1. Introduction

Applications of ion implantation require an understanding of the lattice defects, which largely control the optical and electrical properties of semiconductors. Characterization techniques such as secondary ion mass spectrometry, spreading resistance, carrier and mobility profiling,

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Rutherford backscattering, ion channeling, and transmission electron microscopy with examples of using these techniques to investigate the dopant distribution in the implanted samples, characterize dopants that are electrically active, examine accumulation of the ion beam induced defects, and resolve their structure have been reviewed in the literature [1]. As the main feature of ion implantation is the formation of point defects in the energetic ion collisions, it is natural to present additional methods employed in semiconductor research to study atomic origin and electrical activity of technologically relevant imperfections. The prime attention will be given to characterization techniques invented in technological development of the Si/SiO2 system, though examples of other materials systems, which can be studied by application of positron annihilation spectroscopy, electron spin resonance spectroscopy, and (photo) electrical methods are provided.

### 2. Positron annihilation spectroscopy

Positron annihilation spectroscopy (PAS) is now a well-established tool to characterize electronic and defect properties of bulk solids, thin films, and surfaces. PAS allows studying the electronic structure of defects in solids. The imperfections are represented by small volume defects such as vacancies, vacancy clusters, and free volume defects. Positron beams can be applied to study defects in metals, semiconductors, composite materials, and thin film systems of different crystalline structure and chemical bonding. Methodologically, PAS mainly considers the three experimentally accessible dependences schematically indicated in Figure 1: (i) the time-dependent distribution of annihilating photons; (ii) the angular distribution of annihilating photons; and (iii) the Doppler broadening of the 0.511 MeV annihilation line. While the time-dependent distribution of photons bears information on the electron density in the vicinity of the annihilation event, the latter two photon characteristics provide information on the electron momentum distribution. The positron lifetime gives more integral information than the momentum measurements regarding the region from which the positron annihilates. In the case of a defect-containing sample, the average electron density at a defect site can be rather defect-specific. This suggests position lifetime measurements are suitable for investigating vacancy-clustering processes in rapidly quenched or (ion) irradiated materials. The momentum measurements can also yield detailed defect-specific information. The positron energy may vary allowing examination of the depth distribution of defects in solids and interfaces. Other direct experimental methods including transmission electron microscopy and atomic diffusion are less capable in detecting open volume defects located at interfaces and surfaces. The threshold defects concentration ensured by PAS is 1014 to 1015cm<sup>3</sup> .

The physics of positron annihilation spectroscopy has been explained in textbooks [2, 3] and research articles [4, 5]. A positron injected into a solid becomes thermalized within a few picoseconds by ionizing collisions, plasmon and electron-hole excitations, and phonon interactions. If lattice defects are present in the material, the positron can be trapped by these imperfections. Lattice imperfections (vacancies, vacancy clusters, or dislocations), open volumes, nanoclusters, and the surface states can serve as potential wells, which effectively trap positrons. Within hundreds of picoseconds, a positron in a solid annihilates with an electron yielding two gamma rays.

Figure 1. Schematic representation of positron annihilation indicating the basis for the three experimental techniques of positron annihilation spectroscopy: lifetime, angular correlation, and Doppler broadening.

The distribution of the Δt values for a number of these events, measured in a PAS lifetime experiment, provides the total electron density in the region of positron-electron annihilation. The positron annihilation rate λ is the reciprocal of the positron lifetime and can be described by the overlap integral of the electron ρ�ðrÞ and positron ρþðrÞ densities [4]:

$$
\lambda = \pi r\_0^2 c \iiint \rho^-(\mathbf{r}) \rho^+(\mathbf{r}) d^3 \mathbf{r},\tag{1}
$$

where r<sup>0</sup> is the classical electron radius and c is the velocity of light.

Rutherford backscattering, ion channeling, and transmission electron microscopy with examples of using these techniques to investigate the dopant distribution in the implanted samples, characterize dopants that are electrically active, examine accumulation of the ion beam induced defects, and resolve their structure have been reviewed in the literature [1]. As the main feature of ion implantation is the formation of point defects in the energetic ion collisions, it is natural to present additional methods employed in semiconductor research to study atomic origin and electrical activity of technologically relevant imperfections. The prime attention will be given to characterization techniques invented in technological development of the Si/SiO2 system, though examples of other materials systems, which can be studied by application of positron annihilation spectroscopy, electron spin resonance spectroscopy, and (photo)

Positron annihilation spectroscopy (PAS) is now a well-established tool to characterize electronic and defect properties of bulk solids, thin films, and surfaces. PAS allows studying the electronic structure of defects in solids. The imperfections are represented by small volume defects such as vacancies, vacancy clusters, and free volume defects. Positron beams can be applied to study defects in metals, semiconductors, composite materials, and thin film systems of different crystalline structure and chemical bonding. Methodologically, PAS mainly considers the three experimentally accessible dependences schematically indicated in Figure 1: (i) the time-dependent distribution of annihilating photons; (ii) the angular distribution of annihilating photons; and (iii) the Doppler broadening of the 0.511 MeV annihilation line. While the time-dependent distribution of photons bears information on the electron density in the vicinity of the annihilation event, the latter two photon characteristics provide information on the electron momentum distribution. The positron lifetime gives more integral information than the momentum measurements regarding the region from which the positron annihilates. In the case of a defect-containing sample, the average electron density at a defect site can be rather defect-specific. This suggests position lifetime measurements are suitable for investigating vacancy-clustering processes in rapidly quenched or (ion) irradiated materials. The momentum measurements can also yield detailed defect-specific information. The positron energy may vary allowing examination of the depth distribution of defects in solids and interfaces. Other direct experimental methods including transmission electron microscopy and atomic diffusion are less capable in detecting open volume defects located at interfaces and surfaces.

The threshold defects concentration ensured by PAS is 1014 to 1015cm<sup>3</sup>

The physics of positron annihilation spectroscopy has been explained in textbooks [2, 3] and research articles [4, 5]. A positron injected into a solid becomes thermalized within a few picoseconds by ionizing collisions, plasmon and electron-hole excitations, and phonon interactions. If lattice defects are present in the material, the positron can be trapped by these imperfections. Lattice imperfections (vacancies, vacancy clusters, or dislocations), open volumes, nanoclusters, and the surface states can serve as potential wells, which effectively trap positrons. Within hundreds of picoseconds, a positron in a solid annihilates with an electron yielding two gamma rays.

.

electrical methods are provided.

68 Ion Implantation - Research and Application

2. Positron annihilation spectroscopy

Because energy and momentum are conserved in the annihilation process, the two gamma rays resulting from the electron-positron pair annihilation each have energy equal to the restmass energy of an electron or positron (mc<sup>2</sup> = 511 keV) and � an energy increment <sup>Δ</sup>E; the two gamma rays propagate in opposite directions with some deviation θ. Since the thermal energies of the positions are about kT, the values of ΔE and θ correspond only to the momenta of the annihilating crystal electrons. The similarity of information available from Dopplerbroadening spectra P(ΔE) and angular-correlation curves N(θ) can be inferred by comparing the expressions for N(θ) and P(ΔE) in terms of the independent-particle-model (IPM) probability, R(p), that positron-electron annihilation yields 2γ-emission with total momentum p:

$$R(\mathbf{p}) = \pi r\_0^2 c \sum\_k n\_k |\iint e^{-ipr} \Psi\_+(r) \Psi\_-(r)|^2 d^3r,\tag{2}$$

where Ψ þðrÞ and Ψ �ðrÞ are the positron and electron wave functions, respectively, nk is the Fermi function, and k represents both the electron wave vector k and the band index. The expression for NðθÞ and PðΔEÞ is represented as NðθzÞ ¼ ʃʃRðpÞdpxdpy and PðΔExÞ ¼ ʃʃRðpÞdpydpz. The IPM approximation ignores the effects of positron-electron correlations in the solid assuming the particles act independently. The treatment of the electron-positron correlation, i.e., the enhancement of the electron density at a positron trapped by a defect site has been considered in Ref. [6]. The theory developed in this work considers the two-particle representation of an annihilating positron-electron pair. The IPM approximation is used to calculate the momentum distribution for each electron state. The individual contributions are weighted by the corresponding partial annihilation rates. The partial rates are calculated within the generalized gradient approximation. This approach was found useful when considering the momentum region where the uppermost core electron states dominate. The analysis of the momentum distribution curves up to rather large momenta becomes possible enabling identification of the chemical environment where the annihilation event has occurred. The one-dimensional momentum distribution of the annihilating electron-positron pairs can be extracted from the measurement of the Doppler broadening of the annihilation radiation. Generally, the positron-enhanced electron density can be accounted for if a constant, multiplicative factor (the enhancement factor) is used to take the many-body effects into account, although different enhancement factors must be used for valence and core electrons consistent with their degree of tight-binding.

A typical positron lifetime experiment has been described in work [7]. It can be performed by using a radioactive 22Na as a positron source. The positron source material can be deposited on a sample or sealed in foil, then placed between two identical samples under study. The decaying Na nuclei emit a high energy photon at 1.2745 MeV, which is used as a start signal for the positron lifetime measurement, while a stop signal is characterized by 511 keV photons. The photons serving as start and stop signals are detected by scintillating detectors coupled with photomultiplier tubes. Detectors are chosen to optimize scintillating efficiency and resolution. The use of digitization of the detector pulses significantly simplifies the postmeasurement signal analysis. The measured positron lifetime spectrum is exponential and reveals several features such as the background noise, the time resolution, and annihilations in the source. The background noise is determined by the source activity and arises due to rapid emissions of positrons that produce false coincidences. Further, the data analysis methods are also described in Ref. [7]. Except for the least-squares fitting of the positron life time spectrum, the inverse Laplace transform and the Bayesian-probability methods have been developed. The latter two methods do not require the number of lifetime components to be a priori fixed and can be used if continuous lifetime distributions are expected.

The surroundings of the vacancy defect can be studied with coincidence Doppler broadening spectroscopy measurements. Nonzero electron and positron momentum causes a Doppler shift of the annihilation photons. The Doppler shift is determined by the momentum of electrons since positrons in a solid are thermalized. Analysis of the Doppler broadening of annihilation radiation provides a sensitive method of defect characterization by extracting the momentum distribution of the electrons. It allows examining high-momentum core electrons. The principle of the method lies in the analysis of the positron annihilation line shape, which directly corresponds to the distribution of momentum of electron-positron pairs as shown in Figure 2. The momentum itself is measured from the amount of the Doppler shift of the emitted photons. In the coincidence Doppler broadening spectroscopy developed in works

Figure 2. A typical annihilation line. After Ref. [144].

NðθÞ and PðΔEÞ is represented as NðθzÞ ¼ ʃʃRðpÞdpxdpy and PðΔExÞ ¼ ʃʃRðpÞdpydpz. The IPM approximation ignores the effects of positron-electron correlations in the solid assuming the particles act independently. The treatment of the electron-positron correlation, i.e., the enhancement of the electron density at a positron trapped by a defect site has been considered in Ref. [6]. The theory developed in this work considers the two-particle representation of an annihilating positron-electron pair. The IPM approximation is used to calculate the momentum distribution for each electron state. The individual contributions are weighted by the corresponding partial annihilation rates. The partial rates are calculated within the generalized gradient approximation. This approach was found useful when considering the momentum region where the uppermost core electron states dominate. The analysis of the momentum distribution curves up to rather large momenta becomes possible enabling identification of the chemical environment where the annihilation event has occurred. The one-dimensional momentum distribution of the annihilating electron-positron pairs can be extracted from the measurement of the Doppler broadening of the annihilation radiation. Generally, the positron-enhanced electron density can be accounted for if a constant, multiplicative factor (the enhancement factor) is used to take the many-body effects into account, although different enhancement factors must be used for valence and core electrons

A typical positron lifetime experiment has been described in work [7]. It can be performed by using a radioactive 22Na as a positron source. The positron source material can be deposited on a sample or sealed in foil, then placed between two identical samples under study. The decaying Na nuclei emit a high energy photon at 1.2745 MeV, which is used as a start signal for the positron lifetime measurement, while a stop signal is characterized by 511 keV photons. The photons serving as start and stop signals are detected by scintillating detectors coupled with photomultiplier tubes. Detectors are chosen to optimize scintillating efficiency and resolution. The use of digitization of the detector pulses significantly simplifies the postmeasurement signal analysis. The measured positron lifetime spectrum is exponential and reveals several features such as the background noise, the time resolution, and annihilations in the source. The background noise is determined by the source activity and arises due to rapid emissions of positrons that produce false coincidences. Further, the data analysis methods are also described in Ref. [7]. Except for the least-squares fitting of the positron life time spectrum, the inverse Laplace transform and the Bayesian-probability methods have been developed. The latter two methods do not require the number of lifetime components to be a priori fixed and can be used if continuous

The surroundings of the vacancy defect can be studied with coincidence Doppler broadening spectroscopy measurements. Nonzero electron and positron momentum causes a Doppler shift of the annihilation photons. The Doppler shift is determined by the momentum of electrons since positrons in a solid are thermalized. Analysis of the Doppler broadening of annihilation radiation provides a sensitive method of defect characterization by extracting the momentum distribution of the electrons. It allows examining high-momentum core electrons. The principle of the method lies in the analysis of the positron annihilation line shape, which directly corresponds to the distribution of momentum of electron-positron pairs as shown in Figure 2. The momentum itself is measured from the amount of the Doppler shift of the emitted photons. In the coincidence Doppler broadening spectroscopy developed in works

consistent with their degree of tight-binding.

70 Ion Implantation - Research and Application

lifetime distributions are expected.

[8, 9] determination of energy of both γ rays is done simultaneously. Coincidence measurements of annihilation photons reduce the background signal by several orders of magnitude and allow observation of the high-momentum part of the spectrum, which stems from positrons annihilated by core electrons making possible identification of chemical elements surrounding a positron annihilation site.

The discovery of slow positron emitters enabled analysis of solid surfaces [10, 11]. Slow positron beams are utilized for nondestructive depth profiling of defects in surfaces and interfaces, low energy positron diffraction, and positron remission microscopy studies on surfaces. A moderator single crystal metal film (Au, Cu, W, Ta) was used to produce slow positron beams [12]. The thermalized slow positrons are emitted from the metal surface spontaneously owing to the negative positron-surface affinity. Since slow positron beam generation is a surface process, it is sensitive to surface contaminations such as carbon, oxygen, and the surface defects [13, 14]. Energy loss mechanisms and the positron processes in condensed matter are described in Ref. [15]. Except being ejected from the surface, positrons can form a positronium (Ps) by capturing a surface electron. This bound state decays from either a singlet state, p-Ps ( 1 S0) or a triplet state, o-Ps ( 3 S1), each having unique annihilation characteristics [16]. Positrons can become trapped by the surface states or reflected back to the interior from the surface.

When a slow positron annihilates with a core electron, the released energy can be transferred to another electron, which can be ejected and detected out of the surface. Weiss et al. [17] were first to demonstrate that a low-energy positron creates core holes through matter-antimatter annihilation generating Auger electrons with high efficiency and extremely low secondary electron background. The latter is feasible to obtain by using incident beam energy below the secondary electron emission threshold. Positron-annihilation-induced Auger-electron spectroscopy (PAES) is advantageous due to increased surface selectivity in systems where the localization of the positron at the surface causes the excitation volume to be restricted almost to the top atomic layer. In addition, because calculated PAES intensities are very sensitive to the spatial extent of the positron wave function, PAES measurements provide an important test for models of the positron surface state. This technique has been proved to be a useful tool for determining surface composition, thin film and nanocrystal characterization, and surface diffusion of atoms.

Also, positrons can be used in diffraction experiments having the advantage that interaction with solids can be easier modeled due to the sign of the scattering potential (the scattering potential between the positron and the atomic nucleus is repulsive) and the total reflection, which is only present in the positron diffraction [18, 19]. The interaction of an energetic positron with the solid may differ from that of electrons of the same energy. The differences can be associated with the relative differential and total elastic cross sections and also with the different energy loss processes for the two particles in a solid. At low energy, the inelastic mean-free path of a positron is shorter than that of an electron leading to an increased surface sensitivity of positrons. This is especially useful in examining the features of reconstructed surfaces, adsorbates, single adsorbed layers and their spacing to the substrate as well as layers with a nominal thickness in the submonolayer range. The positron scattering cross sections are marginally dependent on the specific element enabling analysis of compounds comprising unlike atoms.

High energy diffraction of positrons generates two-dimensional (2D) pattern similar to electrons, although there are several differences due to differences in the ion-core interaction and crystal potential between positrons and electrons. Kikuchi lines stemming from multiplescattering of electrons are not observed in diffraction of high-energy positrons. The most notable feature is in the total reflection of positrons at surfaces. The positron diffraction near the critical angle is especially sensitive to the topmost atomic surface layer whereas at the critical angle for total reflection in X-ray diffraction, which is usually less than 0.2 the penetration depth of the photons into the solid still amounts to a few nanometers. Surface sensitivity of positron techniques is especially suited to near-surface measurements, which are particularly relevant to ion beam modified devices.

The technique of positron annihilation spectroscopy in conjunction with a slow positron beam has been proposed for the monitoring of ion implantation dose and uniformity [20]. Positron dosimetry can nondestructively measure doses of implanted ions with significantly higher sensitivity than that available using other techniques. The principle of the technique is that implanted thermalized positrons diffusively move in the material and become trapped by the open-volume vacancy-type defects created by ion implantation. The positron annihilation in vacancy-type defects contributes less to the Doppler broadening of the energy spectrum of annihilation γ rays compared to that in the defect-free bulk material. Doppler broadening parameter S is defined as the ratio of the number of counts in the central part of 511 keV gamma line to the total number of counts under the peak. A single parameter S describing the linewidth of the annihilation gamma ray line at 511 keV is related to the defect concentration. The concentration C of open-volume defects is related to the number φ of ions implanted as C∝φ0.7. The defect depth profiling using positron beams has found applications in materials research to study ion beam damage in both inorganic [21–23] and organic materials [24]. In the latter case, positron beam studies are of particular importance since application of X-ray or electron beams to organic materials may appear invasive [25].

Though modern MOS device technology may rely on ion-implantation free approaches [26, 27], applications of ion implantation are expanding over areas of quantum information processing [28, 29] and photovoltaics [30, 31]. Plasma immersion ion implantation enables fabrication of 3D transistor architectures [32, 33] required for scaling of metal-oxide-semiconductor field-effect transistors (MOSFETs) and is technologically more convenient for the fabrication of shallow pn-junctions. The ion implantation doping and the problems associated with the formation of point defects in the ion collision processes have been reviewed in work [34] highlighting the differences in the defect generation and accumulation in Si and Ge upon ion implantation. The dopant behavior in Ge is dominated by vacancies, while both vacancies and self-interstitials are active in Si. PAS has been applied to study point defects in interfaces between high-k dielectrics and metal [35] and Si [36]. The open volume defects were found to be located at both TiN/SiO2 and Si/SiO2 interfaces [37]. Annealing studies of defects indicated that while the defects in the Si/SiO2 interface could be annealed out, the TiN/SiO2 interface revealed an enhanced defect density due to the formation of the interfacial titanium oxynitride. Open volume defects introduced in SiN<sup>x</sup> films [38] and SiGe/Si interfaces [39] by plasma processing have been also revealed by PAS.

### 3. Electron spin resonance spectroscopy

electron emission threshold. Positron-annihilation-induced Auger-electron spectroscopy (PAES) is advantageous due to increased surface selectivity in systems where the localization of the positron at the surface causes the excitation volume to be restricted almost to the top atomic layer. In addition, because calculated PAES intensities are very sensitive to the spatial extent of the positron wave function, PAES measurements provide an important test for models of the positron surface state. This technique has been proved to be a useful tool for determining surface

Also, positrons can be used in diffraction experiments having the advantage that interaction with solids can be easier modeled due to the sign of the scattering potential (the scattering potential between the positron and the atomic nucleus is repulsive) and the total reflection, which is only present in the positron diffraction [18, 19]. The interaction of an energetic positron with the solid may differ from that of electrons of the same energy. The differences can be associated with the relative differential and total elastic cross sections and also with the different energy loss processes for the two particles in a solid. At low energy, the inelastic mean-free path of a positron is shorter than that of an electron leading to an increased surface sensitivity of positrons. This is especially useful in examining the features of reconstructed surfaces, adsorbates, single adsorbed layers and their spacing to the substrate as well as layers with a nominal thickness in the submonolayer range. The positron scattering cross sections are marginally dependent on the

High energy diffraction of positrons generates two-dimensional (2D) pattern similar to electrons, although there are several differences due to differences in the ion-core interaction and crystal potential between positrons and electrons. Kikuchi lines stemming from multiplescattering of electrons are not observed in diffraction of high-energy positrons. The most notable feature is in the total reflection of positrons at surfaces. The positron diffraction near the critical angle is especially sensitive to the topmost atomic surface layer whereas at the critical angle for total reflection in X-ray diffraction, which is usually less than 0.2 the penetration depth of the photons into the solid still amounts to a few nanometers. Surface sensitivity of positron techniques is especially suited to near-surface measurements, which are particularly

The technique of positron annihilation spectroscopy in conjunction with a slow positron beam has been proposed for the monitoring of ion implantation dose and uniformity [20]. Positron dosimetry can nondestructively measure doses of implanted ions with significantly higher sensitivity than that available using other techniques. The principle of the technique is that implanted thermalized positrons diffusively move in the material and become trapped by the open-volume vacancy-type defects created by ion implantation. The positron annihilation in vacancy-type defects contributes less to the Doppler broadening of the energy spectrum of annihilation γ rays compared to that in the defect-free bulk material. Doppler broadening parameter S is defined as the ratio of the number of counts in the central part of 511 keV gamma line to the total number of counts under the peak. A single parameter S describing the linewidth of the annihilation gamma ray line at 511 keV is related to the defect concentration. The concentration C of open-volume defects is related to the number φ of ions implanted as C∝φ0.7. The defect depth profiling using positron beams has found applications in materials

composition, thin film and nanocrystal characterization, and surface diffusion of atoms.

specific element enabling analysis of compounds comprising unlike atoms.

relevant to ion beam modified devices.

72 Ion Implantation - Research and Application

Being integral to CMOS technology, ion implantation finds its applications at the forefront of materials science for fabrication of quasi-2D materials [40, 41], exploration of electron and nuclear spins of donor atoms in silicon as qubits for quantum information processing [42], and fabrication of light-emitting diodes [43]. Pertaining to MOS device fabrication, ion implantation is known to result in generation of electron and hole-trapping centers, which are detrimental to the device performance [44]. Such trapping centers may reside in a gate oxide and its interfaces with a semiconductor and a gate electrode. In amorphous SiO2, ion implantation induces densification and the amorphous network reconstruction, not fully consistent with the assumption of plastic deformation. Ion implantation forces SiO2 to freeze in a nonequilibrium phase tolerating a substantial reduction in the mean SiOSi angle and a subsequent change in the ring distribution statistics. As such, the radiation response of SiO2 is dependent on the intrinsic structure of the material and the incorporated strain. Possible structural modifications in amorphous SiO2 resulting in irradiation-induced charge have been reviewed in Ref. [45]. When paramagnetic, electrically active defects can be studied by using electron spin resonance (ESR) since the method is restricted to systems with a residual electron spin. For example, molecular solids with singlet ground states are not observable by ESR. This selectivity appears as useful in research on the electronic states of conducting materials, point defects in thin films, interfaces, and nanocrystals [46–50]. For the subject of ESR describing the fundamental theory and also the primary applications of the technique one can refer to the textbooks [51, 52]. The potential of the method in application to interfaces and nanolayers is detailed in Ref. [53].

The actual quantity detected in the ESR experiment is the net magnetic moment per unit volume, the macroscopic magnetization M. The microwave absorption spectrum is described by the spin Hamiltonian consisting of two components. A spin Hamiltonian contains operators for an effective electronic spin and for nuclear spins, the external magnetic field, and parameters. Its eigenfunctions determine the allowed energy levels of the system for an ESR experiment. The characteristics of paramagnetic species are the g-value, the spin-lattice relaxation time, and the line width. The g-value is the magnitude of the electron Zeeman factor for the paramagnetic species considered. The g-value can be determined as E ¼ gμBB, where E is the energy of microwave, μ<sup>B</sup> is Bohr magneton, and B is magnetic field. In the case of free electrons, the g-value becomes 2.0023. For a paramagnetic defect, the g-value is different due to the effect of local magnetic field induced by movement of electrons in their orbits. The structure of the orbits contributes to the g-values via the effect of spin-orbit coupling, which is anisotropic and depends on axis determined by the magnetic field.

The spin-lattice relaxation time characterizes interactions of a spin system with its environment and reflects the strength of the interaction between the spin system and its surroundings. The magnetic environment of an unpaired electron can give rise to the ESR line broadening. The spectral lines are broadened either homogeneously or inhomogeneously. Homogeneous line broadening can be fitted by a single Lorentzian line and indicates that all the spins are described by the same spin Hamiltonian parameters. The line width of homogeneously broadened lines depends on the relaxation time of the spins. In the case of inhomogeneous broadening, the observed signal becomes a superposition of a large ensemble of individual spin packets, which are of slightly different g-values from each other. The inhomogeneous broadening of the spectral line can be caused, for example, by anisotropy of the g-tensor or the unresolved hyperfine structure. The latter may occur when the number of hyperfine components located near nuclei is so large that the hyperfine structure cannot be clearly observed. The large line width can be also observed due to dipole-dipole interactions between the defects spins [54].

As a starting point in defect identification, it is instructive to give an overview of intrinsic and extrinsic point defects of the Si/SiO2 system as the most comprehensively studied system in CMOS technology. Being oxidized, silicon forms network-lattice-induced dangling bond defects at the Si/SiO2 plane. The structure of the Pb defects is dependent on the crystalline orientation of Si. The (111)Si/SiO2 interface can be characterized by dangling bond defects of only one type—Р<sup>b</sup> centers. This is a sp3 silicon-dangling bond directed along the [111]. The defect is of C3v symmetry and can exist in four orientations in the silicon lattice [55, 56]. Thermally oxidized silicon contains the Pb density of approximately 4.9�1012 см�<sup>2</sup> . In contrast to the (111)Si/SiO2 interface, the (100)Si/SiO2 interface is characterized by two ESR active defects, Pb0 and Pb1 as shown in Figure 3. When oxidation of silicon is implemented at 800–970�С, the defect density of both defect types is similar (1012 см�<sup>2</sup> ). The Pb1 defect is also a Si-dangling bond located slightly under the interface plane. Unlike Pb0, it is of monoclinic-I point symmetry [48].

The dangling bond silicon defects, the Pb centers, are often employed as sensitive probes to detect interfacial stress during the Si/SiO2 interface formation. When Si is subjected to oxidation at Т > 900�C, structural relaxations occur at the Si/SiO2, and the density of Pb-centers decreases. At this point, two stages of the silicon oxidation process can be distinguished. Suboxide

Ion-Beam-Induced Defects in CMOS Technology: Methods of Study http://dx.doi.org/10.5772/67760 75

Figure 3. Schematic representation of Pb0 и Pb1 defects at the (100)Si/SiO2 interface. After Ref. [145].

The actual quantity detected in the ESR experiment is the net magnetic moment per unit volume, the macroscopic magnetization M. The microwave absorption spectrum is described by the spin Hamiltonian consisting of two components. A spin Hamiltonian contains operators for an effective electronic spin and for nuclear spins, the external magnetic field, and parameters. Its eigenfunctions determine the allowed energy levels of the system for an ESR experiment. The characteristics of paramagnetic species are the g-value, the spin-lattice relaxation time, and the line width. The g-value is the magnitude of the electron Zeeman factor for the paramagnetic species considered. The g-value can be determined as E ¼ gμBB, where E is the energy of microwave, μ<sup>B</sup> is Bohr magneton, and B is magnetic field. In the case of free electrons, the g-value becomes 2.0023. For a paramagnetic defect, the g-value is different due to the effect of local magnetic field induced by movement of electrons in their orbits. The structure of the orbits contributes to the g-values via the effect of spin-orbit coupling, which is

The spin-lattice relaxation time characterizes interactions of a spin system with its environment and reflects the strength of the interaction between the spin system and its surroundings. The magnetic environment of an unpaired electron can give rise to the ESR line broadening. The spectral lines are broadened either homogeneously or inhomogeneously. Homogeneous line broadening can be fitted by a single Lorentzian line and indicates that all the spins are described by the same spin Hamiltonian parameters. The line width of homogeneously broadened lines depends on the relaxation time of the spins. In the case of inhomogeneous broadening, the observed signal becomes a superposition of a large ensemble of individual spin packets, which are of slightly different g-values from each other. The inhomogeneous broadening of the spectral line can be caused, for example, by anisotropy of the g-tensor or the unresolved hyperfine structure. The latter may occur when the number of hyperfine components located near nuclei is so large that the hyperfine structure cannot be clearly observed. The large line width can be

As a starting point in defect identification, it is instructive to give an overview of intrinsic and extrinsic point defects of the Si/SiO2 system as the most comprehensively studied system in CMOS technology. Being oxidized, silicon forms network-lattice-induced dangling bond defects at the Si/SiO2 plane. The structure of the Pb defects is dependent on the crystalline orientation of Si. The (111)Si/SiO2 interface can be characterized by dangling bond defects of only one type—Р<sup>b</sup> centers. This is a sp3 silicon-dangling bond directed along the [111]. The defect is of C3v symmetry and can exist in four orientations in the silicon lattice [55, 56]. Thermally oxidized silicon

the (100)Si/SiO2 interface is characterized by two ESR active defects, Pb0 and Pb1 as shown in Figure 3. When oxidation of silicon is implemented at 800–970�С, the defect density of both

The dangling bond silicon defects, the Pb centers, are often employed as sensitive probes to detect interfacial stress during the Si/SiO2 interface formation. When Si is subjected to oxidation at Т > 900�C, structural relaxations occur at the Si/SiO2, and the density of Pb-centers decreases. At this point, two stages of the silicon oxidation process can be distinguished. Suboxide

. In contrast to the (111)Si/SiO2 interface,

). The Pb1 defect is also a Si-dangling bond located slightly under

anisotropic and depends on axis determined by the magnetic field.

also observed due to dipole-dipole interactions between the defects spins [54].

contains the Pb density of approximately 4.9�1012 см�<sup>2</sup>

the interface plane. Unlike Pb0, it is of monoclinic-I point symmetry [48].

defect types is similar (1012 см�<sup>2</sup>

74 Ion Implantation - Research and Application

bonding at the Si/SiO2 interface is diminishing when silicon is oxidizing at 850C<Т< 900C. Increasing oxidation temperature to 1050C reduces strain at the macroscale [57]. Spatial uniformity of the dangling bond defects is determined by the temperature conditions during silicon oxidation. ESR studies of Pb defects can be used to determine deformations at the interface from dependence of the ESR line width as a function of magnetic field angle [58, 59].

Pb<sup>0</sup> and Pb<sup>1</sup> defects in (100)Si/SiO2 as well as Pb defects in (111)Si/SiO2 can be passivated in molecular hydrogen [49]. Upon ion implantation or ionizing irradiation, the interface trap generation may occur. A part of the interface states appears to be due to depassivated dangling bond defects. The mechanism of the depassivation reactions has been considered within the "hydrogen model", which assumes defect precursors in SiO2 to create mobile protons interacting with HPb and generating Pb centers. The interface trap generation coincides with the positive charge built-up in the oxide. The model proposes that protons are introduced in SiO2 as a product of reactions of atomic hydrogen with the hole carriers trapped in the oxide; both the atomic hydrogen and the trapped holes are produced by irradiation. It has been concluded that the positive charge trapped in the oxide is present in the form of small polarons (self-trapped holes) in amorphous SiO2 [60]. Though in bulk vitreous SiO2 intrinsic hole-trap centers have been found to be stable at relatively low temperatures, thin films of insulating gate dielectrics in modern MOS devices are formed by low-temperature depositions on semiconductors and could incorporate interfacial strain sufficient to support self-trapped carriers at higher temperatures. The polaronic nature of the oxide-trapped charge in amorphous SiO2 is consistent with the recent theoretical consideration of hole and electron trapping in hafnia. The deep states of electron and hole polarons have been predicted to exist in HfO2 with precursor sites being elongated HfO bonds or under-coordinated Hf and O atoms [61]. This indicates that: (i) similar mechanisms of the defect generation under irradiation or ion beam damage could be operative in MOS devices containing HfO2 and other amorphous oxides. (ii) Dangling bond defects in oxides may not be required for the charge trapping to occur.

Of the dangling bond defects in SiO2, there are point defects associated with a dangling bond localized either on silicon or oxygen. The EX center belongs to the oxygen-related defects in SiO2. The EX defect is the intrinsic network-stabilized defect in SiO2. It is formed in the upper part of the oxide when the oxidation temperature Тox = 700–800�C. Being most prominent in thin oxides, EX is linked to the specific way thermal oxide is grown, i.e., oxidation of c-Si. As a working model, EX can be represented as an excess-O hole defect where an electron is delocalized over the four oxygen atoms bordering a Si vacancy [62], Figure 4. There are also a nonbridging oxygen hole center (O3�Si�O�) [63] and a peroxide-radical (Si�O�O�) [64], which are not naturally present in SiO2 and introduced as damage defects in a postoxidation stage by irradiation with some energetic species (e.g., γ and x photons, electrons, ions).

The E<sup>0</sup> defect is also an extrinsic defect present in crystalline and amorphous SiO2. The E<sup>0</sup> defects in SiO2 have an unpaired electron localized at a hybrid sp3 orbital of silicon, which is bonded to three oxygen atoms (О3�Si�) [65]. Several schematic models of the E<sup>0</sup> centers are depicted in Figure 5. The model representation of Е' as the bridged hole-trapping oxygendeficiency center has not been experientially verified [66]. The model considers a paramagnetic silicon atom connected via oxygen with another silicon atom, which is the trapping center for positive charge carriers, Figure 5(b). Generation of E'defects may depend on hydrogen content in a-SiO2, since dissociation energy of a strained Si�O bond by hydrogen is rather low and amounts to 0.5–1.3 еВ [67]. The defect generation in interfaces and thin films by ionizing radiation or hot electron injection is sensitive to the initial content of the strain bonds in MOS devices [68]. Therefore, ESR studies could be employed to reveal the impact of the interfacial strain on the defect generation.

Since electronic devices explore charge carries in their operation, it appeared natural to establish interrelationship between the silicon-dangling bond defects and the electron states at the

Figure 4. Schematic representation of the EX center.

Of the dangling bond defects in SiO2, there are point defects associated with a dangling bond localized either on silicon or oxygen. The EX center belongs to the oxygen-related defects in SiO2. The EX defect is the intrinsic network-stabilized defect in SiO2. It is formed in the upper part of the oxide when the oxidation temperature Тox = 700–800�C. Being most prominent in thin oxides, EX is linked to the specific way thermal oxide is grown, i.e., oxidation of c-Si. As a working model, EX can be represented as an excess-O hole defect where an electron is delocalized over the four oxygen atoms bordering a Si vacancy [62], Figure 4. There are also a nonbridging oxygen hole center (O3�Si�O�) [63] and a peroxide-radical (Si�O�O�) [64], which are not naturally present in SiO2 and introduced as damage defects in a postoxidation stage by

The E<sup>0</sup> defect is also an extrinsic defect present in crystalline and amorphous SiO2. The E<sup>0</sup> defects in SiO2 have an unpaired electron localized at a hybrid sp3 orbital of silicon, which is bonded to three oxygen atoms (О3�Si�) [65]. Several schematic models of the E<sup>0</sup> centers are depicted in Figure 5. The model representation of Е' as the bridged hole-trapping oxygendeficiency center has not been experientially verified [66]. The model considers a paramagnetic silicon atom connected via oxygen with another silicon atom, which is the trapping center for positive charge carriers, Figure 5(b). Generation of E'defects may depend on hydrogen content in a-SiO2, since dissociation energy of a strained Si�O bond by hydrogen is rather low and amounts to 0.5–1.3 еВ [67]. The defect generation in interfaces and thin films by ionizing radiation or hot electron injection is sensitive to the initial content of the strain bonds in MOS devices [68]. Therefore, ESR studies could be employed to reveal the impact of the interfacial

Since electronic devices explore charge carries in their operation, it appeared natural to establish interrelationship between the silicon-dangling bond defects and the electron states at the

irradiation with some energetic species (e.g., γ and x photons, electrons, ions).

strain on the defect generation.

76 Ion Implantation - Research and Application

Figure 4. Schematic representation of the EX center.

Figure 5. The first model of E´γ center (а), the model of the bridged hole-trapping oxygen-deficiency center (b), and the E´σ center model (c).

semiconductor/insulator (SI) interfaces. For the Si/SiO2 interfaces, it is known that technology chosen for silicon oxidation is crucial for attaining low density of the interface state (Dit), which is directly linked to the density of silicon-dangling bonds at the Si/SiO2 interface. The decrease in Dit and the Pb density was observed when steam oxidation was used to grow SiO2. Also, the higher Dit values are expected at the more closely packed (111)Si surface as compared to the (100)Si one. A direct correlation between the Pb density and the free carrier concentration in the field-effect transistor channel was reported in work [69]. Further studies of electrical activity of the Si/SiO2 defects were undertaken by using various methodologies: capacitancevoltage (CV) measurements [70], deep-level transient spectroscopy [71], and the photoionization threshold method [72]. It was firmly established that Pb0 defects at the (100)Si/SiO2 interface form amphoteric surface states at 0.3 and 0.8 eV above the silicon valence band edge [73]. In respect to the Pb1 centers at the (100)Si/SiO2, the Pb0 и Pb1 defect densities inferred from ESR studies were compared with the interface trap densities determined from CV measurements. It was concluded that Pb1 does not form electrically active states within the silicon band gap [74]. Concerning the E´ center in thermal oxide, it is neutral when paramagnetic and strongly interacts with hydrogen [75]. The model for the E´ center in this case is the Hterminated center denoted as O3Si–H. It has been supposed that the E´ center constitutes the hole trap and releases hydrogen in the form of a proton upon hole-trapping. The released proton can be trapped by the oxide network and form a donor-like surface state. When hydrogen is available in gate oxides as it can be upon an irradiation process, the neutral E´ center may be again passivated serving as a hole-trapping site.

Charge trapping in gate oxides is one of the major obstacles in integration of high-k gate dielectrics in CMOS technology. Among the issues is the enhanced migration of dopant impurities originating from ion implantation steps. As such, ESR studies are indispensable to unravel point defects, which may appear detrimental for MOSFET performance. For example, ESR studies of phosphorous implanted high-k dielectrics reveal that P incorporating in the metal oxide network forms point defects by substituting for Hf or Zr in HfO2 or ZrO2, respectively [76]. Such defects formed due to enhanced migration of dopant impurities during dopant activation thermal steps may potentially trap charge.ESR studies have been applied to diverse ion-implanted systems. In SiO2, a substantial reduction in S and E<sup>0</sup> <sup>γ</sup> centers (Si enrichment in the oxide) was found when in situ ultrasound treatment was applied during implantation of Si+ ions into thermal SiO2 on (100)Si [77]; ESR found a radical mechanism of degradation of the ion-implanted photoresist [78]. Applications of the ESR techniques to study ion-beam-induced implantation damage in carbon-based materials have been described in Ref. [79].

ESR techniques have been explored in studies of spintronic materials fabricated by ion implantation. To probe the spin relaxation, the technique of choice is the pulse-electron spin resonance spectroscopy. ESR studies have been undertaken to measure spin relaxation times of dopants in Si. Shallow donors in Si are known for their long relaxation time suggesting a possible application of spins as qubits. The transverse relaxation time measured for isolated spins is associated with the decoherence time. ESR studies have been used to determine spin relaxation times in Sb-implanted isotopically enriched 28Si [80]. It has been shown that annealing of ultralow dose antimony implants leads to high degrees of electrical dopant activation with minimal diffusion. Spin relaxation times were increased when paramagnetic defects at the Si/ SiO2 interface were passivated by hydrogen. Except for the Si/SiO2 system, pulsed ESR experiments have been used to characterize the coherent spin dynamics of nanofabricated nitrogen vacancy centers in nitrogen implanted high-purity diamond [81].
