Electron paramagnetic resonance (EPR) is one of the by two electrons with opposite spins. If the defects main methods for investigation the microscopic structure of contain even number of electrons their ground state will various point defects in solids, particularly in semiconduc- be nonparamagnetic with spin S = 0. Under band gap tors. Among semiconductor materials the most significant illumination and recombination process the defects can be results were achieved in silicon. Using the EPR technique in the excited spin S = 1 state when two unpaired electrons about three hundreds different EPR spectra of impurity occupy different atomic or molecular orbitals.
atoms, their complexes, radiation and thermal defects in Let us consider the Hamiltonian of two interacting elecsilicon were observed . A part of them were identified trons in magnetic field B and described in reviews [2,3]. Further progress of magnetic H = µBBg1S1 + µBBg2S2 + JS1S2 + S1DS2, (1) resonance spectroscopy of defects in semiconductors was related to the development of the new highly sensitive taking into account the Zeeman interaction between the methods based on the effects of spin dependent recombinaapplied magnetic field B and the electrons spins S1 and S2 tion (SDR) when the recombination rate of nonequilibrium (µB is the Bohr magneton, g1 and g2 are g-tensors of the carriers depends on the spin orientation of the recombination centers . These methods allow us to detect EPR spectra by measuring the intensity of the recombination luminescence or the photoconductivity of samples in magnetic field under saturation of the EPR transitions by the resonance microwave magnetic field.
The detection of microwave photoconductivity of silicon samples by the absorption of the electric component of the microwave field due to the resonance change of the concentration of photoexcited carriers increases the sensitivity of the method by four orders of magnitude . It was found that the main channel of SDR is the recombination through the excited triplet states of the recombination centers. Several new SDR detected EPR spectra of the excited triplet states of different defects have been found in irradiated silicon. Some of them were identified as arising from the excited spin S=1 state of Substitutional carbon–Interstitial silicon–Substitutional carbon (CS–SiI–CS) complex (spectrum Si–PT1 [5,6]), divacancy (spectrum Si–PT5 ), and complex phosphorus + vacancy (spectrum Si–PT3 [5,8]).
In the present paper the advantages and some applications of the SDR–EPR methods for investigation the structure of the recombination centers in irradiated silicon will be described.
1. Excited Triplet States of Defects The irradiation of silicon crystals by fast electrons or -rays gives rise to various structural defects containing Figure 1. Energy levels of a system of two electrons in a magnetic the dangling bonds which can form the molecular orbitals.
field B (a) and the expected positions of the SDR detected lines Each of the latter can be occupied by one electron or of the change of the microwave photoconductivity (b).
Photoelectrically Detected Magnetic Resonance Spectroscopy of the Excited Triplet States of Point... Figure 2. SDR detected lines of microwave photoconductivity in irradiated silicon, observed in different ranges of magnetic field B for various defects. Zero field line and anticrossing (a) and crossing (b) lines correspond to the Si–WL2 center. Anticrossing line and line of the forbidden transition (c) are related to the excited triplet state of the oxygen + vacancy complex (Si–SL1 spectrum). SDR–EPR spectra of the defects with different D-constant are presented in (d).
first and second electrons), the isotropic exchange interaction The exchange interaction between two unpaired electrons JS1S2, and the anisotropic magnetic dipole-dipole interaction leads to formation of a ground singlet S0 state with spin S1DS2, where Dis a symmetric traceless tensor determined S = 0 and an excited metastable triplet state T (S = 1).
by two parameters, D and E, in the principal coordinate In zero magnetic field these states are separated by the frame corresponding to the symmetry of the defects. The energy J W(T ) - W (S0) where J is the exchange = energy levels obtained from the Hamiltonian (1) for the case interaction constant. An additional zero field splitting +1 -1 of two identical electrons (g1 = g2 and S1 = S2 = 1/2) are between T, T, and T states is due to the magnetic shown in Fig. 1, a. dipole-dipole interaction S1DS2. The expected spectrum of Физика твердого тела, 1999, том 41, вып. 776 L.S. Vlasenko the change of photoconductivity of the sample containing defects in the excited triplet state is shown in Fig. 1, b.
The formation of the excited triplet states of defects under illumination and the change of the recombination rate of the photoexcited carriers under saturation of the EPR +1 0 -transitions between magnetic sublevels T, T, and T as well as the change of photoconductivity at the magnetic field B = Bac corresponding to the anticrossing of the sublevels -1 T and T without magnetic resonance (see Fig.1, b) was considered in detail in Refs. [5,6]. In addition, the spin dependent change of photoconductivity can be observed at zero magnetic field (ZFLine), at the magnetic field B = Bc -corresponding to the crossing of excited T state and ground S0 state, and under magnetic resonance between +T and T-1 sublevels (forbidden = ±2 transitions).
The examples of the experimentally detected lines of the SDR related change of photoconductivity are shown in Fig. 2.
Figure 3. Dependence of the fine structure splitting B on the The angular and temperature dependences of intensity and distance r between two interacting electrons.
position of these lines allow us to get additional information about the parameters of the Hamiltonian (1).
2. Parameters of the Spectra and Models of the Defects The components of the g- and D-tensors determined from the experimentally observed angular dependences of the EPR spectra bear an information on the symmetry of point defects. The exchange interaction constant J and the component D of the D-tensor depend of the distance r between interacting electrons, which is important for consideration the models of defects.
The value of J depends exponentially on the distance r and is usually many orders of magnitude higher than the Zeeman energy. For such defects the crossing (C) lines cannot be detected at reasonable strength of the magnetic field. The defects having the value of J comparable with the Zeeman energy were found recently [9,10]. The positions and angular dependences of the anticrossing and crossing lines for such defects (see Fig. 2, a, b) are described by the same parameters of Hamiltonian (1) as the new SDR detected Si–WL2  spectrum shown in Fig. 2, d.
The value of parameter D is proportional to the 1/raveraged over the electron wave function. It can be determined experimentally from the fine structure splitting of the Zeeman lines separated by B 2D as well as from = the position of the anticrossing line (AC) (see Fig. 1, b).
Figure 4. The models of the carbon related defects corresponding The knowledge of D values allows us to estimate the to the SDR–EPR spectra Si–PT1 (a), Si–PT 4 (b), Si–WL1 (c), average distance between two unpaired electrons forming and Si–WL2 (d).
the total spin S = 1 of the defects and to suggest the models of the investigated defects. The comparison of the B values for Si–WL2 and for other SDR–EPR spectra with the theoretical dependence of B on the distance r calculated Carbon impurities play an important role in the forin Ref.  is shown in Fig. 3. The models of some carbon mation of the radiation defects in silicon. One of the related defects derived from the SDR–EPR spectroscopic main defects in the irradiated pure float–zone grown sidata are shown in Fig. 4. licon is the (CI–SiS–CI) complex (Fig. 4, a) giving the Физика твердого тела, 1999, том 41, вып. Photoelectrically Detected Magnetic Resonance Spectroscopy of the Excited Triplet States of Point... SDR–EPR spectrum labeled Si–PT 1. Under isochronal  V.A. Khramtsov, V.N. Lomasov, Ya.Ya. Pilkevich, M.P. Vlasenko, L.S. Vlasenko. Phys. Stat. Sol. (a) 109, thermal annealing in the temperature range of 200-300C 127 (1988).
the spectrum Si–PT 1 decreases and new spectrum Si–PT L.S. Vlasenko, Y.V. Martynov, T. Gregorkiewicz, C.A.J. Amappears simultaneously. It was found that this spectrum merlaan. Phys. Rev. B52, 1144 (1995).
has the symmetry similar to the symmetry of divacancy and  R. Laiho, M.M. Afanasjev, M.P. Vlasenko, L.S. Vlasenko. Phys.
shows the hyperfine structure due to the interaction with Rev. Lett. 80, 1489 (1998).
two equivalent carbon atoms. The model of the defects  Y.H. Lee, J.W. Corbett. Phys. Rev. B13, 2653 (1976).
responsible for the Si–PT 4 spectrum is shown in Fig. 4, b.
This defects can be considered as a complex of two carbon atoms + divacancy.
Two weak spectra Si–WL2 and Si–WL4  shown in Fig. 2, d are observed in the unannealed samples. The models of the defects giving these spectra are shown in Fig. 4, c, d. These models were derived from the trigonal symmetry of the spectra and from the values of the fine structure splitting B = 2D determined by the distance between two electrons forming the total spin of defects S = 1. These electrons can be localized at the carbon atoms occupying the tetrahedral interstitial positions along directions of silicon lattice near the (CI–SiS–CI) complex.
In summary, the spin-dependent effects and detection of the EPR spectra by the change of microwave photoconductivity of samples allow us to observe the spectra of the excited triplet state of defects at their low concentration, which cannot be detected by traditional EPR spectroscopy.
The nonresonat crossing and anticrossing change of photoconductivity allows us to obtain additional information about the parameters of the triplet centers and to suggest their models.
The author thanks B.P. Zakharchenya for helpful discussions, R. Laiho for collaboration and helpful discussions, M.P. Vlasenko and M.M. Afanasjev for help in the experiments.
This work was supported by RFBR Grant N 97-02-18062.
References  C.A.J. Ammerlaan. Paramagnetic centers in silicon. In:
Landolt–Brnstein Numerical Data and Functional Relationship in Science and Technology / Ed. by O. Madelung.
Vol. 22 b, Impurity and Defects in Group IV Elements and III–V Compounds. Springer–Verlag, Berlin (1992). P. 365.
 G.W. Ludwig, H.H. Woodbury. Electron Spin Reconance in Semiconductors. In: Solid State Physics / Ed. by F. Zeitz and D. Turnbull. Academic Press, N.Y. (1992). Vol. 13, p. 223.
 G.D. Watkins. A Review of EPR Studies in Irradiated Silicon.
In: Radiation Damage in Semiconductors / Ed. by P. Baruch.
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