Interactions of ion beams with polymers: the physical picture

The implantation of energetic ions into a solid causes a significant transformation of the structure and properties of its surface layer. The movement of ions penetrating into the solid causes collisions with atoms and electrons of the molecules along the ion path. As a result of these collisions, the atoms and electrons of the ion-implanted material are shifted from their equilibrium positions, leading to atomic displacements and the excitation of vibrational modes. The vibrational energy is dissipated in the material by the propagation of phonons. The collision cascades produced by the ions implanted can be considered according to the theory of particle scattering using a binary collision model to give ion penetration depths, atomic vacancy, phonon, and scattered atom and electron distributions. Estimates of the distribution of radicals created under the surface in polymers can be obtained by examining the distribution of atomic vacancies together with the atom valencies.

Keywords

Ion implantation; polymer; collision; unpaired electron; phonon

An ion beam treatment of a solid target causes a significant transformation of the structure and properties of the treated surface [1–8]. Rutherford reported the first experiments of charged particle penetration into a solid [9]. This and subsequent research has shown that the changes in the solid target depend on the material of the target, the kind of implanting ions, their kinetic energies, the ion flux, the temperature of the target and the gas environment. The movement of penetrating ions in the solid target causes collisions with atoms and electrons of the target molecules. As result of these collisions, the atoms and electrons can be shifted from their equilibrium positions, leading to the excitation of vibrational modes and the resulting phonons propagate to dissipate the energy. Atoms and electrons receiving more energy in collisions can be ejected from their positions in the target if the energy transferred to them by the penetrating ion is higher than the binding energy in the solid or the ionization energy of the target atom, respectively. If the recoiled atoms or electrons have enough kinetic energy, they will interact in the same way with other atoms and electrons of the target, transferring energy in the process, in this way, generating cascades of collisions. The region in the target that contains displaced and recoiled atoms and electrons is called the spur of the penetrating ion. Usually, the volume of the spur has a teardrop shape: narrow at the surface where the ion entered, with a wide waist and obtuse end.

The collision events of ions implanted into the target can be considered according to the theory of particle scattering. The energy lost by the implanting ion in a collision with an atom of the target depends on its angle of incidence, its interactions with atoms and electrons, and the density of the target. If we assume that electron and atomic excitations are not correlated processes, the energy transfer is the sum of electron and nuclear stopping effects:

Edx=N[(Sn(E)+Se(E)] (Eq. 1.1)

where Sn(E) and Se(E) are nuclear and electron cross-sections of stopping, and N is the atomic density of the target [2,8]. Most models for calculating the effects of ion implantation are based on this additive assumption. The nuclear- and electron-stopping cross-sections depend on the interactions between the collided particles. Typically, pair potentials, such as the as Wilson, Haggmark, Biersack (WHB) or Ziegler, Biersack, Littmark (ZBL) potentials, are used to model these interactions in modern computer codes for ion collision calculation. Modern computer simulation codes, such as Transport of ions in matter (TRIM) and Stopping and Range of Ions in Matter (SRIM) [10], give excellent agreement with experimental data for ion penetration depths, defect distributions, phonon distributions, distributions of scattered atoms and electrons, and transmitted ions. TRIM and SRIM are based on the Monte Carlo method and are commonly used for simulation of ion implantation effects in solids, including polymers [2].

For example, Figure 1.1 presents the region affected by a nitrogen ion track in polyethylene calculated with the TRIM code. The nitrogen ion penetrates into the polyethylene, colliding with carbon and hydrogen atoms, and they recoil. The recoiled atoms receive energies high enough to leave their sites in the structure and subsequently collide with other carbon and hydrogen atoms. A tree of collisions forms. Thousands of ions implanting into randomly distributed target atoms are calculated and analyzed (Figure 1.2) to achieve a statistical understanding of these events. A complete statistical analysis of all collisions, stopped ions, and recoiled and displaced atoms and electrons, as well as phonons, is presented. The final distribution of positions at which the implanted ions come to rest (stopped ions) has a maximum under the modified surface layer (Figure 1.3). The profile of stopped ions has been analyzed by experimental methods for many materials, including polymers, with good agreement with the calculated theoretical data observed. For polymer materials, the number of ions per square centimeter penetrating the surface, or fluence, is typically kept low, so the distribution of stopped ions is not very important.

The graph of collision events, which shows the distribution of carbon and hydrogen atom vacancies (Figure 1.4), is of more significance in the case of polymer materials. This gives an indication of the distribution of free valence electrons in the polymer macromolecules, or in another words, the distribution of free radicals created by the propagating impacts. The free radicals are a result of significant structural damage of the polymer macromolecules, and they initiate a complex structural transformation. The graph showing the sum of the target vacancies has no significance for polymers, because recoiled carbon and hydrogen atoms have very different consequences for the structural transformation. If a hydrogen atom is recoiled, the carbon atom to which it was bonded is left with an unbonded valence electron that is very reactive and will readily form new covalent bonds with other unpaired electrons.

However, a recoiled carbon atom (e.g., in a polyethylene macromolecule) generates four unpaired electrons in the macromolecule: two on hydrogen atoms and two on neighboring carbon atoms. The recoiled carbon atom brings four unpaired electrons in a place, where the atom is stopped. In total, eight unpaired electrons are generated.

For a thorough analysis, the total number of free radicals (i.e., electrons not paired in covalent bonds) in the structure of the polymer macromolecule must be taken into account. Because each vacancy generates more than one unpaired electron, the free radical concentration in polymers is significantly higher than the calculated vacancies or recoiled atoms would suggest.

Figure 1.5 presents an example of energy lost due to ionizing interactions. Ionizing interactions due to incoming ions commence at the point of entry immediately under the surface. The free electrons created in ionization events can leave the structure, resulting in a net positive charge on the polymer target. The electrons ejected in this way are called secondary electrons. Usually, the ion interactions cause the ejection of many electrons, and the charge resulting from the implantation of the positive ions has a significantly smaller magnitude than does the charge resulting from the release of electrons. Energetic free electrons can also penetrate deeper into the polymer target, with a range longer than that of the implanted ions. The collisions of these electrons with polymer macromolecules cause structural transformations deep below the surface.

Interactions where there is low energy transfer generate a phonon distribution (Figure 1.6). Interactions with the implanting ion make a small contribution to the phonons, with the majority of phonons being generated by the recoiled atoms of the target. Phonon excitation can be interpreted thermodynamically as a vibrational temperature of the macromolecules. Calculations suggest short-term (<ns) temperature increases of up to 104 K. After a short time...