a colliding neutral
reactive gas molecule to react with an unreacted elemental
target atom at the (1Àht) fraction of the target, q is the
elementary electronic charge and F is multiplied by a factor
of 2 because we assume two atoms per gas molecule. This
equation states that at steady state the sputter erosion rate of
compound molecules from the target must be identical to the
compound formation rate by reactions between neutral
reactive gas molecules and elemental target atoms. To
further illustrate this, we have inserted a small compound
area in front of the arrow corresponding to the incoming
flux of reactive gas, Qt, to the target surface. This symbolizes
the rate of compound formation at the target. We have
also bopened upQ a small hole in the ht fraction area of
the target. This is to illustrate the sputter removal rate of
the compound material from the target. At steady state, the
compound area to the right must breplaceQ the hole to the
left. From Eqs. (1) and (2), it is possible to solve for ht as a
function of partial pressure of the reactive gas.
2.3. Conditions at collecting area (substrate)
We assume that all sputtered material from the target will
be uniformly deposited at the collecting area Ac. At steady
state, the composition of added film material must be
identical to the existing film composition. There are several
ways of describing this situation.
2.3.1. Flux of material approach
By the following arguments, hc may be evaluated. The
descriptions refer to Fig. 4b. The total number of outsputtered
compound molecules per unit time from the target
will be denoted Fc.
Fc ¼
J
q
YchtAt; ð3aÞ
where Yc represents the sputtering yield of the compound
material. We assume that this compound material will be
uniformly distributed onto the collecting surface Ac. Notice,
however, that ( Fchc) will be deposited at the fraction hc of
Ac that already has been defined to consist of compound
material. Adding compound material to the already existing
compound fraction of the collecting area will not change the
local composition. Consequently, the addition of ( Fchc) to
the hc fraction at the collecting area Ac will not influence the
surface fraction hc. This contribution will therefore be
neglected in this treatment.
The remaining fraction Fc(1Àhc) of sputtered compound
material will be deposited onto the fraction (1Àhc)
of the collecting area Ac containing elemental non-reacted
target atoms. This will convert some part of the (1Àhc)Ac
area to become part of the hc fraction of compound
material at the surface Ac. This fraction of the deposited
compound material will thus contribute to an increase in
the value of hc.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230218
2.3.2. Sputtered elemental target atoms
A corresponding argument may be applied to the
sputtered non-reacted elemental target atoms, for which
the total number per unit time in Fig. 4b is denoted by
Fm ¼
J
q
Ym 1 À htð ÞAt ð3bÞ
The fraction of flux Fm(1Àhc) deposited onto the fraction
(1Àhc) of the collecting area Ac will not influence the
value of hc. Adding elemental non-reacted target atoms to
an area already defined to consist of non-reacted atoms
does not change hc. However, the flux Fmhc deposited
onto the fraction hc of compound material at the collecting
area Ac will contribute to a decrease in hc.
Compound formation by reaction between reactive gas
molecules and elemental non-reacted atoms at the collecting
area will consume Qc reactive gas molecules. As for the
target, we assume that no reactions between elemental target
atoms and the reactive gas can take place on the compound
fraction hc of the collecting area. Therefore,
Qc ¼ aF 1 À hcð ÞAc: ð3cÞ
For simplicity, we assume the same value for a as for
the target. Since the reactive gas molecules consist of two
atoms, Qc will contribute with two compound molecules
adding to the value of hc. At steady state, the
contributions supporting an increase in hc must be
identical to the contributions that support a decrease in
hc. This leads to the following balance equation for the
collecting area Ac,
2Qc þ Fc 1 À hcÞ ¼ hcFm:ð ð3Þ
From Eqs. (1)–(3), it is possible to solve for hc as a
function of the partial pressure of the reactive gas.
2.3.3. Material conservation approach
Some arguments have been raised against the above
approach; namely, that the flux of materials approach
described in Sections 2.3.1 and 2.3.2) above neglects some
of the outsputtered material ( Fchc) and Fm(1Àhc). The
following alternative treatment, however, serves to support
the validity of the balance treatment.
The ratio hc/(1Àhc) between the compound and elemental
target atom fractions in the deposited film must be
identical to the corresponding ratio ( Fc+2Qc)/Fm of the
added film material. This relation defines a balance equation
for the collecting area Ac,
hc
1 À hc
¼
Fc þ 2Qc
Fm
ð3VÞ
By solving Eqs. (3) and (3V) for hc, we find that both these
equations result in identical expressions for hc. The bflux of
materialQ and bmaterial conservationQ approaches give rise
to identical mathematical conditions for the steady-state
conditions at the collecting area Ac.
2.4. Deposition rate
Using the above notation, it is easy to define an
expression for the total sputter erosion rate R from the
target (atoms+molecules per unit area and time),
R ¼
J
q
Ym 1 À htÞ þ Ychtð Š:½ ð4Þ
Proper constants may be added to convert R into desired
units (e.g., angstrom/min, etc.). It must be understood,
however, that more material is deposited at the collecting
area Ac than sputter eroded from the target area At. This is
because Qc of the reactive gas is added to the sputtered flux
of material. The difference in mass between sputter eroded
material and the mass of the deposited material will strongly
depend on the content of reactive gas atoms in the
compound molecule per sputtered elemental metal atom.
An expression for the deposition rate D may be obtained in
the following way. The total sputtering rate Rm of metal
atoms (elemental+those included in sputtered molecules) is
Rm ¼
J
q
Ym 1 À htð Þ þ Ycht½ ŠAt: ð5VÞ
Knowing the compound fraction hc at Ac makes it quite
easy to derive an expression for the deposition rate D.
D ¼ c1Rm 1 À hcð Þ þ c2Rmhc; ð5Þ
where c1 and c2 are constants accounting for unit
conversions. The first term in Eq. (5) represents the
contribution by elemental metal atoms, while the second
term represents the contribution by compound material. We
have chosen to express normalized D in units of mass/unit
time.
2.5. Modeling as a function of reactive gas partial
pressure P
From Eqs. (1)–(5), it is possible to calculate R, D, ht and
hc as a function of partial pressure P. Typical curves are
shown in Figs. 5 and 6). Numerical values used for the
calculations are given in Appendix Notice that all curves
Fig. 5. Calculated target erosion rate R and substrate deposition rate D vs.
partial pressure, P, of the reactive gas.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 219
are bwell behavedQ and give single valued results at all
partial pressures. Moreover, the deposition rate curve may
have a maximum value before reaching complete target
poisoning. These curves correspond to the reactive deposition
of AlN.
Unfortunately, it is not easy to experimentally control
the partial pressure of the reactive gas during processing.
Therefore, simple processing curves like Figs. 5 and 6
will not be obtained without quite sophisticated process
control systems. The simplest and most common control
function is the supply of reactive gas to the processing
chamber. This calls for modeling equations based on the
supply of the reactive gas rather than based on the partial
pressure.
2.6. Kinetics of the reactive gas
The relation between the reactive gas supply and the
partial pressure may quite easily be solved from the model
outlined above where the compound formation (reactions
between elemental target atoms and reactive gas molecules)
consumes a fraction of the incoming gas. A schematic
diagram of the reactive gas pathways was shown in Fig. 4a.
The consumption (number of molecules per unit time) at the
target Qt is obtained from Eq. (2),
Qt ¼ aF 1 À htð ÞAt; ð6aÞ
while the consumption Qc at the collecting area Ac is
obtained from Eq. (3c).
Qc ¼ aF 1 À hcð ÞAc: ð6bÞ
The remaining part Qp of the reactive gas will escape
from the processing chamber through the pumping system.
Assuming a pumping speed of S for the system pump gives
Qp ¼ SP: ð6cÞ
The total supply Qtot is the sum of all sources for reactive
gas consumption,
Qtot ¼ Qt þ Qc þ Qp: ð6Þ
2.7. Modeling as a function of the total reactive gas supply
rate Qtot
Adding Eq. (6) to the previous equations makes it
possible to find the relation between Qtot and P, and
consequently calculate R, D, ht, hc, Qt, Qc, Qp and P as a
function of the supply rate of the reactive gas Qtot. Results
are shown in Figs. 7–9. It is obvious that these curves show
a more complex relation to Qtot than the curves in Figs. 5
and 6 did to the partial pressure P. The S-shaped behaviour
defines a region where one value for Qtot may be satisfied
by three different values of R, D, P, ht and hc. This region
corresponds to the hysteresis width shown in Figs. 1 and 2
in the introduction. Four different points, P1–P4, are marked
in Figs. 7–9. In the following, we discuss important
phenomena that take place at these positions. Before
elaborating on this, however, we clarify two different modes
of operation.
It is important to understand the difference between
processes controlled by partial pressure of the reactive gas
and by the supply of the reactive gas. This difference is
illustrated in Fig. 10a–b. Selecting values for the partial
pressure in Fig. 10a corresponding to positions 1, 2, . . ., 9
on the curve result in well-defined single-valued supply
levels Qtot. Thus, by selecting continuously increasing
Fig. 6. Calculated compound fractions ht and hc at the target and substrate,
respectively, as a function of the partial pressure, P, of the reactive gas.
Fig. 7. Calculated target erosion rate R and substrate deposition rate D vs.
total supply rate of reactive gas, Qtot, for conditions identical to those used
in generating Figs. 5 and 6.
Fig. 8. Calculated partial pressure, P, vs. supply rate of the reactive gas,
Qtot.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230220
values of the partial pressure of the reactive gas, the Sshaped
curve shown in Fig. 10a will be generated. This is
the signature of a partial pressure process control.
As previously shown in Fig. 5 in Section 2.5, any
selected partial pressure value also corresponds to a welldefined
single value of the sputter erosion rate R. Thus, it is
possible to obtain paired values (R, Qtot) corresponding to
specifically selected partial pressures. These (R, Qtot) pair
values will define a R vs. Qtot curve with the shape shown in
Fig. 10b. It must be understood that experimentally this
curve can only be generated by stepping values of the partial
pressure not by stepping values of the reactive gas supply. In
practice, this curve can only be obtained for processes
having some feedback control system enabling, in a
controlled way, variations in the reactive gas supply
corresponding to the desired values of the partial pressure.
A different behaviour will result if the supply rate of the
reactive gas Qtot is used as the process control parameter.
Continuously increasing Qtot can not generate the entire Sshaped
curve in Fig. 10b. When Qtot reaches the value
corresponding to position 2 on the curve, a dramatic effect
occurs. A small additional increase in Qtot forces the rate to
avalanche from position 2 down to position 7 on the curve.
An even further increase of Qtot generates R values 8, 9,
etc., following the curve.
Starting at high gas flow values (corresponding to
position 9 on the curve) and then decreasing Qtot generates
values of the erosion rate R following the curve in reverse
order to position 4. However, at this point, a further decrease
in Qtot will result in R avalanching from position 4 to a point
somewhat to the left of position 1. A further decrease in Qtot
will cause the rate R to follow the curve. The fact that the
sharp decrease and increase of R do not occur at the same
value for Qtot illustrates the hysteresis effect with the
hysteresis width defined by the separation between the two
avalanche positions. This is the way that the R responds
experimentally to having the supply Qtot as the input control
parameter. It must also be pointed out that, in this mode of
operation, it is not possible to reach any of the processing
points on the segment between the positions 2 and 4 on the
curve. Instead of following the S-shaped loop on this
segment, the process will by-pass the loop and avalanche
along the dotted lines.
Thus, the positions labeled P1–P4 in Figs. 7–9 denote the
processing region (shown shadowed) in which hysteresis
occurs.
3. Parameters influencing the hysteresis effect
There exist many bpopularQ explanations regarding the
origin of the hysteresis effect in reactive sputtering
processes. A too simplified explanation, however, may
cause the experimentalists to draw wrong conclusions
concerning how to optimize the process. We therefore want
to clarify parametric interactions in somewhat more detail. It
should be pointed out that, although hysteresis is generally
observed in reactive sputter processing, there also exists
conditions under which hysteresis does not occur. It is
possible to use the mathematical model outlined above to
analyze specific processes and predict if hysteresis will
appear or not.
In order to investigate the influence of processing
parameters on the reactive sputtering process, we will
introduce some illustrative curves. Plotting the curves for
Qtot, Qt, Qc and Qp as a function of P may clarify the
gettering situation. This is shown in Fig. 11a where it is
clear that among the supply rate components, only Qc
exhibits a negative derivative dQc/dP in a limited section of
the curve. Qt and Qp do not have negative derivatives. It is
therefore the negative derivative portion of the Qc curve that
Fig. 9. Calculated compound fractions ht and hc for the target and substrate,
respectively, vs. supply of the reactive gas, Qtot. P1–P4 are only marked for
the ht-curve.
Fig. 10. Schematic diagram illustrating the simulation procedure. (a) shows
the general behavior for the reactive gas pressure, P, vs. reactive gas flow
and (b) shows sputtering rate, R, vs. reactive gas flow. By selecting
different values for the partial pressure in (a), the process operates at
different points indicated by 1, 2, . . ., 9. These points correspond to points
1, 2, . . ., 9 in (b).
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 221
causes a negative derivative in the Qtot vs. P curve. Having
(or eliminating) hysteresis may be predicted by investigating
the conditions for the derivative dQtot/dP. If dQtot/dPb0 in
some region, the process will exhibit hysteresis. If dQtot/
dPN0 over the whole processing region, then the process
will not exhibit any hysteresis. In Fig. 11b are shown the
derivatives of Qtot, Qc, Qt and Qp as a function of P. The
following condition is valid,
dQtot
dP
¼
dQt
dP
þ
dQc
dP
þ
dQp
dP
: ð7Þ
Eq. (7) is quite useful when determining whether
hysteresis will appear or not. (Notice that dQp/dP=S, system
pumping speed.)
The functions Qt, Qc and Qp may also be presented as a
function of Qtot. Such a presentation is shown in Fig. 12.
3.1. Influence of target material
The sputtering yields Ym for the elemental target material
and Yc for the compound formed on the target surface are
materials constants. For materials where YcbbYm, hysteresis
is normally more pronounced than if Yc is close to Ym [10].
In Fig. 13, three R vs. Qtot curves calculated for different
values of Yc, keeping Ym constant, are shown. As can be
seen, there is a pronounced difference in hysteresis width for
the curves. The model thus predicts that different target
materials may respond differently in a reactive sputtering
process.
3.2. Influence of reactive gas
Some gases are more reactive to the target material than
others. Normally, O2 is a more aggressive gas than N2. The
influence of gas reactivity may be simulated by changing
the value of the sticking coefficient a in the model formulas.
In Fig. 14, the results of R vs. Qtot for different values of a
are shown. Notice that a decrease in a causes a decrease in
the width of the hysteresis region [11]. Also, a may be
considered as a materials constant. However, this constant
may be influenced by, e.g., target/substrate temperatures,
surface morphology, etc.
3.3. Influence of system pumping speed
In many reactive sputtering processing chambers there is
a throttle valve between the pump and the chamber. The
setting of this valve determines the pumping speed for the
external pump. It is thus possible to experimentally control
the pumping speed. Fig. 15 shows the effect of varying the
pumping speed. The calculations predict that the hysteresis
may be eliminated if the pumping speed is high enough.
This is a well known effect [12] and it can also be seen
directly by inspection of Eq. (7) and Fig. 11a–b. Since
S=dQp/dP, the value of S may always be chosen high
enough to make dQtot/dPN0. Unfortunately, the critical
value of the pumping speed needed to eliminate the
hysteresis is usually unrealistically high.
Fig. 11. (a) shows calculated consumptions of the reactive gas vs. the partial
pressure of this gas and (b) shows calculated derivatives of the consumption
curves shown in (a).
Fig. 12. Calculated consumption of the reactive gas vs. the supply, Qtot, of
this gas.
Fig. 13. Calculated sputter erosion rates, R, vs. the supply, Qtot, of reactive
gas for different values of the sputtering yield Yc for the compound,
Ym=1.5.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230222
3.4. Target to substrate distance
The position of the target in front of the substrate may
also influence the hysteresis width. This is illustrated by
changing the size of the collecting area Ac in the
calculations. An increasing collecting area Ac represents
an increasing target to substrate distance. Fig. 16 shows the
processing curves for two different sizes of Ac. Keeping the
target to substrate distance small will cause a decrease in the
hysteresis width. Notice that there will always be some
spread of the sputtered material. Therefore, the condition
that AcNAt will always exist in this configuration.
Many sputtering systems have shutters relatively close in
front of the sputtering cathodes. It is common practice by
many users to pre-sputter the target behind a shutter before
exposing the substrate to film deposition. The idea is to
obtain stable processing conditions before exposing the
substrate to deposition. The use of a target shutter in reactive
sputter deposition, however, may significantly influence the
processing conditions. Pre-sputtering the target in reactive
mode behind the shutter will be equivalent to sputtering
with a smaller collecting area than the collecting area when
the shutter is removed. The reactive sputtering process will
then QjumpQ from one processing curve corresponding to the
shutter area to another corresponding to the deposited area
when the shutter is removed (illustrated by the arrow in Fig.
16). After the shutter removal, a new stabilization period
will take place before reaching the new steady-state
condition. During this period, the composition of the
deposited film may vary significantly. This initial phase of
deposition determines the film/substrate interface. This may
affect the film adhesion and other film/substrate sensitive
properties.
However, having a protective shutter close to the
substrate instead of close to the target will make it possible
to pre-sputter in reactive mode without any significant
change in mode of operation when the shutter is removed
(minor change in Ac).
3.5. Target ion current
At first, it might seem possible to eliminate the hysteresis
by applying high power to the target and thus reducing the
target poisoning effect by a high sputter erosion rate.
Unfortunately, the process does not respond in this way. In
Fig. 17, results of calculations for different ion current levels
are shown. Increasing the ion current only causes a
magnification of the curves. In fact, the calculations predict
Fig. 15. Calculated sputter erosion rates, R, vs. reactive gas supply, Qtot, for
three different pumping speeds, S.
Fig. 16. Calculated processing curves corresponding to sputtering with a
target shutter (Ac=700 cm2
) and without a shutter (Ac=2500 cm2
).
Fig. 17. Calculated sputter erosion rates, R, vs. reactive gas supply, Qtot, for
different values of the argon ion current, I. Dashed lines represent constant
compositions ht and hc.
Fig. 14. Calculated sputter erosion rates, R, vs. reactive gas supply, Qtot, for
three different values of the sticking coefficient a.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 223
that the target poisoning and the film composition effects
will be identical along straight lines starting from the origin.
It is thus not possible to eliminate the hysteresis by
increasing the target ion current.
The hysteresis effect may also cause confusion in
decisions concerning the processing point. It is often desired
to operate the process close to the avalanche point. A
suitable operating point for the I=2.5 A curve in Fig. 17
should be point X. This point may be reached by first
applying 2.5 A to the target and then slowly increasing Qtot
to c13 sccm. Note, however, that, if 13 sccm of reactive
gas is supplied to the processing chamber before the target
current is applied, the process will end up at processing
point XV. Identical sets of values for Qtot and I yield
different processing conditions. This serves to illustrate that
under certain conditions it is important to report in which
order different parameters are applied to the process.
Sometimes, the target current or power supplied to the
target may be used as a control processing parameter. If a
constant supply of reactive gas is fed to the chamber, this
will give the curves in Fig. 18a–b for the sputter erosion rate
R and partial pressure P as a function of target ion current.
Notice that, for low values of the ion current, the target is
poisoned, while the metallic target mode corresponds to
high values of ion current. This same information can also
be obtained from Fig. 17.
3.6. Target area: hysteresis-free operation
It is possible to select the size of the target. The model
predicts that the shape of the processing curves depend
strongly on the size of the beffectiveQ target area. This is
shown in Fig. 19a. As can be seen, there will be no hysteresis
for a small size target area under these processing conditions
[13]. It must be pointed out that this is not an effect caused by
the corresponding increase in ion current density (having the
same total target current for all target areas). To further
illustrate this, calculations for the small area target for
different target ion currents are shown in Fig. 19b. As can be
seen, the hysteresis is eliminated irrespective of ion current
density values. This is a consequence of the results described
in Fig. 17. Increasing or decreasing the ion current only
causes a magnification or demagnification of the curves. It
does not change the shape of the curves.
A small target exhibits almost ideal processing conditions.
Fig. 19c shows the compound fractions ht and hc
corresponding to the same conditions as in Fig. 19a for
At=3 cm2
. Note that the target remains primarily in the
high rate metallic mode htc0 all the way up to the
position where hcc1 (stoichiometric film formation).
Fig. 18. Calculated processing curves using ion current, I, as the
independent parameter. (a) Target erosion rates, R. (b) Partial pressure of
reactive gas, P.
Fig. 19. (a) Calculated sputter erosion rates, R, vs. reactive gas supply, Qtot,
for different values of the target area, At, assuming a constant total target
ion current, I. (b) Calculated sputter erosion rates, R, vs. reactive gas
supply, Qtot, for different values of target ion current, I, for the 3-cm2
target
in (a). (c) Calculated values for ht and hc vs. reactive gas supply, Qtot, for
the 3-cm2
target in (a).
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230224
It should be noticed, however, that the critical target size
for hysteresis-free operation will depend on several other
processing parameters. The critical size has to be estimated
for the specific reactive sputtering process. Notice also that
the power dissipation over a relatively small area may give
rise to a considerable heating of the target. This has to be
considered when designing a hysteresis-free reactive sputtering
process based on this phenomenon.
4. Dissociation of sputtered compound molecules: effect
on modelling
In the above treatment, we assumed that the sputtered
compound molecules from the target reached the collecting
area without breaking up into free atoms [14]. This is
generally not believed to occur for compound molecules
during sputtering. During the sputter event, the compound
molecule is believed to dissociate into its elemental atoms. It
is easy, however, to modify the above model to take
molecule dissociation into account. This may be illustrated
by the following arguments.
(a) In the case of compound dissociation, there will be no
net gettering of the reactive gas at the target surface.
The reason for this is that the gas molecules that are
consumed to form the compound at the target surface
will return to the gas when the compound molecule is
sputtered and dissociated into its original components.
We simply assume that these bgas atomsQ will return
back to the gas phase.
(b) There will be an additional flux of elemental target
atoms to the collecting area Ac. Compound molecules
will be sputter eroded from the target at a rate
( J/q)Ychc. The metal fraction of these outsputtered
compound molecules will, after compound dissociation,
reach the collecting area as elemental target
metal atoms.
In Fig. 20, results from calculations based on the
dissociation of the compound molecules are compared to
the results based on sputtered compound molecules. It is
observed that there is only a minor difference between the
two curves. Detailed comparisons of ht, hc, Qc, Qt and P as
a function of Qtot give the same minor deviations as for the
R vs. Qtot curve shown in this figure. This illustrates that the
status of the sputtered material does not primarily determine
the general shapes of these curves. Other parameters have a
far more significant influence on the overall process. In the
following treatments, we therefore choose to continue to
allow sputtered compound molecules to reach the substrate
intact.
5. Reactive co-sputtering
Complex compound thin films may be deposited by
reactive co-sputtering from several elemental targets [15].
The processing behaviour for such a set-up can be
predicted by calculations based on the simple model
presented above. It is necessary, however, to somewhat
modify the conditions at the collecting area compared to
that outlined for a single elemental target. We suggest the
following treatment.
A schematic of the model for the processing situation for
a reactive co-sputtering process having two separate targets
is shown in Fig. 21. The notation corresponds to the
definitions given in Fig. 4a–b. Eq. (2) may be used to define
the balances for each separate target.
J1
q
Yc1ht1 ¼ a12F 1 À ht1Þð ð8aÞ
for target 1 and
J2
q
Yc2ht2 ¼ a22F 1 À ht2ð Þ ð8bÞ
for target 2.
The conditions at the collecting area Ac are somewhat
more complicated than for the simple single target process.
We choose to use the material conservation approach
(Eq. (3V)) to solve for the overall composition y of the
collecting area Ac. The total number T1 of sputtered
elemental atoms from target 1 is given by
T1 ¼
J1
q
A1 Ym1 1 À ht1ð Þ þ Yc1ht1½ Š; ð9aÞ
assuming one metal and one gas atom in the compound
molecule. A corresponding equation may be defined for the
second target,
T2 ¼
J2
q
A2 Ym2 1 À ht2ð Þ þ Yc2ht2½ Š: ð9bÞ
From T1 and T2, the fraction y of metal 1 atoms in the
deposited film may be calculated as
y ¼
T1
T1 þ T2
: ð9ÞFig. 20. Calculated sputter erosion rates, R, vs. reactive gas supply, Qtot,
including the effect of molecular dissociation and neglecting this effect.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 225
These equations may then be used to calculate the
compound fractions hc1 and hc2 at the surface fractions
yAc and (1Ày)Ac of the collecting area. Since y was
defined to be the fraction of atoms sputtered from target 1,
we simply assume that all material sputtered from target 1
is collected at the y fraction of Ac. Therefore, collecting of
materials from the two separate targets may be treated
separately.
A relationship between the partial pressure and supply of
the reactive gas can be found that is analogous to the
treatment for one gas and one target. Notice, however, that
all sub-areas At1(1Àht1), At2(1Àht2), yAc(1Àhc1) and
Ac(1Ày)(1Àhc2) consume reactive gas.
Calculations based on the assumptions made here are
shown in Fig. 22. We have chosen processing conditions to
demonstrate that the width and position of the hysteresis
obtained by simultaneous sputtering of both targets (cosputtering)
may deviate significantly from operating any of
the targets individually. Notice also that we only obtain a
single hysteresis and not a complex mixture of two
hystereses.
Due to the different reactivity of the two targets, and also
the different ratios Yc/Ym of the targets, the film composition
y may vary quite dramatically as a function of the reactive
gas supply Qtot. In Fig. 23, the composition y as a function
of reactive gas supply is shown for the co-sputtering curve
shown in Fig. 22. The loop illustrates that quite complex
composition behaviour may be obtained for reactive cosputtering
from two separate targets. Increasing the number
of targets further increases the complexity.
We also want to point out that due to different reactivities
between targets and the reactive gas, it may be impossible to
operate both targets in the metallic mode (high rate
sputtering) and obtain a fully reacted coating. However,
this can only be achieved for certain specific compositions.
This effect will exist for both reactive alloy and co-
sputtering.
6. Reactive sputtering from an alloy target
Due to the materials conservation, modeling of reactive
sputtering from an alloy target is almost as straight forward
as sputtering from a single element target. Under steadystate
conditions, the fraction y of one of the materials in the
deposited film will be constant (identical to the target alloy
composition) and independent of the value of the reactive
gas supply. It should be understood, however, that, due to
differences in reactivity with the reactive gas, the different
metals in the alloy target may end up with quite different
compound fractions hc1 and hc2 in the deposited film.
It should also be pointed out that, during processing, the
surface composition of the alloy target normally will deviate
from the target bulk composition. The fact that the overall
composition of the sputter-eroded material must correspond
to the target bulk composition makes it quite easy to
determine the target surface concentration. The relationship
between the bulk and surface composition may be found
from the condition that the rate of sputtered atom emission
from material 1 divided by the rate of emission from
material 2 must be equal to the target bulk composition. A
detailed description of modelling of reactive alloy sputtering
may be found in Ref. [16].
7. Processing with several reactive gases
Sometimes, it may be desirable to form an alloy such
as an oxy-nitride by reactive sputtering from a metallic
Fig. 21. Schematic diagram of a reactive co-sputtering system having two
targets.
Fig. 22. Calculated partial pressures, P, vs. supply, Qtot, of the reactive gas
for the cases in which the targets are operating individually or both are
operating simultaneously.
Fig. 23. Calculated fraction, y, of material 1 in mixed deposited film vs.
reactive gas supply, Qtot, for reactive co-sputtering (solid line) and reactive
alloy sputtering (dashed line).
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230226
target with more than one reactive gas. The basic model
may easily be modified to define a set of equations
describing such a process. We assume in the following
example a process having a single element metallic target
sputtered in argon and two reactive gases (e.g., oxygen
and nitrogen). A schematic diagram of the target
conditions is shown in Fig. 24. Two reactive gases (gas
1 and gas 2) act on the target surface forming compound
1 at surface fraction ht1 and compound 2 at surface
fraction ht2.
There will be two balance equations defining the target
steady-state condition. Analogous to Eq. (2), the balance for
gas 1 and compound 1 will be:
J
q
Yc1ht1 ¼ a12F1 1 À ht1 À ht2Þð ð10Þ
A corresponding equation may be defined for the second
gas.
The treatment of the situation at the collecting surface
follows the technique outlined in the previous paragraphs.
The results of the calculations show that the process
response is quite complex. The two gases compete for
compound formation at the target and substrate surfaces.
Both gases contribute to target poisoning. The gas
gettering will strongly depend on the non-poisoned
fractions (1Àht1Àht2) of the target and (1Àhc1Àhc2) of
the collecting surfaces. Increasing the supply of gas 1, Q1,
therefore directly influences the gettering of gas 2 even
without altering the supply of gas 2, Q2. This intrinsic
feedback behaviour of the process makes process control
difficult [17,18].
There is a unique phenomenon that can occur during
reactive sputtering with two reactive gases. It is possible
to enter the target poisoning mode by increasing the
supply of the first gas while keeping the second gas
supply constant. During certain conditions, however, it is
not possible to return to the metallic (non-poisoned) mode
even by decreasing the supply of the first gas to zero.
The process may be btrappedQ in the target poisoned
mode. The metallic mode can only be reached again if
the supply of the second gas is decreased markedly below
its original constant value. This phenomenon further
complicates reliable control of the two gas reactive
sputtering process. However, the effect is predicted by
the results of the modelling calculations as shown in
Fig. 25. The trapping effect starts to appear for
approximately 4 sccm of gas 2. Once gas 1 is increased
beyond the point for avalanching to the compound mode,
it is not possible to return to the metallic mode even if
the gas supply of gas 1 is set to zero. It is necessary to
also decrease the supply of gas 2 to be able to return to
the metallic mode [19,20].
8. Transient behaviour: pulsed DC reactive sputtering
During the last decade, pulsed DC reactive sputtering
has become the dominating technique to power the target
during reactive sputter deposition processing. This technique
eliminates, or significantly reduces, the arcing
problem caused by a thin insulating layer building up
on the target surface. In the simulations described above,
we have introduced ht to describe the fraction of the
target consisting of compound material. If this is an
insulating compound layer, it will be positively charged
by the bombarding positively charged inert argon ions. A
certain net charge will cause a voltage drop over the
insulating layer. At a critical electrical field, an electrical
breakdown of the insulating layer will take place giving
rise to arcing. By changing the polarity (applying a
positive voltage) from the power supply over a few
percent of the duty cycle, electrons are attracted to the
target surface. Proper positive voltage and duty time
allow for the complete discharge of the insulating layer.
In this way, arcing is prevented despite having some
areas of insulating material on the target surface. The
frequency of pulsed DC systems is normally in the range
of 10–300 kHz.
Assuming a frequency of 100 kHz and a target
erosion rate of 10 Am/min is equivalent to eroding
Fig. 24. Schematic of the target conditions for reactive sputtering with two
reactive gases.
Fig. 25. Calculated sputter erosion rates, R, vs. reactive gas supplies, Q1
and Q2.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 227
0.0017 2/pulse from the target surface. Such a small
erosion rate per pulse is not enough to markedly change
the poisoning status (ht) at the target. This example
serves to illustrate that ht will not respond to the
frequency of the power supply at these high frequencies.
A more detailed analysis [21] shows that similar
conditions will be valid for the response of uc to the
applied frequency.
It should also be pointed out that there will be a transit
time before sputter eroded material from the target reaches
the collecting area. Due to scattering with gas atoms, there
will be a dispersion in transit times for these sputtered
particles. At a target to substrate distance of 10 cm and a
total pressure of 5 mTorr there will be a substantial spread
in transit times for sputtered Al atoms. This is illustrated in
Fig. 26. The dashed short pulse (duration 0.1 ms) causes
sputter erosion from an Al target. The solid curve shows
the probability distribution, f(t), of the transit time for
sputtered atoms to reach the substrate. This result indicates
that consecutive pulses from the target (frequency N1 kHz)
will supply sputtered material to the collecting area with a
large time overlap. The higher the frequency, the more
overlap between consecutive pulses. The net result will be
that the pulsed-character of arriving sputtered material will
disappear. Instead, there will be a continuous flux of
sputtered material as in the case of pure DC sputtering.
This is illustrated in Fig. 27.
From the above arguments, we can conclude that the
behaviour of the pulsed DC reactive sputtering very much
will be the same as for continuous DC sputtering. The
positive pulse only serves to discharge insulating parts on
the target surface. The gas kinetics and flow of sputtered
material will not respond fast enough to the DC pulses
applied by the power supply. The short positive pulse,
however, may cause some energetic bombardment at the
substrate, which may influence the morphology of the
deposited film. One advantage of pulsed DC operation is,
however, that it allows for higher plasma densities during
the bpulse onQ interval as compared to the plasma density
obtained for a corresponding continuous DC-plasma having
the same average power.
9. Ion implantation: reactive gas
We have described some major effects that take place
during reactive sputtering processes. As mentioned in the
introduction we chose to include as few parameters as
possible in the model, while still obtaining results which
are well correlating with experimental experiences. We are
aware of other effects that also take place during
processing. Some of the reactive gas molecules will be
ionized and gain energy from the electric field in front of
the target and get implanted in the target surface region.
Upon penetrating into the surface region of the target,
these ions can undergo chemical reactions with the target
atoms. This will cause some additional target poisoning
and contribute to an increase in ht. In our simplified
treatment, however, we assumed that the ion current is
solely carried by the argon gas. This is valid when the
partial pressure of the reactive gas is small compared to
the partial pressure of the argon gas in the processing
chamber. A detailed analysis of the effect of ion
implantation of reactive gas molecules have been carried
out by D. Depla and R. De Gryse. Their theoretical
calculations predict that this effect alone may give rise to
a hysteresis in the erosion rate vs. partial pressure curves
[22]. So far, however, there exists no experimental
evidence for such behaviour. The relative importance of
reactive gas ion implantation and chemisorption at the
target surface remains to be further investigated. Our
preliminary studies indicate that the outer 20–50 2 layer
at the target surface will be influenced by bknock-onQ
effect of energetic argon onto chemically adsorbed and/or
implanted reactive gas atoms. However, irrespectively of
reactive gas incorporation mechanism, the gas atoms will
be evenly distributed within the whole altered target
surface layer.
Fig. 27. Results corresponding to Fig. 26 but for a pulsed frequency of 5
kHz (dashed line).
Fig. 26. Probability distribution, f(t), (solid line) of the transit time for
sputtered Al atoms to reach the substrate after one short (0.1 ms) sputtering
pulse (dashed line).
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230228
10. Effect of secondary electrons
When the target surface composition changes, the
amount of secondary electrons emitted by ion bombardment
of the target surface changes. This will, in turn, change the
ratio between ion and electron current. It is not possible to
distinguish the electron and ion currents in the external
electrical circuit. Therefore, a constant total current during
processing does not necessary imply that there is a constant
ion current bombarding the target. If the secondary electron
emission coefficient can be estimated for the different target
surface conditions, this effect can be included in the
modelling work. Some authors have recently done this
[23,24]. The results indicate that this effect does not change
the general shapes of the calculated curves. To some extent,
however, it offers a possibility to include the plasma
conditions into the calculations. It is well known that the
target voltage will change due to target poisoning if a
reactive sputtering process operates in the constant target
current mode. This can be predicted by simple calculations.
We will briefly summarize the treatment by Pflug et al.
[23] who assumed that the total target current IT is composed
of both ions and electrons.
IT ¼ I 1 þ cð Þ; ð11Þ
where I denotes the actual ion current and Ic denotes the
electron current generated by the secondary emission
coefficient c. The secondary electron emission factor c
depends on both the target voltage, U, and the degree of
target poisoning. Pflug et al. [23] suggested the expression
c ¼ cm 1 À htð Þ þ cchtð Þ
U
U0
ð12Þ
in which cm and cc are the secondary electron emission
coefficients at the metal and compound areas, respectively, at
the target surface and U0 is a reference voltage required for
keeping the equation dimensionless. It is possible to combine
these equations with the basic gas kinetic equations outlined
in Section 2 above and calculate the variations in target
voltage as a function of the reactive gas supply for constant
target current. Calculated results following the treatment of
Pflug et al. are shown in Fig. 28. It should be noticed that cm
may be either smaller or larger than cc. Consequently, the
voltage may either increase or decrease for a large supply of
reactive gas. It depends on the target material and the choice
of reactive gas. We may notice, however, that the processing
curve is still S-shaped.
It must be pointed out, however, that the results shown in
Fig. 28 are based on very simplified assumptions about the
electrical characteristics of the plasma. A detailed analytical
analysis can not easily be evaluated.
11. Non-uniform target current
In magnetron sputtering, the ion current is extremely
non-uniform at the target. The current density in the
pronounced erosion zone may be significantly higher than
outside this zone. We therefore normally estimate the area of
the erosion zone and assume that the current acts only on
this zone. The shapes of the modeling curves, however, will
not change if we assume the target to consist of different
segments having different ion current densities. The degree
of target poisoning, however, will be different for the
different segments.
12. Modelling conclusions
The basic model presented in the first sections of this
article serve to predict the general shapes of processing
curves for a wide variety of reactive sputtering processes.
We have also demonstrated that this model can be slightly
modified quite easily to account for more complex reactive
sputtering processes. It must be pointed out that the
simplifications made in the model will, of course, restrict
the validity of the calculated results. To our experience,
however, the theoretical curves remarkable well mirror most
experimental findings.
We are well aware of that much work remains to be done
before there will exist a reliable detailed model which also
accounts for the properties of the plasma, non-uniformities
in gas kinetics, more complex chemical reactions, variations
in secondary electron emission coefficients, ion implantation
of the reactive gas, etc. Several attempts already exist to
use finite element method (FEM) calculations to solve for
some of these effects [25]. We will continue to search for
new simple ways of introducing additional effects into the
description of reactive sputtering processes. The basic idea
is to find an extended reliable process model, which is able
to predict the effects of more individual parameters.
Acknowledgements
The work presented in this article has primarily been
financial supported by the Swedish Foundation for Strategic
Research in the former project bThe Angstrom Consortium
Fig. 28. Calculated target voltage, U, as a function of the supply of the
reactive gas, Qtot, for reactive sputter processing at constant total target
current.
S. Berg, T. Nyberg / Thin Solid Films 476 (2005) 215–230 229
for Thin Film ProcessingQ and the ongoing project bThe
Low-Temperature Thin Film Synthesis ProgramQ. Additional
financial contributions have been obtained from the
Knut and Alice Wallenberg Foundation, the Swedish
Research Council for Engineering Sciences and the Swedish
Agency for Innovation Systems.
Appendix A
The following parameters have been used for calculating
the curves in the figures, unless otherwise is indicated.
Figs. 5–19: S=80 l/s, Yc=0.3, Ym=1.5, a=1, At=150 cm2
,
Ac=2500 cm2
, I=0.5 A. Figs. 21 and 22: S=80 l/s, Yc1=0.3,
Ym1=1.5, Yc2=0.8, Ym2=3.0, a1=1, a2=0.5, At1=150 cm2
,
At2=150 cm2
, Ac=2500 cm2
, I=0.5 A. Fig. 24: S=10 l/s,
Yc1=0.03, Ym1=0.4, Yc2=0.03, Ym2=0.4, a1=1, a2=1, At=18
cm2
, Ac=1650 cm2
, I=2 A. Fig. 27: P=100 W, cm=0.4, cc=1,
S=80 l/s, Yc=0.3, Ym=1.5, a=1, At=150 cm2
, Ac=2500 cm2
.
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