Defects in Functional Materials. Группа авторов

·S+S·D·S+S·A·I (Loubser and van Wyk [44]). The first term represents the electronic Zeemann interaction, the second is the interaction of the electron spin with the crystal fields produced by the surroundings, and the last is the magnetic hyperfine interaction due to the nuclear spins. S and I represent operators related with electron and nuclear spins, respectively. g_e, D and A are tensors, which are to be determined from experiment and carry the information about the defects (impurities). These interactions will add pronounced features and great complexity in the ESR spectrum of a real system. The unpaired electron can gain or lose angular momentum and therefore change the value of the g-factor to be different from that for free electrons. For a spin system with S > 1/2, the spin-spin interaction among the unpaired electrons arises, splitting the energy level in absence of the external magnetic field. The magnetic moment of nucleus with a non-zero nuclear spin (I ≠ 0) will affect any unpaired electrons which have wavefunctions overlapping with that atom. This leads to the hyperfine interaction, splitting the ESR resonance signal into doublets, triplets and so forth. Note that the split of the energy levels caused by nuclear spins is often smaller than that of the electronic Zeeman interaction and spin-spin interaction. Moreover, the g-factor and hyperfine interaction are generally not the same for all orientations of an unpaired electron in an external magnetic field. This anisotropy depends on the electronic structure of the environment of the unpaired electron, thus containing information about the atomic or molecular orbital with which the unpaired electron is associated.

      For over six decades, ESR has played a key role in the study of point defects in semiconductors and many other materials even in liquids. Under optimized conditions with narrow resonance line, the sensitivity can be very high, i.e. as low as the defect concentration of ∼10¹⁰ cm⁻³ at room temperature. The sensitivity can be increased at lower temperatures. The ESR information, which can be obtained, about the defects and impurities in semiconductors was nicely summarized by Loubser and van Wyk [44]:

      

      (1) In the same crystal, different types of paramagnetic centers result in well distinguishable ESR spectra and the intensity of a particular center is proportional to the concentration of this kind of centers.

      (2) The shift of the g-factor is a measure of the orbital contribution to the magnetic moment: is generally negative for electrons and positive for holes.

      (3) From the resolved fine-structure lines, one can obtain the number of unpaired electrons associated with the defect.

      (4) The hyperfine interaction due to the nucleus of spin I associated with the defects leads each fine-structure line split into 2I + 1 hyperfine lines. Therefore, impurities with non-zero nuclear spin can be identified.

      (5) The anisotropy of the spectra, e.g., the angular dependence of g as the crystal is rotated in the external field, gives information about the symmetry of the defects.

      (6) The widths of the ESR resonance lines contain information about the magnetic and exchange interaction between defects and about spin-lattice relaxation.

      The above-mentioned information is essential for the defect identification and understanding its electronic structure. In many cases, the identification of point defects in semiconductors needs additional support from theoretical modelling. A careful correlation between ESR experiments and theoretical calculations allows an unambiguous identification of the defect. Along with the new development of optical and electrical detection methods, the sensitivity of ESR can be further increased (Kennedy and Glaser [45] and Spaeth [46]). For example, single isolated nitrogen-vacancy pair in diamond can be resolved and optically detected (Abe and Sasaki [47]) using the optical confocal microscopy.

      Figure 6 shows another example, which is the ESR spectra of Se⁺ in isotopically pure Si (Nardo [48]). The electronic g factor is g = 2.0057. All stable Se isotopes X Se⁺ (X = 74, 76, 78, 80) have zero nuclear spin and the ⁷⁷Se isotope has nuclear spin I = 1/2 and the isotropic hyperfine coupling of A = 1.6604 GHz with the donor electron spin. The central line (around g = 2) is corresponding to Se isotopes with zero nuclear spin and the hyperfine-split lines are corresponding to ⁷⁷Se. The remaining features in the ⁷⁷Se⁺ ESR spectrum are due to Se-H pairs. Those resonance peaks have a very small linewidth (<5 μT) due to Si isotopic purification.

      Figure 6. ESR spectra of Se⁺ in ²⁸Si for ²⁸Si:Se (upper, nature Se) and ²⁸Si:⁷⁷Se (lower). The natural abundance of ⁷⁷Se is 7.5%, and the remaining isotopes (92.5% abundance) possess zero nuclear spin. In the lower panel, the ⁷⁷Se-doped sample shows predominantly the hyperfine-split lines arising from coupling to the I = 1/2 nuclear spin of ⁷⁷Se. The additional features in the spectrum correspond to the residual isotopes of Se and the presence of Se-H pairs. The measurement was performed at 23 K using the microwave frequency of 9.38 GHz (Nardo [48]).

      With the development of sensitive magnetometry, such as super-conducting quantum interference device (SQUID), the paramagnetism induced by defects or impurities can also be measured in an intergral method. By fitting the experimental data according to the Curie theory, one also can get the momentum number and get some information about the defects. For instance in ion or neutron irradiated SiC, the paramagnetism from defects was measured by SQUID magnetometry. The magnetization is proportional to the concentration of defects. In some cases, the paramagnetic centers can couple with each other ferromagnetically. Defect induced ferro-magnetism has been observed in various materials, such as the results in Chapters 7, 8 and 9.

       6. Conclusions

      As a general conclusion, we wish to emphasize that the defect characterization involves (i) observing the defect related phenomena with specific electrical, optical or magnetic properties, (ii) revealing the nature of the responsible defects, and (iii) studying the creation and evolution of the defects in a material or device fabrication process. These include the experimental spectroscopic methods characterizing the electrical, optical, magnetic and structural properties of the defects and materials. Notably to obtain a comprehensive picture of the defect, correlative studies between different experimental spectroscopic methods are preferable to increase the chances for non-ambiguous identifications.

       References

[1] Agullo-Lopez F., Catlow C. R. A. and Townsend P. D. (1988) Point Defects in Materials. Academic Press.

[2] Kuzmany H. (1998) Solid-State Spectroscopy — An Introduction. Springer Verlag.

[3] Stavola M. Ed. (1999) Identifications of Defects in Semiconductors. Semiconductors and Semimetals 51A and 51B. Academic Press.

[4] Stavola M. (1999(a)) Vibrational spectroscopy of light element impurities