Defects in Functional Materials. Группа авторов

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(SIMS) are widely employed techniques for studying defects in functional materials.

      

      Positron annihilation spectroscopy (PAS) is a non-destructive probe for neutral or negatively charged vacancy type defects in semiconductors, reviewed by Schultz and Lynn [31], Krause-Rehberg and Leipner [32], Coleman [33], and Tuomisto and Makkonen [34]. Positron is the anti-particle of electron having the same mass but opposite charge. Positron-electron annihilation produces two gamma photons (511 keV because of mass-energy conservation), if the positronium process is not involved. Positronium (the hydrogen-like state of a positron and an electron) does not form in metals or semiconductors because the bound positron-electron pair in the degenerate electron gas would polarize the medium and then screen the positron-electron interaction. However, positronium could form in solid surfaces, amorphous materials, some molecules and ionic solids.

      In more details, positrons injected into the sample from a monoenergetic positron beam or a β⁺ radioactive source like ²²Na rapidly thermalized (∼10 ps) and then undergo diffusion. The positron could annihilation in the delocalized state (or bulk state) during the diffusion. Alternatively, neutral or negatively charged vacancy type defect acts as trap for the positively charged positron. If the positron binding energy of the positron trap is large enough to prohibit thermal de-trapping, the positron will finally annihilate in the trapped state. This implies that the annihilation from the different positron states are in competition. The principal of PAS is that the outgoing gamma photons originated from the annihilation between the positron trapped in the defect and its surrounding electron, carry the information of electronic environment of the defect site, which is a fingerprint of the defect. Using the monoenergetic positron beam as the positron source, the positron energy can be varied up to ∼30 keV, i.e. corresponding to the implantation depth of up to several hundred nm e.g. in Si. Thus, the defect depth profile can be obtained by doing sequential measurements varying positron incidence energies. PAS has been used to study the correlations between the materials properties and the vacancy type defects in different materials. For example, Krause et al. [35] studied the EL2 and its metastable state in GaAs; Lawther et al. [36] studied the compensating defect complexes in Group-V heavily doped Si; Tuomisto et al. [37] identified zinc vacancy (V_Zn) as the dominant acceptor in undoped ZnO; Ling et al. [38] identified the shallow acceptors in undoped GaSb; Khalid et al. [39] correlated magnetic data in undoped ZnO with V_Zn-related defects. Kilpeläinen et al. [49] studied the thermal evolution of the defect complexes in P-doped SiGe.

      Two techniques are typically used in PAS, namely the Doppler broadening spectroscopy (DBS) and the positron lifetime spectroscopy (PLS). DBS measures the Doppler broadening of the line shape of the annihilation photopeak of the annihilation gamma ray energy spectrum. Doppler broadening spectrum reveals the electronic momentum distribution seen by the positrons, i.e. where the summation includes all the electronic states i. ψ₊ is the positron wave function and ψi is the electron wave function with state i. The positron momentum is negligible as compared to that of its annihilating electron counterpart, and thus the total momentum of the positron-electron pair before the annihilation is effectively the electronic momentum (p in Fig. 4). Because of the linear momentum conservation, one of the annihilation gamma photons is Doppler blue shifted (p_γ,1 in Fig. 4) and the other one is red shifted (p_γ,2 in Fig. 4). The Doppler shifted energy is given by ΔE = pzc/2, where c is the speed of light and pz is the longitudinal momentum component of p in the direction of the 511 keV annihilation photon emission (i.e. z-direction in Fig. 4). For the Doppler broadening spectrum obtained from a single detector, the high momentum information is usually hidden behind the background noise. Introduction of a second detector for coincidence gating improves the resolution and the signal-to-noise ratio. Coincidence Doppler broadening spectroscopy (CDBS) can thus be used to explore the annihilation events originated from the high momentum electrons (i.e. the core electrons). As the core electron momentum distribution is the characteristic of a given element, CDBS are used to study the impurity decoration of vacancy type defects (for example Uedono et al. [40], Johansen et al. [41], and Rauch et al. [42]).

      Figure 4. Schematics of the DBS momentum conservation, accounting for the momentum before the annihilation p (i.e. effectively the electron momentum), and the momenta of the two annihilation gamma photons p_γ,1 and p_γ,2.

      

      PLS measures the positron lifetime distribution in the sample. The positron lifetime is inversely proportional to the overlapping of the electron and positron density, i.e. where n₋ is the electron density. Since the electron density at the open volume defect is lower than the delocalized bulk state, the characteristic positron lifetime of the defect state is longer than that of the bulk state. The simple trapping model is normally used to analyse the positron lifetime spectrum; as such the positron lifetime spectrum modelled with the exponential components having different decaying time constants. Assuming for simplicity a system having only one positron defect trap, the spectrum is given by: where τ₁ and τ₂ are the constants. The long lifetime component with the decay time constant τ₂ (i.e. τ₂ > τ₁) is the positron defect trap component. Thus, τ₂ is the characteristic positron lifetime of the defect state and is the fingerprint of the defect. Application of PAS to study the vacancy type defects in SiC is discussed in Chapter 8.

       5. Magnetic Characterization

      The resonant absorption of electromagnetic radiation by unpaired electrons is known as electron spin resonance (ESR) [43]. An electron has a spin S of 1/2 and an associated magnetic moment. In an external magnetic field, two spin states have different energies and this is called Zeeman effect. The electron’s magnetic moment (m_S)

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