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Thin Solid Films 515 (

Dynamic behaviour of the reactive sputtering process

T. Kubart *, O. Kappertz, T. Nyberg, S. Berg

The Angstrom Laboratory, Uppsala University, Box 534, S-751 21 Uppsala, Sweden

Available online 27 January 2006

Abstract

Modelling of the dynamic behaviour of the reactive sputtering process is a key issue in many respects. Apart from increasing the basic

understanding, such a model is also important for an active control of the process so that optimal deposition conditions can be maintained. This

work is intended to present a basic model for the dynamic behaviour of the reactive sputtering process. The influence of the processing parameters

on the transient behaviour is discussed. We found that the processing curves depend on the rate by which the processing parameters are varied. In

particular, when measuring pressure–flow curves for increasing and decreasing reactive gas flow, the rate of change of the reactive gas supply

strongly influences the width of the hysteresis region.

D 2006 Elsevier B.V. All rights reserved.

PACS: 81.15.Cd

Keywords: Reactive sputtering; Process simulation; Magnetron

1. Introduction

Reactive sputtering is a widely used technique to deposit

oxides and nitrides, etc. The process is very non-linear and

usually exhibits a hysteresis behaviour with respect to the

reactive gas flow. It is sometimes very beneficial to operate

the process inside the hysteresis region. To be able to do

this, however, a feedback control system has to be used. The

optimum design of such a feedback control system depends

on the dynamic behaviour of the process to be controlled.

This dynamics is in turn affected by a number of different

parameters like the target material, reactive gas, pumping

speed, or chamber volume. It would be very beneficial if the

time dependent behaviour of the reactive sputtering process

could be adequately simulated since this would not only

increase the basic understanding of the process, but also save

time and provide useful input when designing a feedback

control system for such a process. This work is intended to

present a basic model for the dynamic behaviour of the

reactive sputtering process. Steady state hysteresis of

reactive sputtering is reasonably well described by classical

Berg’s model assuming that the main process involved is

0040-6090/$ - see front matter D 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.tsf.2005.12.250

* Corresponding author. Tel.: +46 18 4713164; fax: +46 18 555095.

E-mail address: Tomas.Kubart@angstrom.uu.se (T. Kubart).

chemisorption of reactive gas on metallic surfaces on target

and substrate [1]. Previous dynamic models have only

taken into account reactive gas gettering at the target surface

[2]. Some recent studies show, however, that several additional

effects like implantation of reactive gas atoms into the target

surface and atomic sputtering have a substantial influence on

the dynamic behaviour and should not be neglected in a model

describing the dynamics [3,4]. Their impact on steady state

hysteresis curve is only of second order [5], but they may

determine transition response of the process to changes in e.g.

the reactive gas flow or target power. An indication of the

complexity is the transition time from compound to metallic

measured in experiments, where the process requires some-

times very long time to reach new steady state after the change

in reactive gas flow.

2. Model

The dynamic model is constructed in a similar way to

classical Berg’s model [1]. However, several new mechan-

isms are included. For convenience we use the number of

reactive gas (RG) atoms Na as a basic quantity where the

partial pressure pRG is linearly correlated with the number of

RG atoms through the Ideal Gas law (assuming a certain gas

species, constant temperature T and chamber volume V).

2006) 421 – 424

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T. Kubart et al. / Thin Solid Films 515 (2006) 421–424422

2.1. Gas balance

The time variation of the reactive gas amount Na (number of

RG atoms) in the chamber is described by a balance between

consumed and introduced gas

dNa

dt¼ Q

;

i � Q;

t � Q;

s � Q;

p; ð1Þ

where Q;i is the number of introduced RG atoms per second

(i.e. the reactive gas flow). The number of RG atoms

consumed at the target and substrate surfaces is denoted Q;t

and Q;s respectively. Q

;p= ( pRGSpkRG)/kT is the reactive gas

flow pumped away from the system, and the expressions for

Q;t, Q

;s are explained in the following paragraphs. All

parameters are listed and explained in Appendix A.

2.2. Target balance

The thickness of the compound layer at the target surface is

several tens of Angstroms [6]. In this model, the compound

layer at the target surface is assumed to consist of N layers. The

number of reactive gas atoms in the ith layer is given by the

product of the fraction ht(i) of the layer consisting of

compound, the density of metal atoms ns and stoichiometry

of the compound xc.

Eq. (2) describes the gas balance in target topmost layer. At

the target surface (layer 1) compound is formed by chemi-

sorption at the metallic part of the target surface (1�ht(1))

according to the flux f of RG molecules (term I in Eq. (2)). The

fraction of compound is also increased by compound being

exposed from the layer just below the top surface, which

replaces material sputtered away from the target surface (term

II). The last two terms describe the removal of RG from the

compound by sputtering of RG atoms (term III), having the

sputtering yield Ycc, and by knock-on implantation (term IV)

where Ykcc is the number of RG atoms being knocked into the

target surface, or forward sputtering yield, for knock-on

implantation of RG atoms from compound. In this model we

assume that RG atoms are transferred into the target only if

they are implanted to metallic material i.e. with a probability

corresponding to the fraction of the metal (1�ht(N)) in the

bottom layer.

nsxcdht 1ð Þdt

¼ atm 1� ht 1ð Þð ÞfI

þ jxc Ymcht 1ð Þ þ Ymm 1� ht 1ð Þð Þð Þht 2ð ÞII

� jYccht 1ð ÞIII

� jYkcc 1� ht Nð Þð Þht 1ð ÞIV

; ð2Þ

where j is the density of ion impacts.

Eq. (3) describes the balance of the bottom layer. Again, RG

atoms are assumed to be moved to the bottom layer only if

there are free metal atoms, both for knock-on (term I in Eq. (3))

and directly implanted ions (term II). Both processes move RG

to the bottom layer instantly. Due to sputtering from the

surface, the material from the bottom layer is replaced with

pure metal from the target bulk (III).

xcnsdht Nð Þ

dt¼ jYkcc 1� ht Nð Þð Þht 1ð Þ

I

þ jRGkRG 1� ht Nð Þð ÞII

� jxc Ymcht 1ð Þ þ Ymm 1� ht 1ð Þð Þð Þht Nð ÞIII

; ð3Þ

where the current conducted by ionized molecules

jRG ¼gRGpRG

gRGpRG þ gArpArj ð4Þ

is assumed to be directly proportional to the ratio between the

pressure of the working gas pAr, and the reactive gas pRG, and

their ionization probabilities gAr, gRG [7]. Since intermediate

layers only transport the material, the RG atoms variation in the

ith layer is simply the difference between the composition of

incoming and leaving material

xcnsdht ið Þdt¼ jxc Ymcht 1ð Þ þ Ymm 1� ht 1ð Þð Þð Þ ht iþ 1ð Þ� ht ið Þð Þ:

ð5Þ

The total RG gas consumption at the target Q;t is given by

Q;

t ¼ atm 1� h 1ð Þð Þf þ jRGkRG 1� ht Nð Þð Þ � jYccht 1ð Þð ÞAt:

ð6Þ

2.3. Substrate balance

The RG is supplied to the substrate through two different

mechanisms, chemisorption and sputtering. Since the chemi-

sorbed RG mainly consists of thermalised molecules while the

sputtered RG consists of atoms having a somewhat higher

average energy, two different sticking coefficients are intro-

duced in balance Eq. (7), asm for the background molecular

oxygen (term I) and ams for atomic oxygen sputtered from

compound (II), with the latter close to 1. Atomic oxygen

reflected from the substrate surface is considered to thermalise

and contribute to the background RG pressure. Moreover, the

area covered by compound is reduced by deposition of

sputtered metal onto the compound (III)

nsxcdhsdt¼ asm 1� hsð Þf

I

þ ams jYccht 1ð ÞAt

As

1� hsð ÞII

� jxc Ymcht 1ð Þ þ Ymm 1� ht 1ð Þð Þð Þ At

AsIII

: ð7Þ

Growing layer consumes Q;

s RG atoms per second

Q;

s ¼ asm 1� hsð Þf þ ams jYccht 1ð ÞAt

As

1� hsð Þ� �

As: ð8Þ

3. Experiment

The experiments were carried out using a Von Ardenne CS

600 S sputter deposition apparatus. The chamber was

evacuated by a Pfeiffer TMH 520 turbomolecular pump with

0

0.01

0.02

0.03

0.04

0 200 400 600

p O2

[Pa]

t [s]

M-C

C-M

Fig. 1. Measured transition from metallic to compound mode (M–C, from 2 to

2.2 sccm) and opposite transition back to metallic mode (C–M, from 2.5 to

1.5 sccm). In both cases the flow was abruptly changed in time t =100 s.

0

0.01

0.02

0.03

0.04

0.5 1 1.5 2 2.5 3

q [sccm]

Rate [sccm/min]0.05

0.10.20.6

p O2

[Pa]

Fig. 3. Experimentally determined hysteresis curves for various rates of qRGchange.

T. Kubart et al. / Thin Solid Films 515 (2006) 421–424 423

a nominal pumping speed of 520 l/s for N2 to a pressure of

approximately 10�5 Pa prior to experiments. During deposition

the pumping speed was reduced by a throttle valve to achieve

an Ar pressure of 0.47 Pa (3.5 mTorr) at a constant flow of 40

sccm. Oxygen was added by an Aera FC 7800 mass flow

controller, and the partial pressure was measured by a Zirox

XS22.3H lambda probe. The pumping speed for oxygen was

determined to be 130 l/s under deposition conditions. A

constant discharge current of 0.5 A, provided by a Huttinger

PFG 3.000 DC power supply, was applied to a 125 mm

magnetron cathode equipped with an Al target of 99.99%

purity.

4. Results and discussion

Values of sputtering yield were determined from Trim

simulations, while target and receiving areas were taken from

[2]. The values of all parameters are shown in Appendix A.

In order to investigate the dynamic behaviour, the process

response to an abrupt change in the flow of reactive gas was

studied. Two cases were measured, first the flow was increased

from a value corresponding to operation inside the hysteresis

region to outside the hysteresis. The dynamics of this transition

from metallic to compound mode is illustrated in Fig. 1 by the

curve denoted M–C. It has been observed that the time to reach

0

0.01

0.02

0.03

0.04

0 100 200 300 400t [s]

C-M

M-C

p O2

[Pa]

Fig. 2. Simulated transition from metallic to compound mode (M–C, from 2 to

2.3 sccm) and back (C–M, from 2 to 1.3 sccm). The flow of reactive gas was

changed in time t =100 s.

0

0.01

0.02

0.03

0.04

0.5 1 1.5 2 2.5 3q [sccm]

Rate [sccm/min]0.05

0.10.20.6

p O2

[Pa]

Fig. 4. Hysteresis curves calculated for different rates of RG flow change.

steady state is significantly increased when the process moves

to an operating point close to the hysteresis border. When the

upper flow is just above the transition edge, it took more than

400 s to reach steady state. The same trend can be observed in

results from simulation (M–C curve in Fig. 2). The time it

takes to reach steady state according to the simulations is

however significantly lower, indicating that either the input

values are somewhat incorrect, the simplifications are too

crude, or that there are further mechanisms that are needed to

be taken into account in the dynamic modelling.

Similar experiments were carried out when the process was

shifted from compound state to metallic. The transition is

illustrated in Fig. 1, the curve is denoted C–M. In this case, the

time to reach the steady state in metallic mode is given by the

time it takes to remove the compound layer from target surface.

The different response time for the switching from metallic to

compound mode as compared to switching from compound to

metallic mode is explained by the fact that the removal time of

a compound layer is not necessarily equal to the build up time

of the same layer. The shape of simulated curve again shows

the same trend (Fig. 2).

A very important issue concerns the reproducibility and

comparability of results measured by different experimental-

ists. With modern feedback control systems, hysteresis curves

may be measured completely automatically. Such experimen-

tally obtained curves are shown in Fig. 3 and the corresponding

simulated curves are shown in Fig. 4. It can be seen in Figs. 3

T. Kubart et al. / Thin Solid Films 515 (2006) 421–424424

and 4, that if the rate of change of reactive gas flow is too high,

the measured hysteresis width is substantially wider than for

the same system when the flow is changed at another rate.

Since transition time is different for different apparatus, one

should be aware of this effect when comparing results from

different systems and/or different articles. Accuracy of mea-

sured curve can be verified by a very slow measurement

around previously determined critical flows. Similar effect may

influence the results when the pressure vs. flow curve is

measured by means of a partial pressure feedback control

system where observed curves differ from each other depend-

ing on whether the pressure is decreased or increased [8].

The model will predict the dynamic behaviour more

accurately if some of the mechanisms are treated more

accurately. For instance, the parameter determining the time

constant of a process is ion current density which is considered

to be constant over whole target in our model. In reality,

however, the current density is distributed highly nonuniformly

over the target which means there are areas with substantially

lower erosion rate. Such areas of the erosion track may need

significantly longer time to reach steady state than the

simulations indicate, since the time to change composition of

target surface layer correlates with ion current density.

5. Conclusions

A model describing the dynamic behaviour of the reactive

sputtering process has been described. The model takes into

account two different implantation mechanisms. First, the

implantation that occurs as a result of ionized reactive gas

colliding with the target and secondly, the implantation that

occurs when argon ions collide with the target surface and

knock-in the chemisorbed reactive gas at the top surface.

Moreover, the model assumes that all sputtered species from

the target are atoms. The model can correctly describe the

general dynamic behaviour and the trends that have been

observed from experiments. Moreover, some implications of

dynamic effects during measurement of the hysteresis curve

have been demonstrated. A difference in the absolute time to

reach steady state in experiment and simulations has however

been observed in some cases. Some improvements have been

suggested to overcome these deviations.

Appendix A

The following simulation parameters were used in this

work: target area At =0.014 m2, substrate area As=0.6 m2,

thickness of implanted layer N =16 atomic layers, sticking

coefficient of the RG on the target surface atm=0.3, on the

substrate asm=0.3, sticking coefficient of atomic oxygen

ams=1, sputtering yield of metal from the metallic surface

Ymm=0.8, sputtering yield of metal from the compound

Ymc=0.03, sputtering yield of the RG atoms Ycc=0.09, forward

sputtering yield Ykcc=0.27, stoichiometry of the compound

xc =1.5, ns =3.39e+16 m2, T =300 K, discharge current

J =0.53 A, pumping speed Sp=0.130 m3/s, chamber volume

V=100 l, ionization efficiency gRG=gAr=1, argon pressure

pAr=0.5 Pa, atoms per RG molecule kRG=2.

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