Linköpings universitet
Linköping University | Department of Physics, Chemistry and Biology
Master thesis, 30 ECTS | Applied Physics
Spring term 2021 | LITH-IFM-A-EX–21/4039–SE
Modeling of carbon plasma
discharges in high-power
impulse magnetron sputtering
Henrik Eliasson
Supervisor : Daniel Lundin Examiner : Ulf Helmersson
Datum
Date
2021-06-09
Avdelning, institution
Division, Department
Department of Physics, Chemistry and Biology
Linköping University
URL för elektronisk version
ISBN
ISRN: LITH-IFM-A-EX--21/4039--SE
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Modeling of carbon plasma discharges in high-power impulse magnetron sputtering
Författare Author
Henrik Eliasson
Nyckelord Keyword Sammanfattning AbstractDiamond like carbon (DLC) is a metastable state of amorphous carbon that has very important and wide-ranging thin film applications. DLC has a strong resemblance to pure diamond and exhibits many traits of real diamond, like mechanical hardness and chemical inertness, but with a drastically lower deposition cost. DLC is
characterized by a high fraction of sp3 hybridization. To reach a high fraction of sp3 bonding by sputtering of a graphite target, an energetic ion population and a high ionized flux fraction (Fflux) is beneficial. High-power impulse magnetron sputtering (HiPIMS), an ionized physical vapour deposition technique (iPVD) based on magnetron sputtering, has been shown to produce significantly higher ionized fluxes and more energetic ions compared to the industry standard technique of direct current magnetron sputtering (dcMS). For carbon however, the ionized flux fraction is significantly lower than that of common metal targets like titanium and aluminium, even with HiPIMS.
In this thesis the ionization region model is applied to experimental carbon-argon 50 µs HiPIMS discharges at peak current densities of 1, 2 and 3 A/cm2 to investigate why the fraction of sputtered carbon reaching the substrate as ions is so low. The ionized flux fraction of the experimental discharges was measured by an ion meter to be lower than 5 %. From the computational modeling we find that the ionization probability of a carbon neutral (α) increases with increased peak discharge current densities from 40 % at 1 A/cm2 to over 60 % at 3 A/cm2. However, the back attraction probability of carbon ions (β) is high or above 90 %. The model predicts a higher Fflux than measured for all cases. The modeled Fflux values were 6-8 %, 10-13 % and 13-15 % for peak discharge current densities of 1, 2 and 3 A/cm2, respectively. By the time evolution of the particle densities, it is clear that most of the ionization takes place at the end of the pulse and thus the afterglow plays a significant role, especially for shorter pulses. The main conclusion is that the HiPIMS carbon discharge is mainly governed by the argon working gas and shares many traits with a typical working gas recycling process.
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Abstract
D
iamond-like carbon (DLC) is a metastable state of amorphous carbon that has very im-portant and wide-ranging thin film applications. DLC has a strong resemblance to pure diamond and exhibits many traits of real diamond, like mechanical hardness and chemi-cal inertness, but with a drastichemi-cally lower deposition cost. DLC is characterized by a high fraction of sp3 hybridization. To reach a high fraction of sp3 bonding by sputtering of a graphite target, an energetic ion population and a high ionized flux fraction (Fflux) isben-eficial. High power impulse magnetron sputtering (HiPIMS), an ionized physical vapour deposition technique (iPVD) based on magnetron sputtering, has been shown to produce significantly higher ionized fluxes and more energetic ions compared to the industry stan-dard technique of direct current magnetron sputtering (dcMS). For carbon however, the ionized flux fraction is significantly lower than that of common metal targets like titanium and aluminium, even with HiPIMS.
In this thesis the ionization region model is applied to experimental carbon-argon 50 µs HiPIMS discharges at peak current densities of 1, 2 and 3 A/cm2 to investigate why the fraction of sputtered carbon reaching the substrate as ions is so low. The ionized flux fraction of the experimental discharges was measured by an ion meter to be lower than 5 %. From the computational modeling we find that the ionization probability of a carbon neutral (α) increases with increased peak discharge current densities from 40 % at 1 A/cm2 to over 60 % at 3 A/cm2. However, the back attraction probability of carbon ions (β) is high or above 90 %. The model predicts a higher Ffluxthan measured for all cases. The modeled
Ffluxvalues were 6–8 %, 10–13 % and 13–15 % for peak discharge current densities of 1, 2
and 3 A/cm2, respectively. By the time evolution of the particle densities, it is clear that most of the ionization takes place at the end of the pulse and thus the afterglow plays a significant role, especially for shorter pulses. The main conclusion is that the HiPIMS carbon discharge is mainly governed by the argon working gas and shares many traits with a typical working gas recycling process.
Acknowledgments
I
have had the pleasure of working in an international environment with very competent people whose generous help and positive mindset made this thesis work a great experience. First of all I would like to thank my supervisor Daniel Lundin for guiding me through all parts of my thesis and for introducing me to the scientific society. My examiner Ulf Helmers-son for providing good feedback and giving me the freedom to work independently. Michal Zanaska for all the help in the lab. And the rest of the plasma group at Linköping University, Hao Du, Rommel Viloan, Tetsuhide Shimizu, Sebastian Ekeroth and Robert Boyd for good discussions and for making me feel welcome in the group.The members of the wednesday-Skype meetings deserve a big thank you as well, our discussions have been invaluable to my understanding of the subject. So, thank you Nils Brenning, Tiberiu Minea, Michael Raadu, Hamid Hajihoseini and especially Martin Rudolph and Jon Tomas Gudmundsson for also helping me a lot with the computational modeling.
Last but not least I would like to thank my family and friends for cheering me on and showing interest in my work, even though I am not the best at explaining what it is.
Contents
Abstract iii
Acknowledgments iv
Contents v
List of Figures vii
List of Tables viii
1 Introduction 1
1.1 Thin films and deposition techniques . . . 1
1.2 Computational modeling . . . 2
1.3 Purpose and Outline . . . 2
2 Theory 4 2.1 Sputtering . . . 4
2.2 HiPIMS . . . 7
2.3 Carbon films . . . 9
2.4 The Ionization Region Model . . . 10
2.4.1 Particle balance . . . 10
2.4.2 Power balance . . . 12
2.4.3 The carbon reaction set . . . 12
2.4.4 Fitting with the IRM . . . 15
2.5 The Ion meter . . . 16
3 Method 18 3.1 Finding the ionized flux fraction of carbon . . . 18
3.2 Modeling of carbon discharges using the IRM . . . 22
4 Results 24 4.1 Experimental results . . . 24
4.2 Modeling . . . 25
4.2.1 Model fitting . . . 25
4.2.2 Neutral particle dynamics . . . 27
4.2.3 Electron dynamics . . . 29 4.2.4 Ionization . . . 29 5 Discussion 32 5.1 Experimental results . . . 32 5.2 Modeling . . . 32 5.2.1 Model fitting . . . 32
5.2.3 Electron dynamics . . . 34 5.2.4 Ionization . . . 35
6 Conclusions 36
7 Outlook 37
Bibliography 38
A Complete list of reactions and rate coefficients 41 B SEM and OM images + Empirical deposition rate 44 C Pre-ionization study 47
List of Figures
2.1 Unbalanced planar circular magnetron . . . 4
2.2 Sketch of plasma region and current flows . . . 5
2.3 The sputtering process . . . 6
2.4 HiPIMS vs dcMS voltage waveform . . . 7
2.5 Schematic HiPIMS setup . . . 8
2.6 Comparison of dcMS and HiPIMS deposition rates . . . 8
2.7 sp3hybridization . . . 9
2.8 The collisional energy loss of carbon and argon . . . 15
2.9 An output example from the IRM . . . 16
2.10 Structure differences between the m-QCM and the g-QCM . . . 17
3.1 The experimental setup . . . 18
3.2 The ion meter circuit . . . 19
3.3 The ion meter . . . 20
3.4 Example of linear fit to raw data . . . 21
3.5 Measurement sequence . . . 22
3.6 Input waveforms . . . 23
3.7 The ionization region . . . 23
4.1 Experimental Ffluxvalues . . . 25
4.2 Fitting map and current fit of the best IRM fit to each peak discharge current . . . . 26
4.3 Time evolution of neutral particle densities for ID,pk= 20 A . . . 27
4.4 Time evolution of neutral particle densities for ID,pk= 40 A . . . 28
4.5 Time evolution of neutral particle densities for ID,pk= 60 A . . . 28
4.6 Electron density and temperature . . . 29
4.7 Current composition and temporal evolution of the charged particle densities . . . 30
5.1 Fitting map and current fit with non-zero βafterglowfor ID,pk= 40 A . . . 33
B.1 SEM: Carbon thin film cross section . . . 45
B.2 SEM: Carbon thin film surface morphology . . . 46
List of Tables
2.1 Argon and carbon species in the IRM . . . 10
2.2 The carbon reaction set . . . 14
3.1 Discharge and system parameters . . . 22
4.1 Measured values of Fflux . . . 24
4.2 Optimal combinations of β, f and Fflux . . . 27
4.3 Ionization probability of carbon . . . 29
4.4 Contributions from argon and carbon ions to the total and peak discharge current 31 5.1 Comparison of experimental and modeled Ffluxvalues . . . 33
5.2 Net change of neutral carbon species after the pulse . . . 34
A.1 Complete IRM reaction set . . . 42
Acronyms
AP Anode plasma.
BP Bulk plasma.
dcMS Direct current magnetron sputtering.
DLC Diamond-like carbon.
DR Diffusion region.
EEDF Electron energy distribution function.
HiPIMS High-power impulse magnetron sputtering.
iPVD Ionized physical vapor deposition.
IR Ionization region.
IRM Ionization region model.
OM Optical microscope.
PVD Physical vapor deposition.
QCM Quartz crystal microbalance.
RT Racetrack.
see Secondary electron emission.
1
Introduction
1.1
Thin films and deposition techniques
Thin film deposition is the process of forming layers of material on a substrate. The thickness of a thin film can range from a few atomic layers to a few micrometers. A thin film on a substrate is like butter on a slice of bread. Alone they might not be anything special, but together they form something great. The combination of the thin film’s surface properties and the properties of the bulk substrate is what makes thin films so interesting. Thin films are widely used today for example to enhance a material’s optical, electrical, magnetic, chemical or mechanical properties [1]. They are found everywhere, in advanced applications such as solar cells and semiconductors, but also in more basic applications like increasing hardness of everyday tools. In reality the process of growing a thin film is a bit more complex than spreading butter on toast. The structure nor the thickness should vary too much. However a perfectly uniform film is hard to achieve since no deposition technique is perfect, and typically neither are the substrates.
There are many ways to deposit thin films. There are evaporation techniques, sputter techniques and other physical techniques but also chemical techniques and more [1]. In this work the focus is on physical vapor deposition (PVD) using magnetron sputtering. Physical vapor deposition is a general term for any method based on the condensation of vaporized material onto a substrate. Sputter deposition is a PVD technique that makes use of a plasma to vaporize the target material. The source of the film material in sputter deposition is called the target and is usually shaped as a disc. The sputtering process will be described in depth later but in short the target material gets vaporized by bombarding it with particles from the plasma. The incoming particles knocks out target atoms into the chamber and a fraction of them ends up on the substrate and contributes to thin film growth.
The most widely used deposition technique of metallic and compound thin films today is magnetron sputtering [2]. Magnetron sputtering is a reliable, flexible and effective method of depositing thin films with low surface roughness, high density and overall high film quality [2]. A weakness of magnetron sputtering is that ionization of the sputtered target material is quite low. A large amount of ions can be beneficial to the microstructure of the grown film as well as enabling deposition of uniform films on complex-shaped substrates
1.2. Computational modeling
[2–4]. For example with carbon as target material it has been shown that more ionization and higher energy ions promote sp3hybridization in the deposited film which is important when synthesizing diamond-like carbon (DLC) [5, 6]. A way to increase the ionization in magnetron sputtering is to increase the power of the discharge.
High power impulse magnetron sputtering (HiPIMS) [7] is an ionized physical vapor de-position technique (iPVD ) aimed at increasing the ionization compared to regular direct current magnetron sputtering (dcMS). Instead of applying to the target (cathode) a constant voltage like in dcMS, in HiPIMS the voltage is applied in pulses. This enables HiPIMS to uti-lize much larger peak powers while maintaing the same average power. Typically the peak power exceeds the time averaged power by two orders of magnitude [8]. Another benefit of HiPIMS is that it is quite easy to change from a dcMS setup to a HiPIMS setup, all you need to do is change the power supply. However, pulsing the power often comes with a reduced deposition rate.
Much work has been put in by researchers to try and increase the ionization in HiPIMS and reduce the difference in deposition rate compared to dcMS, both in general and for spe-cific target materials. This thesis focuses on carbon as the target material. Carbon is a tricky material since it is notoriously hard to ionize. The only previously recorded value of the ion-ized flux fraction of carbon in HiPIMS is 4.5 % from a conference proceeding in 2003 [9]. This is very low in contrast to titanium for example where the Ffluxhas been measured to be up to
60 % [10].
1.2
Computational modeling
Computational models are a great tool when investigating processes that are hard or tedious to measure and verify experimentally. A computational model can be used to determine the agreement between theory and experiment.
In the present work I have used the so called ionization region model (IRM) which is a computational model that has been continously developed for more than ten years [11]. The IRM is a time-dependent and volume averaged plasma chemical model of the ionization region in a HiPIMS disharge. The ionization region is defined as the volume adjacent to the cathode target where the dense glowing plasma is trapped by a magnetron’s magnetic field. Previously the IRM has been used to model aluminium and titanium discharges where modeled results show good agreement with measured values [11,12]. The IRM has also been used successfully to study reactive HiPIMS [13,14]. The model will be explained in detail in the theory chapter.
With the IRM it is possible to follow the time evolution of each material species added to the model. The model tracks neutrals and ions of both the target material and the working gas, as well as the electron population in the discharge. The ability to track the population densities of all the particle species in the discharge makes the IRM a very powerful model. The IRM can also yield interesting results related to the ionization within a HiPIMS discharge, like the ionization probability of sputtered species and the ionized flux fraction. A benefit to being a volume averaged model is that the IRM can be used to analyse a discharge in just a few minutes. Compared to fluid models or particle in cell simulations that require great computational power often running for days on end, this is a great benefit. Of course, assuming volume averaged densities also limits the accuracy of the model.
1.3
Purpose and Outline
In this work we would like to investigate carbon HiPIMS discharges using computational modeling with the ultimate goal of increasing the fraction of ionization of the sputtered species.
1.3. Purpose and Outline
The HiPIMS discharge with carbon target is being explored extensively for deposition of diamond-like carbon films [9,15–18] with the aim to increase the ionization fraction of the sputtered carbon which in turn increases the film hardness and density. It has been reported that the ionized flux fraction in an argon HiPIMS discharge with a carbon target is low, typi-cally below 5 % [9]. Also Sarakinos et al.[16] have shown that the dominant ionized species in a HiPIMS discharge with argon (Ar) working gas and graphite target are argon ions (Ar+), while carbon ions (C+) constitute only about 1 % of the total ionic contribution.
In order to alleviate this problem and increase the ionized carbon flux fraction, Aijaz et al. [15] have suggested increasing the electron temperature in a HiPIMS discharge by using neon (Ne) as the working gas instead of Ar. This strategy has been demonstrated to facilitate a sub-stantial increase of carbon ionization in magnetron sputtering discharges, although absolute quantification of the ionized flux fraction of C has so far not been successfully achieved. Still, an energetic C+ion population has been detected indicating a substantial increase in the C+ ion flux as compared to the conventional Ar-based HiPIMS processes [15].
We would now like to model the internal discharges physics of these C/Ar/Ne HiPIMS discharges using the ionization region model (IRM) in order to understand and hopefully optimize these discharges. The IRM is semi-empirical and is constrained by experimental data, such as the discharge voltage-current characteristics and (optionally) the measured ionized flux fraction.
The work will be divided into two parts. The first being an empirical study to collect ID-VD characteristics for the discharge and determine the ionized flux fraction of three
car-bon target HiPIMS-discharges at peak current densities of 1, 2 and 3 A/cm2. As the second
part, the data collected by the experimental study will be used to run the IRM. From the IRM outputs we will specifically focus on the time evolution of the electron population, the neutral particle populations and the charged particle populations. We will also look at the electron temperature and the current composition of the modeled discharge current waveforms.
2
Theory
2.1
Sputtering
Sputtering is a PVD technique for depositing thin films on a substrate [1]. Sputtering is the mechanism used in the common industrial PVD method magnetron sputtering. In magnetron sputtering a plasma discharge is ignited at the so called target, a piece of material (usually in the shape of a disc) which is the source of the film forming material. To ignite the plasma, the chamber is first filled with a working gas to a certain pressure, then a negative voltage of usually several hundred volts is applied to the target (cathode). The applied voltage will give rise to an electric field, which accelerates positive ions towards the target. Upon ion bombardment of the target electrons are emitted out from the target. Some electrons will get caught in the magnetron’s magnetic field where they will excite and ionize the working gas (typically argon), and if the electron density and temperature is high enough, create a plasma. A typical magnetron used in magnetron sputtering discharge is shown in figure 2.1.
Figure 2.1: A cross section and a three dimensional sketch of an unbalanced planar circular magnetron (from Lundin [19]).
The cross sectional image shows etching in the target material. The circular ditch that is formed in the target material by sputtering is known as the racetrack. This is because
2.1. Sputtering
electrons travelling in it will experience it as a racetrack.
An unbalanced magnetron does not perfectly close the magnetic field loops over the tar-get. This is good because it allows a fraction of the electrons to excape the magnetic trap in the vicinity of the target and form a plasma further away from the target which in turn leads to better transport of ions to the substrate [19,20].
The plasma can be divided into regions based on the dominating physics. There is the anode plasma, the bulk plasma, the ionization region and the sheath as visualized in figure 2.2. The sheath (SH) is defined by a large charge imbalance where the density of positive ions is at least more than double the electron density. In the ionization region (IR), most of the ionization occurs. In the bulk plasma (BP), sometimes referred to as diffusion region (DR), the current transport of electrons from the IR across the magnetron’s magnetic field towards the anode plasma (AP) is the main process. And in the anode plasma the electric circuit is closed by the electron flux reaching the anode (substrate or chamber walls) [11,21].
Figure 2.2: A cross sectional schematic sketch of the plasma regions in a magnetron sputtering discharge with voltages and current density flows annotated (From Huo et al. [11]).
The ionization region is the foundation of the computer modeling done in this thesis and will discussed in detail in section 2.4.
As a consequence of igniting the plasma close to the target, the phenomenon of sputter-ing arises. The sputtersputter-ing process is the key mechanism behind thin film deposition in magnetron sputtering and is visualized in figure 2.3 below.
2.1. Sputtering
Figure 2.3: Visualization of the sputtering process (From Lundin [19]). The roman numbers each represent an event that may take place. Blue and green circles represent working gas neutrals and ions while the red circles are metal species.
Starting from the target side, event I and II represent the bombardment of the target surface by working gas ions and metal ions, respectively. The metal ions in our case will be carbon, both singly and doubly ionized. Depending on the sputter yield of the bombarding species they will sputter away different amounts of target material (III), shooting target neu-trals out into the chamber. The sputter yield of argon and carbon is presented in section 2.4.3. On the sputtered target atom’s way to the substrate, there is a probability of it being ionized (IV). This could happen by colliding with an electron. A fraction of the ionized target atoms will have such a low kinetic energy that they cannot resist the attraction from the negatively biased target. These ions will then be back-attracted to the target (V) and proceed to sputter the target (II). When target species sputters the target it is known as self-sputtering. The ions energetic enough to escape the ionization region will travel into the bulk plasma (VI). In the bulk plasma the target ion will either condense on the substrate surface (VII) or collide with the chamber walls. The sputtered neutrals that were not ionized in the IR will make their way to the bulk plasma where they will either be lost to the walls, condense on the surface (IX) or get ionized (VIII). There is also a possibility that a sputtered neutral will collide with the neutral gas background (X). These collisions will increase the heat of the working gas and expand it in a process called gas rarefaction. There is a chance that the bombarding gas ions will not actually sputter anything but only get neutralized at the target surface and reflected back to the plasma again (XI). Finally, a fraction of the reflected gas neutrals will also collide with the neutral background and contribute to the gas rarefaction (XII).
Magnetron sputtering usually operates by the application of direct current (dc) denoted as dcMS (direct current magnetron sputtering). Direct current magnetron sputtering is an inexpensive and easy way of depositing metal films, but has a drawback when it comes
2.2. HiPIMS
to ionizing the sputtered species. The film forming material in a dcMS discharge consists mainly of neutral species and most of the ions that do bombard the substrate are working gas ions [2]. For many applications it is desired to have a high ionization fraction in the film forming material, especially for carbon where more energetic ions are expected to increase the sp3hybridization in the carbon film. The structure and usefulness of carbon films will be
discussed in section 2.3.
2.2
HiPIMS
High power impulse magnetron sputtering (HiPIMS) is a ionized physical vapor deposition technique based on magnetron sputtering. HiPIMS was developed by Kouznetsov et al. [22] in 1999, based on previous works by Mozgrin et al. [23,24], Bugaev et al. [25], and Fetisov et al. [26], as a deposition technique which combines magnetron sputtering with pulsed power technology [27]. In a regular dcMS setup a constant voltage is applied to the cathode (target) to create and maintain the plasma discharge. In HiPIMS the voltage is instead applied in pulses (see figure 2.4). A typical HiPIMS pulse is in the range of 10–500 µs [28].
Figure 2.4: Comparison of the voltage application to the target (cathode) in dcMS and HiP-IMS. In this particular case the average power at the target is not the same for HiPIMS and dcMS. The HiPIMS pulses are 50 µs long and were measured in the present work, the dcMS waveform is artificial.
By pulsing the voltage it is possible to apply a larger voltage (often several hundred volts more) and reaching much higher peak discharge current densities (4–60 mA/cm2for dcMS [2] compared to 1–10 A/cm2for HiPIMS [19]) while still maintaining the same average power at the cathode (target). To distinguish HiPIMS from other pulsed magnetron sputtering tech-niques we use the definition by Anders [8] which goes like this: "HIPIMS is pulsed sputtering where the peak power exceeds the time-averaged power by typically two orders of magni-tude.". The increased peak power increases the ionization and the ion energy of the sputtered material which is the main benefit of HiPIMS [29].
An increase of the ionization of the sputtered material has shown to be beneficial for a wide range of thin film characteristics. It has been shown that more ionization promotes the growth of smooth and dense films [30,31] and enables control of the phase composition [32], microstructure [33] as well as optical [31,32] and mechanical [34] properties. Other benefits are improved film adhesion [35], the possibility of depositing uniform films on complex-shaped substrates [3,4] and a lower deposition temperature [36].
2.2. HiPIMS
To set up HiPIMS on a conventional magnetron sputtering system, all you have to do is change the power supply. Figure 2.5 shows a schematic overview of a HiPIMS set up.
Figure 2.5: A typical HiPIMS setup. The graphite target is mounted on the magnetron facing downwards and below it is the substrate position. The power supply is a dc-unit combined with a HiPIMS pulsing unit.
In general a system running in HiPIMS mode will exhibit a higher ionized flux fraction (Fflux) and a lower deposition rate compared to a dcMS system operated at the same average
power. The relative deposition rate in HiPIMS compared to dcMS is dependent on the target material as displayed in figure 2.6. In some cases the HiPIMS deposition rate has been shown to reach up to 85 % of the deposition rate in dcMS [30].
Figure 2.6: Results from comparisons of the deposition rate in HiPIMS vs dcMS for various target materials, compiled by Samuelsson et al. [30].
The discharge that remains (typically a few microseconds) just after the pulse is turned off is known as the afterglow. During this time period the plasma will decay and the constituents
2.3. Carbon films
of the plasma will diffuse away. The effect of the afterglow is usually neglected for longer pulses but for shorter pulses the afterglow might play a significant role [37]. This will be elaborated on in the results and discussion.
2.3
Carbon films
There are many reasons why you would want to deposit carbon based thin films. Carbon can exist in three hybridizations, sp1, sp2, and sp3. By mixing these hybridization states carbon can form a wide range of crystalline and disordered structures with different film character-istics. The carbon atom has four valence electrons, in the sp1state two of these form σ bonds along the ˘x-axis and the remaining two electrons form π bonds in the y and z directions. In the sp2hybridized state carbon forms three σ bonds triangularly in a plane while the fourth valence electron is in a π orbital normal to that plane. The sp3state arises when all of the car-bon’s four valence electrons form π bonds where the lobes are spread out with the tetrahedral angle 109.5˝ [5,38,39]. The sp3hybridization is a very strong volume structure and is what,
for instance, diamond is formed of. Graphite is based on the sp2hybridization and has a very strong structure within its atomic layer but the layers of graphite are only held together by weak van der Waals bonding [5]. A visualisation of the sp3state of carbon is shown in figure 2.7 below.
Figure 2.7: A visualisation of sp3hybridization, the marbles represent carbon atoms. Tetrahederal amorphous carbon (ta-C) or diamond-like carbon (DLC) is a metastable state of amorphous carbon that contains a significant amount of sp3hybridization (up to 80 ´ ´88 %
as compared to 100 % for pure diamond [5]). This form of carbon is possible to deposit with PVD and exhibits many of the qualities of diamond. A DLC-film has a high mechanical hardness making it suitable for coatings aimed at increasing hardness of a substrate. It also has other benefits like chemical and electrochemical inertness which makes DLC coatings suitable for coatings of medical tools and implants. DLC has a wide band gap, high mass density and is more inexpensive to produce than diamond [5].
It is known that energetic ion bombardment of the substrate is crucial to form a significant amount of sp3hybridization [6]. Therefore, it is important to use a deposition technique that is good at creating energetic ions. As we now know HiPIMS excels at precisely this. Today sputtering is the most common industrial process to form DLC (dc or rf sputtering) [5]. The problem with carbon seems to be that it is very difficult to ionize, even for HiPIMS where the only previously recorded value of the ionized flux fraction is Fflux=4.5 % [9]. Work has
been put into increasing the ionization of carbon and a way to do this could be by using neon instead of argon as working gas as shown by Aijaz et al.[15].
DLC deposited with HiPIMS have shown an sp3 fraction of 45 % [9,16,40] and up to 80 % by adding an arc at the end of the HiPIMS pulse [41]. This can be compared to « 30 % for dcMS [16]. To repel the low energy ions contributing to film growth one could add a substrate bias [5] or try the up and coming technique of bipolar-HiPIMS [42].
2.4. The Ionization Region Model
2.4
The Ionization Region Model
The ionization region model (IRM) is a computational model of the ionization region in a HiPIMS discharge. The model is limited to the ionization region and calculates fluxes of particles travelling in and out of it. The volume of the ionization region (IR) is modeled in the IRM as an annular cylinder with outer radius r2and inner radius r1, and height L=z2´z1
where z1is the distance from the target where the IR begins and z2 its extension into the
chamber. The IRM is capable of modeling the time evolution of a HiPIMS discharge, making it possible to monitor the fluxes and particle densities in the IR over time. The model also tracks the electron temperature and maintains power balance within the discharge.
The IRM already supports the common target materials titanium and aluminium [11] in non-reactive HiPIMS operation using argon (Ar) as working gas, and has also been used to model reactive HiPIMS using argon/oxygen working gas mixtures [14]. In this project the target material was graphite which meant that the IRM had to be updated with a reaction set and discharge parameters for an argon-carbon HiPIMS discharge. All the species considered by the IRM in the argon-carbon case can be found in table 2.1 below.
Table 2.1: Complete list and short explanation of the species tracked in the IRM for graphite as target material and argon as working gas. The notations of the carbon and argon states are based on the electron configuration and are explained in litterature [38,43,44].
Notation Species Comment
eC Cold electron Bulk electrons assumed to have Maxwellian EEDF eH Hot electron Energetic secondary electrons emitted from the target. Ar Ground state argon atom
ArH Hot argon atom Argon entering the discharge with an
energy of a few eV by event XI in figure 2.3 [11]. ArW Warm argon atom Argon entering the discharge with an
energy ď 0.1 eV by event XI in figure 2.3 [11]. Ar(3P0) Metastable argon atom
Ar(3P2) Metastable argon atom
Ar+ Argon ion
C(2s22p2 3P) Ground state carbon atom C(2s22p2 1D) Metastable carbon atom C(2s22p2 1S) Metastable carbon atom C(2s2p3 5S˝) Metastable carbon atom
C+ Singly ionized carbon ion C2+ Doubly ionized carbon ion
2.4.1
Particle balance
The particle balance is the main mechanism of the IRM and is governed by the general equa-tion dn(X) dt = ÿ i R(X)Generation,i´ÿ j R(X)Loss,j (2.1)
for each species X in table 2.1. The change of a species’ particle density over time depends on the two reaction rates R(X)Generation,iand R(X)Loss,jthat describe the generation and loss processes related plasma chemistry with species X within the IR [11]. Each reaction rate, Rjfor a given
2.4. The Ionization Region Model reaction j is defined as Rj=kjˆ ź i nreactant,i (m´3s´1) (2.2)
where nreactant,iis the density of the i:th reactant and kjis the rate coefficient of the reaction.
The rate coefficient of a reaction is calculated by integrating the cross section over an assumed Maxwellian distribution
k=4π ż8
0
σ(v)v3f(v)dv (2.3)
where σ is the collision cross section, v the electron velocity and f(v)the velocity distribution. Often we use the electron energy distribution function (EEDF)
ge(E)dE =4πv2fe(v)dv. (2.4)
Here we assume that the EEDF is Maxwellian. The rate coefficient k can then be fitted to the Arrhenius form
k= ATeBexp(´C/Te) (2.5)
where A, B and C are constants and Tethe electron temperature [45].
Beside chemical reactions in the plasma volume, a few more rates should be included in equation 2.1. The rate at which neutrals are sputtered off the target Rn,sputt, the neutral
particles diffusing out of the IR Rn,diff, a loss rate for each ion sputtering the target Ri,loss
and three rates concerning the working gas Rg,refill, Rg,kick-outand Rg,return. A more thorough
description of their origin and how to calculate them can be found in work by Huo et al. [11] and Gudmundsson et al. [14]. One of the more important rates, Rn,sputt, is calculated as
Rn,sputt=
ř
iΓRTi SRTYi(E)
VIR
. (2.6)
From this relation the rate of sputtered neutrals off the target is a function of the incoming flux of ions i to the target racetrack (RT)ΓRT
i , the surface area of the racetrack SRT, the energy
dependent sputter yield of the bombarding ion Yi(E)and the total volume of the IR, VIR. The
flux to the racetrack of ion species i is defined as
ΓRT i =βni
d qiUIR
mi (2.7)
where niis the density of ion species i, qiis the ion charge, UIRis the potential drop over the
IR, miis the ion mass and β is the back-attraction probability of ions. The parameter β is an
important fitting parameter to the IRM, this will become apparent to the reader in section 2.4.4.
The discharge is assumed to be quasi neutral so the density of cold electrons is given by nec = ÿ i Zin+,i´ ÿ j n-,j´neh (2.8)
where Zi is the relative charge of the positive ion in units of electron charge e. The densities
n+,iand n-,jare the densities of the positive ion i and the negative ion j, respectively. The hot
electron density (neh) is obtained from the electron temperature Tehand the electron energy
density pehas
neh=
peh
eTeh
. (2.9)
2.4. The Ionization Region Model
2.4.2
Power balance
The model must comply with the laws of energy conservation. The power balance is handled in the IRM by equating the power losses due to collisions, de-excitations and Penning ioniza-tions with the power absorbed by the plasma electrons. The electron population is divided into two groups, hot electrons and cold electrons, based on their energy. The benefit of two electron populations is a more accurate energy cost of ionization processes but also makes it possible to account for two mechanisms of electron heating, Ohmic heating within the IR and secondary electron acceleration across the sheath [11]. The power transfer to the electrons Pe
is therefore split into two parts, PSHin the sheath and POhmin the IR, like
Pe=PSH+POhm=/Ohm’s law/= Ie,SHUSH+Ie,IRUIR. (2.10)
The temporal evolution of the power transfer is a quite complex expression that can be found in published work [11,14]. The time evolution is analogous for cold and hot electrons besides a few changes for hot electrons explained by Gudmundsson et al [14]. The potentials falling over the sheat and over the IR are related by the factor f which is one of the fitting parameters used by the IRM. The total discharge current is defined as
UD(t) =UIR(t) +USH(t) = f UD(t) + (1 ´ f)UD(t) (2.11)
and f =UIR/UD, where UIRis the voltage drop over the ionization region, USHis the voltage
drop over the sheath and UD is the total discharge voltage. The electron currents in the
different zones are defined as
Ie,SH(t) =e ÿ i ΓRT i SRTγsee,i(1 ´ r) (2.12) and Ie,IR(t) = AIe ID E ID(t). (2.13)
In equation (2.12) we introduced γsee which is the secondary electron (see) emission yield,
and r that is the electron recapture probability. In the electron current within the IR, xIe/IDy
is the volume average of the fraction of the discharge current in the IR carried by electrons. There are two target specific parameters that are important to the power balance of the IRM, the collisional energy loss and the secondary electron emission yield. The secondary electron emission yield is just what it sounds like, i.e., the number of secondary electrons that are emitted when an ion bombards the target. The collisional energy loss is due to electron impact ionization, excitation and elastic scattering against neutral atoms [46]. The collisional energy loss per electron-ion pair createdEccan be calculated with the ionization
rate coefficient of neutral ground state species X, k(X)iz [14]
Ec(X)=Eiz(X)+ ÿ i Eex,i(X) k(X)ex,i k(X)iz + k(X)el k(X)iz 3me m(X)Te (2.14)
whereEiz(X)is the ionization energy of species X,E (X)
ex,iis the excitation energy and k (X)
ex,ithe rate
coefficient of the i:th excitation process of species X, k(X)el is the elastic scattering rate coefficient of species X, me is the electron mass and m(X) is the mass of species X. Calculated values of
the collisional energy loss for the carbon discharge is given in the next section.
2.4.3
The carbon reaction set
The following carbon species have been added to the IRM: ground state (2s2p2 3P), three
2.4. The Ionization Region Model
ionized C2+. The first ionization energy is 11.26 eV and the second ionization energy is 24.38 eV. We assume that the ground state is composed of the three closely spaced levels of the 2s22p2configuration3P0,3P1and3P2but treat them as one state.
The carbon atoms enter the discharge in one of two ways, either they get sputtered of the graphite target by a bombarding carbon ion, or by a bombarding argon ion. The sputter yield in both cases is approximated by the general form
Y=aEib (2.15)
whereEi is the energy of the incoming ion and a and b are constants depending on the ion
target pair. For argon ions bombarding the graphite target a= 0.0021 and b=0.687 and for carbon ions (self-sputtering) a=0.0562 and b=0.224 [47].
A sputtered carbon atom may experience many different effects on its way through the plasma discharge, all of the implemented reactions that a carbon atom may take part in are compiled in table 2.2. When entering the discharge the carbon atom may experience electron impact excitation (R1-R8) and ionization (R9-R13), charge transfer (R14) as well as Penning ionization (R15-R16).
The rate coefficient for electron impact ionization from the ground state (R9) is calculated from cross sections by Kim and Desclaux [48]. Ionization from the metastable states (R10-R12) use the same cross section but with threshold reduction applied. The cross section for electron impact double ionization (R13) is a fit by Stevefelt and Collins [49] to the data collected by Tawara and Kato [50]. Fits to the rates for electron impact excitation to the three lowest metastable states (R1-R3) by cold electrons are given by Toneli et al. [51]. For hot electrons the rates were calculated for the purpose of this project from the cross sections calculated by Wang et al. [52] downloaded from the LXCat database [53]. Reactions R4, R5 and R6 are inverses of reactions R6, R6 and R6 respectively. For these inverses the rate coefficients were calculated by the principle of detailed balancing. The coefficients of the Penning reactions R15-R16 are based on published cross sections [54–56] and scaled by the square of the atomic radii, the atom mass and the number of valence electrons [57]. For the charge transfer reaction (R14) we use Gaucherel and Rowe’s [58] measured rate coefficients for the charge transfer reaction between argon and oxygen.
2.4. The Ionization Region Model
Table 2.2: Carbon-argon and carbon-carbon reactions implemented in the IRM with corre-sponding rate coefficients for both cold and hot electrons. The top coefficient of each reaction is for cold electrons and the bottom of the two is for hot electrons. Reactions R14-R16 use only one rate for all electron energies. Reactions R14-R16 are implemented for each of the four neutral carbon species.
Reaction Rate coefficient [m3/s] (R1) e + C(2s22p2 3P) Ñ C(2s22p2 1D) + e 3.315 ˆ 10´14T´0.498 e exp(´1.995/Te) 3.489 ˆ 10´15´2.504 ˆ 10´17ˆT e (R2) e + C(2s22p2 3P) Ñ C(2s22p2 1S) + e 4.9 ˆ 10´15T´0.584 e exp(´3.462/Te) 3.543 ˆ 10´16´2.581 ˆ 10´18ˆT e (R3) e + C(2s22p2 3P) Ñ C(2s2p3 5S˝) + e 3.831 ˆ 10´14T´0.813 e exp(´5.057/Te) 1.701 ˆ 10´15´1.2105 ˆ 10´17ˆT e (R4) e + C(2s22p2 1D) Ñ C(2s22p2 3P) + e 6.78 ˆ 10´15T´0.523 e exp(´0.757/Te) 7.1673 ˆ 10´16´5.018 ˆ 10´18ˆT e (R5) e + C(2s22p2 1S) Ñ C(2s22p2 3P) + e 5.193 ˆ 10´15T´0.6205 e exp(´0.8638/Te) 3.7491 ˆ 10´16´2.7709 ˆ 10´18ˆTe (R6) e + C(2s2p3 5S˝) Ñ C(2s22p2 3P) + e 7.275 ˆ 10´15T´0.7829 e exp(´0.9309/Te) 3.7181 ˆ 10´16´2.7095 ˆ 10´18ˆT e (R7) e + C(2s22p2 1D) Ñ C(2s22p2 1S) + e 5.796 ˆ 10´15T´0.2076 e exp(´1.6752/Te) 3.4144 ˆ 10´15´1.0218 ˆ 10´17ˆT e (R8) e + C(2s22p2 1S) Ñ C(2s22p2 1D) + e 2.738 ˆ 10´14T´0.1811 e exp(1.3185/Te) 1.8364 ˆ 10´14´6.0929 ˆ 10´17ˆT e (R9) e + C(2s22p2 3P) Ñ C++ 2e 1.515 ˆ 10´14T0.5868 e exp(´11.8972/Te) 1.4348 ˆ 10´13´3.3441 ˆ 10´17T e (R10) e + C(2s22p2 1D) Ñ C++ 2e 1.4120 ˆ 10´14T0.5991 e exp(´10.70/Te) 1.433 ˆ 10´13´3.33 ˆ 10´17T e (R11) e + C(2s22p2 1S) Ñ C++ 2e 1.21 ˆ 10´14T0.6404 e exp(´9.2267/Te) 1.433 ˆ 10´13´3.33 ˆ 10´17T e (R12) e + C(2s2p3 5S˝) Ñ C++ 2e 1.008 ˆ 10´14T0.6819 e exp(´7.2335/Te) 1.428 ˆ 10´13´3.32 ˆ 10´17T e (R13) e + C+ Ñ C2++ 2e 8.98 ˆ 10´15T0.3872 e exp(´24.56/Te) 1.4838 ˆ 10´13Te´0.2304exp(´67.33/Te) (R14) Ar++ C Ñ Ar + C+ 6.4 ˆ 10´18 (R15) Ar(3P0) + C Ñ Ar + C++ e 4.2 ˆ 10´15 (R16) Ar(3P 2) + C Ñ Ar + C++ e 4.2 ˆ 10´15
The collisional energy loss was calculated using equation (2.14) with the excited states listed in table A.2 and the electron impact ionization cross sections from Kim and Desclaux [48]. The collisional energy loss is plotted as a function of the electron temperature in figure 2.8 below.
2.4. The Ionization Region Model
1
2
3 4 5
10
20 30 50
100 200
500 1000
1
5
10
20
30
50
100
200
500
1000
T
e[V]
E
c[V
]
C
Ar
Figure 2.8: The collisional energy loss per electron–ion pair created,Ec, as a function of the
electron temperature for the ground state carbon atom
Finally, the secondary electron emission yield due to argon ion bombardment is a fit to mea-sured data of a Si(111) surface [59], γsee,Ar+ = 0.0255+1.4609 ˆ 10´5Ei, whereEiis the en-ergy of the bombarding ion. This is scaled for self-sputtering carbon ions by 11.26/15.76 = 0.714, which is the quotient between the ionization energies of carbon and argon, giving
γsee,C+ =0.714 ˆ γsee,Ar+.
2.4.4
Fitting with the IRM
Discharge current and voltage waveforms from a HiPIMS discharge is all that is needed as input to the IRM. Then the model will scan the parameter space defined by four parame-ters, the ionized flux fraction Fflux, back-attraction probability of ions β, the fraction of the
total discharge voltage falling over the IR f (as defined in equation (2.11)) and the secondary electron recapture probability r, to try and recreate the input current as close as possible.
The IRM calculates the current by the fluxes of charged particles just above the racetrack. The current is calculated as
Icalc=e
ÿ
i
ZiΓiSRT(1+ (1 ´ r)γsee,i (2.16)
where γsee,i is the secondary electron emission probability of ion i, SRT is the area of the
racetrack,Γiis the flux of ion i and the sum is taken over all the positive ions.
A fitting run with the IRM may yield, among other graphs, the output seen in figure 2.9. In this particular run the four input variables were varied like this: 0.3 ă β ă 0.99 with steps of 0.069, 0.05 ă f ă 0.2 with steps of 0.015, r= 0.5 and Fflux =0.0255. Since this run was a
pretty rough overview the Ffluxwas allowed to be in the interval 2.55 ˘ 1 % so that the model
2.5. The Ion meter
Figure 2.9: An example of two output plots from the IRM. (a) After the model has scanned the parameter space it will yield a plot like this were the current fits are evaluated by how much they agree with the measured current. A blue area means a better fit. In this example the best fits are found with a combination of 0.1 ă f ă 0.15 and 0.8 ă β ă 0.99. The white lines with black numbers are values of Fflux. In this case the best fits have Ffluxvalues of 2–6%.
The white circle indicates where the best fit close to your experimental Ffluxinput is. (b) The
discharge current waveform measured and the fit developed by the IRM. The modeled and the measured currents agree well.
2.5
The Ion meter
An ion meter is a device based on a quartz crystal microbalance (QCM) and used in this thesis to measure the deposition rate of a discharge and calculate the ionized flux fraction of that discharge. A QCM has the ability to read the film thickness deposited on a monitor crystal. The main mechanism behind a QCM is piezoelectricity. When voltage is applied to the electrodes of a properly shaped piezoelectric crystal, it starts to oscillate [60]. When sputtered material is deposited on the face of the crystal it will add mass and slow down the frequency of these oscillations. The relation between the added mass and decrease in frequency was found to be:
Mf
Mq =
∆ f
fq (2.17)
by Sauerbrey [61] and Lostis [62] in the 1950’s. Here Mf is the mass of the crystal with the
added film, Mq and fq is the mass of the uncoated crystal and its frequency. The frequency
shift is∆ f = fq´fcwhere fcis the frequency of the coated crystal.
By substitution this leads to a simple expression for the film thickness: Tf= K∆ fd
f
(2.18) where Tf is the film thickness and df is the mass density of the film. The constant, K =
NATdq/ fq2where NATis the frequency constant of AT cut quartz, dqis the density of single
crystal quartz. Further work by Behrndt [63] followed by Miller and Bolef [64] and Lu and Lewis [65] lead to the slightly more complex but higher accuracy expression:
Tf= N ATdq πdffcZ arctan Ztan π(fq´fc) fq . (2.19)
In this equation Z= (dquq/dfuf)1/2is the acoustic impedance where uqis the shear modulus
of the quartz crystal and ufis the shear modulus of the film. The FTM-2400 QCM used in this
2.5. The Ion meter
to calculate the film thickness [60]. To get the deposition rate you simply divide the film thickness by the deposition time. A stand alone QCM will measure the total deposition rate of all incoming film forming species Rt. It has no way of measuring only the neutral flux. The
purpose of an ion meter is to measure the two fluxes Rtand Rnso that you may calculate the
ionized flux fraction Fflux. Here Rnis solely the flux of neutral particles condensing on the
crystal electrode surface. The Ffluxis calculated by
Fflux=
Ri
Rt =1 ´
Rn
Rt (2.20)
with the substitution that the total flux Rtis the sum of the ion flux Riand neutral flux Rn.
The two most prominent ion meters are the gridded QCM (g-QCM) and the magnetic QCM (m-QCM) [10]. The g-QCM is a QCM modified with two grids in front of the exposed crystal. The bottom grid is for repelling positively charged ions, and is therefore biased with a positive voltage, typically +60 V. The second grid is for repelling plasma electrons from the QCM and is biased with about -30 V. In an m-QCM the crystal electrode is instead directly biased by + 60 V to repel the ions. And instead of a grid repelling electrons, a strong magnetic field over the exposed crystal captures the electrons. The magnets generating the magnetic field are connected to the anode ground. In both ion meter variations, the total flux of particles Rt is measured by grounding the positive bias and the neutral flux Rn is
measured with the bias applied [7].
Figure 2.10: Comparison of the sensor structure of ion meters based on the m-QCM (left) and the g-QCM (right).
It is important to repel the plasma electrons from the QCM. If the QCM would draw large currents it is likely that it would disrupt the oscillations of the crystal [60]. This is espe-cially important when measuring close to the ionization region where the electron density is very high and is a problem that was encountered during the experimental part of this work. Therefore it is important that the magnetic field in an m-QCM is strong enough to capture the electrons. In their work, Shimizu et al. [66] used an m-QCM with two opposing SmCo mag-nets that generated a magnetic field of 0.4 T protecting the crystal. The magnetic field should however not be so strong that it significally affects the magnetic field of the magnetron as-sembly. In the present work we have used an m-QCM with a magnetic field of 0.25 T. The system setup will be described in section 3.1.
3
Method
The work was divided into two parts. The first being an experimental study to try and find a value for the ionized flux fraction in a carbon target HiPIMS-discharge. The second part would then use the found value to run the Ionization Region Model to investigate the time evolution of the carbon discharge.
3.1
Finding the ionized flux fraction of carbon
An experimental study was conducted to determine the ionized flux fraction (Fflux) of several
HiPIMS carbon discharges operated at different process conditions (see table 3.1). The sputter chamber used in this work was a cylindrical vacuum chamber, 44 cm in diameter and 75 cm high. The magnetron assembly was mounted on the top circular flange of the chamber, facing downwards. The sputter target was a 2 inch graphite target mounted on the magnetron assembly. A dc-unit together with a HiPSTER 6 pulsing unit from Ionautics were used to apply voltage to the target. In figure 3.1 below, the lab setup is shown.
Figure 3.1: The experimental setup.(1) The logger PC. (2) The PicoScope hardware on top of the QCM on top of the crystal’s dc biasing unit. (3) The sputter chamber. (4) The HiPSTER unit and and dc power supply mounted in the cupboard (not visible) and the control PC.
3.1. Finding the ionized flux fraction of carbon
A way to estimate the ionized flux fraction, Fflux, of a discharge is to measure the
deposi-tion rate of neutrals and atoms combined Rtand the deposition rate of only neutrals Rnand
use equation (2.20). The measurements were done using an ion meter based on the m-QCM described in section 2.5. The sensing mechanism of the ion meter is a quartz crystal plated with gold electrodes. The exposed electrode is connected to a dc voltage power supply mak-ing it possible to directly bias the side of the sensor facmak-ing the plasma discharge. A voltage bias of 0 V (directly grounded) was used to measure the combined flux of neutrals and ions. To measure only the neutral flux a bias voltage of 40 V was applied. A magnetic field was generated parallell to the orifice of the crystal holder by two nickel-plated 6 mm neodymium cube magnets on each side. The magnetic field strength over the sensor was measured with a Hall probe to be about 250 mT. The purpose of the magnetic field was to capture and stop electron current going through the QCM. The crystals used were 6 MHz gold coated crystals from Inficon. To read the output signal a FTM-2400 Multi-Channel Quartz Crystal Monitor from Kurt J. Lesker Company was used. A full schematic of the ion meter circuit as well as pictures of the ion meter can be seen in Figures 3.2 and 3.3 below.
Figure 3.2: The ion meter circuit. The crystal and its housing is protected by a grounded metal enclosure insulated by non-conductive tape. Magnets generate a magnetic field protecting the sensor from large electron currents. The dc bias unit is direcly connected through a resistor (R1 = 500Ω) to the crystal housing which is also connected to the upper crystal electrode. This line is also connected to ground through a capacitor (C1 = 100 nF) for high frequency signals. The QCM readout unit is connected to the crystal’s bottom electrode.
3.1. Finding the ionized flux fraction of carbon
Figure 3.3: (a) A picture of the ion meter in position inside the sputter chamber. The magnets in the picture are the two cyldrical objects inside the extruded ring. These were later replaced by four square shaped Nd magnets (two on each side) to increase the magnetic field strength. (b) The ionmeter in operation with a titanium target.
The placement of the ion meter should be as close to the ionization region as possible. This is to have a more accurate comparison between the measured Fflux and the modeled
Ffluxin the IR. Unfortunately due to an increasing noise, it was difficult to get clear readings
closer than 7 cm from the target. The QCM was therefore placed 7 cm below the target under the race track.
The QCM readout unit evaluates the thickness of the deposited film from the determined resonance frequency of the crystal. The obtained thickness value, however, depends on other material-specific parameters (see equation (2.19)), which can be programmed in the QCM. For reference a carbon film was deposited and the experimental deposition rate was calculated by measuring the film thickness with a SEM (see appendix B).
The QCM samples one data point every 0.01 µs. The logger-PC plots the thickness in real time and saves the data in a txt-file. The data is then analysed in the software program Origin where a linear fit is fitted to the data. The slope of this linear fit is the deposition rate of the measurement.
3.1. Finding the ionized flux fraction of carbon
Figure 3.4: An example of a linear fit to the raw data from one measurement. The noise level of the raw data increases with the peak current. This case is from a measurement at a HiPIMS peak current of ID,pk=40 A.
Measurements were done in sequence, handling one peak discharge current at a time. In total three peak currents were measured, ID,pk=20, 40 and 60 A, leading to a peak current density
on a two inch diameter magnetron target (« 20 cm2) of about 1, 2 and 3 A/cm2, respectively.
Measurements were also done for a dcMS discharge at equal average power (80 W) as the HiPIMS discharges. The dcMS measurement was used as a reference since the ionized flux fraction is known to be close to zero [10]. The discharge was never turned off between mea-surements. Since measurements were time consuming, in order to get good statistics, only one peak current was analysed per day. Before starting the measurement sequence for a given peak current, the discharge was allowed to stabilize for 30 minutes. This was to reduce any effect of heating or other transients. Each measurement was 10 minutes long as shown in figure 3.4. The first measurement was always the unbiased case. After measuring unbiased for 10 minutes, the bias voltage was applied, the thickness reading on the QCM readout unit zeroed, and a new measurement was taken. About 20 measurements were done for each peak current. The process is visualised in figure 3.5.
The measurements are spread out 10 minutes in time, so in order to compare them di-rectly an average of the deposition rates from the previous and the next measurement was used. The averaged value is made from measurements of the same sort, meaning biased or unbiased. And the discharge current measurement is of the other sort. The two values were then used to calculate an ionized flux fraction. This was done for all measurements yielding around 20 values of the ionized flux fraction for each HiPIMS peak current and for dcMS. A mean value of the ionized flux fraction was used for each corresponding HiPIMS peak current as input to the IRM.
3.2. Modeling of carbon discharges using the IRM
Figure 3.5: A visualisation of the measurement sequence and the calculation of the ionized flux fractions.
For each HiPIMS measurement the discharge current and voltage waveforms along with the bias voltage was recorded by a digital oscilloscope (PicoScope 4444, Pico Technology). A cur-rent clamp (Chavin Arnoux C160) was used for sensing the discharge curcur-rent. The discharge voltage waveform was measured directly by the oscilloscope after reducing the voltage by a factor of 100 using a resistor voltage divider circuit (1 kΩ and 99 kΩ). The bias voltage was sensed by a passive 1:10 oscilloscopic probe (TPP0101, Tektronix). Each measurement was averaged over 100 waveforms and all the measured data was saved by the logger-PC. The system inputs used in each case are compiled in the table below.
Table 3.1: Inputs to the HiPSTER pulsing unit and the dcMS dc-unit along with the working gas pressure in the chamber for each measurement. dc does not have any frequency nor pulse length as explained in the theory section.
20 A 40 A 60 A dc Pressure 0.7 Pa 0.7 Pa 0.7 Pa 0.7 Pa Power 80 W 80 W 80 W 80 W Voltage 618 V 626 V 637 V 486 V Frequency 520 Hz 350 Hz 280 Hz -Pulse length 50 µs 50 µs 50 µs
-3.2
Modeling of carbon discharges using the IRM
The IRM was used to analyse averaged discharge waveforms corresponding to the three in-vestigated peak currents. First the raw data must be formatted to achieve an input pulse that complies with the model. To do this the input pulses were cut at t = 0 and t = 70 µs. In this way only the interesting part of the measured pulse was included. The voltage and current data was offset by a small 5 V and 300 mA in the first microsecond of the pulse to avoid neg-ative values. From t = 52 µs to t = 65 µs the input voltage was also offset to 5 V and from t = 65 µs to t = 70 µs the input voltage was set to 0.01 V. The current was set to 100 mA from t = 65 µs to t = 69 µs and to zero from t = 69 µs to t = 70 µs. The input waveforms of the HiPIMS peak currents 20, 40 and 60 A are shown in Figure 3.6 as well as a comparison between the three.
3.2. Modeling of carbon discharges using the IRM
Figure 3.6: The input waveforms to the IRM. The shape of the current waveform is similar in all three cases and the voltage value only increases a bit for larger peak currents.
Before using the IRM a reaction set with correct rate coefficients has to be implemented. Values for the secondary electron emission yield, sputter yield and a fit for the cost of ion-ization also have to be pre-calculated by stand alone scripts. These values and the complete reaction set implemented in the code are found in the section 2.4.3 on the carbon reaction set. The volume parameters of the ionization region are set as follows: r1=6 mm, r2=19 mm,
z1=2 mm, z2=13 mm. The parameters define the IR as the volume visualized in figure 3.7.
Figure 3.7: A visualization of the IR located above the racetrack made to scale. The volume parameters are given in the text.
4
Results
4.1
Experimental results
The total deposition rate Rtand the deposition rate of only neutrals Rnwere measured for
dcMS and HiPIMS with peak discharge current of 20, 40 and 60 A. Each measurement was repeated a number of times. From the measured values of Rtand Rn, several values of the
ionized flux fraction for each investigated operational mode was calculated using equation (2.20). The ionized flux fraction for the investigated cases are compiled in table 4.1.
Table 4.1: The measured values of Ffluxin chronological order Fflux,i 20 A 40 A 60 A DC i = 1 -0.22 % 0.18 % 0.79 % -5.57 % 2 0.14 % -1.75 % 0.64 % -4.81 % 3 0.43 % 0.89 % 2.77 % -3.31 % 4 0.11 % -0.14 % 0.80 % -2.13 % 5 -0.24 % 1.27 % 2.03 % -2.43 % 6 -0.07 % 2.17 % 1.27 % -2.58 % 7 0.06 % 0.28 % 0.91 % -2.87 % 8 -1.26 % 0.76 % -0.25 % -2.74 % 9 -1.42 % 1.27 % 1.88 % -2.45 % 10 0.42 % -1.44 % 0.33 % -2.75 % 11 0.80 % -0.23 % 2.16 % -3.19 % 12 0.27 % 1.49 % 2.36 % -2.76 % 13 -0.20 % 0.43 % -0.3 % -1.89 % 14 -0.27 % 0.94 % 2.42 % -1.59 % 15 0.72 % 1.90 % 1.28 % -1.74 % 16 0.76 % 0.40 % 1.20 % 17 -0.83 % 0.64 % 2.09 % 18 -1.81 % -0.15 % 0.82 % 19 -1.45 % -1.65 % 1.09 % 20 -1.08 % 0.17 % 21 -1.18 % 1.23 % 22 0.50 % 23 2.75 % µ -0.30 % 0.38 % 1.26 % -2.85 % σ 0.80 1.11 0.91 1.08
4.2. Modeling
Each case plotted with a normal distribution is visualized in figure 4.1 below. Something worth noting is that for dcMS and 20 A HiPIMS, the ionized flux fraction is negative which is not physical. All the cases have a lower Ffluxcompared to the value of 4.5 % presented
by DeKoven et al. [9]. We will return to this in the discussion. The general trend is that the ionized flux fraction is increasing with increasing peak current. This is in fact expected due to increased ionization with increasing HiPIMS peak discharge current and will be discussed in more detail in section 5.2.4. The relative change in percentage units between the cases are about 2.5 % between DC and 20 A, 0.7 % between 20 A and 40 A, and 0.9 % between 40 A and 60 A.
Figure 4.1: Normal distribution of the measured Ffluxvalues in dcMS as well as in HiPIMS
(three different peak discharge currents: 20 A, 40 A, and 60 A).
4.2
Modeling
4.2.1
Model fitting
The IRM was applied to model the three HiPIMS discharges operated with peak discharge currents 20, 40 and 60 A. The best fit the model could find to the experimental current wave-form of each HiPIMS peak current is displayed in figure 4.2 below.
4.2. Modeling
(a) (b)
Figure 4.2: From top to bottom, the best fits for HiPIMS peak discharge currents of 20, 40 and 60 A. (a) The fitting map showing β versus f . (b) The measured current waveform and the model fit for the current waveform.
As explained in the theory chapter, the most blue zones in the fitting map are the combina-tions of f and β where the modeled discharge current resembles the experimental waveform the best. The most blue zone remains somewhat in the same region (combinations of f and
β) for all investigated currents. It is clear that the model has a hard time fitting the higher
peak currents. This is most apparent in the case of ID,pk = 60 A but the zone of best fit is
also less blue for 40 A compared to that for 20 A. The reason why the fits get worse seems to be the IRM having difficulties reaching the desired peak current. The peak IIRM,pkof the
experimental 60 A case is only a few ampere higher than the fitted current to the 40 A case. The areas in which the best fits are found are constrained by the values of the parameters f ,
4.2. Modeling
Table 4.2: The values of the back attraction probability, β, the fraction of the discharge voltage falling over the IR, f , and the ionized flux fraction, Fflux, of the areas of best fit.
20 A 40 A 60 A
f 12–14 % 12–14 % 12–13 %
β 89–99 % 94–99 % 97–99 %
Fflux, IRM 7–10 % 11–15 % 13–17 %
Fflux, exp -0.30 % 0.38 % 1.26 %
Not only are the fits getting worse for higher peak discharge currents, but the areas in which the possible best fit can be found is also shrinking due to the need of a larger back at-traction probability. The modeled Ffluxvalues are significantly higher than the measured ones
but the trend of higher Ffluxat higher peak currents remains. Reasons why the experimental
and modeled value differs so much will be presented in the discussion.
4.2.2
Neutral particle dynamics
The time evolution of the neutral particles is shown in figures 4.3, 4.4 and 4.5 for the three different peak discharge currents 20 A, 40 A, and 60 A, respectively. The evolution of the particle densities are similar for all peak currents. All carbon densities are increasing as more and more carbon is sputtered off the target during the pulse (continuously increasing dis-charge current). At the end of the pulse there is a significant drop in the density of the carbon ground state atom. The carbon metastables are steadily increasing throughout the pulse and for a few microseconds after the pulse. For the higher peak discharge currents the C(1D) state even overtakes the carbon atom ground state density in the end of the pulse and for a few mi-croseconds afterwards. The drop in the carbon ground state density at the end of the pulse is not seen for the argon atom ground state density. Instead it is steadily decreasing for a longer time with a minimum at the end of the pulse. There is also an increase in the hot and warm argon densities while the cold argon ground state density is decreasing. This is an indication of gas rarefaction which we will return to in section 5.2.2.
Figure 4.3: Time evolution of the neutral particle densities for a HiPIMS discharge with peak discharge current of 20 A.
