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The di-vacancy in particle-irradiated, strain-relaxed SiGe
Nuclear Instruments and Methods in Physics Research B 186 (2002) 195±200 www.elsevier.com/locate/nimb
The di-vacancy in particle-irradiated, strain-relaxed SiGe H. av Skardi a, A. Bro Hansen a, A. Mesli b, A. Nylandsted Larsen a
a,*
Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark b Laboratoire LPSE, 4 rue des Fr eres Lumi ere, F-68093 Mulhouse Cedex, France
Abstract The di-vacancy is known to introduce three energy levels in the energy-band gap of Si. Using deep level transient spectroscopy (DLTS) on particle-irradiated p n and n p diodes, we have followed these levels in epitaxially grown, strain-relaxed Si1 x Gex as a function of x for 0 6 x 6 0:5. Both the single- and double-acceptor levels located in the upper half of the band gap in Si move gradually deeper into the gap with increasing x. While the double-acceptor level remains in the upper half of the band gap of the alloys, the single-acceptor level crosses the mid-gap for x 0:25. The donor level becomes gradually more shallow, but remains pinned to the conduction band. The anneal temperature of the divacancy is found to be independent of composition in the investigated composition range. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Si1 x Gex ; Irradiation; Di-vacancy; DLTS; Annealing
1. Introduction The di-vacancy is one of the most abundant defects in Si following particle irradiation at room temperature, and as it is, moreover, a rather stable defect with an anneal temperature of about 250 °C it always gives rise to concern when Si-based components are exposed to irradiations [1]. It exists in four dierent charge states in Si (, 0, , ) corresponding to three levels in the band gap: 0= a donor level V2 at EV 0:20 eV and two acceptor levels at EC 0:24 eV V2= and EC =0 0:41 eV V2 (EV and EC are the valence- and
*
Corresponding author. Tel.: +45-46-8942-3720. E-mail address: [email protected] (A. Nylandsted Larsen).
conduction-band edges, respectively) [2]. The deep single-acceptor level at EC 0:41 eV is a feared recombination-generation center. Only little is known about the di-vacancy in Ge. Arguments have recently been put forward that a level at EC 0:29 eV, observed by deep level transient spectroscopy (DLTS) in irradiated n-type Ge, can be assigned to the di-vacancy [3]. However, whether it is a donor or an acceptor level has not been established. The existence of di-vacancyrelated levels in the lower half of the band gap of Ge has, to our knowledge, not been demonstrated. The compositional dependence of the donor level of the di-vacancy in strain-relaxed SiGe alloy layers has previously been studied in epitaxially grown, p-type Si1 x Gex for x 6 0:15 [4]. Although the level was found to become gradually more shallow with increasing x, it remains pinned to the
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conduction band, demonstrating that the decrease of the hole-ionization enthalpy with increasing x is fully accounted for by the band-gap shrinkage of the alloy. The eect of strain on the single-acceptor level of the di-vacancy has recently been studied in strained, epitaxial Si0:87 Ge0:13 [5]. It was found that the ionization enthalpy relative to the conduction-band edge decreased as compared to that of Si, opposite to what was observed for the PV-pair. To the best of our knowledge there has been no further investigation of the dependency of the di-vacancy levels on strain or composition in SiGe. This report presents the ®rst results from a comprehensive DLTS study of the di-vacancy in Si1 x Gex . They include a study of the eect of composition on all three di-vacancy levels in strain-relaxed, epitaxially grown Si1 x Gex for x 6 0:5.
3. Results and discussion 3.1. Results from the p n diodes The DLTS spectra of the irradiated p n-diodes change dramatically in going from Si0:84 Ge0:16 to Si0:75 Ge0:25 as demonstrated in Figs. 1(a) and (b). The Si0:84 Ge0:16 DLTS spectrum (Fig. 1(a)), and also those for x K 0:16, resembles those of a typical Si spectrum consisting of a dominant E-center line at a temperature of about 280 K (which also contains a small contribution from the singleacceptor line of the di-vacancy), a smaller line at about 190 K from the double-acceptor level of the di-vacancy, and the line related to the Ci center at about 100 K (the Ci defect in Si0:84 Ge0:16 is stable to 350 K as demonstrated in [8]). A careful computer analysis of the dominating line (the E-center line) shows that the hidden di-vacancy line has an intensity almost identical to that of the ( / )-
2. Experimental details Strain-relaxed Si1 x Gex layers with x varying from 0 to 0.5 were grown on (1 0 0) Si substrates by molecular-beam epitaxy (MBE) using the compositional-grading technique, as described elsewhere [6,7]. The DLTS investigations were done on n pand p n-mesa diodes. The mesa diodes were fabricated by ®rst growing 4 lm thick n- or p-type doped, strain-relaxed Si1 x Gex layers on top of a compositionally graded buer. These layers were doped with either Sb or B to concentrations of about 5 1015 cm 3 . The p and n layers were ®nally grown to a thickness of 0:5 lm and doped to very high concentrations of B and Sb, respectively 1 1019 cm 3 . The diodes were irradiated at room temperature with either 2-MeV electrons or protons to doses of 3 1015 cm 2 or 4 1012 cm 2 , respectively, or with 2.5 MeV aparticles to a dose of 1 1011 cm 2 . Apart from dierences in the intensities of the DLTS lines resulting from the irradiations with the dierent particles no other eects of changing the projectiles were observed. The DLTS measurements were carried out with a Semitrap spectrometer using the lock-in principle to process the capacitance transient signal.
Fig. 1. DTLS spectra of p n-mesa diodes of (a) Si0:84 Ge0:16 and (b) Si0:75 Ge0:25 after 2-MeV a-particle irradiations. The spectra were measured using a repetition rate of 2390 Hz.
H. av Skardi et al. / Nucl. Instr. and Meth. in Phys. Res. B 186 (2002) 195±200
acceptor line at 190 K. The major change in going from Si0:84 Ge0:16 to Si0:75 Ge0:25 is that the E-center line disappears allowing both charge states of the di-vacancy to emerge with equal intensities. The behavior of the E-center as a function of x will be the topic of a forthcoming paper, however, we may already now reveal that the ( /0)-acceptor level of the E-center moves gradually deeper into the gap with increasing x, as already demonstrated in [9], and crosses the mid-gap for x somewhere between 0.20 and 0.25, in which case the E-center changes from being an electron trap for x K 0:25 to become a hole trap for x J 0:25. The two acceptor levels of the di-vacancy behave in a similar way at least while they are primarily interacting with the conduction band. They move gradually deeper into the gap with increasing x, and seem to remain approximately equidistant from each other by the so-called Hubbard energy of 0.2 eV, as illustrated in Fig. 2. It is clear from Fig. 2 that none of the levels are pinned to any of the band edges. Above a Ge fraction of about 0.30, the single-acceptor level crosses the mid-gap and begins to signi®cantly interact with the valence band, necessitating the use of minority-carrier transient spectroscopy (MCTS) based on optically induced minority carriers. Unfortunately, this method is not without ambiguity in the present case for two main reasons. Firstly, both types of
Fig. 2. Extracted ionization enthalpies relative to the conduction band as a function of the Ge content from p n diodes. The data points is a second-order polynomial line through the V= 2 ®t; the same polynomial has been shifted to ®t the V2 =0 data points.
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carriers are simultaneously injected into the depletion region and quantitative interpretations of spectra related to mid-gap levels may become doubtful. Secondly, the overlap between the lines of the E center and the single-acceptor level of the di-vacancy introduces the same kind of ambiguity as in the case when both these levels are acting as electron traps. A way of overcoming these dif®culties is oered by using p-type materials for x P 0:30, as discussed in Section 3.2. The anneal temperature of the di-vacancy as a function of composition can be unambiguously determined by following the double-acceptor line. The results are displayed in Fig. 3. It appears that, within a narrow range of about 20 °C, the stability is independent of composition. Apparently, the charge state of the di-vacancy does not play any signi®cant role in its stability as it is predominantly neutral during the annealing in the low-x materials and predominantly singly negative during the annealing in the high-x material. It is surprising that the anneal temperature is independent of the Ge content. The anneal temperature of the di-vacancy in Si is known to be sensitive to the impurity content of the samples, most probably because the impurities act as sinks and annihilation centers for the diusing di-vacancies [10]. Without exception, the anneal temperature or diusivity of all the defects and impurities which we have previously studied in strain-relaxed SiGe layers has been somehow in¯uenced by the presence of the Ge (V [11], Ci [8], SbV [9], B [12], Sb [13], Ge [14]). So why is the anneal temperature of the di-vacancy
Fig. 3. Anneal temperature of the di-vacancy as a functin of the Ge content, determined from the intensity of the V= line. The 2 anneal time was always 15 min.
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independent of the Ge content? We do not have an answer to this question as yet. 3.2. Results from the n p-diodes As demonstrated by Monakhov et al. [4] for x J 0:10 the DLTS lines from the donor levels of Ci and the di-vacancy cannot be separated. This is also demonstrated in Fig. 4(a) which shows a typical spectrum from a Si0:84 Ge0:16 diode. The line at about 100 K is made up by a large contribution from Ci and a smaller contribution from the di-vacancy. However, it was always possible to anneal the Ci defect without in¯uencing the divacancy in the composition range in which we have followed the donor level of the di-vacancy (x K 0:3). The line labelled ``unknown'' in Fig. 4(a), situated at a temperature of about 260 K, has not yet been identi®ed. However, its variation with irradiation dose, Ge composition, and B concentration points to the triple complex Ge±V±B as the origin of the line. Increasing the Ge content x further, the two lines move to lower temperatures as demonstrated in Fig. 4(b) and for x J 0:25 a
Fig. 5. Extracted ionization enthalpies relative to the valence band as a function of the Ge content from n p diodes. The lines between the data points are only to guide the eye.
new line appears in the spectrum, at a temperature of about 250 K. This line is most probably associated to the single-acceptor level of the divacancy. Our investigations so far demonstrate that the line has approximately the same intensity as the donor level of the di-vacancy and it anneals at about 250 °C as does the double-acceptor state of the di-vacancy. Unfortunately, at such a deep position in the band gap, a single-acceptor level, acting as a hole trap, does not exhibit a Poole± Frenkel eect which is strong enough to be observed in the present, moderately doped materials (the most optimistic expected lowering is of the order of DEPF 0:03 eV, which is small compared to the ionization energy of 0.45 eV). Nevertheless, we assign this line to the single-acceptor state of the di-vacancy as its appearance also corresponds to the disappearance of the electron trap from the upper half of the gap. The hole-ionization enthalpies of the two di-vacancy lines are shown in Fig. 5. They both move gradually nearer to the valence band nicely following each other. This peculiar behavior introduces, however, a clear cut between the observations in n- and p-type materials which has so far never been demonstrated for other point defects. 3.3. Discussion of the ionization enthalpies
Fig. 4. DTLS spectra of n p-mesa diodes of (a) Si0:84 Ge0:16 and (b) Si0:73 Ge0:27 after 2-MeV electron irradiations. The spectra were measured using a repetition rate of 250 Hz.
We have seen in the previous sections that the ionization enthalpies of the di-vacancy levels in the
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upper half of the band gap follow each other with increasing Ge content x while shifting away from the conduction band. However, as soon as the single-acceptor level crosses the mid-gap, starting to act as a hole trap, it follows the donor level which, surprisingly, has a totally dierent behavior from the doubly negatively charge state. It remains indeed pinned to the conduction band while the latter moves away from the conduction band. This is, to our knowledge, the ®rst time that such a peculiar behavior is demonstrated for a defect of multiple charge states. Other cases like Au [15], Zn [16] or interstitial carbon, Ci [17] have their different charge states pinned to each other. For the sake of clarity we may express all the ionization enthalpies with reference to the conduction band edge by using the energy-conservation law EC Et EV Et ECV , where ECV is the band-gap enthalpy. In agreement with van de Walle and Martin [18] it is here assumed that the reduction of the band gap exclusively takes place in the valence band and that the band-gap enthalpy ECV x; T is given by [15,19] ECV x; T 1:17
abT 2 = b T 2
0:206x eV;
2
0:43x 1
where a 4:9 10 4 (eV/K) and b 655 K [20]. The results are shown in Fig. 6. The band-gap
Fig. 6. Ionization enthalpies of the dierent di-vacancy-charge states relative to the conduction band. The two fat lines represent, from the bottom, the energy of the valence band edge and the energy of the middle of the band, respectively, relative to the conduction band.
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enthalpy used for Fig. 6 has been calculated for a temperature of 250 K which is a reasonable = =0 value for V2 , and V2 but a too high value for 0= V2 , implying an underestimation of the ionization enthalpy of the donor level. This has, however, no eect on the general trend. We recall that the experimental data plotted in Fig. 6 have been extracted assuming temperature independent capture-cross-sections. We will come back to this point later on. Two points from the plots in Fig. 6 need to be commented on. Firstly, the observation, already mentioned above, that the double-acceptor and single donor, both belonging to the same defect, behave clearly dierently, is con®rmed. What is peculiar is that the single-acceptor as a function of x follows the former when acting as an electron trap while it follows the latter when it acts as a hole trap. In [16] it was proposed that very deep levels, due to the localized nature of the electron or hole in these levels, should be horizontally aligned in the band gap with x while shallow levels should not be so due to the delocalized nature of the electron or hole. We can see that the behavior of the two di-vacancy levels in the lower half of the band gap is not in agreement with this proposal. Secondly, it is also clear from Fig. 6 that there is a discontinuity of 0.07 eV in the position of the =0 V2 level when it crosses the mid-gap. The absolute uncertainties of the ionization enthalpies are less than 0.02 eV, so this discontinuity is signi®cant. Two eects can account for such a discrepancy: When the single-acceptor acts as a hole trap, it is electrically attractive to the carrier, while it is neutral when interacting with the conduction band. The simplest approach accounting for the attractive character of the defect is to attribute a coulombic potential to it. In that case, Abakumov et al. [21] have predicted that the hole-capture cross-section should vary as rp / 1=T 2 , while it is expected to be temperature independent for neutral centers. This eect reduces the measured ionization enthalpy by 0.05 eV. In addition, as a consequence of the coulombic interaction between the ionized defect and the hole, the emission process is in¯uenced by the Poole±Frenkel eect. In the present case, this eect might lower the ionization enthalpy by 0.03, as already mentioned
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in Section 3.2. Thus, when considering these two mechanism together we can account for the discontinuity reported in Fig. 6. This leaves us with only the question of why the dierent charge states of the same defect behave dierently. 4. Summary The energy levels of the di-vacancy have been followed in epitaxially grown, strain-relaxed Si1 x Gex as a function of x for 0 6 x 6 0:5, using deep level transient spectroscopy (DLTS) on particleirradiated p n and n p diodes. The two acceptor levels situated in the upper half of the band gap in Si are found to move gradually deeper into the gap with increasing x and the single-acceptor level crosses the mid-gap for x 0:25, from then on it changes its slope with x. The donor level in the lower half of the band gap becomes gradually more shallow, pinned to the conduction band. The anneal temperature of the di-vacancy is found to be independent of composition in the investigated composition range. Acknowledgements This work was supported by the Danish National Scienti®c Research Council. References [1] S.J. Watts, Nucl. Instr. and Meth. B 386 (1997) 149. [2] See G.D. Watkins, in: W. Schr oter (Ed.), Materials Science and Technology, a Comprehensive Treatment, Vol. 4:
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
Electronic Structure and Properties of Semiconductors, VCH, Weinheim, 1991, p. 105. J. Fage-Pedersen, A. Nylandsted Larsen, A. Mesli, Phys. Rev. B 62 (2000) 1. E.V. Monakhov, A. Nylandsted Larsen, P. Kringhùj, J. Appl. Phys. 81 (1997) 1180. E.V. Monakhov, A.Yu. Kuznetsov, B.G. Svensson, J. Appl. Phys. 87 (2000) 4629. See e.g. E.A. Fitzgerald, S.B. Samavedam, Thin Solid Films 294 (1997) 3. E.V. Monakhov, S.Yu. Shiryaev, A. Nylandsted Larsen, J. Hartung, G. Davies, Thin Solid Films 294 (1997) 43. T.P. Leervad Pedersen, A. Nylandsted Larsen, A. Mesli, Appl. Phys. Lett. 75 (1999) 4085. P. Kringhùj, A. Nylandsted Larsen, Phys. Rev. B 52 (1995) 16333. J. Lalita, B.G. Svensson, C. Jagadish, A. Hallen, Nucl. Instr. and Meth. B 127±128 (1997) 69. A. Mesli, A. Nylandsted Larsen, Phys. Rev. Lett. 83 (1999) 148. N. Zangenberg, J. Fage-Pedersen, J. Lundsgaard Hansen, A. Nylandsted Larsen, Defect and Diusion Forum 94±99 (2001) 703. A. Nylandsted Larsen, P. Kringhùj, Appl. Phys. Lett 68 (1996) 2684. N. Zangenberg, J. Fage-Pedersen, J. Lundsgaard Hansen, A. Nylandsted Larsen, Phys. Rev. Lett. 87 (2001) 125901-1. A. Mesli, P. Kringhùj, A. Nylandsted Larsen, Phys. Rev. B 56 (1997) 13202. S. Voû, H. Bracht, N.A. Stolwijk, P. Kringhùj, A. Nylandsted Larsen, Appl. Phys. Lett. 73 (1998) 2331. A. Nylandsted Larsen, A. Bro Hansen, D. Reitze, J.-J. Goubet, F. Fage-Pedersen, A. Mesli, Phys. Rev. B 64 (2001), to be published. C.G. van de Walle, R.M. Martin, Phys. Rev. B 34 (1986) 5621. J. Weber, M.I. Alonso, Phys. Rev. B 40 (1989) 5683. V. Alex, S. Finkbeiner, J. Weber, J. Appl. Phys. 79 (1996) 6943. V.N. Abakumov, V.I. Perel, I.N. Yassievich, in: V.M. Agranovich, A.A. Maradudin (Eds.), Nonradiative Recombination in Semiconductors, Vol. 33, 1991, p. 62.
The di-vacancy in particle-irradiated, strain-relaxed SiGe H. av Skardi a, A. Bro Hansen a, A. Mesli b, A. Nylandsted Larsen a
a,*
Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark b Laboratoire LPSE, 4 rue des Fr eres Lumi ere, F-68093 Mulhouse Cedex, France
Abstract The di-vacancy is known to introduce three energy levels in the energy-band gap of Si. Using deep level transient spectroscopy (DLTS) on particle-irradiated p n and n p diodes, we have followed these levels in epitaxially grown, strain-relaxed Si1 x Gex as a function of x for 0 6 x 6 0:5. Both the single- and double-acceptor levels located in the upper half of the band gap in Si move gradually deeper into the gap with increasing x. While the double-acceptor level remains in the upper half of the band gap of the alloys, the single-acceptor level crosses the mid-gap for x 0:25. The donor level becomes gradually more shallow, but remains pinned to the conduction band. The anneal temperature of the divacancy is found to be independent of composition in the investigated composition range. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Si1 x Gex ; Irradiation; Di-vacancy; DLTS; Annealing
1. Introduction The di-vacancy is one of the most abundant defects in Si following particle irradiation at room temperature, and as it is, moreover, a rather stable defect with an anneal temperature of about 250 °C it always gives rise to concern when Si-based components are exposed to irradiations [1]. It exists in four dierent charge states in Si (, 0, , ) corresponding to three levels in the band gap: 0= a donor level V2 at EV 0:20 eV and two acceptor levels at EC 0:24 eV V2= and EC =0 0:41 eV V2 (EV and EC are the valence- and
*
Corresponding author. Tel.: +45-46-8942-3720. E-mail address: [email protected] (A. Nylandsted Larsen).
conduction-band edges, respectively) [2]. The deep single-acceptor level at EC 0:41 eV is a feared recombination-generation center. Only little is known about the di-vacancy in Ge. Arguments have recently been put forward that a level at EC 0:29 eV, observed by deep level transient spectroscopy (DLTS) in irradiated n-type Ge, can be assigned to the di-vacancy [3]. However, whether it is a donor or an acceptor level has not been established. The existence of di-vacancyrelated levels in the lower half of the band gap of Ge has, to our knowledge, not been demonstrated. The compositional dependence of the donor level of the di-vacancy in strain-relaxed SiGe alloy layers has previously been studied in epitaxially grown, p-type Si1 x Gex for x 6 0:15 [4]. Although the level was found to become gradually more shallow with increasing x, it remains pinned to the
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 8 9 3 - X
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conduction band, demonstrating that the decrease of the hole-ionization enthalpy with increasing x is fully accounted for by the band-gap shrinkage of the alloy. The eect of strain on the single-acceptor level of the di-vacancy has recently been studied in strained, epitaxial Si0:87 Ge0:13 [5]. It was found that the ionization enthalpy relative to the conduction-band edge decreased as compared to that of Si, opposite to what was observed for the PV-pair. To the best of our knowledge there has been no further investigation of the dependency of the di-vacancy levels on strain or composition in SiGe. This report presents the ®rst results from a comprehensive DLTS study of the di-vacancy in Si1 x Gex . They include a study of the eect of composition on all three di-vacancy levels in strain-relaxed, epitaxially grown Si1 x Gex for x 6 0:5.
3. Results and discussion 3.1. Results from the p n diodes The DLTS spectra of the irradiated p n-diodes change dramatically in going from Si0:84 Ge0:16 to Si0:75 Ge0:25 as demonstrated in Figs. 1(a) and (b). The Si0:84 Ge0:16 DLTS spectrum (Fig. 1(a)), and also those for x K 0:16, resembles those of a typical Si spectrum consisting of a dominant E-center line at a temperature of about 280 K (which also contains a small contribution from the singleacceptor line of the di-vacancy), a smaller line at about 190 K from the double-acceptor level of the di-vacancy, and the line related to the Ci center at about 100 K (the Ci defect in Si0:84 Ge0:16 is stable to 350 K as demonstrated in [8]). A careful computer analysis of the dominating line (the E-center line) shows that the hidden di-vacancy line has an intensity almost identical to that of the ( / )-
2. Experimental details Strain-relaxed Si1 x Gex layers with x varying from 0 to 0.5 were grown on (1 0 0) Si substrates by molecular-beam epitaxy (MBE) using the compositional-grading technique, as described elsewhere [6,7]. The DLTS investigations were done on n pand p n-mesa diodes. The mesa diodes were fabricated by ®rst growing 4 lm thick n- or p-type doped, strain-relaxed Si1 x Gex layers on top of a compositionally graded buer. These layers were doped with either Sb or B to concentrations of about 5 1015 cm 3 . The p and n layers were ®nally grown to a thickness of 0:5 lm and doped to very high concentrations of B and Sb, respectively 1 1019 cm 3 . The diodes were irradiated at room temperature with either 2-MeV electrons or protons to doses of 3 1015 cm 2 or 4 1012 cm 2 , respectively, or with 2.5 MeV aparticles to a dose of 1 1011 cm 2 . Apart from dierences in the intensities of the DLTS lines resulting from the irradiations with the dierent particles no other eects of changing the projectiles were observed. The DLTS measurements were carried out with a Semitrap spectrometer using the lock-in principle to process the capacitance transient signal.
Fig. 1. DTLS spectra of p n-mesa diodes of (a) Si0:84 Ge0:16 and (b) Si0:75 Ge0:25 after 2-MeV a-particle irradiations. The spectra were measured using a repetition rate of 2390 Hz.
H. av Skardi et al. / Nucl. Instr. and Meth. in Phys. Res. B 186 (2002) 195±200
acceptor line at 190 K. The major change in going from Si0:84 Ge0:16 to Si0:75 Ge0:25 is that the E-center line disappears allowing both charge states of the di-vacancy to emerge with equal intensities. The behavior of the E-center as a function of x will be the topic of a forthcoming paper, however, we may already now reveal that the ( /0)-acceptor level of the E-center moves gradually deeper into the gap with increasing x, as already demonstrated in [9], and crosses the mid-gap for x somewhere between 0.20 and 0.25, in which case the E-center changes from being an electron trap for x K 0:25 to become a hole trap for x J 0:25. The two acceptor levels of the di-vacancy behave in a similar way at least while they are primarily interacting with the conduction band. They move gradually deeper into the gap with increasing x, and seem to remain approximately equidistant from each other by the so-called Hubbard energy of 0.2 eV, as illustrated in Fig. 2. It is clear from Fig. 2 that none of the levels are pinned to any of the band edges. Above a Ge fraction of about 0.30, the single-acceptor level crosses the mid-gap and begins to signi®cantly interact with the valence band, necessitating the use of minority-carrier transient spectroscopy (MCTS) based on optically induced minority carriers. Unfortunately, this method is not without ambiguity in the present case for two main reasons. Firstly, both types of
Fig. 2. Extracted ionization enthalpies relative to the conduction band as a function of the Ge content from p n diodes. The data points is a second-order polynomial line through the V= 2 ®t; the same polynomial has been shifted to ®t the V2 =0 data points.
197
carriers are simultaneously injected into the depletion region and quantitative interpretations of spectra related to mid-gap levels may become doubtful. Secondly, the overlap between the lines of the E center and the single-acceptor level of the di-vacancy introduces the same kind of ambiguity as in the case when both these levels are acting as electron traps. A way of overcoming these dif®culties is oered by using p-type materials for x P 0:30, as discussed in Section 3.2. The anneal temperature of the di-vacancy as a function of composition can be unambiguously determined by following the double-acceptor line. The results are displayed in Fig. 3. It appears that, within a narrow range of about 20 °C, the stability is independent of composition. Apparently, the charge state of the di-vacancy does not play any signi®cant role in its stability as it is predominantly neutral during the annealing in the low-x materials and predominantly singly negative during the annealing in the high-x material. It is surprising that the anneal temperature is independent of the Ge content. The anneal temperature of the di-vacancy in Si is known to be sensitive to the impurity content of the samples, most probably because the impurities act as sinks and annihilation centers for the diusing di-vacancies [10]. Without exception, the anneal temperature or diusivity of all the defects and impurities which we have previously studied in strain-relaxed SiGe layers has been somehow in¯uenced by the presence of the Ge (V [11], Ci [8], SbV [9], B [12], Sb [13], Ge [14]). So why is the anneal temperature of the di-vacancy
Fig. 3. Anneal temperature of the di-vacancy as a functin of the Ge content, determined from the intensity of the V= line. The 2 anneal time was always 15 min.
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H. av Skardi et al. / Nucl. Instr. and Meth. in Phys. Res. B 186 (2002) 195±200
independent of the Ge content? We do not have an answer to this question as yet. 3.2. Results from the n p-diodes As demonstrated by Monakhov et al. [4] for x J 0:10 the DLTS lines from the donor levels of Ci and the di-vacancy cannot be separated. This is also demonstrated in Fig. 4(a) which shows a typical spectrum from a Si0:84 Ge0:16 diode. The line at about 100 K is made up by a large contribution from Ci and a smaller contribution from the di-vacancy. However, it was always possible to anneal the Ci defect without in¯uencing the divacancy in the composition range in which we have followed the donor level of the di-vacancy (x K 0:3). The line labelled ``unknown'' in Fig. 4(a), situated at a temperature of about 260 K, has not yet been identi®ed. However, its variation with irradiation dose, Ge composition, and B concentration points to the triple complex Ge±V±B as the origin of the line. Increasing the Ge content x further, the two lines move to lower temperatures as demonstrated in Fig. 4(b) and for x J 0:25 a
Fig. 5. Extracted ionization enthalpies relative to the valence band as a function of the Ge content from n p diodes. The lines between the data points are only to guide the eye.
new line appears in the spectrum, at a temperature of about 250 K. This line is most probably associated to the single-acceptor level of the divacancy. Our investigations so far demonstrate that the line has approximately the same intensity as the donor level of the di-vacancy and it anneals at about 250 °C as does the double-acceptor state of the di-vacancy. Unfortunately, at such a deep position in the band gap, a single-acceptor level, acting as a hole trap, does not exhibit a Poole± Frenkel eect which is strong enough to be observed in the present, moderately doped materials (the most optimistic expected lowering is of the order of DEPF 0:03 eV, which is small compared to the ionization energy of 0.45 eV). Nevertheless, we assign this line to the single-acceptor state of the di-vacancy as its appearance also corresponds to the disappearance of the electron trap from the upper half of the gap. The hole-ionization enthalpies of the two di-vacancy lines are shown in Fig. 5. They both move gradually nearer to the valence band nicely following each other. This peculiar behavior introduces, however, a clear cut between the observations in n- and p-type materials which has so far never been demonstrated for other point defects. 3.3. Discussion of the ionization enthalpies
Fig. 4. DTLS spectra of n p-mesa diodes of (a) Si0:84 Ge0:16 and (b) Si0:73 Ge0:27 after 2-MeV electron irradiations. The spectra were measured using a repetition rate of 250 Hz.
We have seen in the previous sections that the ionization enthalpies of the di-vacancy levels in the
H. av Skardi et al. / Nucl. Instr. and Meth. in Phys. Res. B 186 (2002) 195±200
upper half of the band gap follow each other with increasing Ge content x while shifting away from the conduction band. However, as soon as the single-acceptor level crosses the mid-gap, starting to act as a hole trap, it follows the donor level which, surprisingly, has a totally dierent behavior from the doubly negatively charge state. It remains indeed pinned to the conduction band while the latter moves away from the conduction band. This is, to our knowledge, the ®rst time that such a peculiar behavior is demonstrated for a defect of multiple charge states. Other cases like Au [15], Zn [16] or interstitial carbon, Ci [17] have their different charge states pinned to each other. For the sake of clarity we may express all the ionization enthalpies with reference to the conduction band edge by using the energy-conservation law EC Et EV Et ECV , where ECV is the band-gap enthalpy. In agreement with van de Walle and Martin [18] it is here assumed that the reduction of the band gap exclusively takes place in the valence band and that the band-gap enthalpy ECV x; T is given by [15,19] ECV x; T 1:17
abT 2 = b T 2
0:206x eV;
2
0:43x 1
where a 4:9 10 4 (eV/K) and b 655 K [20]. The results are shown in Fig. 6. The band-gap
Fig. 6. Ionization enthalpies of the dierent di-vacancy-charge states relative to the conduction band. The two fat lines represent, from the bottom, the energy of the valence band edge and the energy of the middle of the band, respectively, relative to the conduction band.
199
enthalpy used for Fig. 6 has been calculated for a temperature of 250 K which is a reasonable = =0 value for V2 , and V2 but a too high value for 0= V2 , implying an underestimation of the ionization enthalpy of the donor level. This has, however, no eect on the general trend. We recall that the experimental data plotted in Fig. 6 have been extracted assuming temperature independent capture-cross-sections. We will come back to this point later on. Two points from the plots in Fig. 6 need to be commented on. Firstly, the observation, already mentioned above, that the double-acceptor and single donor, both belonging to the same defect, behave clearly dierently, is con®rmed. What is peculiar is that the single-acceptor as a function of x follows the former when acting as an electron trap while it follows the latter when it acts as a hole trap. In [16] it was proposed that very deep levels, due to the localized nature of the electron or hole in these levels, should be horizontally aligned in the band gap with x while shallow levels should not be so due to the delocalized nature of the electron or hole. We can see that the behavior of the two di-vacancy levels in the lower half of the band gap is not in agreement with this proposal. Secondly, it is also clear from Fig. 6 that there is a discontinuity of 0.07 eV in the position of the =0 V2 level when it crosses the mid-gap. The absolute uncertainties of the ionization enthalpies are less than 0.02 eV, so this discontinuity is signi®cant. Two eects can account for such a discrepancy: When the single-acceptor acts as a hole trap, it is electrically attractive to the carrier, while it is neutral when interacting with the conduction band. The simplest approach accounting for the attractive character of the defect is to attribute a coulombic potential to it. In that case, Abakumov et al. [21] have predicted that the hole-capture cross-section should vary as rp / 1=T 2 , while it is expected to be temperature independent for neutral centers. This eect reduces the measured ionization enthalpy by 0.05 eV. In addition, as a consequence of the coulombic interaction between the ionized defect and the hole, the emission process is in¯uenced by the Poole±Frenkel eect. In the present case, this eect might lower the ionization enthalpy by 0.03, as already mentioned
200
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in Section 3.2. Thus, when considering these two mechanism together we can account for the discontinuity reported in Fig. 6. This leaves us with only the question of why the dierent charge states of the same defect behave dierently. 4. Summary The energy levels of the di-vacancy have been followed in epitaxially grown, strain-relaxed Si1 x Gex as a function of x for 0 6 x 6 0:5, using deep level transient spectroscopy (DLTS) on particleirradiated p n and n p diodes. The two acceptor levels situated in the upper half of the band gap in Si are found to move gradually deeper into the gap with increasing x and the single-acceptor level crosses the mid-gap for x 0:25, from then on it changes its slope with x. The donor level in the lower half of the band gap becomes gradually more shallow, pinned to the conduction band. The anneal temperature of the di-vacancy is found to be independent of composition in the investigated composition range. Acknowledgements This work was supported by the Danish National Scienti®c Research Council. References [1] S.J. Watts, Nucl. Instr. and Meth. B 386 (1997) 149. [2] See G.D. Watkins, in: W. Schr oter (Ed.), Materials Science and Technology, a Comprehensive Treatment, Vol. 4:
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
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