Plasma diagnostics and simulations
Determination of titanium atom and ion
densities in sputter deposition plasmas by
optical emission spectroscopy
Tasks
1. Measure the overview optical emission spectrum (300 – 800 nm) in dcMS and HiPIMS discharge
for two sets of experimental conditions – 1 Pa, 0.5 kW and 5 Pa, 1.5 kW; identify the
spectral lines in the ranges of 320 – 340 nm, 360 – 380 nm, 430 – 480 nm and 690 – 800 nm.
2. Determine the titanium atom and ion number densities of HiPIMS discharge at 5 Pa and
1.5 kW from two chosen sets of spectral lines measured in task 1.
3. Measure the intensities of selected titanium atom spectral lines in dcMS as a function of
applied power for the pressure of 5 Pa and as a function of working pressure for the applied
power of 1.5 kW. Determine the evolution of titanium atom number densities using
EBF method and compare it to the evolution of titanium atom spectral line (399.86 nm)
intensity.
4. Measure the evolutions of titanium atom and ion spectral lines as a function of duty cycle
(from dcMS to HiPIMS discharge) and determine the titanium atom and titanium ion
number densities.
5. Study the reproducibility of the experiment. Measure a selected spectra 10 times with only
1 accumulation and ones with 10 accumulations. Compare the evolution of spectral lines
intensities and calculated number densities for averaged and non-averaged spectra.
Introduction
Plasma is optically active medium, where the light can be either generated or absorbed. Usually,
the ideal plasma is assumed, where the light is only generated or only absorbed while the second
effect is neglected. However, in the real plasma both events can occur simultaneously. The
process in which some of the radiation emitted by plasma is absorbed by the plasma itself is
called self-absorption. The effect of self-absorption causes the decrease of the plasma emissivity.
Only spectral transition ending at the energy state with the long time of life such as ground or
metastable states can suffer from the self-absorption. The simulation of intensities of two titanium
atom resonant lines computed not taking and taking into account the effect of self-absorption is
depicted in figure 1a) and 1b), respectively. The self-absorption depends on the line strength,
length of the absorbing media and on the number of particles capable to absorb the emitted
photon.
Effective branching fractions method
Theory
The method of effective branching fractions (EBF method) was developed originally for measurement
of metastable and resonant state densities of argon atoms from self-absorbed optical
Laboratory guides (verze June 26, 2019) 2
0 1 2 3 4 5 6 7 8 9 1 0
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
4 5 0Intensity[a.u.]
T i 3 9 8 . 1 7 n m
T i 4 0 0 . 8 9 n m
L [ c m ]
a )
0 1 2 3 4 5 6 7 8 9 1 0
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
4 5 0
Intensity[a.u.]
T i 3 9 8 . 1 7 n m
T i 4 0 0 . 8 9 n m
L [ c m ]
b )
Figure 1: Simulated evolution of two titanium atom resonant spectral lines intensities with the
length of optically active media a) without self-absorption and b) with self-absorption of the
radiation.
emission spectra [1, 2]. In contrast to absorption methods measuring the attenuation of light
passing through the plasma from an external light source, self-absorption methods consider the
studied plasma as both light emitting and absorbing medium. When optical depth of a transition
is kL 1 (k is absorption coefficient and L is plasma depth in the direction of observation),
photons emitted in the discharge may be significantly re-absorbed by atoms in the lower state
of the transition before escaping the plasma. Unlike classical self-absorption methods comparing
intensities of transitions with the same lower level, the EBF method compares intensities of
transitions from a common upper level i by means of branching fractions
Γij =
Φij
l Φil
, (1)
where Φij is photon emission rate of transition i → j and the summing is performed over all possible
lower states l. In the absence of absorption, the photon emission rates are simply proportional
to the product of Einstein coefficient for spontaneous emission Aij and the number of atoms in
the excited states. The branching fractions equal
Γfree
ij =
Aij
l Ail
, (2)
the branching fractions for absorption-free plasma are therefore simply determined by the Einstein
coefficients of spontaneous emission.
When the self-absorption of radiation occurs in plasma, apparent branching fractions of escaping
radiation may be altered, since the light of different transitions is absorbed to a different extent.
The self-absorption in plasma is often estimated using the concept of escape factors developed by
Holstein [3]. The effective branching fraction of spectral line in the presence of self-absorption is
calculated as
Γeff
ij =
g(k0
ijL)Aij
l g(k0
ilL)Ail
, (3)
where g is the (radiation) escape factor depending on the absorption coefficient k0
il evaluated at the
spectral line centre and L is a sensed plasma depth. The EBF method was applied on magnetron
sputtering system [4], where the accurate evaluation of self-absorption is a non-trivial problem.
In order to keep the method simple, the commonly used approximative formula of Mewe [5] was
adopted
Laboratory guides (verze June 26, 2019) 3
g(k0
ijL) =
2 − e−k0
ijL/1000
1 + k0
ijL
. (4)
The formula assumes a uniform spatial distribution of atoms in both upper and lower states of
transition. In our case, the distributions of atoms in chamber are inhomogeneous with most of the
atoms located just above the racetrack. When the optical fibre is directed along the tangent line
of the race track (and parallel with the target), the fibre senses a region of enhanced density of a
depth L. This value is taken into calculations as the absorption path; however, the uncertainty of
this absorption path determination can contribute significantly to the measurement error. Since
Doppler broadening is the dominant broadening mechanism at pressure of ≈ 1 Pa, the absorption
coefficient k0
il at the line centre is calculated as
k0
ij =
λ3
ij
8π3/2
m0
2kbT
gi
gj
Aijnj, (5)
in which m0 is atomic mass, λij wavelength of the transition in the line center, T is kinetic
temperature of atoms and gi and gj are statistical weights of upper and lower level, respectively.
The density of the lower state nj is the searched unknown quantity.
In order to determine the density of a specific atomic state, intensities of spectral lines of
spontaneous transitions ending in the studied state and of their competitive transitions from the
same upper level must be measured. Since such transitions will end on several lower states, several
densities nj are typically simultaneously determined. It is recommended to measure more spectral
lines and fit the effective branching fractions (3) by least squares method to the measured values
Γexp
ij =
Iij/hνij
l Iil/hνil
. (6)
hνij are photon energies. The measured intensities Iij should be corrected for spectrometer
spectral sensitivity and integrated over the spectral profiles.
For ease of use the EBF fit software, enabling the calculation of branching fractions from
measured line intensities and their fit by the least squares method, was developed [6]. The software
enables us to determine the titanium atom and ion ground state density from optical emission
spectra. A database of spectral lines with wavelengths, Einstein coefficients, statistical weights
etc. needed for calculation of branching fractions of titanium atom and ion is included in the
software.
Application to ground state Ti atoms
The ground state of titanium neutral atom, originating from electron configuration 1s22s22p63s2
3p63d24s2, is a 3F2. Other levels a 3F3 and a 3F4 of the triplet term lie 0.021 and 0.048 eV above
the ground state, respectively.
The optical spectrum of titanium in UV-VIS range is plentiful. The selected spectral lines
sorted according to their upper state, fulfilling the condition of one transition going to the ground
state, are summarized in 1. The utilizable lines have to meet several requirements: high transition
probability (Einstein coefficient of spontaneous emission), no overlapping with surrounding spectral
features in the measured spectra, ease of measurement and instrument calibration etc. Close
wavelengths provide a low impact of varying instrument sensitivity on the measured intensity
values.
The selected transitions of neutral Ti atom with their upper and lower levels are shown in
a diagram in 3a). In order to calculate the effective branching fractions from formula (3), the
densities of all three a 3F levels must be taken into account. Since the energy splitting of the
levels is low, the levels are assumed to be in local thermodynamic equilibrium with the densities
following the Boltzmann law
Laboratory guides (verze June 26, 2019) 4
nj = n0
gj
g0
e
−
Ej−E0
kbTexc ,
where Texc is excitation temperature of a 3F triplet state and n0 is density of a 3F2 level. By fitting
13 branching fractions of selected transitions (see table 1), n0 and Texc quantities are determined.
Since populations of a 3F3 and a 3F4 levels are not negligible, the sum of densities of all three
levels is taken as the resulting density of titanium atoms [Ti].
Application to ground state Ti ions
The ground state of singly ionized titanium, originating from electron configuration 1s22s22p63s2
3p63d24s, is a 4F3/2. Other levels a 4F5/2, a 4F7/2 and a 4F9/2 of the quartet term lie 0.012, 0.028
and 0.049 eV above the ground state, respectively.
Spectral lines of Ti ion sorted according to their upper state, fulfilling the condition of one
transition going to the ground state, are summarized in table 2, 19 selected transitions with their
upper and lower levels are shown in a diagram in 3b). In order to calculate the effective branching
fractions, densities of all a 4F levels must be evaluated. As in case of neutral titanium, Boltzmann
law is taken to decrease the number of fitted parameters. The sum of densities of all four levels is
taken as the resulting density of titanium ions [Ti+].
Magnetron sputtering
Magnetron sputtering belongs to the group of physical vapor deposition (PVD) techniques, which
generally involve the condensation of vapor created from a solid state source, often in the presence
of a glow discharge or plasma. Nowadays, in many cases the magnetron sputtered films
outperform the films deposited by other PVD processes offering the same functionality as much
thicker films produced by other coating techniques. Thin films deposited by magnetron sputtering
find application in numerous technological domains including hard, wear-resistant, optical,
corrosion-resistant coatings or coatings for microelectronics, etc.
The sputtering process is shown in figure 2. The ions are generated in plasma and are accelerated
by the electric field towards the target surface. The incident ion bombards the target surface
causing collision cascade resulting in physical ejection of atoms or small clusters of atoms from
the target surface which are deposited onto substrate.
neutralized atom
secundary electron
sputtered atom sputtered atom
surface
incident ion
Figure 2: Diagram of sputtering process.
Before being deposited onto the samples, the film forming species should follow a certain
pathway. On their pathway these particles may be ionized, neutralized or they can chemically
react with other particles in the gas phase. During their transport, it is also very likely that they
exhibit gas-phase collisions with background gas atoms.
High power impulse magnetron sputtering (HiPIMS) is one of the PVD techniques. The
applied power is focused into a short pulse (microseconds or 10’s of microseconds) or into a long
Laboratory guides (verze June 26, 2019) 5
pulse (hundreds of microseconds), but both with duty cycles less than 5%. In HiPIMS, very
high instantaneous power density (several kW cm−2) is applied to the target, while keeping an
averaged power density similar to the one used in conventional dc magnetron sputtering (dcMS).
Higher actual applied power results in higher plasma density and hence higher fraction of ionized
sputtered species compared to dcMS, which is the major advantage of HiPIMS. Coatings prepared
by HiPIMS have improved properties in terms of film density, adhesion, surface roughness and
higher hardness.
Experimental setup
The measurements is done on the magnetron sputtering system Alcatel SCM 650. The sputtering
system is equipped with Ti target (99.95% purity) of rectangular shape (25×7.5 cm) and unbalanced
magnetic field configuration. The discharge is powered by a Melec SIPP 2000 HiPIMS
generator operated in both dcMS and HiPIMS mode. The Melec generator is equipped with a
current and voltage probe for electric measurements.
The deposition chamber is evacuated by a turbo-molecular pump backed with a Roots pump
down to a pressure of 10−4 Pa. The buffer gas is argon (99.999%). The working pressure can be
varied from 0.3 Pa to 5.4 Pa by the gas flow-meter (1 – 140 sccm) and measured by MKS Baratron.
The optical emission spectroscopy (OES) is carried out using a Andor Shamrock spectrometer
(Czerny-Turner configuration) with 0.75 m focal length, 2400 grooves.mm−1 grating and CCD
detector. The total integration time is set to achieve sufficient line intensities. The optical fiber
is placed on a movable holder to collect the light from 10 mm above the target and it is directed
along the tangent line of the racetrack paralell with the target to achieve the longest optical depth.
Measurement and data processing
Measurement
• Turn on spectrometer.
• Turn on cooling of magnetron and generator.
• Set working pressure.
• Turn on generator (program Melec).
• Set arc limit.
• Set operation mode (dcMS, HiPIMS), and pulse parameters.
• Set discharge parameters (voltage, current, power).
• Ignite discharge.
Data processing
• Identify the selected spectral lines and determine their intensities (for example using Spectrum
analyzer [8, 9]).
• Create *.txt file with two columns - wavelength and corresponding intensity
• Determine [Ti] or [Ti+] using EBF fit, L ≈ 23 cm, T ≈ 500 K, fit also Texc.
• For spectral line intensity evolution, normalize spectra for the same integration time and
number of accumulations.
Laboratory guides (verze June 26, 2019) 6
References
[1] Schulze M, Yanguas-Gil A, von Keudell A and Awakowicz P 2008 J. Phys. D: Appl. Phys.
41 065206
[2] Boffard J B, Jung R O, Lin C C and Wendt A E 2009 Plasma Sources Sci. Technol. 18
035017
[3] Holstein T 1947 Phys. Rev. 72 1212
[4] Vašina P, Fekete M, Hnilica J, Klein P, Dosoudilová L, Dvořák P and Navrátil Z 2015 Plasma
Sources Sci. Technol. 24 065022
[5] Mewe R 1967 Br. J. Appl. Phys. 18 107
[6] Software EBF fit. http://www.physics.muni.cz/~zdenek/ebffit/
[7] Kramida A, Ralchenko Yu, Reader J and NIST ASD Team 2018. NIST Atomic Spectra
Database (ver. 5.5.6) [Online] http://physics.nist.gov/asd.
[8] Navrátil Z, Trunec D, Šmíd R and Lazar L 2006 Czech. J. Phys. 56 B944–51
[9] Software Spectrum Analyzer http://www.physics.muni.cz/~zdenek/span/
Appendix
Transition λ (nm) Aij (107 s−1) Γij
3d2(3P)4s4p(3P◦) z 5S◦
2 →3d24s2 a 3F2 398.24806 0.45000 0.764
3d2(3P)4s4p(3P◦) z 5S◦
2 →3d24s2 a 3F3 400.96565 0.13900 0.236
3d2(3F)4s4p(1P◦) y 3F◦
2→3d24s2 a 3F2 398.17616 4.42000 0.846
3d2(3F)4s4p(1P◦) y 3F◦
2→3d24s2 a 3F3 400.89273 0.80700 0.154
3d2(3F)4s4p(1P◦) y 3F◦
3→3d24s2 a 3F2 396.28508 0.47100 0.083
3d2(3F)4s4p(1P◦) y 3F◦
3→3d24s2 a 3F3 398.97586 4.48000 0.794
3d2(3F)4s4p(1P◦) y 3F◦
3→3d24s2 a 3F4 402.45709 0.69100 0.122
3d2(3F)4s4p(1P◦) y 3F◦
4→3d24s2 a 3F3 396.42694 0.36400 0.070
3d2(3F)4s4p(1P◦) y 3F◦
4→3d24s2 a 3F4 399.86366 4.81000 0.930
3d3(4F)4p y 3D◦
2 →3d24s2 a 3F2 392.98740 0.85100 0.197
3d3(4F)4p y 3D◦
2 →3d24s2 a 3F3 395.63343 3.46000 0.803
3d3(4F)4p y 3D◦
3 →3d24s2 a 3F3 392.45268 0.81000 0.141
3d3(4F)4p y 3D◦
3 →3d24s2 a 3F4 395.82016 4.88000 0.852
Table 1: Einstein coefficients of spontaneous emission and branching fractions for transitions of
isolated titanium atom [7]. Lines are divided into groups with a common upper level.
Laboratory guides (verze June 26, 2019) 7
Transition λ (nm) Aij (107 s−1) Γij
3d2(3F)4pz 4G◦
5/2 →3d2(3F)4s a 4F3/2 338.37584 13.90000 0.833
3d2(3F)4p z 4G◦
5/2→3d2(3F)4s a 4F5/2 339.45721 2.69000 0.161
3d2(3F)4p z 4G◦
7/2→3d2(3F)4s a 4F5/2 337.27927 14.10000 0.830
3d2(3F)4p z 4G◦
7/2→3d2(3F)4s a 4F7/2 338.78334 2.81000 0.165
3d2(3F)4p z 4G◦
9/2→3d2(3F)4s a 4F7/2 336.12121 15.80000 0.920
3d2(3F)4p z 4G◦
9/2→3d2(3F)4s a 4F9/2 338.02766 1.37000 0.080
3d2(3F)4p z 4F◦
3/2 →3d2(3F)4s a 4F3/2 324.19825 14.70000 0.782
3d2(3F)4p z 4F◦
3/2 →3d2(3F)4s a 4F5/2 325.19078 4.09000 0.218
3d2(3F)4p z 4F◦
7/2 →3d2(3F)4s a 4F5/2 322.28413 3.07000 0.162
3d2(3F)4p z 4F◦
7/2 →3d2(3F)4s a 4F9/2 325.42453 2.17000 0.115
3d2(3F)4p z 4F◦
9/2 →3d2(3F)4s a 4F7/2 321.70543 2.09000 0.109
3d2(3F)4p z 4F◦
9/2 →3d2(3F)4s a 4F9/2 323.45146 17.10000 0.891
3d2(3F)4p z 2D◦
5/2→3d2(3F)4s a 4F5/2 313.07985 0.82000 0.547
3d2(3F)4p z 2D◦
5/2→3d2(3F)4s a 4F7/2 314.37546 0.62000 0.414
3d2(3F)4p z 4D◦
5/2→3d2(3F)4s a 4F3/2 305.73929 0.19800 0.012
3d2(3F)4p z 4D◦
5/2→3d2(3F)4s a 4F7/2 307.86442 13.40000 0.807
3d2(3F)4p z 4D◦
7/2→3d2(3F)4s a 4F5/2 305.97353 0.24000 0.014
3d2(3F)4p z 4D◦
7/2→3d2(3F)4s a 4F7/2 307.21071 2.13000 0.123
3d2(3F)4p z 4D◦
7/2→3d2(3F)4s a 4F9/2 308.80256 15.00000 0.864
Table 2: Einstein coefficients of spontaneous emission and branching fractions for transitions of
titanium ion [7]. Lines are divided into groups with a common upper level.
a3F
J = 4
J = 3
J = 2
y3F°
J = 4
J = 3
J = 2
y3D°
J = 3
J = 2
J = 1
z5S°
J = 2
398.24nm
400.96nm
399.86nm
396.42nm
402.45nm
398.97nm
396.28nm400.89nm
398.17nm
395.82nm
392.45nm
395.63nm
392.98nm
(a)
a4F
J = 7/2
J = 5/2
J = 3/2
J = 9/2
z4F°
J = 9/2
J = 7/2
J = 5/2
J = 3/2
z4G°
J = 11/2
J = 9/2
J = 7/2
J = 5/2
z4D°
J = 7/2
J = 5/2
J = 3/2
J = 1/2
z2D°
J = 5/2
J = 3/2
338.37nm
338.02nm336.12nm
337.27nm
338.78nm
339.45nm
324.19nm
322.28nm
325.42nm
323.45nm
325.19nm
321.70nm313.07nm
314.37nm
305.73nm
307.86nm
305.97nm
308.80nm
307.21nm
(b)
Figure 3: Energy levels and selected transitions for density measurement of a) Ti neutral atom
and b) Ti ion.