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Chapter 2 Ion solid interactions: Ion implantation, production of radiation damage and annealing of damage.
Introduction
Ion implantation is regarded as the main technique used to introduce controlled concentrations of impurities into solids. Atoms from the desired material are ionized, then accelerated and directed towards a target. The kinetic energy of the ions enables them to penetrate into the lattice of the target material. Energetic particles impinging on a target, penetrating into it until they come to rest somewhere within the target are said to have been implanted. During these ion-solid interactions, ions gradually lose energy when they interact with target atoms as they move through the solid until they stop at a certain depth within the solid.
A variety of other processes can also take place during interactions between projectile ions and solid targets [Gna99]. Some target materials are of a crystalline nature, meaning that their constituent atoms are positioned at specific points known as lattice sites in periodic arrays leading to long range order [Cal07]. Implantation into such materials may result in target atoms being temporarily or permanently displaced from their original lattice sites leading to the formation and accumulation of defects in the target. Accumulation of the defects can lead to the total loss of this systematic and regular arrangement of the atoms and this absence of long range order is known as the amorphous state [Cal07]. Incident ions may also supply target atoms close to the surface with enough energy to overcome the surface potential barrier and escape from the target. This emission of surface atoms on impact of energetic particles is known as sputtering [Hof76,Cal07]. A term known as the sputter yield, defined as the mean number of atoms removed from the target surface per unit incident ion is used to quantify the surface erosion [Beh83]. The sputter yield depends on the target material, the experimental geometry, ion species and ion energy of the incident ion beam [Fel86]. An excellent review of the sputtering of compound semiconductor surfaces is given by Malherbe [Mal94].
Energy loss of ions in solids
There are two major processes which result in the incident ions losing energy when energetic ions enter a solid. The ions lose energy when they undergo elastic collisions with lattice atoms and the ions also lose energy in inelastic interactions with electrons in the solid in which the electrons are excited. These processes are referred to as nuclear energy loss and electronic energy loss respectively. The two processes are generally viewed as being independent from each other [Wil73].In nuclear stopping, elastic coulomb interactions between the nuclei of the ion and target atom result in relatively large amounts of energy and momentum transfer. This leads to significant changes in ion‟s direction as well as displacements of target atoms from their lattice positions. Nuclear stopping depends on the distance of closest approach of the ion to the target atom as the interaction potentials are strongly dependant on the distance separating the two nuclei. In the case of electronic stopping, the collisions are characterized by relatively small amounts of energy and momentum transfer due to the small electron mass. For such collisions, deflections of the ions will be negligible.The average energy loss per unit length of penetration into a homogenous medium by a charged particle or projectile is the quantity most often referred to as the stopping power of the medium [Kam84]. The total stopping power for an ion coming to rest at a depth x below the target surface [Dea73] is given by.
where N is the atomic density of the target, Sn (E) and Se (E) the nuclear and electronic stopping powers respectively. The total stopping cross section (ε) can be calculated by dividing the total stopping power by the target density N and are therefore defined by:The stopping power is greatly influenced by the ion energy E. At low energies, nuclear stopping is the dominant mechanism. At higher energies nuclear stopping is overtaken by electronic stopping which then dominates. This shift in the dominant energy loss mechanism is shown in figure 2.1. It is clearly observed in the figure that electronic stopping begins to dominate above the critical energy Ec. The electronic stopping then reaches a maximum and then decreases again towards the high energy region described by the Bethe-Bloch equation [Bet30] where the ion has a shorter time to interact with the target atoms at the high ion velocities. The mechanisms of electronic and nuclear stopping are discussed in more detail in sections 2.1.1 and 2.1.2.
Electronic Stopping
In this energy loss mechanism, energetic ions penetrating a material lose their energy via inelastic interactions with target electrons. A number of processes facilitate this transfer of kinetic energy from the incident ion to the target electrons [Zie85]. These include electron-electron collisions, excitation or ionization of target atoms and excitation, ionization or electron–capture of the incident ion.A model based on the ion velocity is used to describe the energy loss process. The basis of which arises from comparing the ion‟s velocity with the Bohr velocity v0 = e2 / . Here, e and ħ are the electron charge and the Planck‟s constant h/2π respectively. The first part of the model deals with the low energy region (L in figure 2.1) where the ion‟s velocity v1 is such that v1 < v0 z 23 . z here is the atomic number of the ion . v0 z 2 / 3 for cesium ions is 3.16 × 10 9 cm/s. At 360 keV, cesium ions have an initial velocity of 7.2 × 10 7 cm/s which is less than v0 z 2 / 3 . At these ion velocities, the ion cannot transfer sufficient energy to electrons that are far lower in energy than the Fermi level. As a result only electrons in energy levels close to the Fermi level are involved in the inelastic energy loss process. In calculating the electronic stopping for this low energy region, a free electron gas with a density ρ is assumed [Lin53, Lin61]. The electronic stopping cross section e e of an ion with Z1 is then [Zie88]:
where I is the stopping interaction function of an ion of unit charge with velocity v, ρ is the electron density of each volume element the target dV, Z1(v) shows that the charge state of the ion is velocity dependant as the stripping of its electrons depends on its velocity. The integral is performed over each volume element of the target dV.The second region of the model deals with the so-called intermediate region where the ions velocity v1 is such that v1 » v0 z 23 . In this energy region, the ion is partly ionized and the electronic stopping reaches it maximum (figure 2.1).Very high velocities where the ion‟s velocity is now given by the condition v1 >> v0 z 23 make up the third region in the model and this region is described by the Bethe-Bloch equation [Boh13, Bet30, Blo33, Kam84]. The Bethe-Bloch equation shows that the energy loss in this case is proportional to Z1 2 as given in equation 2.4where me is the mass of the electron, v1 the velocity of the projectile, Z2 is the mass of the target atom, b = vc , c being the speed of light and C/Z2 is the shell correction to compensate for the lower contribution to the stopping power of electrons in the inner shells. d2 is the density effect correction at very high kinetic energies to account for the decrease in stopping power due to dielectric polarization of the stopping medium. I is the mean excitation energy defined as [Kam84 where fn is the dipole oscillator strength for transitions from the ground state E0 to energy state En . Many models have been used estimate I. A common approximation for I is given by Block‟s rule [Bloc33]:
For the work presented in this thesis, we are interested in the low and intermediate energy regimes. The low energy regime for the implantation of 360 keV ions and the intermediate energy regime for the ion beam analysis technique Rutherford backscattering spectroscopy (RBS) in which we use 1.6 MeV alpha particles.
Nuclear Stopping
As the projectile ion penetrates through the solid, the interaction between the incident ion and a target atom is taken to be isolated from the rest of the target atoms. This assumption allows the ion scattering and energy transfer to be treated as a simple two-body collision event. Nuclear scattering can then be described by the potential between the ion and the target electrons. There are many interatomic potentials that have been suggested over the years in literature [Gna99] and generally take the form of the screened coulomb potential given in equation 2.7 below.
electron density distribution in the two atoms [Gna99]. The interatomic potentials for a number of atomic pairs have been calculated using the Hartree-Fock Methods [Zie85].The collision between the incident ion of mass M1 and target atom of mass M2 results in the transfer of kinetic energy T. This transfer obtained from the conservation of energy and momentum, is a function of the masses of the ion and target atom along with the projectile energy E0 and the scattering angle α in the centre of mass system [Tow94, Fri01] as shown in equation 2.10The scattering angle (α) in equation 2.8 can be calculated as a function of collision parameter b for a given potential such as the one given in equation 2.7.For an incident ion penetrating through an amorphous target having a density of N atoms/unit volume, and during its movement through a slab of the target material of thickness dx, (figure 2.2), the number of atoms with collision parameters in an interval db is given by [Was07].
Energy loss in compounds
Our work in this thesis revolves around silicon carbide. In dealing with the energy loss processes, we are therefore interested in the energy loss behaviour in multi element targets or compounds. In such targets, collisions are still considered to be independent encounters taking place one at a time. The collisions are distributed among the various elements and weighted proportionally to the elemental distribution of the compound. This is known as the Bragg rule [Bra05]. For a compound with composition AmBn, the stopping cross section where A and B are the elements in the compound and m and n are the relative molar fractions of the compound.Deviations from this Bragg rule have been found experimentally. This is due to the fact that the rule assumes that the projectile ion-target atom interaction is independent of the environment [Tes95]. However, during the interactions, the chemical and physical state of the medium, influence the energy loss. Marked deviations from the Bragg rule, in the order of 10%-20% around the stopping maximum have been observed. Such cases involved light organic gasses, as well as solid compounds in which there are large differences between the atomic masses of the constituents such as in the case of oxides and nitrides of heavy metals [Tes95]. Ziegler and Manoyan [Zie88], developed the „Cores and Bonds‟ model (CAB) to accommodate the chemical state effects. In this model for the stopping of ions in compounds, it is assumed that two contributions are involved. These are the effects of the non-bonding closed shell „core‟ electrons and the bonding valence electrons. If the bond structure of a compound is known, the CAB correction can be determined.
Energy Straggling
An energetic particle moving through a medium loses energy via many individual interactions with the medium‟s atoms. The discreteness of such interactions leads to statistical fluctuations. Identical energetic particles initially having the same energy when entering the medium will not have the same energy after traversing the same thickness (x) of the same medium. This phenomenon is known as straggling [Fel86].For electronic energy loss where the energy loss process is subject to statistical fluctuations of the electronic interactions, the straggling has been derived from the Bloch-Bethe equation [Boh48, Zie85, Fel86]. This so-called Bohr straggling, W2B , is given by:Here, W2B is the variance of the average energy loss of a projectile travelling through a target thickness x. The distribution of energy loss for many independent collisions is approximately Gaussian when the energy loss is small compared to the incident energy [Fel86]. The full width at half maximum (FWHM) of the energy loss distribution is then given by 2WB 2 ln 2 . This Bohr theory of straggling has since been extended to include corrections for energies where earlier assumptions may not be valid. Some of these extended models include works by [Lin53] and [Chu76]. In compound targets, the total energy straggling is through a similar linear additivity rule to the Bragg‟s rule for energy loss [Chu76. Tes95].
Range of implanted ions
The penetration length of ions with initial incident energy E0 known as the range, R, of ions moving through a target medium of atomic density N, is given by equation 2.14 [Gib75] below.
The standard practice when dealing with penetration depths of ions into targets is to consider the projection of the distance travelled into the medium by an ion (the range R of the ion)
onto the direction of incidence. This projection is referred to as the projected range RP of the ion (figure 2.3).
Chapter 1: Introduction and Background
1.1 Motivation for new generation nuclear reactors
1.2 The Pebble Bed Modular Reactor (PBMR)
1.3 Silicon Carbide (SiC)
1.4 Motivation for simulation of neutron irradiation effects in reactor conditions with heavy ion irradiation as a surrogate
1.5 Radiation damage in SiC
1.6 Radiological significance of chosen fission product elements
1.7 Diffusion of fission product elements in SiC
1.8 Outlay of this Thesis
References
Chapter 2: Ion solid interactions: Ion implantation,production of radiation damage and annealing of damage
2.1 Energy loss of ions in solids
2.1.1. Electronic stopping
2.1.2. Nuclear stopping
2.1.3. Energy loss in compounds
2.1.4. Energy straggling
2.1.5. Range of implanted ions
2.2. Ion Channeling
2.3 The distribution of implanted ions
2.4. Radiation damage
2.4.1. Point defects and extended defects
2.4.2 Amorphisation
2.4.3. Homogenous and Heterogeneous models for amorphisation
2.4.4. Amorphisation: Fluence dependence
2.4.5. Armophisation: Temperature dependence
2.5. Structure of amorphous SiC
2.6 Annealing of radiation damage
References
Chapter 3: Diffusion
3.1 The diffusion coefficient
3.2 Evaluation of the diffusion coefficient
3.3 Mechanisms of diffusion in solids
3.3.1 Diffusion in crystalline materials
3.3.2 Vacancy mechanism
3.3.3 Interstitial mechanism
3.4. Diffusion in defective and damaged crystals
3.5 Diffusion in polycrystalline materials References
Chapter 4: Experimental- Analysis Techniques
4.1 Scanning Electron Microscopy (SEM)
4.1.1 Electron beam-specimen interactions
4.1.2 The Field Emission Gun (FEG)
4.1.3. Electron beam optical column
4.1.4. Condenser lenses
4.1.5. The objective lenses and scanning coils
4.1.6. In-lens detector
4.2. Atomic Force Microscopy (AFM)
4.2.1. Basic principle of the AFM set up
4.3 Atom Probe Tomography (APT)
4.3.1 The physics of Atom Probe Tomography
4.3.2. Fabrication of the atom probe samples with a dual beam focused ion beam(FIB) instrument
4.4 Rutherford backscattering spectroscopy-Channelling (RBS-C)
4.4.1 The accelerator, scattering chamber and detector system-RBS experimental
4.4.2 The physics of RBS
4.4.3 The kinematic factor
4.4.4 Depth profiling
4.4.5 The differential cross section
4.4.6 Rutherford backscattering combined with Channelling (RBS
4.4.7 Data acquisition in RBS
4.4.8 Data analysis
4.5 Time-of-Flight -Heavy Ion Elastic Recoil Detection Analysis (ToF-ERDA)
4.5.1 ToF-ERDA set-up at the iThemba Labs, Gauteng 6Mev Tandem Accelerator
4.6 Secondary Ion Mass Spectroscopy (SIMS)
4.6.1 General principles of SIMS
4.6.2 Secondary ion yield
4.6.3 Mass spectrometry
4.6.4 Depth profiling in SIMS
4.7 X-ray Photoelectron Spectroscopy (XPS)
4.7.1 Physics of XPS (photoionization)
4.8. Raman spectroscopy
References
Chapter 5: Sample preparation
5.1 Ion implantation
5.2 Annealing of samples and the annealing system
5.2.1 Webb 77 graphite furnace
References
Chapter 6: Results- Diffusion Studies
6.1 Introduction
6.1.1 Isochronal annealing results of cesium implanted single and polycrystalline
silicon carbide
6.1.2 Isothermal annealing results of cesium implanted single and polycrystalline silicon carbide
6.2 Results of the high temperature isochronal annealing studies of iodine and silver ions implanted in to 6H-SiC: Synergistic effects on the diffusion behaviour in SiC
6.2.1 RBS-C results
6.2.2. Heavy ion ERDA results of silver and iodine ions co-implanted in to 6H-SiC
6.2.3 SIMS Results of silver and iodine ions co-implanted in to 6H-SiC
6.2.4 APT Results of silver and iodine ions co-implanted in to 6H-SiC
References
Chapter 7: Results-Surface microstructure studies of ion implanted SiC
7.1 SEM studies on the annealing behaviour of ion implanted 6H-SiC
7.2 XPS studies on I and Ag co-implanted samples
7.3 Raman spectroscopy studies on the recrystallization and thermal decomposition of silicon carbide
References
Chapter 8: Conclusions
Chapter 9: Research outputs
