- Email: [email protected]
Self-interstitials and Frenkel pairs in electron-irradiated germanium
ARTICLE IN PRESS
Physica B 401–402 (2007) 495–498 www.elsevier.com/locate/physb
Self-interstitials and Frenkel pairs in electron-irradiated germanium A. Carvalhoa,, R. Jonesa, J. Gossb, C. Jankea, J. Coutinhoc, S. O¨bergd, P.R. Briddonb a
School of Physics, University of Exeter, Stocker Rd., Exeter EX4 4QL, UK School of Natural Sciences, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK c Department of Physics, University of Aveiro and I3N, 3810 Aveiro, Portugal d Department of Mathematics, Lule˚a University of Technology, Lule˚a S-97187, Sweden
b
Abstract First principles calculations were used to study the structures and electrical levels of the self-interstitial in Ge. We considered the possibility of structural changes consequent with change in charge state and show these have important implications in the mobility and electrical activity of the defect. The theoretical model is compared to the results of low temperature electron irradiation in germanium reported in the literature. r 2007 Elsevier B.V. All rights reserved. PACS: 61.80.Az; 61.80.Ed; 61.80.Fe; 61.82.Fk Keywords: Self-interstitial; Germanium; Frenkel pair; Irradiation
1. Introduction Vacancies and self-interstitials are very mobile and highly reactive, complexing with dopants and mediating their diffusion at high temperatures. Thus, knowing their basic properties, such as equilibrium charge states and diffusion energies is essential to understand and control the defect reactions taking place in a wide temperature range. One difficulty is that both germanium self-interstitials (I’s) and vacancies (V’s) become mobile at 220 K or below [1], readily recombining or reacting with impurities. Thus, observation of the isolated defects require near-threshold gamma (g-) or electron (e-)irradiation at very low temperatures [2]. Frenkel pairs are electrically active. They are the deep acceptors responsible for up to 95% of the conductivity loss below 65 K in e-irradiated n-Ge [3]. However, it seems that e-irradiation at 4 K initially introduces neutral I–V pairs both in n- and p-type Ge, since thermal activation or other type of excitation is required to observe conductivity changes [3,4]. In p-type material annealed in the dark, compensation is only observed at 100 K. At 100–200 K, a Corresponding author.
E-mail address: [email protected] (A. Carvalho). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.09.007
curious ‘two-state defect’ appears [4–6]. This is believed to be a long lived electron trap that can be cycled between two charge states. Its ionization level was placed at E c 0:2 or E c 0:1 eV [4–6], and we suggest that it is the selfinterstitial (I). In fact, it seems to be an intrinsic donor, since it was observed in B, Al, Ga, In and Tl doped samples and the spin-12 state was identified with the P1 electron paramagnetic resonance (EPR) center [6], observed both in Ga-doped and undoped samples after strong irradiation. Recently, the perturbed angular correlated spectroscopy (PACs) technique was used to monitor of the trapping of V and I by radioactive probes as a function of the Fermi level. An acceptor level of the vacancy was placed at E v þ 0:2 eV and a transition level of the I was placed at E c 0:04 eV [1]. Here we address the charge-dependent properties of the self-interstitials, their interaction with vacancies, and show how these relate to the puzzling properties of e-irradiation damage in Ge.
2. Method We employ density functional pseudopotential calculations, carried out using the AIMPRO code [7]. A Pade´
ARTICLE IN PRESS A. Carvalho et al. / Physica B 401–402 (2007) 495–498
496
parameterization of the exchange-correlation functional of Perdew-Wang was used together with the dual space separable pseudopotentials of Hartwigsen et al. [8]. A non-linear core-correction (NLCC) was included to account for the 3d semicore electrons of Ge [9]. The germanium crystal was modeled by large hydrogenpassivated Ge329 H172 and Ge338 H184 clusters, centered on a lattice site and an interstitial T-site, respectively. The results obtained with both clusters are in excellent agreement. The surface germanium atoms and their hydrogen terminators were kept fixed, and all the other atoms were allowed to move during structural optimizations. Donor and acceptor levels were calculated using the marker method [10]. The markers used were substitutional S for donor levels and substitutional Au for acceptor levels [11,12]. Migration and transformation barriers were calculated using the nudged elastic band method [13]. The symmetry was not restricted during the structural relaxations. To avoid rounding errors, we quote energies with more digits than the real accuracy associated with the underlying approximations. 3. Results We investigated several split-interstitial configurations as well as self-interstitials occupying the open cages of the Ge lattice [14]. The latter included the high symmetry hexagonal (H) and tetrahedral (T) interstitials and distortions of those. The total energies of the various defect forms were compared for each charge state. Only the defects found to be relevant will be discussed here. The h1 1 0i split-interstitial or dumbbell (D) configuration is the most stable in the neutral charge state (Table 2), as found by previous theoretical work [15,16]. However, open-cage configurations are the lowest in energy in the
positive charge states. In the interstitial cage, the energy minimum is at the H site for neutral I, at the T site for Iþþ , and in a C3v hexagonal configuration for Iþ (Fig. 1). The T site was the only energy minimum found for Iþþ . The calculated electrical levels are shown in Table 1. We first analyze the vertical levels of the dumbell and caged interstitial defects. These are the electronic levels calculated assuming that before and after ionization the selfinterstitial is in the same defect form. There is an energy barrier preventing the transformation from D to a caged site (H/T). However, at the caged site, the self-interstitial moves between T and H upon ionization without additional activation energy (Fig. 1). At low temperatures, the transformation I0D ! I0H ðW ¼ 0:53 eVÞ can be neglected, and the dumbbell (I0D ) and caged defects (I0H , Iþ H, ) exist independently. The dumbbell self-interstitial is Iþþ T electrically inactive, having neither donor nor acceptor levels. In contrast, the open-caged self-interstitial (IT=H ) is a double donor with levels within 0.2 eV from the conduction band, consistent with recent PACs studies [1]. The double donor level of the self-interstitial was not found by previous theoretical modeling which investigated the electrical activity of the dumbell only [15,16] (see Tables 1 and 2). The bistability has different implications in a higher temperature regime. At high temperatures, the self-interstitial has enough thermal energy to overcome the barrier between the D and T or H sites. The Ið0=þÞ level is thus a thermodynamic level associated with a reconfiguration to the lowest energy structure of the final charge state: I0D þ Table 1 Calculated vertical levels (eV) of IT=H and ID , along with the thermodynamic levels of the self-interstitial (I) assuming transitions between the lowest energy structure of each charge state (see text), and the experimental (Exp.) value from Ref. [1] IT=H
1.2 1
ID
I
E c Eðþ= þ þÞ
0.08
–
E c Eð0=þÞ
0.24
0.10
Exp. 0.08 0.04
0.8 I0 + 2h+
0.6
0.02
E (eV)
0.4 0.2
Table 2 Calculated relative energies (eV) of different configurations of the selfinterstitial. In the þ charge state, D and H configurations are distorted [14]
I+ + h+
0 -0.2
Cluster
-0.4 I++
-0.6 -0.8
T
0 + ++
Charge 0
þ
þþ
Ge329 H172
D H T
0.00 0.50 H
0.08 0.00 H
T T 0.00
Ge338 H184
D H T
0.00 0.48 H
0.11 0.00 H
T T 0.00
H
Fig. 1. (Color online) Energy profiles of I along the h1 1 1i direction (Ge338 H184 cluster). The initial and final positions of all the atoms (½R~T and ½R~H ) were optimized subject to symmetry constraints and the intermediate points were allowed to relax perpendicular to ½R~H ½R~T . Transition energies were calculated using the marker method (Table 1).
Defect form
Letters indicate an unstable form and the configuration it relaxes to.
ARTICLE IN PRESS A. Carvalho et al. / Physica B 401–402 (2007) 495–498
−
+
Ev-0.02
~ Ec+0.3
Ec-0.08
Ef (eV)
++
0
F (eV) Ev
Ec
Fig. 2. (Color online) Formation energy (E f ) versus Fermi level position (F) for the germanium self-interstitial. E c E v is taken to be 0.74 eV.
hþ ! I þ H or the reverse. Although the respective transition level lies below the valence band (Table 1), it is in negative U order relative to the ðþ= þ þÞ level; this means that Iþ will not be thermodynamically stable, since the reaction 0 þþ 2Iþ is exothermic. Consequently, for Fermi H ! ID þ IT levels above the ð0= þ þÞ occupancy level, which is close to mid-gap (Fig. 2), the defect will be neutral, and double positive charged otherwise. The activation energy for the transformation from neutral D to H is 0.53 eV. Simultaneously, we have to take into account the mobility of the self-interstitial. The neutral self-interstitial can undertake long-range migration by reconfiguring between D and H forms, and therefore the migration energy is 0.53 eV also. The thermodynamically unstable Iþ H is the most mobile species, diffusing along the h1 1 1i with an activation energy of about 0.3 eV only. The double positive self-interstitial, however, has to overcome a barrier of 1.2 eV to jump between T sites. We know from experiment that at about 200 K the interstitial is already mobile (probably when the most mobile species Iþ H starts diffusing), and reacts with impurities and other traps [1]. However, above 100 C self-interstitials reappear, released by the dissociation of interstitial-dopant and other complexes [1]. In this temperature range, the self-interstitial is a negative-U defect. We also investigated caged and split-interstitial defects in the single and double negative charge states, but we found no acceptor level [14]. 4. Comparison with experiment We now compare our results to the low temperature (4 K and 78 K) e-irradiation data.
497
In n-type material below 65 K, the majority of the selfinterstitials are close to their vacancy, such that the I–V distance is smaller than the average distance to dopants and other traps [17]. The self-interstitial is neutral in n-Ge, and we know from previous calculations that the vacancy is a double acceptor [18]. Thus Frenkel pairs are double acceptors as found by experiment [3], and we expect that ð0=þÞ the fI2Vgð¼=Þ level corresponds to the IT –V¼ transition. The measured E c 0:070 eV derived from the Fermi level dependence and the 65 K annealing rate [19] is consistent with our IH=T level Eð0=þÞ ¼ E c 0:24 eV, within the accuracy of the method. Both are close to the experimental level at E c 0:04 eV reported by the PACs study [1]. In p-Ge under equilibrium conditions, I is in the þþ state. However, the capture cross section of the second hole is quite small [5], because conductivity changes are only seen above 50 K under light excitation or above 100 K in the dark [4]. We suggest that the self-interstitial is the ‘twostate’ defect observed between 100 and 200 K. Its ‘0’ state was identified with the spin-12 P1 EPR center [6], implying that Iþ and Iþþ are to be identified with the ‘0’ and ‘þ’ states of Ref. [4]. The capture of a hole requires the ionization of a chemical acceptor as well as a switch of ID to IH . We suggest that this only takes place above 100 K. Injecting electrons into the conduction band leads to the conversion of Iþþ to Iþ , which ionizes over a time scale of minutes above 100 K. This model is consistent with (i) the observation of the P1 center both in doped and undoped Ge, (ii) the measured capture cross sections for electrons of 1015 cm2 , and o1027 cm2 for holes of the ‘0’ state (Iþ ), (iii) the ionization level of the ‘two-state’ defect about 0.1 or 0.2 eV below E c and (iv) the loss of the ‘two-state’ defect at 200 K—temperature at which the V becomes mobile [4–6]. Further, Iþ H is very close to the T site and the reorientation barrier is very small (Fig. 1). It is likely that the defect has effective Td symmetry, and other effects not taken into account by our calculations, such as spin–orbit coupling, may account for a further distortion and justify the unusual C2v symmetry of the P1 EPR center. The I model does not explain the loss of Ga acceptors found by Ref. [20], that we think may be associated with other reactions taking place in the same temperature range. 5. Conclusion We have shown that I in Ge is bistable having an electrically inert h1 1 0i-split configuration, but behaving as a double donor when at a cage site. The donor levels of the self-interstitial are consistent with the PACs trapping experiments [1], the ionization level of Frenkel pairs [19], and with the properties of the ‘two-state’ defect [4–6]. At higher temperatures, the self-interstitial is expected to be a negative-U defect with ð0= þ þÞ level at about midgap.
ARTICLE IN PRESS 498
A. Carvalho et al. / Physica B 401–402 (2007) 495–498
Acknowledgments AC thanks Profs. D.W. Palmer and V.V. Emtsev for helpful discussions and comments. Fundac- a˜o Calouste Gulbenkian and FCT are acknowledged for financial support. References [1] H. Haesslein, R. Sielemann, C. Zistl, Phys. Rev. Lett. 80 (1998) 2626; R. Sielemann, Nucl. Instr. and Meth. 146 (1998) 329; R. Sielemann, H. Haesslein, Ch. Zistl, M. Mu¨ller, L. Stadler, V.V. Emtsev, Physica B 308 (2001) 529. [2] V.V. Emtsev, Mater Sci Semicond. Process. 9 (2006) 580. [3] T. A Calcott, J.W. Mackay, Phys. Rev. B 161 (1967) 698. [4] T.M. Flanagan, E.E. Klontz, Phys. Rev. 167 (1967) 789. [5] W.L. Brown, W.M. Augustyniak, T.R. Waite, J. Appl. Phys. 30 (1959) 2158. [6] D.L. Trueblood, Phys. Rev. 161 (1967) 828. [7] P.R. Briddon, R. Jones, Phys. Stat. Sol. (b) 217 (2000) 131. [8] C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (1998) 3641.
[9] S.G. Louie, S. Froyen, M.L. Cohen, Phys. Rev. B 26 (1982) 738. [10] J.P. Goss, M.J. Shaw, P.R. Briddon, Topics Appl. Phy. 104 (2007) 69. [11] E. Simoen, C. Claeys, in: Germanium-based Technologies: From Materials to Devices, Elsevier, London, 2007 (chapter 5). [12] H.G. Grimmeiss, L. Montelius, K. Larsson, Phys. Rev. B 37 (1988) 6916. [13] G. Henkelman, H. Jo´nsson, J. Chem. Phys. 113 (2000) 9978. [14] A. Carvalho, R. Jones, J.P. Goss, C. Janke, S. O¨berg, P.R. Briddon, Phys. Rev. Lett., in press. [15] A.J.R. daSilva, A. Janotti, A. Fazzio, R.J. Baierle, R. Mota, Phys. Rev. B 62 (2000) 9903. [16] M.D. Moreira, R.H. Miwa, P. Venezuela, Phys. Rev. B 70 (2004) 115215. [17] J. Zizine, in: F.L. Vook (Ed.), Radiation Effects in Semiconductors, Proceedings of the Conference Santa Fe´ USA, Plenum Press, New York, 1968, p. 186. [18] J. Coutinho, R. Jones, V.J.B. Torres, M. Barroso, S. O¨berg, P.R. Briddon, J. Phys.: Condens. Matter 17 (2005) L521. [19] J. Bourgoin, F. Mollot, Phys. Stat. Sol. (b) 43 (1971) 343. [20] E.D. Vasil’eva, V.V. Emtsev, T.V. Mashovets Fiz. Tekh. Poluprovodn. 17 (1983) 35 [Sov. Phys. Semicond. 17 (1983) 21].
Physica B 401–402 (2007) 495–498 www.elsevier.com/locate/physb
Self-interstitials and Frenkel pairs in electron-irradiated germanium A. Carvalhoa,, R. Jonesa, J. Gossb, C. Jankea, J. Coutinhoc, S. O¨bergd, P.R. Briddonb a
School of Physics, University of Exeter, Stocker Rd., Exeter EX4 4QL, UK School of Natural Sciences, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK c Department of Physics, University of Aveiro and I3N, 3810 Aveiro, Portugal d Department of Mathematics, Lule˚a University of Technology, Lule˚a S-97187, Sweden
b
Abstract First principles calculations were used to study the structures and electrical levels of the self-interstitial in Ge. We considered the possibility of structural changes consequent with change in charge state and show these have important implications in the mobility and electrical activity of the defect. The theoretical model is compared to the results of low temperature electron irradiation in germanium reported in the literature. r 2007 Elsevier B.V. All rights reserved. PACS: 61.80.Az; 61.80.Ed; 61.80.Fe; 61.82.Fk Keywords: Self-interstitial; Germanium; Frenkel pair; Irradiation
1. Introduction Vacancies and self-interstitials are very mobile and highly reactive, complexing with dopants and mediating their diffusion at high temperatures. Thus, knowing their basic properties, such as equilibrium charge states and diffusion energies is essential to understand and control the defect reactions taking place in a wide temperature range. One difficulty is that both germanium self-interstitials (I’s) and vacancies (V’s) become mobile at 220 K or below [1], readily recombining or reacting with impurities. Thus, observation of the isolated defects require near-threshold gamma (g-) or electron (e-)irradiation at very low temperatures [2]. Frenkel pairs are electrically active. They are the deep acceptors responsible for up to 95% of the conductivity loss below 65 K in e-irradiated n-Ge [3]. However, it seems that e-irradiation at 4 K initially introduces neutral I–V pairs both in n- and p-type Ge, since thermal activation or other type of excitation is required to observe conductivity changes [3,4]. In p-type material annealed in the dark, compensation is only observed at 100 K. At 100–200 K, a Corresponding author.
E-mail address: [email protected] (A. Carvalho). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.09.007
curious ‘two-state defect’ appears [4–6]. This is believed to be a long lived electron trap that can be cycled between two charge states. Its ionization level was placed at E c 0:2 or E c 0:1 eV [4–6], and we suggest that it is the selfinterstitial (I). In fact, it seems to be an intrinsic donor, since it was observed in B, Al, Ga, In and Tl doped samples and the spin-12 state was identified with the P1 electron paramagnetic resonance (EPR) center [6], observed both in Ga-doped and undoped samples after strong irradiation. Recently, the perturbed angular correlated spectroscopy (PACs) technique was used to monitor of the trapping of V and I by radioactive probes as a function of the Fermi level. An acceptor level of the vacancy was placed at E v þ 0:2 eV and a transition level of the I was placed at E c 0:04 eV [1]. Here we address the charge-dependent properties of the self-interstitials, their interaction with vacancies, and show how these relate to the puzzling properties of e-irradiation damage in Ge.
2. Method We employ density functional pseudopotential calculations, carried out using the AIMPRO code [7]. A Pade´
ARTICLE IN PRESS A. Carvalho et al. / Physica B 401–402 (2007) 495–498
496
parameterization of the exchange-correlation functional of Perdew-Wang was used together with the dual space separable pseudopotentials of Hartwigsen et al. [8]. A non-linear core-correction (NLCC) was included to account for the 3d semicore electrons of Ge [9]. The germanium crystal was modeled by large hydrogenpassivated Ge329 H172 and Ge338 H184 clusters, centered on a lattice site and an interstitial T-site, respectively. The results obtained with both clusters are in excellent agreement. The surface germanium atoms and their hydrogen terminators were kept fixed, and all the other atoms were allowed to move during structural optimizations. Donor and acceptor levels were calculated using the marker method [10]. The markers used were substitutional S for donor levels and substitutional Au for acceptor levels [11,12]. Migration and transformation barriers were calculated using the nudged elastic band method [13]. The symmetry was not restricted during the structural relaxations. To avoid rounding errors, we quote energies with more digits than the real accuracy associated with the underlying approximations. 3. Results We investigated several split-interstitial configurations as well as self-interstitials occupying the open cages of the Ge lattice [14]. The latter included the high symmetry hexagonal (H) and tetrahedral (T) interstitials and distortions of those. The total energies of the various defect forms were compared for each charge state. Only the defects found to be relevant will be discussed here. The h1 1 0i split-interstitial or dumbbell (D) configuration is the most stable in the neutral charge state (Table 2), as found by previous theoretical work [15,16]. However, open-cage configurations are the lowest in energy in the
positive charge states. In the interstitial cage, the energy minimum is at the H site for neutral I, at the T site for Iþþ , and in a C3v hexagonal configuration for Iþ (Fig. 1). The T site was the only energy minimum found for Iþþ . The calculated electrical levels are shown in Table 1. We first analyze the vertical levels of the dumbell and caged interstitial defects. These are the electronic levels calculated assuming that before and after ionization the selfinterstitial is in the same defect form. There is an energy barrier preventing the transformation from D to a caged site (H/T). However, at the caged site, the self-interstitial moves between T and H upon ionization without additional activation energy (Fig. 1). At low temperatures, the transformation I0D ! I0H ðW ¼ 0:53 eVÞ can be neglected, and the dumbbell (I0D ) and caged defects (I0H , Iþ H, ) exist independently. The dumbbell self-interstitial is Iþþ T electrically inactive, having neither donor nor acceptor levels. In contrast, the open-caged self-interstitial (IT=H ) is a double donor with levels within 0.2 eV from the conduction band, consistent with recent PACs studies [1]. The double donor level of the self-interstitial was not found by previous theoretical modeling which investigated the electrical activity of the dumbell only [15,16] (see Tables 1 and 2). The bistability has different implications in a higher temperature regime. At high temperatures, the self-interstitial has enough thermal energy to overcome the barrier between the D and T or H sites. The Ið0=þÞ level is thus a thermodynamic level associated with a reconfiguration to the lowest energy structure of the final charge state: I0D þ Table 1 Calculated vertical levels (eV) of IT=H and ID , along with the thermodynamic levels of the self-interstitial (I) assuming transitions between the lowest energy structure of each charge state (see text), and the experimental (Exp.) value from Ref. [1] IT=H
1.2 1
ID
I
E c Eðþ= þ þÞ
0.08
–
E c Eð0=þÞ
0.24
0.10
Exp. 0.08 0.04
0.8 I0 + 2h+
0.6
0.02
E (eV)
0.4 0.2
Table 2 Calculated relative energies (eV) of different configurations of the selfinterstitial. In the þ charge state, D and H configurations are distorted [14]
I+ + h+
0 -0.2
Cluster
-0.4 I++
-0.6 -0.8
T
0 + ++
Charge 0
þ
þþ
Ge329 H172
D H T
0.00 0.50 H
0.08 0.00 H
T T 0.00
Ge338 H184
D H T
0.00 0.48 H
0.11 0.00 H
T T 0.00
H
Fig. 1. (Color online) Energy profiles of I along the h1 1 1i direction (Ge338 H184 cluster). The initial and final positions of all the atoms (½R~T and ½R~H ) were optimized subject to symmetry constraints and the intermediate points were allowed to relax perpendicular to ½R~H ½R~T . Transition energies were calculated using the marker method (Table 1).
Defect form
Letters indicate an unstable form and the configuration it relaxes to.
ARTICLE IN PRESS A. Carvalho et al. / Physica B 401–402 (2007) 495–498
−
+
Ev-0.02
~ Ec+0.3
Ec-0.08
Ef (eV)
++
0
F (eV) Ev
Ec
Fig. 2. (Color online) Formation energy (E f ) versus Fermi level position (F) for the germanium self-interstitial. E c E v is taken to be 0.74 eV.
hþ ! I þ H or the reverse. Although the respective transition level lies below the valence band (Table 1), it is in negative U order relative to the ðþ= þ þÞ level; this means that Iþ will not be thermodynamically stable, since the reaction 0 þþ 2Iþ is exothermic. Consequently, for Fermi H ! ID þ IT levels above the ð0= þ þÞ occupancy level, which is close to mid-gap (Fig. 2), the defect will be neutral, and double positive charged otherwise. The activation energy for the transformation from neutral D to H is 0.53 eV. Simultaneously, we have to take into account the mobility of the self-interstitial. The neutral self-interstitial can undertake long-range migration by reconfiguring between D and H forms, and therefore the migration energy is 0.53 eV also. The thermodynamically unstable Iþ H is the most mobile species, diffusing along the h1 1 1i with an activation energy of about 0.3 eV only. The double positive self-interstitial, however, has to overcome a barrier of 1.2 eV to jump between T sites. We know from experiment that at about 200 K the interstitial is already mobile (probably when the most mobile species Iþ H starts diffusing), and reacts with impurities and other traps [1]. However, above 100 C self-interstitials reappear, released by the dissociation of interstitial-dopant and other complexes [1]. In this temperature range, the self-interstitial is a negative-U defect. We also investigated caged and split-interstitial defects in the single and double negative charge states, but we found no acceptor level [14]. 4. Comparison with experiment We now compare our results to the low temperature (4 K and 78 K) e-irradiation data.
497
In n-type material below 65 K, the majority of the selfinterstitials are close to their vacancy, such that the I–V distance is smaller than the average distance to dopants and other traps [17]. The self-interstitial is neutral in n-Ge, and we know from previous calculations that the vacancy is a double acceptor [18]. Thus Frenkel pairs are double acceptors as found by experiment [3], and we expect that ð0=þÞ the fI2Vgð¼=Þ level corresponds to the IT –V¼ transition. The measured E c 0:070 eV derived from the Fermi level dependence and the 65 K annealing rate [19] is consistent with our IH=T level Eð0=þÞ ¼ E c 0:24 eV, within the accuracy of the method. Both are close to the experimental level at E c 0:04 eV reported by the PACs study [1]. In p-Ge under equilibrium conditions, I is in the þþ state. However, the capture cross section of the second hole is quite small [5], because conductivity changes are only seen above 50 K under light excitation or above 100 K in the dark [4]. We suggest that the self-interstitial is the ‘twostate’ defect observed between 100 and 200 K. Its ‘0’ state was identified with the spin-12 P1 EPR center [6], implying that Iþ and Iþþ are to be identified with the ‘0’ and ‘þ’ states of Ref. [4]. The capture of a hole requires the ionization of a chemical acceptor as well as a switch of ID to IH . We suggest that this only takes place above 100 K. Injecting electrons into the conduction band leads to the conversion of Iþþ to Iþ , which ionizes over a time scale of minutes above 100 K. This model is consistent with (i) the observation of the P1 center both in doped and undoped Ge, (ii) the measured capture cross sections for electrons of 1015 cm2 , and o1027 cm2 for holes of the ‘0’ state (Iþ ), (iii) the ionization level of the ‘two-state’ defect about 0.1 or 0.2 eV below E c and (iv) the loss of the ‘two-state’ defect at 200 K—temperature at which the V becomes mobile [4–6]. Further, Iþ H is very close to the T site and the reorientation barrier is very small (Fig. 1). It is likely that the defect has effective Td symmetry, and other effects not taken into account by our calculations, such as spin–orbit coupling, may account for a further distortion and justify the unusual C2v symmetry of the P1 EPR center. The I model does not explain the loss of Ga acceptors found by Ref. [20], that we think may be associated with other reactions taking place in the same temperature range. 5. Conclusion We have shown that I in Ge is bistable having an electrically inert h1 1 0i-split configuration, but behaving as a double donor when at a cage site. The donor levels of the self-interstitial are consistent with the PACs trapping experiments [1], the ionization level of Frenkel pairs [19], and with the properties of the ‘two-state’ defect [4–6]. At higher temperatures, the self-interstitial is expected to be a negative-U defect with ð0= þ þÞ level at about midgap.
ARTICLE IN PRESS 498
A. Carvalho et al. / Physica B 401–402 (2007) 495–498
Acknowledgments AC thanks Profs. D.W. Palmer and V.V. Emtsev for helpful discussions and comments. Fundac- a˜o Calouste Gulbenkian and FCT are acknowledged for financial support. References [1] H. Haesslein, R. Sielemann, C. Zistl, Phys. Rev. Lett. 80 (1998) 2626; R. Sielemann, Nucl. Instr. and Meth. 146 (1998) 329; R. Sielemann, H. Haesslein, Ch. Zistl, M. Mu¨ller, L. Stadler, V.V. Emtsev, Physica B 308 (2001) 529. [2] V.V. Emtsev, Mater Sci Semicond. Process. 9 (2006) 580. [3] T. A Calcott, J.W. Mackay, Phys. Rev. B 161 (1967) 698. [4] T.M. Flanagan, E.E. Klontz, Phys. Rev. 167 (1967) 789. [5] W.L. Brown, W.M. Augustyniak, T.R. Waite, J. Appl. Phys. 30 (1959) 2158. [6] D.L. Trueblood, Phys. Rev. 161 (1967) 828. [7] P.R. Briddon, R. Jones, Phys. Stat. Sol. (b) 217 (2000) 131. [8] C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (1998) 3641.
[9] S.G. Louie, S. Froyen, M.L. Cohen, Phys. Rev. B 26 (1982) 738. [10] J.P. Goss, M.J. Shaw, P.R. Briddon, Topics Appl. Phy. 104 (2007) 69. [11] E. Simoen, C. Claeys, in: Germanium-based Technologies: From Materials to Devices, Elsevier, London, 2007 (chapter 5). [12] H.G. Grimmeiss, L. Montelius, K. Larsson, Phys. Rev. B 37 (1988) 6916. [13] G. Henkelman, H. Jo´nsson, J. Chem. Phys. 113 (2000) 9978. [14] A. Carvalho, R. Jones, J.P. Goss, C. Janke, S. O¨berg, P.R. Briddon, Phys. Rev. Lett., in press. [15] A.J.R. daSilva, A. Janotti, A. Fazzio, R.J. Baierle, R. Mota, Phys. Rev. B 62 (2000) 9903. [16] M.D. Moreira, R.H. Miwa, P. Venezuela, Phys. Rev. B 70 (2004) 115215. [17] J. Zizine, in: F.L. Vook (Ed.), Radiation Effects in Semiconductors, Proceedings of the Conference Santa Fe´ USA, Plenum Press, New York, 1968, p. 186. [18] J. Coutinho, R. Jones, V.J.B. Torres, M. Barroso, S. O¨berg, P.R. Briddon, J. Phys.: Condens. Matter 17 (2005) L521. [19] J. Bourgoin, F. Mollot, Phys. Stat. Sol. (b) 43 (1971) 343. [20] E.D. Vasil’eva, V.V. Emtsev, T.V. Mashovets Fiz. Tekh. Poluprovodn. 17 (1983) 35 [Sov. Phys. Semicond. 17 (1983) 21].