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Positron annihilation study of vacancies in type IIa diamonds illuminated with monochromatic light
Diamond and Related Materials 10 Ž2001. 2113᎐2117
Positron annihilation study of vacancies in type IIa diamonds illuminated with monochromatic light S. Dannefaer U , A. Pu, D. Kerr Department of Physics, Uni¨ ersity of Winnipeg, Winnipeg, MB, Canada R3B 2E9 Received 12 May 2000; accepted 26 April 2001
Abstract Electron irradiated type IIa diamonds were investigated by positron lifetime and Doppler broadening spectroscopies during illumination in the photon energy range 2.2᎐3.5 eV. Illumination caused neutral vacancies to become negatively charged, and at photon energies close to 2.85 eV the charging was most effective. This suggests that the electronic level for the negatively charged monovacancy is situated 2.85 eV above the valence band. The photon flux dependency of the charging at the photon energy of 2.83 eV depends strongly on temperature and is attributed to recombination between holes and negatively charged monovacancies. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Monovacancy; Illumination; Positron annihilation
1. Introduction Positron annihilation in conjunction with illumination provides a unique opportunity for investigating charge states of vacancies in semiconductors or insulators. Early investigations demonstrated this in the case of color centers in KC1 w1,2x and more recently in GaAs and Si w3᎐5x. The strength of the method rests on the facts that a vacancy-specific response is obtained from positron annihilation measurements, and that the intensity of the response depends on the charge of the vacancies: if, for example, vacancies are neutral without illumination and turn positive upon illumination, the positron response will disappear because of repulsion with the positively charged positron, whereas an illumination-
induced negative charge will enhance the intensity of the response. The capability of simultaneously identifying the vacancy-type defect that changes charge as well as the sign of the charge are features neither photoconductivity, deep level transient spectroscopy, nor electron paramagnetic resonance possess. A restriction is that high-resistivity samples are necessary to prevent free carriers from rapidly ‘nullifying’ the photon-introduced charge, and that restriction was met in the works mentioned above w1᎐5x. Monochromatic light allows in principle for the determination of energy levels within the band gap for vacancy-like defects without restrictions to their depth within the band gap or to sample temperature.
2. Experimental U
Corresponding author. Tel.: q1-204-786-9754; fax: q1-204-7837981. E-mail address: [email protected] ŽS. Dannefaer..
Two type IIa natural diamonds were irradiated at 8⬚C by 2.3-MeV electrons to a dose of 1.4= 10 18 cmy2 . The samples were illuminated using light with a band
0925-9635r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 1 . 0 0 4 8 9 - 7
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
2114
width of 20 nm, and the photon flux was monitored with a thermopile detector external to the cryostat. The photon flux entering into the samples was calculated from the transmittance of the CaF2 window and the refractive index of diamond. The lifetime spectrometer had a prompt width at half maximum of 200᎐205 ps and the strength of the positron source was l6 Ci Ž0.6 MBq.. The contribution to the lifetime spectra from the source was only 1.5% and had no noticeable effect on data analyses, which were done using the program RESOLUTION w6x. Positron lifetime spectra were accumulated in six successive time intervals each of duration 3.3 h with the purpose of investigating if illumination-induced effects depend on the accumulated photon dose over 19.8 h. Since no dependency was found to within statistical error, the first three and the last three of the lifetime spectra were added together to produce two lifetime spectra, each containing Ž8᎐10. = 10 6 counts. Analyses of these spectra gave identical results to within statistical error, which is approximately half of that for the individual spectra. Doppler broadened spectra of the annihilation ␥quanta were also accumulated in six successive 3.3-h intervals giving 2 = 10 6 counts per spectrum in the annihilation peak, and analyses were done in terms of the S parameter which provides a measure for the valence electron momentum distribution in the bulk as well as close to a vacancy; We refer the reader to the literature w7x for a more extensive introduction to positron annihilation and simply point out that an increase in the S parameter reflects an increase in the fraction of positrons that annihilate in vacancies.
3. Results and discussion In Fig. 1 Doppler results are shown as a function of photon energy using a constant photon flux of Ž9 " 2. = 10 15 cmy2 sy1 entering into the samples at 25 K. The measured S parameter is normalized to SRef s 0.380, a value estimated to be close to the value of S in
Fig. 1. Doppler data obtained at 25 K with the samples in the dark and when illuminated with a photon flux of 9 = 10 15 cmy2 sy1 for photon energies between 2.35 and 3.3 eV.
defect-free diamond w7x. A significant increase in SrSRef is observed close to 2.8 eV whereas at 2.4 or 3.3 eV there is little effect compared to the value without illumination, i.e. in the dark. Lifetime measurements were also made as a function of photon energy and the results are listed in Table 1. In the dark three lifetimes could be resolved, 1 , 2 and 3 with associated intensities I1 , I2 and I3 , respectively. These lifetimes originate according to Pu et al. w7x from positrons annihilating in the bulk Ž 1 ., or in the radiation-produced neutral monovacancies Ž 2 ., or in highly disordered regions Ž 3 ., and their respective intensities reflect the relative importance of these annihilation sites. Illumination decreases slightly the value of 2 but increases significantly its intensity and for photon energies between 2.61 and 3.05 eV, I2 is so large that 1 cannot be resolved. Based on the data shown in Fig. 1 the fraction, F, of positrons trapped by monovacancies can be calculated according to F s Ž SrSref y 1 . r Ž S vrSRef y 1 . ,
Ž1.
where S v is the vacancy-specific S parameter for the monovacancy. According to Pu et al. w7x S vrSRef is
Table 1 Lifetime results for different illumination conditions Condition Dark
1 Žps. 70 " 5
2 Žps. 143 " 8
3 Ž"10 ps. 370
I1 Ž%. 51 " 3
I2 Ž%. 42 " 3
I3 Ž%. 7 " 0.5
Photon energy 2.40 eV 2.61 eV 2.76 eV 2.83 eV 2.90 eV 3.05 eV 3.21 eV
50 " 5 Unresolved Unresolved Unresolved Unresolved Unresolved 50 " 5
128 " 5 128 " 7 142 " 4 137 " 4 145 " 5 142 " 3 133 " 4
348 376 365 348 348 342 318
25 " 3 0 0 0 0 0 19 " 4
67 " 3 89 " 1 90 " 1 89 " 1 91 " 1 92 " 1 73 "3
8 " 0.4 11 " 1 10 " 1 11 " 1 9"1 8"1 8 " 0.8
The photon flux was the same as for the Doppler data shown in Fig. 1 Ž9 = 10 15 cmy2 sy1 . and the sample temperature was 25 K.
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
2115
Fig. 2. Fraction of positrons trapped as calculated from the data in Fig. 1 using Eq. Ž1..
Fig. 4. w Vyx rw V 0 xdark as a function of photon energy. The photon flux was 9 = 10 15 cmy2 sy1 and the sample temperature was 25 K.
equal to 1.079 and is the same for both neutral and negatively charged monovacancies. Fig. 2 depicts F as a function of photon energy and the peak value of 0.8 Ž1.0 is the maximum value for F . demonstrates that photons at 2.85 eV significantly increase the trapping efficiency of monovacancies. The temperature dependence of SrSRef is shown in Fig. 3 in both the dark and illuminated conditions Žphoton flux and energy are 9 = 10 15 cmy2 sy1 and 2.83 eV, respectively.. The significant increase in SrSRef at low temperatures is characteristic for trapping by negatively charged vacancies, whereas the nearly temperature independent results for the dark show that the monovacancies are neutral, as expected for type IIa diamond w8x. To gain further insight into the trapping by negatively charged monovacancies, the data in Fig. 3 for the illuminated diamonds were fitted by an analytical w9x model based on the theoretical work by Puska et al. w10x. Several parameters are determined by the fitting program, but the one of relevance in the present context is the fraction of neutral monovacancies that become negatively charged due to illumination, i.e. the
ratio w Vyx rw V o xdark , where w V o xdark is the concentration of neutral vacancies in the dark. A value of 0.1" 0.02 is determined for the photon energy of 2.83 eV and by adjusting the ratio Žwhile keeping all other fitting parameters constant. to obtain agreement with the data in Fig. 1, w Vyx rw V o xdark is obtained as a function of photon energy. Fig. 4 shows that Vy is formed within a photon energy range of 0.3 eV Žfull width at half maximum. centered at 2.85 eV, suggesting that the electronic level for Vy is situated 2.85 eV above the valence band. Since this level is essentially at mid-gap photons can excite Žvalence. electrons to create Vy as well as remove an electron from Vy by exciting it into the conduction band, so the peak results from the photon energy dependencies of these competing processes. The positron experiments verify that the hole conductivity observed by Farrar and Vermeulen w11x arises from negative charging of neutral monovancies. They are also in agreement with the photon-excitation results of Baldwin w12x, who found that photons with an energy above 2.8 eV give rise to a new electron paramagnetic resonance which, according to the later work by Isoya et al. w13x, arises from Vy ŽBaldwin misinterpreted his results to arise from Vq. . Light-on, light-off Ži.e. dark. experiments were also done in connection with the data shown in Fig. 3 at sample temperatures of 25, 100 and 300 K. Cycling at each of these temperatures showed that within ; 0.5 h of the duration of each measurement Ž3.3 h. the S parameter reached the light-on and the light-off levels displayed in Fig. 3. The discharging within 0.5 h of V y to V 0 contrasts to Baldwin’s w12x observation that Vy persisted for several days in the dark and might be a consequence of electron hole generation due to the energetic Ž; 300 keV. positrons. Optical absorption measurements were also done before and after illumination by measuring the absorption at 70 K of the GR1 zero phonon line due to neutral vacancies. After illumination the absorption was reduced by 5᎐8% which is in
Fig. 3. Doppler data as a function of temperature for samples in the dark and when illuminated with a photon energy of 2.83" 0.07 eV at a flux of 9 = 10 15 cmy2 sy1 . The curve shows a fit using the model described in Dannefaer and Pu w9x.
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S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
good agreement with the Ž10 " 2.% reduction deduced from the positron experiments. The above described positron experiments were done using a constant photon flux but it is of interest also to investigate the flux dependency of w Vyx rw V 0 xdark since that might give insight into the details of Vy formation. A constant photon energy of 2.83" 0.07 eV was used in these experiments for two sample temperatures, 25 and 293 K. Fig. 5 shows the flux dependency of SrSRef and based on these data w Vyx rw V o xdark can be obtained in the same way as described above for the photon energy dependency ratios. The results are shown in Fig. 6, and to explain these we apply a simple model in which it is assumed that V 0 is charged to Vy by a rate r 1 s C1 where C1 is the optical cross-section and is the photon flux. A photon-induced ‘back reaction’ via r 2 s C2 is also invoked, i.e. an electron can be removed from Vy by excitation to the conduction band by the same photon energy. Finally, a photon flux-independent rate r 3 is introduced to take into account the return of Vy to V 0 in the dark. This model gives the differential equation for the concentration of Vy d w Vy x s r 1 w V 0 x y r 2 w Vy x y r 3 w Vy x , dt
Ž2.
which together with conservation of vacancy concentration w Vyx q w V 0 x s w V 0 xdark and steady state Žwithin the time frame of 0.5 h. gives w Vy x r w V 0 x dark s C1r Ž C1 q C2 q r 3r . .
Ž3.
For the data obtained at 293 K ŽFig. 5., Eq. Ž3. describes well the flux dependency of w Vyx rw V 0 xdark ŽFig. 6. for values of C1rŽ C1 q C2 . s 0.1 and r 3rŽ C1 q C2 . s 0.5= 10 15 cmy2 sy1. The first number Ž0.1. indicates that the optical cross-section, C2 , for removing an electron from Vy is nearly 10 times that for charging a
Fig. 6. w Vyx rw V 0 xdark calculated from the data in Fig. 5 using the model described in Dannefaer and Pu w9x. The curve is a fit by the model described in text.
neutral vacancy at the photon energy of 2.83 eV. As to the second number an interpretation is not possible because r 3 cannot be determined from the data due to the 3.3-h duration of data accumulation. From the data obtained at 25 K ŽFig. 5. similar calculations were only realistic up to the photon flux of 6 = 10 15 cmy2 sy1 , above which uncertainties in the values for w Vyx rw V 0 xdark became very large. Much smaller values are found than at 293 K ŽFig. 6. and increase linearly with photon flux. In terms of Eq. Ž3. r 3r is much larger than Ž C1 q C2 . and a straight line fit gives a value for r 3rC1 of 1.2= 10 17 cmy2 sy1 . Assuming that the optical cross-sections are temperature independent, the ratio between the r 3 values at 25 and 293 K, i.e. r 325 K rr 3293 K , can be calculated to have the value of 24. This result suggests that recombination of holes with Vy is much more efficient at 25 K than at 293 K, analogous to the case of positron trapping by negatively charged vacancies.
4. Conclusion Photons are capable of converting neutral monovacancies in type IIa diamonds into negatively charged vacancies with maximum efficiency at 2.85 eV, indicating that its electronic level is situated at 2.85" 0.10 eV above the valance band. Vy is formed much less efficiently at 25 K than at 293 K, and this is suggested to arise from rapid recombination between holes and Vy.
Acknowledgements
Fig. 5. Doppler data as a function of photon flux for two sample temperatures. The photon energy was 2.83" 0.07 eV.
We are indebted to the Gemological Institute of America for lending us the type IIa diamonds. This work was financially assisted by the Natural Sciences and Engineering Research Council of Canada, and by the University of Winnipeg.
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
References w1x L. Bosi, A. Dupasquier, L. Zappa, J. Phys. Colloque. Paris G-9 34 ŽSuppl. 11-12. Ž1973. 295. w2x S. Dannefaer, G. Trumpy, R.M.J. Cotterill, J. Phys. C: Solid State Phys. 7 Ž1974. 1261. w3x K. Saarinen, S. Kuisma, P. Hautojarvi, ¨ C. Corbel, C. LeBerre, Phys. Rev. Lett. 70 Ž1993. 2794. w4x H. Kauppinen, C. Corbel, J. Nissila, K. Saarinen, P. Hautojarvi, ¨ Phys. Rev. B57 Ž1998. 12911. w5x S. Dannefaer, V. Avalos, Phys. Rev. B. 60 Ž1999. 1729. w6x P. Kirkegaard, N.J. Pedersen, M. Eldrup, PATFIT-88 Risø Report M-2740, Risø, DK-4000 Roskilde, Denmark, 1988. w7x A. Pu, T. Bretagnon, D. Kerr, S. Dannefaer, Diam. Relat. Mater. 9 Ž2000. 1450.
2117
w8x G. Davies, N.B. Manson, in: G. Davies ŽEd.., Properties and Growth of Diamond. INSPEC Data reviews series no 9, INSPEC, United Kingdom, 1994, p. 173. w9x S. Dannefaer, A. Pu, Nucl. Instrum. Methods Phys. Res. 462r3 Ž2001. 596. w10x M.J. Puska, C. Corbel, R.M. Nieminen, Phys. Rev. B 41 Ž1990. 9980. w11x R.G. Farrar, L.A. Vermeulen, J. Phys.C: Solid State Phys. 5 Ž1972. 2762. w12x J.A. Baldwin, Jr., Phys. Rev. Lett. 10 Ž1963. 220. w13x J. Isoya, H. Kanda, Y. Uchida et al., Phys. Rev. B 45 Ž1992. 1436.
Positron annihilation study of vacancies in type IIa diamonds illuminated with monochromatic light S. Dannefaer U , A. Pu, D. Kerr Department of Physics, Uni¨ ersity of Winnipeg, Winnipeg, MB, Canada R3B 2E9 Received 12 May 2000; accepted 26 April 2001
Abstract Electron irradiated type IIa diamonds were investigated by positron lifetime and Doppler broadening spectroscopies during illumination in the photon energy range 2.2᎐3.5 eV. Illumination caused neutral vacancies to become negatively charged, and at photon energies close to 2.85 eV the charging was most effective. This suggests that the electronic level for the negatively charged monovacancy is situated 2.85 eV above the valence band. The photon flux dependency of the charging at the photon energy of 2.83 eV depends strongly on temperature and is attributed to recombination between holes and negatively charged monovacancies. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Monovacancy; Illumination; Positron annihilation
1. Introduction Positron annihilation in conjunction with illumination provides a unique opportunity for investigating charge states of vacancies in semiconductors or insulators. Early investigations demonstrated this in the case of color centers in KC1 w1,2x and more recently in GaAs and Si w3᎐5x. The strength of the method rests on the facts that a vacancy-specific response is obtained from positron annihilation measurements, and that the intensity of the response depends on the charge of the vacancies: if, for example, vacancies are neutral without illumination and turn positive upon illumination, the positron response will disappear because of repulsion with the positively charged positron, whereas an illumination-
induced negative charge will enhance the intensity of the response. The capability of simultaneously identifying the vacancy-type defect that changes charge as well as the sign of the charge are features neither photoconductivity, deep level transient spectroscopy, nor electron paramagnetic resonance possess. A restriction is that high-resistivity samples are necessary to prevent free carriers from rapidly ‘nullifying’ the photon-introduced charge, and that restriction was met in the works mentioned above w1᎐5x. Monochromatic light allows in principle for the determination of energy levels within the band gap for vacancy-like defects without restrictions to their depth within the band gap or to sample temperature.
2. Experimental U
Corresponding author. Tel.: q1-204-786-9754; fax: q1-204-7837981. E-mail address: [email protected] ŽS. Dannefaer..
Two type IIa natural diamonds were irradiated at 8⬚C by 2.3-MeV electrons to a dose of 1.4= 10 18 cmy2 . The samples were illuminated using light with a band
0925-9635r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 1 . 0 0 4 8 9 - 7
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
2114
width of 20 nm, and the photon flux was monitored with a thermopile detector external to the cryostat. The photon flux entering into the samples was calculated from the transmittance of the CaF2 window and the refractive index of diamond. The lifetime spectrometer had a prompt width at half maximum of 200᎐205 ps and the strength of the positron source was l6 Ci Ž0.6 MBq.. The contribution to the lifetime spectra from the source was only 1.5% and had no noticeable effect on data analyses, which were done using the program RESOLUTION w6x. Positron lifetime spectra were accumulated in six successive time intervals each of duration 3.3 h with the purpose of investigating if illumination-induced effects depend on the accumulated photon dose over 19.8 h. Since no dependency was found to within statistical error, the first three and the last three of the lifetime spectra were added together to produce two lifetime spectra, each containing Ž8᎐10. = 10 6 counts. Analyses of these spectra gave identical results to within statistical error, which is approximately half of that for the individual spectra. Doppler broadened spectra of the annihilation ␥quanta were also accumulated in six successive 3.3-h intervals giving 2 = 10 6 counts per spectrum in the annihilation peak, and analyses were done in terms of the S parameter which provides a measure for the valence electron momentum distribution in the bulk as well as close to a vacancy; We refer the reader to the literature w7x for a more extensive introduction to positron annihilation and simply point out that an increase in the S parameter reflects an increase in the fraction of positrons that annihilate in vacancies.
3. Results and discussion In Fig. 1 Doppler results are shown as a function of photon energy using a constant photon flux of Ž9 " 2. = 10 15 cmy2 sy1 entering into the samples at 25 K. The measured S parameter is normalized to SRef s 0.380, a value estimated to be close to the value of S in
Fig. 1. Doppler data obtained at 25 K with the samples in the dark and when illuminated with a photon flux of 9 = 10 15 cmy2 sy1 for photon energies between 2.35 and 3.3 eV.
defect-free diamond w7x. A significant increase in SrSRef is observed close to 2.8 eV whereas at 2.4 or 3.3 eV there is little effect compared to the value without illumination, i.e. in the dark. Lifetime measurements were also made as a function of photon energy and the results are listed in Table 1. In the dark three lifetimes could be resolved, 1 , 2 and 3 with associated intensities I1 , I2 and I3 , respectively. These lifetimes originate according to Pu et al. w7x from positrons annihilating in the bulk Ž 1 ., or in the radiation-produced neutral monovacancies Ž 2 ., or in highly disordered regions Ž 3 ., and their respective intensities reflect the relative importance of these annihilation sites. Illumination decreases slightly the value of 2 but increases significantly its intensity and for photon energies between 2.61 and 3.05 eV, I2 is so large that 1 cannot be resolved. Based on the data shown in Fig. 1 the fraction, F, of positrons trapped by monovacancies can be calculated according to F s Ž SrSref y 1 . r Ž S vrSRef y 1 . ,
Ž1.
where S v is the vacancy-specific S parameter for the monovacancy. According to Pu et al. w7x S vrSRef is
Table 1 Lifetime results for different illumination conditions Condition Dark
1 Žps. 70 " 5
2 Žps. 143 " 8
3 Ž"10 ps. 370
I1 Ž%. 51 " 3
I2 Ž%. 42 " 3
I3 Ž%. 7 " 0.5
Photon energy 2.40 eV 2.61 eV 2.76 eV 2.83 eV 2.90 eV 3.05 eV 3.21 eV
50 " 5 Unresolved Unresolved Unresolved Unresolved Unresolved 50 " 5
128 " 5 128 " 7 142 " 4 137 " 4 145 " 5 142 " 3 133 " 4
348 376 365 348 348 342 318
25 " 3 0 0 0 0 0 19 " 4
67 " 3 89 " 1 90 " 1 89 " 1 91 " 1 92 " 1 73 "3
8 " 0.4 11 " 1 10 " 1 11 " 1 9"1 8"1 8 " 0.8
The photon flux was the same as for the Doppler data shown in Fig. 1 Ž9 = 10 15 cmy2 sy1 . and the sample temperature was 25 K.
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
2115
Fig. 2. Fraction of positrons trapped as calculated from the data in Fig. 1 using Eq. Ž1..
Fig. 4. w Vyx rw V 0 xdark as a function of photon energy. The photon flux was 9 = 10 15 cmy2 sy1 and the sample temperature was 25 K.
equal to 1.079 and is the same for both neutral and negatively charged monovacancies. Fig. 2 depicts F as a function of photon energy and the peak value of 0.8 Ž1.0 is the maximum value for F . demonstrates that photons at 2.85 eV significantly increase the trapping efficiency of monovacancies. The temperature dependence of SrSRef is shown in Fig. 3 in both the dark and illuminated conditions Žphoton flux and energy are 9 = 10 15 cmy2 sy1 and 2.83 eV, respectively.. The significant increase in SrSRef at low temperatures is characteristic for trapping by negatively charged vacancies, whereas the nearly temperature independent results for the dark show that the monovacancies are neutral, as expected for type IIa diamond w8x. To gain further insight into the trapping by negatively charged monovacancies, the data in Fig. 3 for the illuminated diamonds were fitted by an analytical w9x model based on the theoretical work by Puska et al. w10x. Several parameters are determined by the fitting program, but the one of relevance in the present context is the fraction of neutral monovacancies that become negatively charged due to illumination, i.e. the
ratio w Vyx rw V o xdark , where w V o xdark is the concentration of neutral vacancies in the dark. A value of 0.1" 0.02 is determined for the photon energy of 2.83 eV and by adjusting the ratio Žwhile keeping all other fitting parameters constant. to obtain agreement with the data in Fig. 1, w Vyx rw V o xdark is obtained as a function of photon energy. Fig. 4 shows that Vy is formed within a photon energy range of 0.3 eV Žfull width at half maximum. centered at 2.85 eV, suggesting that the electronic level for Vy is situated 2.85 eV above the valence band. Since this level is essentially at mid-gap photons can excite Žvalence. electrons to create Vy as well as remove an electron from Vy by exciting it into the conduction band, so the peak results from the photon energy dependencies of these competing processes. The positron experiments verify that the hole conductivity observed by Farrar and Vermeulen w11x arises from negative charging of neutral monovancies. They are also in agreement with the photon-excitation results of Baldwin w12x, who found that photons with an energy above 2.8 eV give rise to a new electron paramagnetic resonance which, according to the later work by Isoya et al. w13x, arises from Vy ŽBaldwin misinterpreted his results to arise from Vq. . Light-on, light-off Ži.e. dark. experiments were also done in connection with the data shown in Fig. 3 at sample temperatures of 25, 100 and 300 K. Cycling at each of these temperatures showed that within ; 0.5 h of the duration of each measurement Ž3.3 h. the S parameter reached the light-on and the light-off levels displayed in Fig. 3. The discharging within 0.5 h of V y to V 0 contrasts to Baldwin’s w12x observation that Vy persisted for several days in the dark and might be a consequence of electron hole generation due to the energetic Ž; 300 keV. positrons. Optical absorption measurements were also done before and after illumination by measuring the absorption at 70 K of the GR1 zero phonon line due to neutral vacancies. After illumination the absorption was reduced by 5᎐8% which is in
Fig. 3. Doppler data as a function of temperature for samples in the dark and when illuminated with a photon energy of 2.83" 0.07 eV at a flux of 9 = 10 15 cmy2 sy1 . The curve shows a fit using the model described in Dannefaer and Pu w9x.
2116
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
good agreement with the Ž10 " 2.% reduction deduced from the positron experiments. The above described positron experiments were done using a constant photon flux but it is of interest also to investigate the flux dependency of w Vyx rw V 0 xdark since that might give insight into the details of Vy formation. A constant photon energy of 2.83" 0.07 eV was used in these experiments for two sample temperatures, 25 and 293 K. Fig. 5 shows the flux dependency of SrSRef and based on these data w Vyx rw V o xdark can be obtained in the same way as described above for the photon energy dependency ratios. The results are shown in Fig. 6, and to explain these we apply a simple model in which it is assumed that V 0 is charged to Vy by a rate r 1 s C1 where C1 is the optical cross-section and is the photon flux. A photon-induced ‘back reaction’ via r 2 s C2 is also invoked, i.e. an electron can be removed from Vy by excitation to the conduction band by the same photon energy. Finally, a photon flux-independent rate r 3 is introduced to take into account the return of Vy to V 0 in the dark. This model gives the differential equation for the concentration of Vy d w Vy x s r 1 w V 0 x y r 2 w Vy x y r 3 w Vy x , dt
Ž2.
which together with conservation of vacancy concentration w Vyx q w V 0 x s w V 0 xdark and steady state Žwithin the time frame of 0.5 h. gives w Vy x r w V 0 x dark s C1r Ž C1 q C2 q r 3r . .
Ž3.
For the data obtained at 293 K ŽFig. 5., Eq. Ž3. describes well the flux dependency of w Vyx rw V 0 xdark ŽFig. 6. for values of C1rŽ C1 q C2 . s 0.1 and r 3rŽ C1 q C2 . s 0.5= 10 15 cmy2 sy1. The first number Ž0.1. indicates that the optical cross-section, C2 , for removing an electron from Vy is nearly 10 times that for charging a
Fig. 6. w Vyx rw V 0 xdark calculated from the data in Fig. 5 using the model described in Dannefaer and Pu w9x. The curve is a fit by the model described in text.
neutral vacancy at the photon energy of 2.83 eV. As to the second number an interpretation is not possible because r 3 cannot be determined from the data due to the 3.3-h duration of data accumulation. From the data obtained at 25 K ŽFig. 5. similar calculations were only realistic up to the photon flux of 6 = 10 15 cmy2 sy1 , above which uncertainties in the values for w Vyx rw V 0 xdark became very large. Much smaller values are found than at 293 K ŽFig. 6. and increase linearly with photon flux. In terms of Eq. Ž3. r 3r is much larger than Ž C1 q C2 . and a straight line fit gives a value for r 3rC1 of 1.2= 10 17 cmy2 sy1 . Assuming that the optical cross-sections are temperature independent, the ratio between the r 3 values at 25 and 293 K, i.e. r 325 K rr 3293 K , can be calculated to have the value of 24. This result suggests that recombination of holes with Vy is much more efficient at 25 K than at 293 K, analogous to the case of positron trapping by negatively charged vacancies.
4. Conclusion Photons are capable of converting neutral monovacancies in type IIa diamonds into negatively charged vacancies with maximum efficiency at 2.85 eV, indicating that its electronic level is situated at 2.85" 0.10 eV above the valance band. Vy is formed much less efficiently at 25 K than at 293 K, and this is suggested to arise from rapid recombination between holes and Vy.
Acknowledgements
Fig. 5. Doppler data as a function of photon flux for two sample temperatures. The photon energy was 2.83" 0.07 eV.
We are indebted to the Gemological Institute of America for lending us the type IIa diamonds. This work was financially assisted by the Natural Sciences and Engineering Research Council of Canada, and by the University of Winnipeg.
S. Dannefaer et al. r Diamond and Related Materials 10 (2001) 2113᎐2117
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