3346 G. Brauer et al. /Applied Surface Science 252(2006)3342-3351 preferential positron annihilation in graphite com pared to 3C-SiC, a linear dependency may be dislocation loop Composite =(1-m)S3C-Sic msgraphite (1) From the comparison of bulk S values shown in Fig. 2a it is found that m=016+0.04. Then. a similar o。o assumption can be made regarding the measured positron diffusion length L+ of the composite provided the two phases form parallel channels to the surface E(kev) Composite=(1-m)L3c-Sic mLgraphi Fig 3. Lineshape parameter S for different silicon carbide samples Inserting all numbers, one obtains atrue' value of and pyrolytic g function of incident positron energy For comparison, alues of dislocation loops and Si +C L+ N 213 nm for 3C-SiC. This remarkably large num- ber indicates that defect-free grains should have a diameter of at least twice this value. i.e. a426 nn but most probably are formed much larger in size by 3.3. Slow positron implantation spectroscopy the sintering process. Indeed, this may be the case as the fibres and some particles have a size similar to the SPIS results of the SiC/SiC sample are presented in estimated effective diffusion length. Thus, grain Fig. 3. For comparison, SPIS data from a very clean boundaries, which might perhaps act as trapping sites pyrolytic graphite sample (of unknown origin) and for positrons too, are evenly distributed through the crystalline 6H-SiC (provided by CREE Research Inc, macroscopic sample made up of defect-free grains and Durham, NC, USA;(000 1)-oriented (3.5 off), Si- do not play any significant role faced, n-type) are given Although dislocation loops and Si+C divacancies A positron diffusion length of L+=186+ 6 nm is (V2) have S values above the bulk value of 6H-SiC and calculated for the composite, which needs to be the composite(see Fig 3), they are unlikely to exist in compared to the values of epi-6H-SiC (L+=157 the composite due to its preparation from 3C-Sic t 36 nm) and crystalline 6H-SiC (L+=54+ 3 nm), nano-crystalline material at high temperature condi- respectively [12]. This comparison already suggests tions To judge whether they exist or not, one option is that the composite has the lowest defect concentration. an improved approach for the analysis of SPis However, it seems to be a contradiction that at higher Doppler broadening data introduced by using a positron implantation energies the bulk value of the combination of Doppler broadening lineshape para composite is found to be slightly above the bulk value meters S and W[17, 18]. These results are shown in of the 6H-SiC sample. On the other hand, from Fig. 4 previous positron lifetime calculations [16] it became Any material state, like the bulk or a certain defect, clear that differences in the structure of the Sic is characterized by a given set of lineshape parameters, polytypes 3C, 4H and 6H are below the detection limit i.e.(S, W) values, which are required to be deduced in of ordinary PAS, and thus the same bulk value for 3c the same way from experimental data. In case of and 6H has to be expected. Therefore, a most natural silicon carbide, from previous work(see ref. [9] and explanation of the results from Fig. 3 is that positron references therein) it became possible to include in annihilation is occurring partly in graphite, which is Fig. 4 the(S, W)values for dislocation loops and the definitely still contained in the composite sample V2 defect, both being of 'open volume type'although according to XRd results to different extents. When only two distinct annihila From the results shown in Fig. 3, a positron tion characteristics, described by (SI, W1)and diffusion length of L+=42+9 nm is calculated for (S2, W2), contribute to a set of experimental data,3.3. Slow positron implantation spectroscopy SPIS results of the SiC/SiC sample are presented in Fig. 3. For comparison, SPIS data from a very clean pyrolytic graphite sample (of unknown origin) and crystalline 6H–SiC (provided by CREE Research Inc., Durham, NC, USA; (0 0 0 1)-oriented (3.58 off), Si￾faced, n-type) are given. A positron diffusion length of L+ = 186 6 nm is calculated for the composite, which needs to be compared to the values of epi-6H–SiC (L+ = 157 36 nm) and crystalline 6H–SiC (L+ = 54 3 nm), respectively [12]. This comparison already suggests that the composite has the lowest defect concentration. However, it seems to be a contradiction that at higher positron implantation energies the bulk value of the composite is found to be slightly above the bulk value of the 6H–SiC sample. On the other hand, from previous positron lifetime calculations [16] it became clear that differences in the structure of the SiC polytypes 3C, 4H and 6H are below the detection limit of ordinary PAS, and thus the same bulk value for 3C and 6H has to be expected. Therefore, a most natural explanation of the results from Fig. 3 is that positron annihilation is occurring partly in graphite, which is definitely still contained in the composite sample according to XRD results. From the results shown in Fig. 3, a positron diffusion length of L+ = 42 9 nm is calculated for the pyrolytic graphite. Supposing that there is no preferential positron annihilation in graphite com￾pared to 3C–SiC, a linear dependency may be assumed: Scomposite ¼ ð1  mÞS3CSiC þ mSgraphite (1) From the comparison of bulk S values shown in Fig. 2a it is found that m = 0.16 0.04. Then, a similar assumption can be made regarding the measured positron diffusion length L+ of the composite provided the two phases form parallel channels to the surface: Lcomposite ¼ ð1  mÞL3CSiC þ mLgraphite (2) Inserting all numbers, one obtains a ‘true’ value of L+ 213 nm for 3C–SiC. This remarkably large num￾ber indicates that defect-free grains should have a diameter of at least twice this value, i.e. 426 nm, but most probably are formed much larger in size by the sintering process. Indeed, this may be the case as the fibres and some particles have a size similar to the estimated effective diffusion length. Thus, grain boundaries, which might perhaps act as trapping sites for positrons too, are evenly distributed through the macroscopic sample made up of defect-free grains and do not play any significant role. Although dislocation loops and Si + C divacancies (V2) have S values above the bulk value of 6H–SiC and the composite (see Fig. 3), they are unlikely to exist in the composite due to its preparation from 3C–SiC nano-crystalline material at high temperature condi￾tions. To judge whether they exist or not, one option is an improved approach for the analysis of SPIS Doppler broadening data introduced by using a combination of Doppler broadening lineshape para￾meters S and W [17,18]. These results are shown in Fig. 4. Any material state, like the bulk or a certain defect, is characterized by a given set of lineshape parameters, i.e. (S, W) values, which are required to be deduced in the same way from experimental data. In case of silicon carbide, from previous work (see ref. [9] and references therein) it became possible to include in Fig. 4 the (S, W) values for dislocation loops and the V2 defect, both being of ‘open volume type’ although to different extents. When only two distinct annihila￾tion characteristics, described by (S1, W1) and (S2, W2), contribute to a set of experimental data, a 3346 G. Brauer et al. / Applied Surface Science 252 (2006) 3342–3351 Fig. 3. Lineshape parameter S for different silicon carbide samples and pyrolytic graphite as a function of incident positron energy E. For comparison, the S values of dislocation loops and Si + C divacancies (V2) in 6H–SiC are given.