2. Review of Ion Implantation
2.1. Ion implantation of polymers
2.1.1. Polymer structure
The term “polymer” describes an extremely diverse group of materials, defined by their being composed of high-molecular weight molecules. Further distinction from other groups of materials is difficult since polymers may be amorphous or crystalline, liquid or solid, organic or inorganic, conductive or insulating. The largest category of polymers, and the one which shall be dealt with in this work, is carbon based, formed by polymerisation of organic precursors. They may be described as amorphous agglomerations of long carbon chains, or backbones, with functional or passive side- groups attached to the carbon atoms. Average molecular masses of individual macromolecules in polymers range from 104 to 106 u. Although predominantly amorphous, crystalline domains exist within semicrystalline polymers and some polymers are completely crystalline.
The simplest of the organic polymers is polyethylene, formed by polymerisation of ethylene (CH2CH2) into polymer molecules many thousands of repeating units long. It may be described by [-CH2CH2-]n, where n is a number usually greater than ten thousand. Bulk properties of the material are dependent on the length of the polymer chains. Increasing melting temperature is exhibited by low molecular weight (or low density) polyethylene (LDPE), medium density polyethylene (MDPE) and high
4 density or ultra-high molecular weight polyethylene (UHMWPE) respectively.
Substitution of one or more of the hydrogen side-groups by using a different precursor gas results in variants with distinctive bulk properties. For example, substitution of hydrogen for a methyl group gives polypropylene, for a cyano group gives polyacrylonitrile (Acrylic), and for chlorine gives poly(vinyl chloride) (PVC).
Substitution of all four hydrogen atoms for fluorine results in poly(tetrafluoroethylene) or PTFE, trade name “Teflon”. Substitution of carbon atoms in the backbone with oxygen, nitrogen, sulphur and carbon ring structures, and combinations of polymer unit sequences, termed co-polymers, provides almost unlimited variation in structure, and subsequent physical and chemical properties
An important concept when considering the physical state of a polymer is the notion of a glass transition temperature (Tg). The glass transition temperature for some common polymers is given in table 2.1. Cooling of a polymer melt decreases the vibrational energy of the constituent molecules. Due to strong long-range intermolecular forces, the transition from the liquid to the solid state occurs over a large temperature range. The glass transition temperature is assigned according to readily observable changes in the thermodynamic properties of the polymer. For example, the heat capacity and expansivity change discontinuously at the glass transition temperature. Mechanical properties also change rapidly. At room temperature, poly(methyl methacrylate) (PMMA) is below its Tg and is relatively hard and brittle, whilst above its Tg PMMA is soft and rubbery. The degree of crystallinity of a polymer is affected by the rate of cooling through the glass transition temperature. Rapid quenching of a polymer melt results in a highly amorphous solid phase, whilst slow cooling encourages the growth of microcystalline domains.
5 Table 2.1: Some common polymers, their repeating units, chemical structure and glass transition temperatures
Name Repeating unit Chemical structure Tg (°K)
Polyethylene [-CH2CH2-]n 140-270
Poly(vinyl [-CH2CH(Cl)-]n 354
chloride)
Polystyrene [-CH2CH(C6H5)-]n 373
Polypropylene [-CH2CH(CH3)-]n 250
Polycarbonate [-OC6H4C(CH3)2 421
C H OC(O)-] 6 4 n
Poly(tetrafluoro- [-CF2CF2-]n N/A
ethylene)
Bulk properties of polymers are as varied as the chemical structures of which they are composed. In general, polymers exhibit relatively low density when compared to other classes of solid. This is due to the random arrangement of large molecules, resulting in large areas of empty space. Chemical inertness, especially resistance to attack by acids, is another common property of polymers. Whilst extremely useful in
6 some respects, this property limits the applicability of polymers to many conventional processing techniques. For example, adhesion of metal films to polymer surfaces is an area of great interest for applications in microelectronics. Traditional metallisation processes often result in low film adhesion due to lack of interaction between the film and the substrate. Plasma processing of the surface prior to deposition by plasma condensation results in an improved adhesion [1]. Plasma processing and ion implantation are non-contact processes that have successfully been applied for surface modifications of polymers. A review and discussion follows.
2.1.2. Ion-polymer interactions
Low-energy plasma treatments (ion energy < 100eV), such as exposure of a polymer surface to DC or RF glow discharge plasmas, affect only the near surface regions.
Impacting low-energy ions can break covalent bonds at the surface, exposing functional groups that affect the surface energy, and subsequently modify the surface hydrophobicity [2]. Chemically reactive ions can become incorporated into the surface chemical structure, functionalising the surface for specific interactions with molecules, proteins and cells [3]. High doses of low energy ions can adsorb on or near the surface, congregating together to form islands, eventually resulting in thin film growth.
Conventional ion implantation uses a series of high voltage grids to extract ions from a plasma and accelerate them as an ion beam toward a target material in a low- pressure environment. Medium- (100eV-100keV) and high-energy (>100keV) ions implant beneath the surface, affecting the target material in a number of different
7 ways. Since polymers are a relatively soft material, composed of, on average, 20% free space, implanting ions travel a comparatively large distance before coming to rest. In the absence of thermodynamic constraints present in traditional materials processing, introduction of a foreign species into the target material can form new compounds. High doses into metals can form new alloys or ceramics. Foreign species act as dopants in semiconductors, which is currently the primary commercial application of ion implantation. High doses of metal ions in polymers can increase the conductivity by forming conductive networks.
A more important consideration for polymers, than the presence of foreign ions or atoms, is the “damage” to the polymer molecules that the ions cause before they come to rest. Impacting medium- to high-energy ions lose energy by multiple interactions with the target material. A convenient measure of the energy deposited by an ion along its path inside the target material is the linear energy transfer (LET), often expressed in units of eV/nm. Interactions can be classified into two categories; interactions of the ion with the target nuclei are known as nuclear stopping processes, and interaction with target electrons are known as electronic stopping processes.
Electronic (Se) and nuclear (Sn) stopping powers (measured in LET) can be calculated by considering the interaction cross-sections as a function of incident ion species, ion energy and target atoms.
Electronic stopping occurs by two processes, both involving electromagnetic interaction between the positively charged ion and target electrons. Relatively frequent low-energy-transfer inelastic glancing collisions usually result in excitation of orbital electrons to a higher energy level (plasmons). High-energy-transfer elastic
8 knock-on collisions, whilst more infrequent, transfer a much greater momentum to the target electrons and are more likely to result in ionisation. Ionisation results in the creation of a molecular ion and the liberation of secondary electrons, which either exit the target material or relocate to another region in the target.
Nuclear stopping involves the transfer of momentum from the ion to a host matrix atom, or recoil atom. If the momentum transfer is small the energy imparted to the recoil atom will be dissipated by phonons. Higher energy transfer collisions may result in irreversible displacement of the recoil atom from its original site. This process requires enough energy to break the bonds that held the atom in place. The displaced atom may remain bound to other atoms or dissociate completely. Displaced recoils are capable of creating further recoils and ionisation. Calculation of the total Sn by an incident ion must include the contribution from recoils as well as the primary ion. Increasing the ion atomic number linearly increases the nuclear interaction cross- section, subsequently increasing the recoil displacement probability.
A Monte-Carlo simulation program, TRIM 2003 (Transport of Ions in Matter) [4] calculates the Se and Sn for a given ion species, energy and target material. An example of electronic and nuclear stopping energy as a function of target depth for
10kV argon ions into PMMA (parameters typical of the experiments presented in this thesis) is shown in figure 2.1 for both the incident ion and recoil ions, averaged for
100,000 ions. The sum of the total energy under the six curves equals the 10kV of the incident ion. Electronic stopping is highest near the surface when the ion energy is highest. Incident ion nuclear stopping shows a distinct peak at a depth where the ion energy is reduced to a value corresponding to the maximum interaction cross-section.
9 This is because nuclear stopping becomes important when the ion slows down to approximately the Bohr velocity (orbital electron velocity), which is of the order of 2 x 106 ms-1 [5]. TRIM has also been used to predict the relative contributions of electronic and nuclear stopping for 100keV and 1MeV argon ion irradiation of polypropylene [4]. The results suggest that an increase in ion energy results in an increase of Se relative to Sn, especially in the near surface regions. Nuclear stopping is more pronounced near the end of the ion track for higher energy ions.
Figure 2.1: TRIM simulation of 10kV Argon ion implantation into PMMA showing the relative contributions to LET from nuclear and electronic stopping.
10 Damage events such as ionisation and recoil displacement result in the modification of the original polymer structure. Ionisation and plasmons can result in the formation of new covalent bonds, often between adjacent molecular chains (figure 2.2(a)). This process, termed cross-linking, increases the molecular weight and can increase the hardness and wear resistance of a polymer [6] Displacement causes molecular chain scission and side group dissociation, resulting in a reduction in the molecular weight
(figure 2.2(b)). Scission can lead to a degradation of the polymer and leave is susceptible to chemical attack. For example, PMMA is used as a photoresist because it undergoes chain scission when exposed to electron bombardment or gamma radiation. In contrast, it has been observed that when PMMA is exposed to high- energy argon ions, cross-linking hardens the surface [5].
Cross-links Scission
Figure 2.2: Schematic of energetic-ion induced cross-linking (a) and scission (b).
For tribological improvements, cross-linking is the desirable form of modification when attempting to alter the surface properties of a polymer. It would therefore appear that ions with high Se would be preferable, since, according to the above arguments, electronic stopping should encourage cross-linking more than nuclear stopping processes. Whilst this is generally accepted, it turns out that some polymers
11 preferentially exhibit cross-linking over chain scission, irrespective of the impacting ion [6]. There is no theoretical rule as to which polymers exhibit enhanced cross- linking when subjected to ion impacts. Empirical observations suggest that side chains play an important role in enhancing the likelihood of scission, possibly due to side chains introducing a strain on the molecule making them more susceptible to breaking of the main chain [6]. The numbers of cross-links and scissions is also proportional to the ion dose, up to a point of saturation.
Medical ion irradiation treatment of biological tissue aims to use scission to denature proteins, which are polypeptide polymers, at a desired location. The technique takes advantage of the relatively small nuclear cross sections at high energies to target a specific region within the biological tissue. Near surface regions are relatively unaffected, deceleration of the ion occurring by electronic stopping processes until nuclear stopping processes contribute to the LET at the end of the ion track. Thus, excitation and ionisation occur along the ion track whilst scission occurs in significant amounts only at the end of the ions path. In contrast, for ion energies of interest in this thesis (<100keV) nuclear stopping contributes relatively evenly along the ion path
(figure 2.1).
2.1.3. Thermal considerations
For substrates that are good thermal conductors the temperature at the surface of the substrate can, for most deposition and implantation cases, be considered to be essentially the same as the bulk of the substrate temperature [7]. If the substrate is placed on an actively cooled holder or heat sink the temperature at the surface of the
12 substrate can, to some extent, be controlled during the deposition process. On the other hand, if the substrate is a thermal insulator there may exist significant temperature gradients, contributing to an increased surface temperature. The implication for polymer substrates is that the temperature in the surface region may rise above the glass transition temperature whilst the bulk substrate remains at or near room temperature. This has dramatic implications for the distribution of the implanted ions since diffusion may occur if the surface region becomes fluid.
The problem of calculating the change in temperature of a substrate due to energetic ion impacts is a complicated one, and as such necessarily requires simplifying assumptions. An obvious complication arises from the definition of temperature as a macroscopic concept, making it difficult to define the temperature at the substrate surface, since we must first define the region that we call the “surface”. We define a slab of material of thickness, l, with thermal diffusivity, α. A solution to the diffusion equation for the problem of conduction in a slab can be found by dimensional analysis, not reproduced here [8]. The solution suggests that a slab may be considered semi-infinite for a given time, t, if l is greater than (tα)1/2. Defining the slab as semi- infinite allows a simplified analysis of the problem.
For a 10µs plasma immersion ion implantation pulse (discussed below), this length is of the order of 2µm for glass and 50µm for metals. These values are much less than typical substrate thicknesses which are of the order of 1mm. Using such a simplifying assumption, Blanchard [9] predicts the substrate surface temperature increase during plasma immersion ion implantation for stainless steel, silicon and Ti-6Al-4V, for heat fluxes up to 3x107 W.m-2. In the limit that there is no heat loss from the substrate
13 during the implantation pulse (justified in the same work) the temperature increase at the surface of the substrate is shown to be around 10°C per 10µs pulse. For the cases considered in this thesis, heat fluxes are of the order of 5x105 W.m-2, considerably lower than those in Blanchard’s analysis.
Using the same formulation and assumptions as Blanchard, predictions of the temperature increase at the surface of Pyrex glass and HDPE were made for a 10kV,
10µs plasma immersion ion implantation pulse for heat fluxes of the order of 5x105
W.m-2. The thermal constants for glass and HDPE were taken from reference [8]. The results are plotted in figure 2.3, along with that for stainless steel and alumina.
14
Figure 2.3: Temperature rise at the surface of substrates with widely varying thermal conductivities during a 10kV, 10µs, plasma immersion ion implantation pulse. For the experiments presented in this work the heat flux is of the order of 5x105W.m-2.
It is clear that the surface temperature rise per pulse for Pyrex and HDPE is much greater than that for stainless steel and alumina. To calculate the final bulk substrate temperature it is necessary to calculate the temperature loss between pulses. Such a calculation has been performed previously for thermally conductive substrates [9].
However, we are concerned here with thermal insulator surface temperature.
Unfortunately such work has not yet been undertaken. We may surmise by stating that the issue of temperature is relevant for ion implantation of polymers and should be considered in any discussion of modification mechanisms.
15
There is a great deal more research to be undertaken before the understanding of the effects of ion interactions with polymers matures. The general approach in the literature review presented below is to subject a given polymer to an impacting ion species, vary the dose and ion energy, and document the observed changes.
Eventually we will be able to model the effects and predict the outcome of an interaction process. However with a materials group as complex and varied as polymers, this will inevitably take some time.
2.1.4. Examples in the literature
Polymer surface modifications by ion implantation include tribological improvements, optical and electronic changes, and increases in wettability and biocompatibility. A brief description of these major applications and some characteristic examples is presented here.
Low-energy RF plasmas are becoming widely accepted as a method of modifying polymer surface properties. In particular, the hydrophobicity of the surface can be tailored in this way. This is especially attractive for biocompatibility enhancements since cell adhesion is dependent on the surface energy of the polymer. Chan, Ko and
Hiraoka give a good overview of this topic up to 1996 [2]. Inert gas, oxygen, nitrogen and fluorine plasmas are all utilised for such purposes. Recently this technology has been exploited to impart micro-scale patterns on polystyrene surfaces that influence the areas of cell growth and adhesion [10]. This has applications in the novel areas
16 such as tissue engineering, biosensors and array technologies for the diagnosis of disease.
0.6-1.2 keV argon ion implantation into polystyrene Petri dishes in oxygen ambient encouraged significant improvement in rat pheochromocytoma cell growth compared to unirradiated polystyrene [11]. This effect closely matched the observed changes in water contact angle, a factor fundamentally related to surface energy. 35keV argon ions implanted into polyurethane and polyethersulphone up to a fluence of 5 x 1015 ions.cm-2 induce a strong improvement in cell adhesion, spreading and proliferation above a threshold fluence of 1 x 1015 ions.cm-2 [12]. XPS and Raman analysis suggest that the observed improvements were due to the formation of a substantial amount of hydrogenated amorphous carbon phase in the polymer surface. Silver ions between 5 and 30 keV implanted into polystyrene at a constant dose of 3 x 1015 ions.cm-2 encouraged human umbilical vascular endothelial cell growth and proliferation, whilst no growth was observed on untreated samples [13]. The effect increased with increasing ion energy up to 20keV, but decreased at 30keV, closely following the water contact angle measurements.
Higher energy ion implantation of fluorine ions into polystyrene at 150keV to a fluence of 5 x 1014 ions.cm-2 showed a slight increase in adhesion and growth of vascular smooth muscle cells [14], whilst fluorine implanted into PMMA at 40-
100keV up to a fluence of 1 x 1015 ions.cm-2 showed a decrease in neutral granulocyte and macrophage number with increasing dose, exhibiting a minimum at around 4 x
1014 ions.cm-2 [15]. Once again, this effect closely followed the water contact angle dependence on dose.
17
For high fluences and ion energy, graphitisation of the surface, observable as a darkening of the polymer, occurs on a broad scale. This is attributed to the irreversible liberation of hydrogen and methyl groups and cross-linking of polymer carbon backbones [6]. For tribological improvements, cross-linking is an important effect.
XPS and FTIR studies of 4keV hydrogen, helium and nitrogen ion implantation into
UHMWPE and linear polyethylene up to fluences of 2 x 1017 ions.cm-2 indicated graphitisation of the surface and an increase in nitrogen content for nitrogen ion implantation [16]. Tribological improvements in UHMWPE surface properties is of great interest due to large volumes of the polymer being used as acetabular cups in artificial hip implants. Significant wear of the cup surface causes degradation and ultimately failure of the implant, warranting ongoing widespread research.
Improvements in surface hardness and wear resistance of polymers have been reported by a number of authors. A “state-of-the-art overview” was published by
Dong and Bell in 1999 outlining improvements in hardness, elastic modulus, wear and friction, amongst other properties [6]. A few of the early applications of PIII to polymers are included. The authors conclude by noting PIII as a potentially important technology for polymer surface modification if a number of problems can be overcome. These problems, and potential solutions, will be outlined later in this work.
Electrical conductivity has been observed to increase with increasing fluence and energy in a lage number of publications [eg.[17],[18],[19]] the effect usually being attributed to graphitisation. Darkening of the polymer with increasing fluence and energy is also observed. Conductivity studies were usually undertaken with high-
18 energy ions (>100keV). Applications of conductivity modifications include the creation of patterned microcircuits.
Optical waveguides are another application that holds great promise for ion implanted polymers. Dorothee Rück and co-workers in Darmstadt, Germany, have made significant progress in the creation of buried waveguides in PMMA and PMMI using high-energy hydrogen and helium ions. Localised changes in the refractive index have resulted in the production of in-plane light splitters and Mach-Zehnder interferometers
[20]. The same group has used similar technology to improve the adhesion of metal films on polymer surfaces. This is another area where ion implantation holds great promise. Low energy plasma treatments have also been shown to modify the surface energy of polymers before metal film deposition, increasing the adhesion of the film
[21],[22].
Whilst it is apparent that important advances have been made in the area of conventional ion implantation of polymers, plasma immersion ion implantation of polymers has been only briefly explored. Other than those presented later in this work, a few noteworthy cases deserve mention. One of the first attempts to apply the
PIII process to polymer surfaces was by Han, Lee and co-workers in Korea [23]. They successfully modified the wettability of a range of polymer surfaces by implanting gaseous ions up to 10keV. A similar result was achieved by Lacoste et. al. by implanting oxygen ions into polystyrene [24]. The results are similar to the observed changes for low-pressure, low-energy plasma treatments mentioned earlier.
Iskanderova et. al. were the first to combine PIII and metal vacuum arcs for metal ion implantation of polymers. They improved the oxidation resistance of polyimide and
19 PET by 2keV implantation of aluminium ions from a cathodic arc [25]. Anders, in his review book “Handbook of plasma immersion ion implantation and deposition”, notes that the field of PIII application to polymers “will expand rapidly over the next years”
[26].
2.2. Plasma Immersion Ion Implantation
2.2.1. Introduction
In the mid 1980’s, J.R. Conrad and co-workers at the University of Wisconsin, U.S.A. developed a process termed plasma immersion ion implantation (PIII) (also known as plasma source ion implantation (PSII) or plasma based ion implantation (PBII)) [27].
It was designed as a low cost alternative to conventional beam-line ion implantation, which had previously been demonstrated to be an effective method for modifying the surface properties of solid materials. Beam-line ion implantation uses a series of high voltage grids to extract ions from a plasma source and accelerate them toward a target in a low-pressure environment. Ions are uni-directional and the process is line-of- sight; i.e. only the target surfaces within the line of sight of the ion source will be implanted. Implantation of complex work-pieces requires that the target be mechanically manipulated to expose all the surfaces to the ion beam. Large-area implantation requires the beam to be rastered to achieve uniform coverage of the target surface.
Unlike traditional methods of materials preparation, the ion implantation process is not limited by thermodynamic constraints such as diffusion and as a result it is
20 possible to produce novel materials. Additionally, by modifying only the surface region of a material, desirable properties of the bulk material can be retained whilst selectively optimising the surface characteristics. Despite the extensive scientific literature espousing the virtues of conventional ion implantation, the technology received only limited acceptance within industrial circles. One explanation was the relatively high cost of beam-line implanters compared to other surface modification processes. In response to this, Conrad and co-workers developed the PIII process as a low cost alternative.
In PIII the target material is immersed in the plasma and a high-voltage bias is applied directly to the target. Ions from the plasma are accelerated through the plasma sheath and implant into the target surface (figure 2.4). Due to the extraction of ions from the plasma surrounding all areas of the target, conformal implantation can be achieved and the line-of sight limitation is thus avoided. Cost reduction arises from the relative simplicity of the technique; the lack of requirement for extraction grids, beam manipulation systems, target manipulators and relatively large vacuum vessels.
Plasma Substrate Sheath
b) Substrate a) -10kV c) Holder
Figure 2.4: Schematic showing the concept of PIII. a) Immersion of the sample and sample holder in the plasma. b) Application of a high negative potential pulse to the sample holder results in an expanding plasma sheath. c) Positive ions uncovered by the expanding sheath are accelerated by the high voltage and conformally implant into the substrate and holder.
21 Essential to the understanding of PIII is the concept of a plasma sheath. A sheath is a region in the plasma where space-charge neutrality is violated. In PIII, when the high voltage is applied to the target, a sheath forms around the target and begins to grow into the plasma as ions are implanted into the target surface. For low-density plasmas, if the sheath were allowed to grow unchecked it would eventually reach the walls of the processing vessel and the source of ions would be depleted. Momentarily switching off the high-voltage allows the sheath to contract, replenishing the available ions. Another reason for limiting the sheath expansion is to retain the advantage of conformal implantation. When the sheath width approaches the radius of curvature of the target surface, the advantageous effect of conformal implantation is lost.
Adjusting the pulse width to limit the sheath expansion overcomes this problem. An additional advantage of pulsing the high-voltage is that any arcing that may occur is suppressed, minimising damage to the target surface.
2.2.2. The Physics of Plasma Sheaths
Plasmas are characterised by their charged particle density, ni and ne (subscript “i” denotes ions and “e” denotes electrons) measured in particles/m-3. For a charge- neutral plasma, ni = ne = no, when the ion charge state (Q) is equal to one (ie. ions are singly ionised). When thermal equilibrium is established between each species, their temperatures, Te and Ti, are equal (i.e. Te = Ti). In stars and interstellar plasmas thermal equilibrium is common whilst in most laboratory plasmas Te > Ti due to enhanced electron response to the external power source. The fraction of ionisation is described by
22 ni xiz = (2.1) ng + ni where ng is the neutral gas density. xiz ranges from very small for weakly ionised plasmas to close to unity for highly ionised plasmas. A characteristic length scale in a plasma is the electron Debye length, λDe. Over distances of the order of a Debye length charged particle distributions within the plasma will act to shield out external applied potentials.
1 ε T 2 o e λDe = (2.2) eno where εo is the permittivity of vacuum and e is the electron charge. It can be shown that in the absence of large external potentials, and for scales much larger than a
Debye length, ni = ne and the plasma tends to remain neutral [28]. This is the basic statement of quasineutrality of a plasma, often called the plasma approximation. In some instances, quasineutrality is violated due to external perturbations by electric fields or physical intrusions into the plasma. One consequence of this violation is the establishment of a plasma sheath.
If a quasineutral plasma (ne = ni, Te ≥ Ti) is electrically perturbed by a surface, the charge neutrality in a thin region surrounding the surface is broken. This region is called the sheath and the physical behaviour of sheaths governs much of the dynamics associated with PIII. It is therefore essential to understand sheaths in detail. Different situations will arise depending on whether the surface is electrically isolated or grounded, or held at a particular potential with respect to the plasma. To demonstrate the principle of sheath formation, the case for a small electrically isolated (floating) wire immersed in a quasineutral plasma is illustrated here.
23
Initially the charge density is in equilibrium and the macroscopic electric field is zero everywhere in the plasma. As a result the charged particles are not confined and are free to impact the wire surface. In a typical plasma the electrons are heated by the source while the ions are at near equilibrium with the background gas. The electrons temperature is then of a few eV, while the ions are cold. Due to difference in mass and temperature, the thermal velocity of the electrons
1 2 eTe ve = (2.3) m where m is the electron mass, is much greater than that of the ions
1 2 eTi vi = (2.4) M where M is the ion mass. More electrons are therefore incident on the surface than ions, causing the wire to charge negatively, and an electric field is thus established between the wire and the plasma. Electrons are subsequently repelled back toward the plasma. If the wire is small with respect to the plasma dimensions the bulk plasma potential will not be altered.
As the potential difference increases, only the highest energy electrons within the thermal energy distribution are able to overcome the electric field and reach the surface, causing an electron density gradient to be established across the region of the electric field. Conversely, the electric field accelerates the slow moving ions toward the surface, creating an ion density gradient. When the number of incident ions balances the number of high-energy electrons incident on the surface, equilibrium is established and the wire potential stabilises at the floating potential, Vf. The region
24 where the electric field is present near the surface is defined as the sheath, of thickness so typically of the order of a few Debye lengths. Since slow moving ions take longer to traverse the sheath than electrons, a positive space charge is now present within the sheath region.
To illustrate the concept of PIII, discussion of sheath dynamics and equations will be limited to DC sheaths in one dimension. Since plasma dynamics and processes are complex and often non-linear, simplifying assumptions are required to derive the equations. These will be presented along with brief derivations of the main equations used throughout this thesis for modelling sheath dynamics. For more complete derivations the reader is referred to reference [28].
In the case where the background gas density, ng, is small, we can make the assumption that ions transit the sheath free of collisions with gas molecules. Since the plasmas used in this work derive from cathodic vacuum arcs, ng is very small and this assumption, termed the collisionless sheath assumption, is valid. Collisional sheaths will not be considered here. We develop the equations for an infinite one-dimensional surface, of potential Vw, immersed in a quasineutral plasma. Setting the sheath boundary (defined as the interface between neutral and non neutral regions) at x = 0, then ni (0) = ne(0). At x = 0 the potential, V, is defined as zero and the ions have a velocity uis.
Assuming the electrons are Maxwellian with temperature Te, and the ions are singly ionised (Q=1) and cold (Ti = 0), conservation of energy gives the ion energy while the ion transits the sheath as
25 1 1 Mu 2 (x) = Mu2 − eV (x) (2.5) 2 i 2 is and the continuity of ion flux as
ni(x)ui(x) = nisuis (2.6) where nis is the ion density at x = 0.
b) a) so
c) s d) s c Figure 2.5: Child-law sheath evolution showing; a) uniform plasma b) ion matrix sheath c) expanding sheath and d) Child-law sheath. (adapted from [26]). S denotes the sheath boundary.
In PIII the target is immersed in a plasma of density no and a pulsed with a high negative potential, Vo, which is assumed to be much greater than the electron temperature such that the number of electrons with sufficient energy to overcome Vo approaches zero. Electrons are expelled from the region surrounding the target leaving behind a more-or-less uniform array of positively charged ions. This sheath,
26 known as an ion matrix sheath (figure 2.5(b)), is formed, on a timescale of the order of the inverse plasma frequency for electrons, ωpe.
1 2 2 e ne ω = pe (2.7) ε om
In most processing plasmas ωpe is of the order of a few nanoseconds. Assuming ni is constant within the sheath, the matrix sheath thickness so is given by,
1 2ε V 2 o o so = (2.8) eni
In terms of the Debye length we see that (from (2.2)),
1 2V 2 o so = λDe (2.9) Te
On a longer timescale, of the order of the inverse plasma ion frequency, ωpi,
1 e 2 n 2 ω = i (2.10) pi ε o M ions will be accelerated by the electric field in the matrix sheath and implant into the target surface. Depletion of the ions in the matrix sheath reduces the ion density, making it non-uniform. Assuming the ion energy as the ions enter the sheath is much smaller than Vo, the last term in equation (2.5) can be ignored, and (2.5) and (2.6) reduce to
1 Mu 2 (x) = −eV (x) (2.11) 2 i and
eni(x)ui(x) = Jo (2.12) where Jo is the ion current to the surface, which must remain constant by continuity.
Combining (2.11) and (2.12) and solving for ni(x), we get
27 1 − 2 Jo 2eV ni (x) = − (2.13) e M
Poisson’s equation in one dimension is
d 2V ρ(x) 2 = (2.14) dx ε o where
ρ(x) = eni(x) (2.15) since we assume the sheath is devoid of electrons. Combining (2.13), (2.14) and
(2.15) we get
1 2 − 2 d V Jo 2eV 2 = − − (2.16) dx ε o M
Letting V = Vo at x = s and manipulating (2.16) (see [28]) we obtain
1 3 2 2 4 2e Vo Jo = ε o (2.17) 9 M s2
Equation (2.17) is known as the Child law of space-charge-limited current in a planar diode. Although it was developed originally for electron diodes, it can used to predict the sheath thickness when a high-voltage is applied to a surface immersed in a plasma. It is thus commonly used for PIII modelling. If the initial ion energy is not insignificant when compared to Vo, equation (2.11) does not hold and the ion energy must be included in the derivation.
The Bohm sheath criterion [28] states that the velocity of the ions at the sheath, uis, must be greater than, or equal to, the ion sound speed (Bohm velocity).
1 2 eTe uis ≥ ub = (2.18) M
28 To satisfy (2.18) the ions must gain energy as they approach the sheath edge and there must therefore be a small but finite electric field in a region, typically much wider than the sheath, called the presheath. An important consequence of the presheath requirement is a reduction in the plasma density from the bulk density, no, at the sheath boundary. It can be shown that the density is smaller by a factor of approximately 0.61 due to the ion acceleration that occurs in the presheath, bringing the ions to the Bohm velocity.
(2.17) can be solved for s in terms of the Debye length giving
3 2 2V 4 o s = λDe (2.19) 3 Te
Comparing this to (2.9) we see that the Child law sheath thickness is larger than the
1/4 matrix sheath by a factor of the order of (Vo/Te) . Thus there is an expansion of the sheath from the initial matrix sheath thickness to the static Child law sheath thickness.
We describe the expanding sheath as a quasistatic Child law sheath. Ion current is supplied to this sheath by the uncovering of ions at the moving sheath edge and by ions crossing the sheath boundary at the Bohm velocity.
ds J o = eni + ub (2.20) dt
Equations (2.17) and (2.20) form the basis of the models used for simulating PIII sheath expansion in this thesis. Equating them and solving for the sheath velocity we find
ds 2s2u = o o − u (2.21) dt 9s2 b where so is the matrix sheath thickness (equation (2.8)) and uo is the characteristic ion velocity
29 1 2 2eVo uo = (2.22) M
Integrating (2.21) we can determine the steady-state child law sheath thickness, sc, to be
1 2u 2 o sc = so (2.23) 9ub
The above derivation assumed singly charged ions. In the case of multiply charged ions (Q > 1), to maintain charge neutrality the ion density, ni, is in fact no/Q, and the ion charge is Qe. Including the effects of multiply charged ions, (2.17) modifies to
1 3 2 2 4 2Qe Vo Jo = ε o (2.24) 9 M s2
Equation (2.20) remains the same since the reduced ion density counters the increased charge of the ions.
2.2.3. Metal plasma immersion ion implantation and deposition
Cathodic arc plasmas exhibit some unique characteristics that require consideration in the application of the above models. Apart from possessing multiply charged ion species (up to Q = 5 in some cases [29]), cathodic arc plasmas have highly directed drift velocities. The reasons for this will be discussed in the next chapter. A major consequence when utilising plasmas with a highly directed drift velocity for PIII is the partial loss of conformal implantation. As it turns out the advantages gained from utilising cathodic arc plasmas can outweigh the aforementioned loss.
30 Cathodic arc plasmas have been traditionally used as a source for thin metal film coatings. When combined with PIII, metal deposition and ion implantation occur simultaneously. During the off-time between PIII pulses, the high voltage is removed from the substrate and deposition occurs during this period. The combination of deposition and implantation (not purely restricted to cathodic arc plasmas) has been dubbed plasma immersion ion implantation and deposition (PIIID) When the plasma ions are metallic the prefix “Me” is added (MePIIID). Pioneering work in this area was primarily conducted by Ian Brown, Andre Anders and co-workers at LBL,
Berkeley, California. Due to the combined effects of implantation and deposition, the growing film is subjected to bombardment by energetic ions inducing changes in the thermodynamic properties. Films grown in this manner consequently exhibit changes in morphological structure, which can result in changes in the intrinsic stress and preferred orientation of the film [30]. One important application of this has been the production of low-stress, adherent, amorphous carbon films [31].
For the models presented above, incorporation of the effects of ions with a high directed velocity has some important consequences. For a cathodic arc plasma, the directed velocity is generally large compared to the Bohm velocity and the ions traverse the sheath boundary at speeds greater than the ion sound speed. Hence, the
Bohm sheath criterion is already satisfied. Subsequently, the presheath no longer needs to develop and the ion density at the sheath boundary is equal to the bulk plasma ion density. For the case of a cathodic arc plasma, the Bohm velocity, ub, is replaced with the directed ion drift velocity, uc, in equations describing sheath growth.
31 From the (2.23) we can see that the effect of the increase in the directed velocity is to reduce the thickness of the sheath. The cathodic arc plasma source allows a steady- state sheath to be established in a short time period, theoretically removing the requirement to pulse the high voltage power supply. Investigations into the practicalities of applying a DC voltage to the substrate in a cathodic arc plasma suggest that other factors may limit this option [32]. For high plasma densities the sheath thickness can be small enough that the electric field across the sheath is significantly large. Surface protrusions can become “emission centres” emitting large amounts of electrons that facilitate a short circuit of the sheath. This results in sheath breakdown, which manifests as arcing and can damage the substrate surface. For extended periods of ion bombardment, heating of the substrate changes the surface work function and secondary electron coefficient, which can enhance the effectiveness of the emission centres [33]. Whilst there is no conclusive evidence to suggest a maximum allowable electric field strength, a recent study by Anders [33] suggests sheath electric fields in excess of 107 V/m are sufficient to cause surface breakdown if field enhancement due to surface roughness is present. Anders also gives evidence for breakdown being due to sheath contraction at higher plasma density increasing the field strength [34]. Using this value, ion density and applied voltage limits have been determined for PIII in a cathodic arc plasma [35]. These have not been tested experimentally.
One of the primary assumptions in the derivation of the Child law sheath equation
(2.17) was that the initial ion energy is much smaller than the applied voltage, Vo. For cathodic arc plasmas ion energies are of the order of tens of electron volts. Thus, for applied voltages less than 1kV the initial ion energy is of consequence. Equation
32 (2.11) is then no longer valid and only analytical solutions can be found to Poisson’s equation. For most PIII applications, voltages of greater than 1kV are used and the
Child law assumption results in only very small errors in the sheath dynamics.
One of the major advantages of using cathodic arcs as a plasma source for PIII is the high fraction of ionisation in the plasma. The degree of ionisation, xiz, is usually very close to unity at the source. Combined with a magnetic macroparticle filter most remaining neutrals are filtered out, resulting in pure implantation during the pulse on time. Other sources of metal ions usually exhibit much lower xiz, which results in combined deposition and implantation during the high voltage pulse. With fully ionised plasmas the proportion of implantation and deposition is determined by the
PIII duty cycle. Another important consequence of using cathodic arc plasma sources is the large proportions of multiply charged ions present in the plasma. Multiply charged ions are accelerated across the sheath and impact with energies proportional to their charge state.
Εi = V1Qe (2.25)
Implantation depths are proportional to the ion energy. Utilising highly charged ions can therefore increase the depth of surface modification.
2.2.4. Plasma immersion ion implantation of insulators
The original focus of this thesis was to utilise the cathodic arc plasma source and the
PIII process to implant polymer surfaces with the aim of modifying the surface properties. It became clear quite early in the work that there were some properties
33 specific to polymers that complicated this relatively straightforward aim. The most obvious of these properties is the electrically insulating nature of most polymers. PIII relies on the high voltage induced on the surface of the substrate to extract ions from the plasma. Incident ions carry charge to the surface, which must be neutralised to maintain the applied voltage. On an insulator surface this charge is not neutralised and the applied potential reduces as the charge accumulates. Eventually the potential at the substrate surface will be completely extinguished by the accumulated charge and the sheath will collapse. Measurements of the sheath collapse for insulating substrates in a cathodic arc plasma will be presented in chapter 6.
Another adverse property of polymers is their high dielectric capacitance. Of the few experimental studies of PIII with polymers, the predominant method of applying a voltage to the substrate surface has been to place the substrate on a conductive holder and apply the high potential to the holder. A voltage is then induced on the substrate surface, but it is reduced due to the capacitance of the substrate. For very thin substrates this capacitance is small but as the thickness of the substrate increases the voltage reduction becomes more pronounced.
Emmert, studying the application of PIII to semiconductor processing and the problem of charge accumulation on silicon oxide, modeled a slab of dielectric material, thickness, d, with dielectric constant, κ, on a conductive block [36]. From
Gauss’ law, if a potential, Vo(t), is applied to the block, the voltage on the dielectric surface at time t will be
Ed (t)d σ (t)d V1(t) = Vo (t) − + (2.26) κ ε oκ
34 where Ed(t) is electric field in the plasma at the surface of the dielectric, and σ(t) is the charge density on the dielectric surface. The electric field can be calculated from
(2.17). Combining (2.17) and (2.26) and rearranging we obtain
V (t) −{[σ (t)d]/(ε κ)} V (t) = o o (2.27) 1 1+{(4d) /[3x(t)κ}}
From (2.27) it is apparent that there are a number of time dependent variables required to determine V1, some of which are interdependent. The charge density is dependent on the sheath thickness by
σ (t) = niQe[x(t) + ubt] (2.28)
In his formulation, Emmert neglected to include the secondary electron co-efficient of the dielectric surface. The secondary electron co-efficient is defined as the number of electrons emitted from the surface per incident ion. Linder and Cheung included the secondary electron co-efficient, γ, in their later model. (2.28) then becomes
σ (t) = ni (Qe + γ )[x(t) + ubt] (2.29)
Lacoste and Pelletier [24] recently noted that γ is dependent on the energy of the arriving ions, Ei, given by (2.25). Thus, there is a further interdependence between the accumulated charge and the surface voltage. It shall be shown in chapter 4 that by applying a thin conductive film that is in contact with the substrate holder to the polymer surface, the charge accumulation problem is alleviated.
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38