EPR identification
of intrinsic defects in SiC

1 Introduction
Electron paramagnetic resonance (EPR) has been proved to be the most successful technique in identifying deep centers in silicon. The abundance of isotopes with non-zero nuclear spin ( 29 Si, I = 1/2, natural abundance 4.67%) is just right to keep the linewidth nar- row enough for sufficient sensitivity and resolution and to observe the satellite lines due to hyperfine (HF) interac- tions easily. EPR has been also powerful in identifying point defects in diamond which supply smaller linewidth, although 13C (I = 1/2, 1.11%) enriched crystals were cru- cial for the identification in several cases [1–4]. As dem- onstrated typically by negatively charged vacancies [1, 5, 6] lattice relaxations involved in intrinsic defects are sig- nificantly different between silicon and diamond. The energy gap of SiC (E g = 3.28 eV for 4H-SiC) is between that of silicon ( E = 1.12 eV) and diamond ( E α = 5.47 eV). Thus, it is expected that the comparison of the same defect among silicon, diamond, and SiC should be useful for un- derstanding the reconstruction of structure relaxations in- volved in intrinsic defects. Moreover, SiC is richer in the variety of intrinsic defects arising from two sublattices (Si and C), abundant polytypes (3C-, 4H-, and 6H-SiC), and the presence of defects specific in compound semiconduc- tors such as antisites (Si c, C si ) and antisite-vacancy pairs. SiC is unique among compound semiconductors in having narrow EPR linewidths (ΔB ρρ ~ 0.03 mT) and non-zero nu- clear spin isotopes with reasonable ( 29 Si, 4.7%) and toler- able ( 13 C, 1.1%) natural abundance. SiC is a promising semiconductor material for high- power, high-temperature, and radiation-tolerant devices. High-purity semi-insulating (SI) substrates are attained by utilizing intrinsic defects [7, 8]. To improve the efficiency of ion implantation doping, understanding the behavior of defects is critically important. The EPR spectrum of phos- phorus-ion implanted 6H-SiC demonstrates the observation of residual defects after post-implantation annealing (Fig. 1). In EPR spectra of intrinsic defects in SiC, several sets of 29Si and/or 13C HF lines are expected to appear as satel- lite lines of strong primary lines. The angular dependence of the line positions of primary lines are described by the spin-Hamiltonian for an electron spin S, H = β S · g · B + [S · D · S] . The first term represents the electron Zeeman interaction. The second term, representing the fine structure interaction, InterScience which splits the primary lines into 2S lines and splits the energy levels even at zero-magnetic field (zero-field split- ting, ZFS), is included for a case with S ≥ 1. Based on the g-values and hence the resonant line positions specific for each EPR center, different EPR spectra arising from differ- ent defects can be distinguished (Fig. 2). The primary lines with high intensities are used to in- vestigate how the concentration of defects varying upon different processing conditions, such as electron irradiation conditions (electron energy, dose and temperature), heat treatment, and light illumination. Before the microscopic structure is established, the EPR spectra are often tenta- tively referred by the labels such as Tn, Pn, Kyn, (n = 1, 2, 3, ….) by using the initials of the research group, EIn, HEIn, SIn for those found in samples irradiated by elec- trons at room temperature or high temperatures and in SI samples, respectively, whereas IDn indicating intrinsic de- fects. Although the g and D tensors are useful parameters for determination of the local symmetry and the spin multi- plicity and hence the charge state, the primary lines lack definite chemical identity (Si or C). The detailed geometric and electronic structure identification comes from the HF interaction. For deep-level intrinsic defects in SiC, the wave function of the unpaired electron is extended to several atoms, Si 1 , Si 2 , ... and C 1 , C 2 , ... .. It is naturally expected that several major atoms comprising the defect such as four nearest-neighbors of vacancies and six nea¬ rest-neighbors of divacancies should have a HF splitting large enough to be resolved from the primary lines. Since the natural abundance of 29 Si and 13 C is low and the num- ber of major atoms of deep intrinsic defects is not large, each set of satellite lines arises from the case that one and only one of the major atoms is occupied by 29 Si/13 C. The line positions of the i-th satellite lines are described by the spin-Hamiltonian
H = β S · g · B + [S · D · S] + [S · A i · I i – g n j β r I · B] ,
where nuclear spin I = 1/2 for both 29Si and 13C and g (29Si) = −1.1106,  g (13C) = 1.40483  [13].  The  third  and fourth terms represent the HF interaction with the nucleus of the i-th atom and the nuclear Zeeman interaction, re- spectively. For structure determination of intrinsic defects, the observation of 29Si/13C HF satellite lines from all of the major-component atoms of the defect is desired. Although the wave function of the unpaired electron extends to fur- ther atoms, their HF interactions are often too weak result- ing in unresolvable HF structures which contribute only to the linewidth of the primary and satellite lines. The pri- mary lines are usually arising from a combination that all of major-component atoms are occupied by isotopes with zero nuclear spin. The intensity ratio between the satellite lines and the primary lines is important to determine the chemical identity (which gives the HF interaction, 29 Si or 13C) and the number of equivalent atoms. Among major Si/C atoms of a defect, some are sym- metry-related as in the case of three basal silicon atoms Si 2 4 in the positively charged carbon vacancy (S = 1/2, C 3v symmetry at 150 K) in 4H-SiC (Fig. 3) [14]. For the mag- netic field B ||[0001], these three atoms are equivalent and their 29 Si satellite lines are superimposed as s hown in Fig. 3. From the fit of the angular dependence of the line positions of the satellite lines, usually obtained with B ro- tating in high-symmetric planes such as (1 100) or (1120), the HF tensor A , is determined. Upon rotation from [0001], the 29 Si 2 4 HF lines split, and the symmetry of A 2 4 is de- termined to be C 16 from the pattern of roadmap of the HF lines. Here, the presence of 29Si on one of three basal sili- con atoms (Si 2 4 ) lowers the symmetry. We determine A i of one site (for example, Si 2 ). The line positions of the other symmetry-related sites (Si 3 and Si 4 ) are converted to those which should be obtained for the selected site (in this case, Si,) by the rotation of the magnetic field in the other plane(s). Thus, A i with the symmetry lower than C 3V is also determined by a single rotation. A i of other sites symmetry- related to the selected site is obtained by symmetry opera- tion. The pattern of the rotational plots shown in Fig. 3 is characteristic of the HF lines of the nearest-neighbors of monovacancy having C 3 v symmetry. The wave function of the unpaired electron is satisfac- torily described by linear combination of atomic orbitals (LCAO)
Ψ = Σιηλαι ψει + βιψει),
where α i and β i (α i + β i =1) are the s- and p-orbital contri- butions of the i-th atom and the total spin density η 2 indi- cates the degree of the spin localization on the i -th atom. The HF tensor of the i -th atom A i has usually axial symme- try with the principal values A l ( i ) and A l ( i ) or nearly uniax- ial. The HF interaction is divided into isotropic part A isot and anisotropic part b , © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim where we use A o = 134.77 mT, b = 3.83 mT for 13C and A 0 = −163.93 mT, b 0 = −4.075 mT for 29Si [13]. In addition to the spin density η 2 and sp-hybrid ratio β 2 /α 2 , the direc- tion of the p r orbital is determined from the principal axes of A . Thus, the observation of the HF structure, which gives the orbital parameters, is crucial for the structure identification of defects. As typically demonstrated in the case of the neutral di- vacancy, [V si V c] , in which the unpaired electrons are mostly localized on three nearest C neighbors of V sj among the six nearest-neighbors [15], the wave function of un- paired electrons might extend quite unevenly among the major atoms comprising the intrinsic defects. In such a case, the identification of the defect from EPR data is not straightforward, since a part of the major atoms which do not give the 29Si/13C satellite lines are invisible in the EPR spectra. Now, the first principles calculations provide not only the predicted structure of intrinsic defects but also the expected HF parameters [16]. Thus, the comparison of HF parameters obtained by experiments and theoretical studies is often crucial for the defect identification (see Fig. 4). For some of major-component atoms which exhibit a weak isotropic HF splitting with the anisotropy hidden un- derneath the linewidth, only the number of equivalent at- oms and η ⁄ α ⁄  are obtainable. Nevertheless, such informa- tion is still important in comparison with that obtained by theoretical studies. To extract the HF interactions hidden underneath the linewidth, we have applied pulsed ENDOR (electron nuclear double resonance) of pulsed EPR tech- niques which have much higher resolutions than that of the conventional EPR. The first-order ENDOR frequencies are determined as
hVendor = | MsAcfr − g,β,β,β |
here h is the Planck constant, β n the nuclear magneton and A rg the effective HF splitting. Since the nucleus is unambi- guously determined from the observed nuclear Zeeman frequency ( g β B/h ), ENDOR is useful for identifying the nucleus ( 29 Si or 13 C) giving rise to the resolved HF satellite 1300 lines. Since the ENDOR frequencies depend on M S (±1/2 for S = 1/2, ±1 and 0 for S = 1, ±1/2 and ±3/2 for S = 3/2), the spin multiplicity ( S ) can be determined. Actually, this technique was employed for the case of silicon vacancies (V si and Tv 2a , S = 3/2) [17, 18]. The intensities of the 29 Si/ 13 C HF lines, which do lead to the decisive structure determination, are severely limited by their low natural abundances. To produce the defect of interest selectively at sufficient concentrations, we performed electron irradiation at various temperatures (−160 °C to 800 °C), with different doses (1 × 10 17 – 1 × 10 19 e/cm 2 ), and post-irradiation heat-treatment pro- cesses (100-1500 °C) and used thick single-crystal sam- ples (typically 3 × 10 × 1.5 mm) of both n- and p-type of different dopant concentrations. 2 Isolated vacancy The lattice vacancy which is one of most fundamental intrinsic defects is also the primary defect produced upon irradiation with energetic particles. The mobility of isolated vacancy is remarkably different among diamond, SiC, and silicon. In SiC and diamond iso- lated vacancies are observable after electron irradiation at room temperature, at which divancancies and impurity- vacancy complexes are formed in silicon. A variety of isolated vacancies arising from different sublattices (Si and C), inequivalent sites (hexagonal site h and cubic site k ), and having different charge states is ex- pected in 4H-SiC. The difference in the electron negativity (2.55 for C and 1.9 for Si on the Pauling scale) favors the negative charge state (−1) for the silicon vacancy (V si ) and the positive charge state (+1) for the carbon vacancy (V c ). So far, several V si, V c and V centers have been identified by EPR in 3C-, 4H- and 6H-SiC. First, let us consider the isolated vacancies in silicon. Features of the EPR spectra of V t (D 2d , S = 1/2) labeled Si- Gl and V-(C 2 , S = 1/2) labeled Si-G2 [5, 6, 19] were suc- cessfully explained with a dominant Jahn–Teller distortion by using simple one-electron LCAO models illustrated in Fig. 5. Tetrahedral crystal field splits the defect molecular orbitals into a singlet a 1 and a triplet t 2 . In the positively charged vacancy (V + ), under undistorted T d symmetry, two electrons enter into a 1 and the third electron enters into t 2 . Thus, V + in silicon, which is subjected to a Jahn– Teller distortion, undergoes a tertragonal distortion and the resulting symmetry is Dンd (Fig. 5(b)). The orbital occupied by the unpaired electron ( b 2 ) spreads equally over the  four 1301 nearest-neighbors with the spin density η ² = 14.6% and the sp-hybrid ratio β 2 /α 2 = 5.5 on each silicon. In the 〈100〉. axial symmetry, the two atoms in two pairs (b, c and a, d) are pulled together [19]. Since the b 2 orbital can accommodate one more elec- tron, the neutral vacancy with four electrons has D 2 d sym- metry and S = 0. Under D 2d symmetry, the fifth electron of the negatively charged vacancy (V − ) goes into a degenerate e level. Thus, further Jahn–Teller distortion lowers the symmetry to C 2v , resulting in the effective spin S = 1/2 (Fig. 6(a)). The distortion is pulling one pair of atoms (b and c) together toward each other and separating the other pair of atoms (a and d) slightly. The unpaired elec- tron is localized mainly on two (a and d) of the four near- est-neighbors with the spin density η ² = 27.3% and the sp-hybrid ratio β 2 /α 2 = 2.52 [5, 6]. In both V + and V − , The sum of the spin densities of the nearest-neighbors is similar between V + (58.4%) and V − (54.6%). V − in diamond has T d symmetry with the effective spin S = 3/2 (three electrons in the triply degenerate t 2 level) as shown in Fig. 6(b) left. The orbitally nondegenerate 4A, state is not subjected to a Jahn–Teller distortion. The large fraction (~83%) of the unpaired electron is localized on the four nearest-neighbors [1]. The electron-electron repul- sion due to the strong localization favors the high spin state in which three electrons occupy three different orbitals. In silicon, the energy gain is obtained by Jahn-Teller distor- tion, while the electron–electron repulsion is lowered by a large delocalization. The extent of the wave function of the unpaired electron was confirmed by ENDOR measure- Figure 5 (online colour at: www.pss-b.com) Energy levels of the positively charged va- cancy in a simple model of one-electron mo- lecular orbital constructed by the four dan- gling bonds shown in (a). Under T d symme- try, both tetragonal and trigonal distortions would remove the degeneracy. Under C 3, symmetry, further distortion is required if a doublet e is lower than a ′ . © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1302 ments up to the 17-th atom along the 〈110〉 zigzag chain [6]. Thus, important factors which govern the geometric and the electronic structures are the degree of structure relaxa- tion and the electron–electron repulsion. 2.1 Silicon vacancy in SiC In SiC, negatively charged silicon vacancies (V si ) are found in 3C- [20, 21], 4H-, and 6H-SiC [17, 18, 22]. Basically, they are similar to V – in diamond in taking the ground state of high spin state ( S = 3/2). The T d symmetry of V si in 3C-SiC (the T1 cen- ter) was confirmed by the angular dependence of 13 C HF lines of the nearest-neighbors [20, 21]. In the T d symmetry, all three ΔΜ s = ±1 transitions of S = 3/2 are superimposed since the ZFS vanishes. The effective spin S = 3/2 of V si in 4H-SiC was confirmed by the ENDOR measurements [17]. This high spin state has been ascribed to predominant tet- rahedral character of the local structure which is indicated by isotropic g-value, isotropic 29 Si HF interactions of next- nearest-neighbors, and the absence of ZFS. By measuring the angular dependence of 13 C HF lines of the nearest- neighbors, two spectra labeled V si (I) and V si (II) are distin- guished (Fig. 7) [22]. It is emphasized that the V Si centers are very similar between 6H-SiC and 4H-SiC (Figs. 8(a) and (b)). From the intensity ratio of the corresponding spectra in 6H-SiC, V s i (I) and V s i (II) are assigned to be arising from V ξ i ( h ) and V ξ i ( k ), respectively. In both types, the C 3 , symmetry is demonstrated by the inequivalence in η ž and β ž /α ž between C 1 and C 2 4 (Table 1, Fig. 9). Thus, the arrangement of nearest-neighbors of V si in 4H-SiC is slightly distorted from regular tetrahedron. The T v 2 a center can be observed by photoluminescence (PL), which is called the V2 line (1.352 eV). The corre- spondence between T V2a and V2 was demonstrated by opti- cally detected magnetic resonance (ODMR) [23]. The T V2a Figure 8 (online colour at: www.pss-b.com) Angular maps for silicon vacancy centers in 6H- and 4H-SiC. (a) V ε ; centers in center which does exhibit ZFS (|D| = 35.1 MHz) [23] has been identified as a family of V si having S = 3/2 [18, 24]. Similar to the V si center, the EPR spectra of T v 2a center have 29Si satellites arising from twelve equivalent Si atoms in the next-nearest-neighbor-shell of V si , which are drawn
in Fig. 9. In both V si and T v 2a , the 29 Si HF splitting is iso- tropic within the resolution of cw-EPR and the satellite lines arising from two 29 Si nuclei  on  among  these twelve silicon atoms are also observed. The angular dependence of three primary lines and the 13 C satellites of four nearest- neighbors (C 1_4 ) is shown in Fig. 8(c). The complete analy- sis of the T v 2a spectrum was achieved by utilizing the en- hancement of the signal intensity due to electron spin po- larization by light illumination [24, 25]. However, the cen- tral primary line of T v 2a was often missing, because it was not enhanced by illumination and was usually hidden un- derneath the V si signal. This misled to that T v2a originates from V si with S = 1 [25]. The observation of the central primary line can be achieved by a pulsed-ELDOR tech- nique shown in Section 3. The spin multiplicity of T v 2a has been determined to be S = 3/2 by the nutation method of pulsed-EPR [24] and by pulsed ENDOR [18]. The C 3 v symmetry of T v 2n , which was already manifested by the ZFS, has been supported by the larger deviation from a regular tetrahedral angle (109.5° → 107.5°, see Table 1). The defect wave function is rather delocalized for V si in SiC (62–65% on C 1-4 atoms, see Table 1) than for V − in diamond (83%). The sp-hybrid ratio is larger than that (~7) of V – in diamond. Four carbon dangling bonds of V si are well separated in SiC [26, 27], preserving the high spin state of V si . This situation is strikingly contrast to the case of carbon vacancies explained in the next section. 2.2 Carbon vacancy in SiC Positively charged car- bon vacancies (V c , S = 1/2) have been found in 4H- and 6H-SiC but not in 3C-SiC. In 4H-SiC, a negatively charged carbon vacancy (V - , S = 1/2) was also found. The EI5 [28] and EI6 [29] centers in 4H-SiC have been established to be V c at cubic ( k ) and hexagonal ( h ) sites, respectively [14, 30]. Similarly, the Ky1/2 and Ky3 centers in 6H-SiC have been identified as V c at two cubic ( k 1 , k 2 ) and one hexagonal sites, respectively [31]. All of these spectra exhibit 29Si HF satellite lines arising from four Si neighbors of a V c . Angular dependences of the primary and 29Si HF lines are summarized in Fig. 10(a) to (d). Again we can find a close similarity between the EPR spectra in 6H-SiC (Fig. 10(a)) and 4H-SiC (Fig. 10(b)). The Vぞcenters are typical examples in which the struc- ture relaxation is remarkably different between the in- equivalent sites (Fig. 11) and the assignment of EPR spec- tra has been achieved by agreement between the observed 1304 29Si HF tensors and those obtained by the first principles calculations [16, 30]. As shown in Table 2, the HF param- eters obtained from the first principles calculation are con- sistent with those from EPR measurements at low tempera- tures. We owe to the contributions of theoretical groups that two EPR spectra EI5/EI6 significantly different in the symmetry and the spin distribution among four-nearest- neighbors are assigned to Vぞ(k) /Vぞ(k) [16, 30]. In 4H-SiC, for both C( h ) and C( k ) sites, there are two magnetically distinguishable orientations of [CSi 4 ] tetrahe- dron, [Si 1 C( h/k )Si 2 Si 3 Si 4 ] and [Si 1 C( h ′ /k ′ )Si 2 Si 3 Si 4 )]. In analyzing the angular dependence of the 29 Si HF lines of Vc, the presence of two orientations needs to be consid- ered. However, instead of going into these technical details, we discuss the structure relaxation by using one tetrahe- dron composed of the nearest-neighbors [Si 1 (Si 2 Si 3 Si 4 )], where Si 1 is the unique silicon atom located on the [0001] direction. An example of the angular-dependence measurement is shown in Fig. 12 for the EI5 center at 5 K. The angular de- pendence for this center (V c ( k )) is classified into two phases: one is observed below 50 K (C 1h symmetry, Fig. 10(b)), and another is seen above 50 K (C 3 , symmetry, Fig. 10(c)) [30]. As the effect of lowering the local sym- metry from C 3 V to C 1 h , in the first place, Si 2 is not symme- try related to Si 3,4 where Si 3 and Si 4 are mirror-symmetric with respect to the (1120) plane (Fig. 11). As a result, with B||[0001], three sets of 29Si HF lines, Si 1 , Si 2 and Si 3,4 are observed as is seen in Fig. 12, while Si 2 -4 become equiva- lent for B ‖[0001] under C 3 v symmetry (Fig. 3). In the sec- ond place, the number (orientational degeneracy) of sym- metry-related sites, which have an identical structure ex- cept orientations in the lattice, is increased. Upon rotation with B ⊥ [T100], the primary line and the set of 29Si 1 , the set of Si 2 split into three lines. The set of Si 3,4 splits into six lines. These behaviors are shown in Fig. 10(b). From the obtained HF parameters (Table 2), the spin density ( η ² ), sp-hybrid ratio ( β 2 / α 2 ), and the direction of p-orbital [polar angles of θ or (θ, φ)] of nearest-neighbor silicon atoms are estimated (Table 3). As is drawn in Fig. 11, the p-orbital directions of Si 1 and Si 2 indicate that two dangling bonds of Si 1 and Si 2 are tilted to approach each other to form a Si 1 –Si 2 bond. A similar reconstructed bond between Si 3 and Si 4 is formed by tilting of Si 3 and Si 4 dangling bonds. At high temperatures, rapid thermally-activated re- orientations (bond  switching Si 3 − Si 4 ] ↔ [Si 1 -Si 2 , [Si 1 −Si 3 , Si 4 −Si 2 ] ↔ [Si 1 −Si 4 , Si 2 −Si 3 )]) results in C 3 v symmetry. Features characteristic to reorientation effects, such as the lifetime broadening of the low-temperature spectrum and the motional narrowing of the high- temperature spectrum were observed as a function of tem- perature. From the analysis of the reorientation time, the activation energy of the reorientation was estimated to be 0.015 eV [30].
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
On the other hand, V (h) (the EI6 center) keeps C 3v symmetry at 5 K [14], although the first principles calcula- tion predicted a possible configuration having C 1h symme- try [16]. As is seen in Fig. 10(d), 29Si HF splittings are much larger for Si 1 than other three Si neighbors (Si 2 4 ) of a V c , indicating a strong localization on the Si 1 atom ( η ² = 33.4–47.3%, see Table 3). The displacement of Si 1 along the [0001] direction away from Si, 4 is the major part of the structure relaxation. Due to the strong spin localiza- tion on Si 1 , 29 Si HF interaction from Si 5 , 7 atoms behind Si 1 (see Fig. 11) can be also observed. Using a pulsed ENDOR technique, the anisotropy of the Si , , HF lines was resolved as shown in Fig. 13. The EI6 EPR spectrum is strongly temperature dependent. As temperature increases, the spin distribution on Si, is shifted to Siン4 (Table 3). Accordingly, with B ||[0001], the 29 Si HF splitting decreases for Si 1 and Si 5_7 , and increases for Si 2_4 . At a low temperature limit, the sum of η ² of four nearest-neighbors is the same for Vぞ( h ) and V (k) (68.0% and 67.6%, respectively), exhibiting a stronger localization than the case of V + in silicon (58.5%). In 4H-SiC, a negatively charged carbon vacancy can be also observed (Fig. 2(a)), which was named the HEI1 cen- ter (S = 1/2) [32]. Two angular maps of this center are shown in Figs. 10(e) and (f). Depending on temperature, the HEI1 EPR spectrum exhibits C 1h and C 3V symmetries, as similarly to V c ( k ). The transition temperature is about 70 K. In the C 1h configuration (<70 K), the unpaired elec- tron is mainly localized on two Si neighbors (Si 1 and one of Si 2 4 ) of V c . This is just the same trend as observed for V − in silicon [5, 6]. As a result, two sets of 29Si HF lines are clearly appeared (Fig. 10(e)). The structure relaxation takes place as to form a Si 1 –Si 2 (or Si 1 –Si 3 or Si 1 –Si 4 ) pair. Likewise the case of V c ( k ), thermally activated reorienta- tion results in C 3 , symmetry at high temperatures. Further- more, the 29 Si, satellite line disappears due to the lifetime broadening (Fig. 10(f)). From the lifetime analysis, the re- orientation activation energy was estimated to be 0.020 eV, which is slightly larger than that for V ĉ ( k ). The sum of η 2 of the two nearest-neighbors is 60.7%, which is larger again than the case of silicon (55.8%). Comparing with the theoretical A tensors, this V c − center is assigned to V − ( h ) (Table 2) [32]. The first principles calculation predicted that the V c ( k ) center is distinguishable due to its different HF signature, however, the corresponding EPR signal has not been identified. 3 Pulsed ELDOR of T v2a : Observation of missing The EPR spectrum of T v 2n (S = 3/2, central line |D| = 35.1 MHz) is expected to be composed of three lines arising from three ΔM s = ±l transitions, +3/2 ↔ +1/2, +1/2 ↔ −1/2, −1/2 ↔ −3/2. The echo-detected EPR spec- trum (130 K, B||[0001]) of n-type 4H-SiC irradiated by electrons (3 MeV, 4 × 10¹ 8 e/cm²) at room temperature is shown in Fig. 14. In dark (Fig. 14(b)), the central line of Tv 2n (+1/2 ↔ −1/2 transition) is hidden underneath the strong signal of V si ( S = 3/2, D ~ 0) due to lower concen- trations. Under illumination of laser light (808 nm), the in- tensity of the two outer lines of T V 2a is strongly enhanced by electron spin polarization to surpass that of V ξ j as shown in Fig. 14(a). However, the +1/2 ↔ −1/2 transition is not enhanced by illumination. Thus, the central line cor- responding to the +1/2 ↔ −1/2 transition of T V2a has not been revealed [23–25, 33]. The polarization under illumination is explainable by selective population onto two levels, either ± l/2 ( D > 0) or ±3/2 ( D < 0), among four M s levels of S = 3/2. Here, 1306 we assume that the ±1/2 levels should be selectively populated and D > 0. Then, the low-field line exhibit- ing strongly enhanced absorption is assigned to the +3/2 ↔ +1/2 transition (higher level is much less popu- lated, p (+3/2) ≪ p (+1/2)) and the high-field line exhibiting strong emission (the higher level has much larger popu- lation, p (−1/2) ≫ p (−3/2)) is assigned to the −1/2 ↔ −3/2 transition. Here, p ( M s ) denote the population of the M s level. Since the microwave-induced transition probability is the same for both of the ΔM s = ± l transitions (upward and downward transitions), the EPR signal intensity is propor- tional not only to the concentration of the defect but also to the population difference of the two M s levels involved in the transition. The strong signal enhancement indicates that the absolute values of the population difference |p(+3/2) - p(+1/2)| and |p(-1/2) - p(-3/2)| is much larger than those in thermal equilibrium. No appearance of the +1/2 ↔ −1/2  transition  of  Ty2a  indicates  that  no  extra population difference is created under illumination. For simplicity, we assume that the ±1/2 levels are equally populated under illumination ( p (+1/2) ~ p (−1/2)). If the large population difference between the −1/2 and −3/2 levels (or between the +3/2 and +1/2 levels) attained by illumination should be created also for between the +1/2 and –1/2 levels, as inferred from Fig. 14, the intensity of the +1/2 ↔ −1/2 transition of T V2a can exceed that of the strong V si signal. We have tried to transfer the polarization of the +3/2 ↔ +1/2 transition (−1/2 ↔ −3/2 transition) to the +1/2 ↔ −1/2 transition by using 180° pulse of the +3/2 ↔ +1/2 (−1/2 ↔ −3/2) transition. Here, the 180° pulse is used to swap the populations of the levels between which the transition is induced. Then, we need a micro- wave pulse with frequencies different from the one used for observing the signal of the +1/2 ↔ −1/2 transition (Fig. 15). We have carried out pulsed ELDOR (electron- electron double resonance) experiments at 130 K under illumination of laser light (808 nm). In the first place, the frequency-swept ELDOR ex- periments were carried out with the magnetic field fixed at the central signal (Fig. 16). For observing the signal of the +1/2 ↔ −1/2 transition of T v 2a which is expected to appear overlapped with that of V ξ i , a pulse sequence of 3-pulse inversion  recovery,  (180° – to – 90° – τ – 180° – τ – echo, where t 0 = 4 µs and τ = 1 µs are fixed), was employed, here, t is sufficiently shorter than the spin–lattice relaxation time.  Hahn-echo (90° – τ – 180° – τ – echo)  generated  by the second and the third pulses, which has usually a role to make the z component of the magnetization M, at time t o observable, is used to measure the polarization of the +1/2 ↔ −1/2 transition of T v 2a induced by the ELDOR pulse. When no ELDOR pulse is applied, the signal corre- sponding to the inversion of the V si signal was observed. The 180° pulse (duration 80 ns) at t = 0 inverts the popula- tion difference of V si, however does not alter the zero- intensity of the +1/2 ↔ −1/2 transition of Tv2a since p(+1/2) ~ p(-1/2). Thus, the baseline in Fig. 16 corre- sponds to the echo height of the inverted V si signal. The ELDOR pulse, of which duration (116 ns) was chosen to attain the flipping angle of ~180°, was applied at t = 1 μs. The frequency (9.705 GHz) of the 3-pulse inver- sion recovery sequence as well as the coherent detection is tuned to that of the resonator loaded with the sample. The resonator has a large bandwidth due to low- Q which is in- herent to pulse experiments for achieving a short deadtime. When the frequency of the ELDOR pulse was varied (Fig. 16), the echo height is significantly affected at 9.635 GHz and at 9.775 GHz as well as at 9.705 GHz. The change brought at 9.705 GHz is caused by the flipping of the central signal mainly due to V sj. The signal of the +1/2 ↔ −1/2  transition  of  Tv 2a,  which  is  also  resonant to 9.705 GHz, was not affected by the flipping by the ELDOR pulse of 9.705 GHz since p (+1/2) ~ p (−1/2). Two frequencies, 9.635 GHz and 9.775 GHz correspond to the −1/2 ↔ −3/2 and +3/2 ↔ +1/2 transitions of T V2 , re- spectively, at the magnetic field of the central signal (Fig. 15(c)). We note that these frequencies are The change of the echo intensity ~9.705 GHz ± 2|D|. brought by the ELDOR pulse of these frequencies, stimu- lated emission at 9.635 GHz and stimulated absorption 1307 at 9.775 GHz, is ascribed to the appearance of the strong signal from the +1/2 ↔ −1/2 transition of T v 2a In the second place, the field-swept ELDOR experi- ments were carried out to obtain the spectral features of the +1/2 ↔ −1/2 transition of Tv2a. We have three signals, the signal of +3/2 ↔ +1/2 of T v 2a , the central signal (+1/2 ↔ −1/2 of T V22 overlapped with V Si ), and the signal of −1/2 ↔ −3/2 of T v 22 . The first 180° pulse (width 80 ns) is strong enough to invert one of the three signals when the magnetic field is set to the signal, however is not sufficient to flip the other two signals, simultaneously. The intensity of the echo of 3-pulse inversion recovery was measured as a function of the magnetic field strength without ELDOR pulse (Fig. 17(c)) and with applying the ELDOR pulse (Fig. 17(a) and (b)). Although the microwave pulses have the excitation bandwidth exceeding the linewidth of the signals, the resolution of the conventional EPR is achieved by using a large window width for integrating the echo. The frequency (9.635 GHz and 9.775 GHz) and the width of the ELDOR pulse are selected to achieve the flipping angle of ~180° for the ±3/2 ↔ ±1/2 transitions at the mag- netic field of the central signal. Without applying ELDOR pulse, we obtained the spectrum shown in Fig. 17(c) which is inverted one of the spectrum shown in Fig. 14(a). We note that the ELDOR pulses at 9.635 GHz and 9.775 GHz did cause a significant change of the central signal. By us- ing the 180° ELDOR pulse of 9.635 GHz, the emission (p(+1/2) ≥ p(−1/2)) of +1/2 ↔ −1/2 transition of T v 2 a is added to the inverted signal of V sj and the amplitude of the negative signal at the central line is strongly increased. By using the 180° ELDOR pulse of 9.635 GHz, the enhanced absorption ( p (+1/2) ≫ p (−1/2)) of the +1/2 ↔ −1/2 transi- tion of T v 2a dominates over the inverted signal of V s. Thus, in Fig. 17(a), the central line is the pure signal of the +1/2 ↔ −1/2 transition of Tv2a. In the field-swept spectra, the effect of the ELDOR pulse on the outer signals is somewhat more complicated. In the case of the ELDOR pulse of 9.635 GHz, the low Figure 17 (online colour at: www.pss-b.com)  Echo-detected  EPR spectrum. The intensity of the 3-pulse inversion recovery was monitored as a function of the magnetic field. 1308 field line corresponding to the +3/2 ↔ +1/2 transition was affected. At the magnetic field, at which the +3/2 ↔ +1/2 transition is resonant to 9.705 GHz, the +1/2 ↔ −1/2 tran- sition is within the bandwidth of the ELDOR pulse of 9.635 GHz. The 180° pulse of 9.705 GHz at t = 0 inverts the polarization of the +3/2 ↔ +1/2 signal from the strong stimulated absorption p (+3/2) ≪ p (+1/2) to the strong stimulated emission p (+3/2) ≥ p (+1/2). This large popula- tion difference is decreased by the ELDOR pulse at t = 1 μs  which  transfers  the  population  of −1/2  level  to +1/2 level. In the case of the ELDOR pulse of 9.775 GHz, the high field line corresponding to the −1/2 ↔ −3/2 transi- tion was affected. At the magnetic field at which the −1/2 ↔ −3/2 transition is resonant to 9.705 GHz, the +1/2 ↔ −1/2 transition is flipped by the ELDOR pulse of 9.775 GHz. Thus, the population difference p (−1/2) ≪ p (-3/2) after the 180° pulse of 9.705 GHz was nearly cancelled by the ELDOR pulse at 9.775 GHz which trans- fers the population of +1/2 level to −1/2 level. We note that both the line position (or the g-value) and the 29Si HF structure of the +1/2 ↔ −1/2 transition of T ν 2a is similar to those of V ξ i as already known from the spin- Hamiltonian parameters determined from the fit of the outer lines. It should be noted that the line width of the +1/2 ↔ −1/2 transition of T V 2n is smaller than that of the outer lines and the 29 Si HF structure of second-nearest neighbours is more clearly observed for the signal of the +1/2 ↔ −1/2 transition than for the outer lines. Thus, the distribution of the zero-field splitting ( D ) contributes sig- nificantly to the line broadening of the outer lines. In the third place, the Rabi oscillations (nutations) of −3/2 ↔ −1/2 and +3/2 ↔ +1/2 transitions, respectively, of T v 2n driven by the ELDOR pulses at 9.635 GHz and 9.775 GHz, respectively were measured by monitoring the polarization of the +1/2 ↔ −1/2 transition. The magnetic field was fixed at the central signal of Fig. 14. In pulsed experiments, the behaviour of the magnetiza- tion is described using a coordinate system rotating with the microwave frequency around the external magnetic field ( z || B 0 , x || B 1 ). At the resonance condition, the micro- wave pulse rotates the magnetization around the x-axis through the angle
θ(tp) = (2πgβcB1/h) tp = ωntp
here, t o is the pulse width, B 1 the microwave rotating field, ω  the nutation frequency. The flipping by the microwave pulse changes the z -component of the magnetization which is related to the population difference of the two levels be- tween which transition is induced. For the usual case start- ing from thermal equilibrium ( M = M o ), the oscillation of the z-component of the magnetization is
M 2 α M 0 cos ( ω t p ) .
In our case, we start from large | M f | (| M f | ≫ M o ), with the sign either positive (absorption) or negative (emission) due to polarization, p (+1/2) ~ p (−1/2) ≥ p (+3/2), p (−3/2). The oscillation of M z corresponding to the −1/2 ↔ −3/2 transi- tion by using the ELDOR pulse of 9.635 GHz or that corresponding to the +3/2 ↔ +1/2 transition using the ELDOR pulse of 9.775 GHz causes the oscillation of the population difference between the +1/2 and −1/2 levels. The population difference between the +1/2 and −1/2 levels is directly related to the signal height of the +1/2 ↔ −1/2 transition of T V 22 . Thus, the Rabi os- cillations  of  −1/2 ↔ −3/2  (9.635 GHz)  and  +3/2 ↔ +1/2 (9.775 GHz) transitions are monitored by measuring the echo signal of the +1/2 ↔ −1/2 transition (9.705 GHz). The height of the 3-pulse echo at the magnetic field of the central signal was measured as a function of the pulse width of the ELDOR pulse (Fig. 18). The Rabi oscillations were observed for ~1 µs. In Fig. 18, the signal height at zero pulse width (i.e. ELDOR pulse off) corresponds to the height of the inverted signal of V sj . The fact that the induced signal exhibits the Rabi oscillations of the −3/2 ↔ −1/2 and +3/2 ↔ +1/2 transitions confirms that the signal of the +1/2 ↔ −1/2 transition is indeed induced. The difference of the nutation frequency for the two ELDOR frequencies 9.635 GHz and 9.775 GHz is likely to be caused by the difference of B 1 for the two frequencies in the pulsed ELDOR setup. 4 Divacancy In silicon, positively and negatively charged divacancies, [VV] + and [VV] − , have been identi- fied by EPR to have C 2h symmetry with S = 1/2. Removing two adjacent Si atoms produces six dangling bonds ( a, b, d, d', b', and d'). Unrelaxed divacancy of D 3d symmetry has two singlets a 1g and a 1g in the valence band, and two dou- blets e g and e u in the energy gap, with e g higher than e u . Since the e n level is partially occupied (V 2 : e n , V 2 : e 3 ), a Jahn–Teller distortion, which reconstructs pair bonds be- tween a and d, d ′ and d ′ , lowers the symmetry to C 2h . In both [VV]+ and [VV]+, the unpaired electron is localized mainly on atoms b and b ′ in the mirror plane of C 2h sym- metry. The spin density η 2 and the sp-hybrid ratio β 2 /α 2 on 1309 these atoms ( b and b ′ ) are 27.5%, 7.5 for [VV] + and 24.6%, 4.8 for [VV]" [34–36]. The neutral vacancy in silicon is diamagnetic ( S = 0). It should be noted that, if [VV] 0 of D 3d symmetry had taken non-orbitally-degenerate 3 A 2g (S = 1) state arising from electronic configuration e α , then no Jahn−Teller distortion is expected. The neutral divacancy in diamond has S = 1, however, the symmetry is lowered to C 2h [4]. The unpaired electron is mainly localized on four atoms ( a, d, a ′ , and d ′ ) which are not in the mirror plane, with η ⁄ = 20% and β 2 /α 2 = 9. The P6/P7 centers ( S = 1) in 4H-SiC have been estab- lished to be originating from the ground state of the neutral divancancy [V siVc ] °, the closest pair of the silicon vacancy (V Si ) and the carbon vacancy (V c ), through the cooperation between the first principles calculations which supplied the predicted HF parameters and the careful EPR measure- ments of the 13C HF lines, both the angular dependence and the intensity relative to the primary lines. Four configura- tions ( hh, kk with C 3V symmetry, hk, kh with C 1h symmetry) are distinguishable by EPR. The divacancy was suggested as a model for the P6/P7 EPR centers in heat treatment 6H-SiC in the early 1980s by Vainer and Il'in [37]. However, the identification was based only on the observed symmetry of the centers (C 16 for P6 and C 3 v for P7). Since light illumination was needed for detecting the spectra, the centers were believed to be related to the excited triplet states of the divacancy [37]. These centers are also commonly detected in n-type 6H-SiC by ODMR [38] or in high-purity semi-insulating (HPSI) 4H- and 6H-SiC substrates by EPR [39, 40]. In a later study using MCDA (magnetic circular di- chroism of the absorption)-detected EPR and first princi- ples calculations by Lingner and co-workers [41], P6/P7 EPR spectra in 6H-SiC were claimed to be the carbon- antisite carbon-vacancy pair in the double positive charge state ([CsiVc] 2*). Figure 19(a)  shows  the  P6/P7  spectra  in  as-grown HPSI 4H-SiC substrates detected at 77 K for the magnetic field B ||[0001] under illumination of light of photon ener- gies in the range 2.0–2.8 eV. In the 4H polytype, there are two configurations with C 3 v symmetry (P6b and P6'b) and two configurations with C 1 h symmetry (P7b and P7'b). The P6/P7 centers have the same g-value g = 2.003 and slightly different fine-structure parameters D and E (in unit of 10 –4 cm –1 ): D(P6b) = D(P7b) = 447, D(P6'b) = 436, D(P7'b) = 408, E(P7b) = 90 and E(P7'b) = 10. The angle between the principal axis of the fine structure tensor and the c axis for P7b and P7'b is 109.5° and 109°, respectively. Recently, detailed HF structures of the P6 and P7 centers in 4H- and 6H-SiC have been observed [15, 43]. Typical HF structures for parts of the P6b and P6'b spectra in 4H-SiC are shown in Fig. 19(b). As shown in the figure, the large splitting HF lines are from the interaction with three nearest C neighbours of V sj . The inner HF lines are due to the interaction with nine next-nearest Si neighbors, of which three Si atoms on the bonds along the c -axis has a slightly larger splitting. The HF interaction with three nearest Si neighbours of V C is small and not resolvable. The principal values of the HF tensors determined for the P6b, P6'b and P7'b centers in 4H-SiC are shown in Table 4. The observed HF constants are in good agreement with the values obtained from the supercell calculations of the neu- tral divacancy model [15, 44]. The P6/P7 centers were therefore identified as different configurations of the neu- tral divacancy ([VsiVc] b ). Comparing the observed HF con- stants with the calculated values for different configura- tions, it was possible to assign the P6b and P6'b centers to 1310
the axial C 3 v configurations at the hexagonal and cubic sites  [P6b: V si (h) – V c (h),  P6'b:  V si (k) – V c (k)]  and  the P7b and P7'b centers to the monoclinic C 1h configurations, V sj ( h ) – V c ( k )    and    V sj ( k ) – V c ( h ),    respectively [15]. Figure 20 shows schematic atomic models for the [VsiVc]° centers. Using the linear combination of atomic orbital analysis, the spin density on a nearest C neighbor is deter- mined as: ~1.8–1.9% on the s-orbital and ~18–19% on the p-orbital for P6b, P6'b and P7'b. The sp-hybrid ratio is ( β 2 / α 2 ) ~ 10 for all the configurations. The total spin den- sity on the three nearest C neighbors of the neutral diva- cancy is ~60% for the C 3 v configuration (P6b/P6'b) and ~62% for the C 1h configuration (P7'b). In the C 3V configu- rations, the spin density is equally distributed among the three nearest C neighbors and the direction of p-orbitals (θ = 107°) with respect to the vacancy-vacancy direction (see Fig. 20) is slightly smaller than the tetrahedral angle (109.5°). In the case of P7'b center, the localization of spins at the C atom along the c -axis is slightly smaller than that at the other two C atoms on the inclined bonds. In both C 3 v and C 1 h configurations, the spin localization on three nearest Si neighbors of V c is negligible (~1%). With elec- trons on the e level arising from C dangling bonds of V si, the spin localization for the neutral divacancy is similar to that of V s i : ~60−62% on three nearest C neighbors of V si in the divacancy and ~62–65% on four nearest C neighbors for V si In as-grown samples, the observation of the P6/P7 cen- ters requires illumination with light of photon energies lar- ger than ~1.1 eV. However, in some irradiated 4H- and 6H-SiC samples, the spectra could be detected in the dark even at low temperatures (1.5–8 K) [15, 45]. This con- firms that the spectra are related to the ground state, in agreement with the supercell calculations of the neutral di- vacancy [15, 39]. In the divacancy, three C dangling bonds and three Si dangling bonds create six defect levels. In the axial configuration with C 3 v symmetry, two a 1 levels fall in the valence band and two double generate e levels lie in the band gap. The lower e level arises from the C dangling bonds of the Si vacancy and the upper e level arises from the Si dangling bonds of the C vacancy. In the neutral charge state, there are six electrons, four of them fill the two resonance a 1 levels in the valence band and the other two occupy the lower degenerate e level, giving rise to the spin S = 1 for the ground state. In 4H-SiC, the calculations found the (+/0) and (0/-) levels to be at ~0.5 eV and ~1.4 eV above the valence band, respectively [15, 44]. Re- cent EPR studies in irradiated HPSI 4H-SiC substrates [46] show that in the dark at 77 K only the V  signal was ob- served. However, increasing the temperature to 293 K while keeping the sample in darkness, the [VsiVc] 1 signal could be weakly detected. This suggests that the (0/–) level of V C V si may lie slightly below the (+/0) level of V C at ~ E v + 1.47 eV [47] so that at room temperature it could be partly thermally ionized. Consequently, a part of the total concentration of the divacancy is changed to the neutral charge state and could be detected. This EPR estimation is close the theoretical prediction of the (0/-) level at ~Ev + 1.4 eV. Recently, the divacancy has been identified as a prominent defect responsible for the semi-insulating properties in HPSI 4H-SiC substrates with thermal activa- © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim tion energies of ~1.5–1.6 eV, which may be associated to the single acceptor level (0/–) of [VsjVc] [46]. The no-phonon lines related to the P6 centers in irradi- ated n-type 6H-SiC substrates were found to reach their maximum intensity after annealing at ~900 °C and to be disappeared after an 1200 °C anneal [48]. In electron- irradiated HPSI 4H- and 6H-SiC substrates, the EPR sig- nals of the divacancy were annealed out at higher tempera- tures (~1400 °C), whereas in as-grown HPSI materials with low concentrations of defects and residual impurities (N and B) their intensities only started decreasing after an- nealing at 1600 °C [46]. In 6H-SiC, the relation between the P6/P7 triplet states and the no-phonon lines of the near-infrared photolumines- cence (PL) band has been confirmed (P6a-c: 1.075, 1.048 and 1.011 eV; P7a-c: 1.049, 1.030 and 0.999 eV) [41]. In 4H-SiC samples with strong EPR signals of the neutral divacancy, five strong absorption lines were also detected at 0.9975, 1.0136, 1.0507 and 1.0539 eV [49]. These lines were also weakly detected in PL. Weak PL emissions may be the reason why the P6/P7 centers in 4H-SiC have not been detected by optical detection of magnetic resonance. In 4H-SiC, the correlation between these no-phonon lines and the P6/P7 EPR centers has not been confirmed. 5 Antisites and antisite-vacancy pairs Antisites and antisite-vacancy (AV) pairs are fundamental native de- fects in compound semiconductors. In SiC, both carbon an- tisite (C s i ) and silicon antisite (Si c ) can be easily formed [50, 51]. For AV pairs, carbon AV pairs (C si V c ) can be sta- ble [52, 53]. Carbon antisite is expected to be one of the most com- mon and abundant defects in SiC, because of its lowest formation energy among various native defects [50, 51]. However, the presence of Csj has not been clear yet, be- cause the first principles theory [50, 51] predicted that C si has no gap states and it will be invisible for any electrical and optical measurements. Recently, however, in neutron irradiated 6H-SiC after 700 ℃ anneal, a C si center (S = 1/2) was reported by Baranov et al. [54]. A single strong  13C HF interaction ( A = 8.1 mT, A 1 = 3.0 mT, see Fig. 21(a)) was detected in the EPR spectrum of this center, suggesting the contribution of a C si atom to this HF inter- action. However, this is not a final proof of the C Si center, because carbon AV pairs [55] (see the text in later) and di- vacancies [56] can show similar strong 13C HF interactions when they are positively charged. Nevertheless, C si is a particularly interesting defect, because it is the "anion" antisite in SiC. An anion antisite in GaAs (As ca , the EL2 center) exhibits a famous bistability [57], in which the As Ga atom can stay either a four-fold-coordinated position or a three-fold-coordinated position. This bistability is accom- panied with a change in the electrical and optical activity of the antisite center. By analogy with this phenomenon, an inactive C Si center (sp 3 -coordinated position) may trans- form into an active one (sp²-coordinated position) in SiC. The Baranov's center may be explained by the latter one. Still we may not understand a complete nature of C si in SiC, so that further studies will be necessary from experi- mental and theoretical view points. On the other hand, silicon antisite attracts less attention than Csi, because their influences will be limited to a heav- ily p-doped region. All its gap levels are close to the va- lence band edge [50]. There is only one probable assign- ment for the Si c center; a series of the H centers (E v + 0.18 ~ 0.51 eV) in the deep level transient spectros- copy (DLTS) spectrum of neutron irradiated 3C-SiC may originate from Si c in different charge states [50]. For the Si center (S = 1/2), a detectable 29Si HF interaction ( A l = 3.2−3.4 mT, A l = 0.7−0.9 mT) due to a Si c atom was predicted by first principles theory [16]. How-ever, such a signature was not reported for any p-type samples. An AV pair is a fundamental native defect, because it is a counterpart of a monovacancy in compound semicon- ductors [53]. For example, in an AB compound semicon- ductor, an A vacancy and a B antisite–B vacancy pair can 1312 be transformed from one to another by simply moving a B atom. Carbon AV pair (anion AV pair in SiC) is expected to be important in p-type and SI SiC. In p-type SiC, a CsiVc pair is energetically rather favorable than a Vsi [52, 58]. This relationship is also true for some SI SiC sub- strates, depending on their Fermi levels [46, 52, 53]. Such a trend is commonly seen in anion AV pairs in GaAs [59] and in ZnO [60], according to theoretical calculations. However, the presence of AV pairs has been confirmed only in SiC. By means of a combination of EPR and first principles calculation, the HEI9/10 centers ( S = 1/2) in ir- radiated p-type 4H-SiC were identified as the C siVc pairs [55]. Figure 22 shows schematic atomic structures of the CsiVc centers. Their typical spectrum is shown in Fig. 2(b). Since there are four inequivalent configurations ( kk , hh , kh , and hk ) for any pairing center in 4H-SiC, four types of HEI9/10 (9a, 9b, 10a, and 10b) can be resolved. The HEI9a and 9b centers correspond to hh and kk configura- tions ( c -axial pairs, C 3v symmetry), while HEI10a and 10b are kh and hk ones (basal pairs, C 1h symmetry). All of them exhibit a single strong 13C HF interaction due to a C si atom (Fig. 21(b) and (c)). Their 13C HF interactions ( A l = 8.2– 9.9 mT, A 1 = 2.2–3.7 mT) indicate a very strong localiza- tion (55–58%) and a very strong p-character ( β 2 /α 2 = 12–16) on the C Si atom as shown in Table 5. The 2nd and 3rd largest HF interactions arise from 29Si atoms in the V c side and outer shells. Accordingly, the HEI9/10 EPR spectrum involves many 29Si HF satellites ( A = 1.7– 2.9 mT). The C Si V t centers were often more abundant than V t  (see  Fig. 2(b)). However, their EPR signals were greatly underestimated at low temperatures owing to a strong saturation effect. In 6H-SiC, there are no reports for the relevant centers, however, the Baranov's center men- tioned above [54] may be consistent with a c -axial C siV c pair in 6H-SiC, because we can find a close similarity be- tween Figs. 21(a) and (b). In 4H-SiC, the electronic levels (the a and a ' levels for c -axial and basal pairs, respec- tively) of CsiV ε were deduced to be E V + 1.4-1.5 eV (E v + 1.2–1.3 eV in theory) [55]. The C si V ≥ centers are annealed out at 1100–1200 °C in irradiated SiC, which is almost the same behavior as V [55]. Other charge states of C si V c will be also detectable in EPR or optical measurements. The SI5 EPR center (the © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
SI-5 center in SI 4H-SiC [61] or the HEI4 center in irradi- ated n-type 4H-SiC [62]) was assigned to a c -axial C si V c center (S = 1/2) [53]. In the negative charge state, an un- paired electron occupies a doubly-degenerate level (the e level) originating from Si neighbors of V C . As a result, a strong 29Si HF interaction is observed in the SI5 EPR spec- trum (Fig. 21(d)), in contrast with the positive charge state already mentioned. Furthermore, there are two possible Jahn–Teller distorted configurations with C 1h symmetry, which are named as "LT (low-temperature)" and "HT (high temperature)" configurations [53]. In the LT one, an unpaired electron is localized on two Si neighbors of Vc (Si , 4 , mirror symmetric with respect to (1120)), while in the HT one, it considerably extends over a C si atom and outer parts (see Table 5). The HT configuration is strongly temperature dependent, and a thermal average causes an apparent C 3 , symmetry as shown in Fig. 21(e). Above 150 K, the HT spectrum is hardly observed due to the sig- nal broadening. The transition between the LT and HT configurations occurs at around 50 K. The ²9Si HF interac- tion of the LT configuration ( A l = 13 mT, A l = 10 mT) in- dicates that the degree of localization (60.6%) and the sp-hybridization ratio (3.5, see Table 5) are quite similar to those of V ح(Table 3). It should be mentioned that the SI5 center is extremely sensitive to photo illumination. In SI and n-type 4H-SiC ( E F ~ E C − 1.1 eV), the C siV c − centers ( S = 0) are dominantly formed, and they can be easily con- verted into C siV  by photo excitation of electrons to the conduction band [53]. This causes a drastic increase in the SI5 signal as is seen in Fig. 2(a). Such a photo sensitivity cannot be seen in the HEI9/10 signals (Fig. 2(b)). Judging from the photo response of the SI5 center, the (–/–2) and (0/-) ionization levels were deduced to be E C – 1.05– 1.35 eV and E c − 1.24−1.4 eV, respectively [46] (E c − 0.9 eV and E c – 1.0 eV in theory, respectively [53]). Due to these two levels, the C si V c pairs can contribute to the SI mechanism that exhibits a carrier activation energy of 1.1–1.3 eV [46]. In the last place of this section, we mention that the CsiVc centers will be detectable in other spectroscopic techniques. In electron irradiated n-type 6H-SiC after 1000 ℃ anneal, the presence of a c -axial C siV c pair was strongly suggested by two-dimensional angular correlation of positron annihilation technique [63]. The basal CsiVc pairs were not observed in this study, and in n-type 4H-SiC, too [53]. The reason why the basal pairs are hidden in n-type samples remains an unresolved problem. 6 Conclusion Vacancy-related defects such as monovacancy, divacancy, and antisite-vacancy pairs in 4H-SiC have been studied by EPR. The comparison of the obtained HF parameters with those predicted from the first principles calculations played a critical role in identifica¬ tion of Vぞ(h)/Vぞ(k), Vぞ(h), [V siV c] 0 , [C siV c] + and [C siV c] − . The measurements of the angular dependence of the 13 C/29 Si satellite lines from the nearest-neighbors, which are crucial for identification, have revealed the detailed geometric and electronic structures. From the orbital parameters estimated from the ¹³C/²³Si hyperfine tensors by using a simple LCAO model, the fol- lowing points, which were predicted to a considerable ex- tent by theoretical studies, have been evidently confirmed. (1) The localization of spin densities on the nearest- neighbors ( η - ω ll-l ) of monovacancies in 4H-SiC is larger than that in silicon and significantly smaller than that in diamond. (2) The positively charged vacancy (V c ) has slightly larger localization and higher p-character than the nega- tively charged vacancy (V c ), similarly to V + and V − in sili- con; η φ cl -1 and the sp-hybrid ratio β 2 /α 2 are 68%, 5.3–5.9 for V č ( h )/V č ( k ), 61%, 3.6 for V č ( h ), and 58%, 5.6 and 54.6%, 3.4 for V + and V − in silicon [5, 6, 19]. (3) Similar to V + and V − in silicon, Jahn− Teller distor- tion is significant for both V ς ( h )/V ς ( k ) and V ς ( h ) in 4H- SiC, and hence V c ( h ) takes low spin configuration (S = 1/2). On the other hand the electron-electron repul- sion favors the high spin configuration for V sj (S = 3/2), similar to V − in diamond. The distance 3.08 Å between the nearest-neighbors of unrelaxed vacancy is not strikingly larger than Si–Si bond length (2.35 Å in silicon), however, fatally larger than C-C bond length (1.54 Å in diamond). Thus, silicon dangling bonds in V c form pairing bonds eas- ily while carbon dangling bonds in V sj are likely to be parted from each other [27]. It should be noted that the dis- tance between the nearest-neighbors of unrelaxed vacancy in 4H-SiC is shorter than that of silicon (3.83 Å) and longer than that of diamond (2.52 Å). (4) The Jahn–Teller distortion is remarkably different between Vぞ( h ) (C 3v ) and Vぞ( k ) (C 1h ) in 4H-SiC. The slight difference in the small distortion from tetrahedral structure between V͡s ( h ) and V͡s i ( k ) has been revealed. (5) The sp-hybrid ratio (~12) for the nearest-neighbor carbon atoms in V si is significantly higher than that (~5) of the nearest-neighbor silicon atoms in V t . The large p- character in V si is ascribed to the outward displacement of carbon atoms forming more sp 2 -like bonds with the next- nearest-neighbors which results in more p-like contribution to the wave function of the unpaired electron. (6) The neutral divacancy [VsiVc] 0 in 4H-SiC, in which the unpaired electrons are mainly confined on car- bon atoms of nearest-neighbors of V si , takes high-spin state (S = 1), whereas Jahn-Teller distortion gives rise to the ground state of S = 0 for [VV] 0 in silicon. The localization (~60%) on the six nearest-neighbors (with negligibly small spin density on three silicon atoms) is smaller that that of [VV] 0 in diamond (82%) [4] and slightly larger than that in silicon (59.3% and 54.6 % for [VV]+ and [VV]+, respec- tively) [34]. Antisite–vacancy (AV) pairs, which are unique to compound semiconductors, have been identified. The determination of the spin multiplicity of Tv 2 n to be S = 3/2 by the nutation method of pulsed EPR and pulsed ENDOR has revealed that T v 2a belongs to a family of V si. The assigning of T v2n to V si with S = 1 was misled by the missing of the central line of T v2a . It is demonstrated that the central line has been observed by the population trans- fer using pulsed ELDOR technique. Acknowledgements Here we review our works from the experimentalist side. Our identification of point defects has been achieved with collaboration with theoretical groups, A. Gali (Budapest University of Technology and Economics) and M. Bockstedte (Universität Erlangen-Nürnberg). We would like to thank Dr. H. Hara (Bruker Biospin, Japan) for his help with the pulsed-ELDOR experiments.