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WDS'07 Proceedings of Contributed Papers, Part II, 212–217, 2007.
ISBN 978-80-7378-024-1 © MATFYZPRESS
Measuring the Ion Current to the Substrate During
Deposition of Thin Films by Hollow Cathode Plasma
Jet
P. Virostko and M. Tichý
Charles University in Prague, Faculty of Mathematics and Physics, Czech Republic.
Z. Hubička, M. Čada, and P. Adámek
Institute of Physics of the Academy of Sciences of the Czech Republic, v.v.i., Prague, Czech
Republic.
Abstract. Measurements of positive ion flux to the substrate during deposition
of thin films by hollow cathode plasma jet are presented. Different methods of
obtaining negative bias of substrate and measuring the resulting ion flux are
compared and discussed — pulsed DC bias, RF bias, and pulse-modulated RF bias
of substrate. For determination of current and voltage waveforms on the substrate
when the RF bias is applied, an electric circuit model of power feed line to the
substrate is presented.
Introduction
A knowledge of plasma parameters and parameters describing an interaction of plasma with a
substrate during deposition of thin films contributes to better understanding of deposition processes as
well as to the reproducibility of deposited films. An important parameter that describes the plasmasubstrate interaction is a positive ion flux to the substrate. A bombardment of substrate with positive
ions is often used to modify properties of deposited films. To enhance the bombardment, the substrate
is negatively biased with respect to the bulk plasma potential by applying an external voltage to the
substrate. For conducting substrate and deposited film, a DC voltage is used. For substrate from
dielectric material or for dielectric deposited film, the negative DC bias is created by applying radiofrequency (RF) voltage to the substrate through a blocking capacitor.
To obtain the ion current for the RF bias, it is necessary to determine RF current and voltage
waveforms directly on the substrate, but RF current and voltage probes cannot be placed directly onto
the substrate in the vacuum chamber. We present an electric circuit model of the power feed line to
the substrate for determination of RF current and voltage waveforms on the substrate from RF current
and voltage waveforms measured outside of the reactor chamber. We used a shielded feed line to the
substrate, which we modeled as a coaxial transmission line with a capacitance on its end accounting
for a parasitic capacitance between the substrate and a grounded reactor. The model is more realistic
than for example a circuit model of an RF power feed line by Spiliopoulos et al. [1996], where the feed
line was characterized as an inductor, thus neglecting the length of the feed line in comparison with the
wavelength of RF voltage waveform. On the other hand, our model is simpler than a general two-port
circuit model and a procedure to determine the impedance between the measuring point and the RF
electrode proposed by Sobolewski [1992].
The ion current to the substrate was determined from the RF current waveform on the substrate
according to Sobolewski [1998] as the current at time t0 when the simultaneously measured RF voltage on
the substrate reached its minimum. The ion current measured using this method for continuous RF bias
was compared to the ion current measured for pulsed DC bias, and for pulse-modulated RF bias using
the method of Braithwaite et al. [1996]. In this case, the ion current is determined from discharging of
a blocking capacitor when the RF voltage is turned off. The ion current was measured in the hollow
cathode plasma jet deposition system [Bárdoš et al., 1993; Hubička et al., 2003] for different substrate
bias and discharge conditions.
Experimental setup
A schematic view of the hollow cathode plasma jet system for thin film depositions can be seen in
Fig. 1. The main part of the deposition system is a nozzle made of material to be sputtered. The nozzle is
connected to a power generator. A working gas flows through the nozzle and an intensive hollow cathode
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VIROSTKO ET AL.: MEASURING THE ION CURRENT TO THE SUBSTRATE
Figure 1. The experimental setup of the hollow cathode plasma jet deposition system.
Figure 2. A schematic view of power feed line to the substrate for RF bias. RF GEN — pulse-modulated
RF generator, MATCH — matching unit, R0 — auxiliary resistor, C — blocking capacitor, URF , IRF
— RF voltage and current sensors, Zc — shunt circuit, Us,1 — oscilloscopic probe, Zl , ll — coaxial
transmission line, Cp — parasitic capacitance between the substrate and the grounded reactor.
discharge is ignited at the nozzle outlet. The discharge is carried out into a grounded continuously
pumped UHV reactor and a plasma jet is formed. Downstream from the nozzle a substrate is placed, on
which a thin film is deposited. A DC mode of discharge excitation was used, with titanium nozzle, and
argon as the working gas. The flow rate of argon was QAr = 138 sccm and the pressure in the reactor
was held at p = 2.7 Pa. Discharge currents were set in the range ID = 0.1–0.6 A, corresponding to power
PD = 20–120 W absorbed in the discharge.
A planar substrate of circular cross-section with diameter ds = 40 mm was placed 34 mm downstream
from the nozzle, coaxially with the nozzle. A cylindrical Langmuir probe with diameter dp = 380 µm
and length lp = 3.5 mm was used to determine the plasma parameters. The probe was placed 18 mm
downstream from the nozzle, 20 mm from the joint axis of the nozzle and the substrate. The substrate
was connected either to a pulsed DC source through a resistor R, or to a pulse-modulated RF (frequency
13.56 MHz) generator through a blocking capacitor C (see Fig. 1). In case of pulsed DC bias, the
substrate voltage was square-modulated with repetition frequency 35 kHz. The substrate was held on
negative voltage UDC,S in the active part of modulation cycle, and it was grounded in the off-time. The
pulsed DC voltage was used because of possibility to measure the ion current also for thin dielectric
deposited layers.
A schematic view of electrical circuit used for RF bias of the substrate can be seen in Fig. 2.
An RF generator was connected through a matching unit to a capacitor C, on which a negative DC bias
was induced due to non-linear properties of sheath around the substrate. The RF voltage and current
waveforms URF (t), IRF (t) were measured by a calibrated voltage sensor and a Rogowski coil. A tunable
shunt circuit [Sobolewski, 1992] was used to compensate an influence of parasitic capacitance Cp between
the substrate and the grounded reactor. The impedance Ẑc 1 of the shunt was set to minimize the
1 The
hat indicates a complex quantity.
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VIROSTKO ET AL.: MEASURING THE ION CURRENT TO THE SUBSTRATE
measured RF current amplitude IRF when the RF voltage was applied to the substrate without burning
discharge. The voltage sensor, the Rogowski coil, and the shunt circuit were placed outside of the reactor
chamber as close as possible to a vacuum feedthrough for the power feed line to the substrate. The power
feed line in the reactor between the feedthrough and the substrate was shielded. An oscilloscopic probe
was mounted on the feed line before the feedthrough to measure a decay of substrate voltage Us1 (t) after
the RF bias was turned off in the modulation cycle. The repetition frequency of the modulation cycle
was 200 Hz (period 5 ms) and the active part of RF bias was 1 ms.
Methods of determination of ion current to the substrate
The ion current to the substrate was obtained directly from the voltage drop on the resistor R in
the active part of modulation cycle for the pulsed DC bias of substrate. When the RF voltage through
a blocking capacitor C was used, the DC bias of substrate UDC,S was determined as the time averaged
value of voltage Us1 (t). First method to obtain the ion current to the substrate for the RF bias was the
method by Braithwaite et al. [1996] that requires pulse-modulation of the RF voltage. They have shown
that the ion current Ii can be determined from the slope of Us1 (t) voltage decrease, when the RF voltage
is turned off, as:
dUs1
Ii = C
.
(1)
dt
A blocking capacitor with the capacitance C = 23.5 nF was used so that the time of discharging from
the DC bias UDC,S to the plasma potential Vpl was τ = 0.2–3.5 ms for all discharge and bias conditions.
The ion current was determined according to Eq. (1) from the first 100 µs after the RF voltage was
turned off, where the decay of Us1 (t) was linear.
Second method to determine the ion current for the RF bias was a method by Sobolewski [1998], in
which the ion current is determined as the current to the substrate Is (t) at time t0 when the simultaneously measured RF voltage on the substrate Us (t) reaches its minimum. The advantage of this method
is that it does not require the RF voltage to be switched off. A following electric circuit model was used
to determine the RF voltage and current waveforms on the substrate Us (t), Is (t) from the waveforms
URF (t), IRF (t) measured on the feed line outside of the reactor chamber. The power feed line between the
measuring point and the substrate was considered as a lossless homogeneous coaxial transmission line of
length ll and characteristic impedance Ẑl , with a capacitance Cp on its end accounting for parasitic capacitance between the substrate and the reactor (see Fig. 2). Complex amplitudes of Fourier components
ˆ
of voltage and current waveforms Û (x), I(x)
in a transmission line are described by equations:
Û (x) = V̂1 exp (−γ̂x) + V̂2 exp (γ̂x) ,
V̂1
V̂2
ˆ
I(x)
=
exp (−γ̂x) −
exp (γ̂x) ,
Ẑl
Ẑl
(2)
where x is the position along the transmission line, V̂1 and V̂2 are the amplitudes of forward and backward
wave in the line, and γ̂ is the wave propagation constant. For a lossless homogeneous transmission line,
Ẑl is real and frequency independent, and γ̂ is imaginary and linearly dependent on frequency. We chose
x = 0 at the position of measurement of URF (t) and IRF (t). The Eqs. (2) can be for x = 0 rewritten to:
Û (0) = ÛRF = V̂1 + V̂2 ,
ˆ = IˆRF − ÛRF = V̂1 − V̂2 .
I(0)
Ẑc
Ẑl
Ẑl
(3)
A current drawn by the shunt circuit ÛẐRF has to be included in Eq. (3). The Fourier amplitudes of
c
voltage and current waveforms at the substrate, which is at the position x = ll , are described by:
Ûs = Û(ll ) = V̂1 exp (−γ̂ll ) + V̂2 exp (γ̂ll ) ,
ˆ l ) − Ûs = V̂1 exp (−γ̂ll ) − V̂2 exp (γ̂ll ) − Ûs , (4)
Iˆs = I(l
Ẑp
Ẑl
Ẑl
Ẑp
where Ẑp is the parasitic impedance represented by the capacitor Cp ; the current drawn by this parasitic
impedance ẐÛs is included in Eq. (4). Assuming the shunt impedance Ẑc , the parameters of the transp
mission line Ẑl , γ̂ll , and the parasitic capacitance Cp are known, the Us (t) and Is (t) waveforms can be
determined as follows. The Fourier components ÛRF , IˆRF are computed from the measured waveforms
Us (t), Is (t) for the base frequency (13.56 MHz) and its harmonics. Then the amplitudes V̂1 , V̂2 are
determined according to Eq. (3) and the Fourier components of waveforms on the substrate Ûs , Iˆs are
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VIROSTKO ET AL.: MEASURING THE ION CURRENT TO THE SUBSTRATE
a)
b)
Figure 3. a) RF voltage and current waveforms URF (t), IRF (t), measured on the power feed line for
discharge current ID = 0.6 A and DC bias UDC,S = −110 V; b) RF voltage and current waveforms Us (t),
Is (t) on the substrate determined from URF (t), IRF (t) using the presented electric circuit model. At time
t0 , when the voltage Us reaches its minimum, the ion current to the substrate Ii is determined from Is .
computed from Eq. (4). Finally, the waveforms Us (t) and Is (t) are obtained by inverse Fourier transform
from Ûs , Iˆs for the base frequency and its harmonics.
The impedance of shunt Ẑc was measured by an impedance meter for the base frequency and its
harmonics. To determine Ẑl , γ̂ll and Cp , the following equation for change of complex impedance along
the transmission line of length ll was used:
ẐRF =
ÛRF
Ẑs + Ẑl tanh (γ̂ll )
=
,
ˆ
s
IRF
1 + Ẑ
tanh (γ̂ll )
Ẑ
(5)
l
where ẐRF is the measured complex impedance at x = 0 and Ẑs is the impedance at x = ll .
The impedance ẐRF was measured at 13.56 MHz without burning discharge for three different impedances
Ẑs – for bare substrate, for substrate and capacitance C1 connected between the substrate and the
grounded substrate support, and for substrate and another capacitance C2 connected. The impedance
Ẑs was represented by a capacitance Cp , by a capacitance Cp + C1 , and by a capacitance Cp + C2 respectively. By simultaneously solving Eq. (5) for the three pairs of measured and end impedances ẐRF
and Ẑs , the parameters Ẑl , γ̂ll and Cp are obtained.
Results and discussion
The determined model parameters were: Cp = 12 pF, Ẑl = 107 Ω, and γ̂ll = n · 0.437j, where
n is the number of harmonic and j is the imaginary unit. An example of measured RF voltage and
current waveforms URF (t), IRF (t) and calculated waveforms at the substrate Us (t), Is (t) is in Fig. 3.
The depicted waveforms were measured for the hollow cathode discharge current ID = 0.6 A and DC
bias of substrate UDC,S = −110 V.
A dependence of positive ion flux to the substrate ji on the DC bias UDC,s measured for the discharge
current ID = 600 mA is depicted in Fig. 4 and a dependence of the ion flux on the discharge current ID
measured for the bias UDC,s = −100 V is depicted in Fig. 5. The ion flux determined for RF bias from
the current Is at time t0 is in Figs. 4a, 5a, and the ion flux determined for pulsed DC bias and for pulsemodulated RF bias from discharging of blocking capacitor is in Figs. 4b, 5b. The ion fluxes determined
for DC bias and pulse-modulated RF bias correspond well in the range UDC,s = −80 V – 0 V (see Fig. 4b).
In this range, the ion flux reached an approximately constant value, which is in agreement with the theory
for saturated ion current to a planar Langmuir probe. Below the value UDC,s = −80 V, there was a
step-like change of ion flux to a higher value for the pulsed DC bias, but not for the pulse-modulated
RF bias. This difference was also observed for different discharge currents ID at UDC,s = −100 V (see
Fig. 5b). Thus the rise of the measured current is caused by a process dependent on the energy of ions
impinging on the substrate and not by the discharge itself. Further investigation is needed to assess the
effect in more detail. However, we can conclude that the ion flux is determined unambiguously by these
two methods for UDC,s from −80 V to 0 V.
The ion flux determined in the RF bias was several times higher than for pulsed DC bias and pulsemodulated method for RF bias (compare Figs. 4a, 5a with Figs. 4b, 5b). One possible explanation for
this is an influence of the RF voltage on the plasma (e.g. by an additional ionization around the RF
biased substrate). In the Fig. 6, plasma parameters measured simultaneously with the ion fluxes by the
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VIROSTKO ET AL.: MEASURING THE ION CURRENT TO THE SUBSTRATE
a)
b)
Figure 4. The ion flux to the substrate ji for the discharge current ID = 600 mA and different DC
bias of substrate UDC,s . a) ion flux determined for RF bias from the current Is at time t0 ; b) ion flux
determined for pulsed DC bias and for pulse-modulated RF bias from discharging of blocking capacitor.
a)
b)
Figure 5. The ion flux to the substrate ji for the DC bias UDC,s = −100 V and different discharge
current ID . a) ion flux determined for RF bias from the current Is at time t0 ; b) ion flux determined for
pulsed DC bias and for pulse-modulated RF bias from discharging of blocking capacitor.
a)
b)
c)
Figure 6. Plasma parameters measured in the bulk plasma simultaneously with the ion fluxes depicted
in Fig. 5. Squares — for pulsed DC bias in the active pulse; circles — for RF bias; triangles — for
pulse-modulated RF bias at time τ = 100 µs after the end of active pulse. a) electron density ne ; b)
electron temperature Te ; c) plasma potential Vpl .
Langmuir probe in the bulk plasma are depicted. The plasma parameters were measured in the middle
of active pulse for pulsed DC bias, for the RF bias, and at time τ = 100 µs after the end of active pulse
for the pulse-modulated RF bias, when the ion current was calculated in this method. It can be seen that
the RF bias influenced the bulk plasma parameters of the continuously burning DC discharge. When
compared between the RF bias present on the substrate and the off-time after the RF pulse, the electron
density, electron temperature, and plasma potential increased when the RF bias was on. The higher
charged particle density and electron temperature mean higher ion current to the substrate. However,
the electron density and electron temperature were also higher for the pulsed DC bias but the ion flux
is several times lower for the DC bias than for the RF bias.
Another source of error might be the procedure to determine the ion flux for the RF bias. The calculated waveforms on the substrate Us (t), Is (t) (Fig. 3b) are comparable to waveforms measured by Gahan
and Hopkins [2007] for an RF electrode in an inductively coupled low-temperature plasma. They used
a more complex general two-port network method by Sobolewski [1992] to describe the power feed line
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VIROSTKO ET AL.: MEASURING THE ION CURRENT TO THE SUBSTRATE
and parasitics between the point of measurement and the electrode surface. However, when determining
the ion flux from the current and voltage waveforms on the substrate Is (t), Us (t), the waveforms IRF (t),
URF (t) have to be measured very precisely. Test calculations showed that the precision of measurement
of current amplitude IRF and of the phase between the current and voltage φRF at the fundamental
frequency have the main influence on the resulting ion flux. The relative error of current and voltage
amplitude for 13.56 MHz was determined to be 10 %, and the error of measurement of the phase between
the current and voltage was determined to be less than 5◦ for 13.56 MHz. When the amplitudes and the
phase of the measured waveforms were varied in the range of determined errors, the ion flux changed
significantly — it was between 0.5 to 1.5 times of original value. In this way, the relative error of ion
flux measurement for the continuous RF bias method was estimated to be 50 %.
The ion current to the substrate is also assumed to be constant in time in the method. This
assumption is valid for ion plasma frequency ωi ≪ ω the angular frequency of the RF voltage. In
our case, the ion plasma frequency calculated for argon ions for the highest charged particle density
was ωi = 3.6 · 107 rad·s−1 , which is already comparable to the angular frequency of the RF voltage
ω = 8.5 · 107 rad·s−1 . The frequency dependence of the method was comprehensively discussed by
Sobolewski [2001]. He showed that for ωi ≈ ω the ion current and the ion density in the sheath are
changing in time and the ion current determined from Is (t) at time t0 is different from the average ion
current. For similar low-temperature plasma, he observed that the RF method yielded the ion flux up
to two times higher than the pulsed DC method when the ion plasma frequency was close to the angular
frequency of the RF bias. The effect of several times higher ion flux determined by the RF method can
therefore be explained partly by the heating of plasma when the RF is on, partly by the inaccuracy of ion
flux determination, and partly due to ion plasma frequency being already comparable with the driving
frequency, which yield higher values of ion flux as was shown by Sobolewski [2001].
Conclusion
Measurements of positive ion flux to the substrate during deposition of thin films by hollow cathode
plasma jet are presented. Different methods of obtaining negative bias of substrate and measuring the
resulting ion flux are compared. For determination of the current and voltage waveforms on the substrate
when the RF bias is applied, an electrical model of power feed line to the substrate is presented. Ion flux
determined for RF bias according to Sobolewski [1998] is much higher than the ion flux determined for
the same conditions for pulsed DC bias and for pulse-modulated RF bias determined from discharging
of a blocking capacitor. This can be partly attributed to the additional ionization and heating of plasma
around the substrate by the RF voltage, which can be seen from Langmuir probe measurements. Other
contribution to the higher ion flux determined for the RF bias can be a relatively high inaccuracy of the
RF bias method, and the fact that the ion flux is not constant during one period of RF voltage, because
the ion plasma frequency is comparable to the angular frequency of RF voltage.
Acknowledgments. This work was supported by project KAN400720701 of the Academy of Sciences of
the Czech Republic and by grant GACR 202/06/0776 of the Czech Science Foundation.
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