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Vacancies and self-interstitials in germanium: a picture derived from radioactive probes
Physica B 308–310 (2001) 529–534
Vacancies and self-interstitials in germanium: a picture derived from radioactive probes R. Sielemanna,*, H. H.assleina, Ch. Zistla, M. Muller . a, L. Stadlera, V.V. Emtsevb a
Hahn-Meitner-Institut Berlin GmbH, Glienicker Strasse 100, 14109 Berlin, Germany b Joffe Institut St. Petersburg, Russia
Abstract Several experimental methods based on radioactive probes have been used and combined to study vacancies and selfinterstitials in Ge. Central to the studies is the perturbed angular correlation spectroscopy. Defects are created and detected by electron irradiation with subsequent trapping at 111In probe atoms and the neutrino-recoil technique. From combination of both types of techniques defect identification is achieved and numerous microscopic defect parameters of the isolated defects and defect–impurity pairs are extracted. Additional information on electrical levels is obtained by applying deep level transient spectroscopy (DLTS) to samples containing radioactive 111In probes (radiotracer-DLTS). r 2001 Elsevier Science B.V. All rights reserved. Keywords: Germanium defects; Perturbed angular correlation; Deep level transient spectroscopy
1. Introduction Though point defects in Ge have attracted intensive research for a long time and numerous results have been obtained, mostly by electrical and capacitance techniques [1,2], no microscopic identification of either vacancy or self-interstitial has yet been accomplished. Thus, a definite assignment of the collected data to the respective defects is still missing and interpretation of the results has remained largely speculative. It is clear, however, that a better knowledge would be of considerable interest not only for Ge itself but also with respect to Si for which a large amount of definite data exist [3]. Recently, another approach to identify and study the intrinsic defects in Ge has been presented. Several experimental techniques based on the radioactive probe nuclei have been employed. Primarily, the perturbed
*Corresponding author. Tel.: +49-30-8062-2725; fax: +4930-8062-2293. E-mail address: [email protected] (R. Sielemann).
angular correlation (PAC) technique has been used which is based on the fact that defects in the immediate vicinity of a radioactive probe atom (111In) can be studied via the induced hyperfine interaction. In this way, structural and electronic defect properties can be obtained. Vacancies and self-interstitials were produced either by electron irradiation or by using the PAC probe itself as primary knock-on atom (PKA) effected by the emission of a neutrino in a preceeding nuclear transmutation. From the combination of both types of experiments, identification of both the vacancy and the selfinterstitial is achieved and numerous defect properties are obtained. A further experimental technique used is DLTS applied to Ge samples doped with radioactive 111 In probes. In this contribution, we will first shortly present the experimental techniques. In the following, we list and discuss the properties of the vacancy and self-interstitial and how these properties were extracted from the various experiments. Finally, we touch recent results obtained by other experimental techniques and mention work in progress which calculates the geometrical structure and electronic properties of the relevant defect–probe pairs.
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2. Experimental techniques 2.1. Perturbed angular correlation spectroscopy (PAC) The PAC method is based on the measurement of the nuclear quadrupole interaction of a radioactive probe nucleus with the charge distribution in its immediate environment. The charge distribution yields information on the probe’s lattice site and defects, which might be situated around it in the form of an electric field gradient (EFG) tensor. The tensor parameters measured are the strength (frequency) nQ ; the asymmetry parameter Z and the crystallographic orientation which yields microscopic information on the probe–defect structure. In addition, the fraction of probes with a certain defect configuration can be determined. The probe nucleus used throughout the experiments is 111In decaying to 111 Cd on which the hyperfine parameters are measured. A recent review of the PAC technique can be found in Ref. [4]. 2.2. Defect production by electron irradiation Vacancies and self-interstitials were produced in two different ways: either by irradiation with 1.2 MeV electrons or by the neutrino recoil technique. In the first case, irradiations of the samples were performed at cryogenic temperatures (in some cases at room temperature) to fluences of typically 5 1016 e/cm2. Following the irradiations, isochronal anneals were performed monitored by PAC to search for trapping at the 111In probes. 2.3. Defect production by neutrino recoil The direct neighbourhood between probe atom and defect is essential for PAC. A full exploitation of this fact is made by a defect production technique which is centered on the probe atom [5]. This is accomplished by using a probe atom which also serves as PKA. Fig. 1 shows the principle: instead of using 111In as parent activity, the precursor 111Sn is used. In the electron capture decay to 111In a high energy neutrino is emitted which leads to a monoenergetic recoil of 29 eV on the 111 In probe. This is an energy close to or above the threshold Td for single Frenkel pair formation in most materials in immediate vicinity of the 111In probe. For Ge Td is known to be about 20 eV. 2.4. Deep level transient spectroscopy (DLTS) on radioactive probes A current weakness of DLTS is the fact that it does not contain information on the chemical nature and microscopic structure of an observed defect. This deficiency makes it difficult to correlate DLTS with
Fig. 1. Partial decay scheme illustrating the neutrino recoil effect. The neutrino emitted in the decay of 111Sn carries an energy of 2.5 MeV leading to 29 eV recoil on the PAC probe 111 In.
structure sensitive methods. In recent developments, it was shown that information on the chemical nature can be added by applying DLTS to radioactive atoms [6]. In the present case, we have used samples like those prepared for PAC with radioactive 111In probes subjected to electron irradiation and isochronal anneals. DLTS spectra were measured on these samples during a period of several days covering the decay of 111In (T1=2 ¼ 2:8 d). One expects that the concentration of deep levels related to 111In should decrease and those related to 111Cd increase as function of time.
2.5. Probe production and recoil implantation All methods described above are based on the incorporation of radioactive probe atoms in Ge [5]. This is done by a recoil implantation technique: A heavy ion beam of high energy (50–100 MeV) produces 111In (or 111Sn) atoms. In this process, the radioactive ions receive recoil energies between 1 and 10 MeV and become well separated from the primary heavy ion beam. The high recoil energies lead to implantation depths of typically 1–5 mm and low probe concentrations: typically between 1013 and 1014 cm3. Following implantation, the Ge samples are annealed at slightly above 6001C to remove the implantation damage and relax the probes to substitutional sites. This process is well monitored and leads to completely unperturbed probe incorporation.
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3. Experimental results and discussion 3.1. Identification of vacancy and self-interstitial Combining the results of the neutrino recoil experiments with those from the trapping experiments, identification of vacancy and self-interstitial is possible. In the recoil experiment, 111Sn was implanted in p- and n-type samples with subsequent annealing of the implantation damage. Following this procedure, the probe is cooled to 4.2 K so that the decay of 111Sn to 111 In takes place at this temperature. The result is shown in Fig. 2. 11% of the probes display an interaction frequency nQ1 ¼ 54 MHz with axial symmetry (Z ¼ 0), showing that a defect is present at the probe. From additional experiments, the orientation of the probe– defect complex can be inferred to be in a /1 1 1S direction. This defect production is restricted to p-Ge, in n-type and intrinsic material no defect production occurs. Isochronal anneals show that the defect is stable to 205 K [7] and then disappears. Since the threshold for Frenkel pair formation is known to be around 20 eV, only one Frenkel pair, one vacancy and one interstitial can be produced. The probe atom as the PKA can either knock a neighbouring atom out of its site and take its position, leaving a vacancy behind (adjacent to the probe), or it may itself end up in an interstitial position. So the defect (54 MHz) connected with nQ1 must be the association of the probe with a vacancy or represents the probe on some type of interstitial site. Theory has until recently not been able to calculate the EFGs pertaining to specific defect situations with sufficient accuracy, this situation, however, is presently changing [8,9]. Remedy of this ambiguity, however, can be obtained by combining the results from neutrino recoil with those from the trapping experiments described in the following.
Fig. 3. PAC spectrum of 111In/111Cd and Fourier transform after electron irradiation in p-Ge measured at 293 K. The spectrum shows both nQ1 and nQ2 :
In these experiments, the 111In-implanted and subsequently annealed samples were electron irradiated (mostly at 77 K). Isochronal annealing was executed and monitored by PAC in a range up to several hundred K. These experiments were performed with p-(Ga), n(Sb) type, and also with high purity material. Depending on doping either one or two defects are trapped at the probes [10]: the already known defect from neutrino recoil (54 MHz) and a second one with nQ2 ¼ 420 MHz (Z ¼ 0 and orientation /1 1 1S), Fig. 3. Since nQ1 ¼ 54 MHz occurs in both the recoil and the trapping experiment, the probe has to occupy a position compatible with both types of defect formation. This leaves only the substitutional site for the probe atom and identifies nQ1 with a monovacancy nearest neighbour to the probe. For nQ2 ; such an identification is not possible since this defect is not produced by neutrino recoil. From extended series of experiments [10], it could be excluded that unintentional impurity trapping is observed. Thus, by exclusion of that possibility one can associate nQ2 with a self-interstitial trapped at the probe in /1 1 1S direction. Additional corroboration of this identification will be discussed below. 3.2. Electrical properties of vacancy and self-interstitial
Fig. 2. PAC spectrum of 111In/111Cd measured at 4.2 K after neutrino recoil in p-Ge. The spectrum shows a defect with nQ1 ¼ 54 MHz.
Given the above identification of vacancy and selfinterstitial microscopic defect parameters can be extracted from the data [10]. The defects’ trapping behaviour was studied as function of the carrier concentration (Fermi level) in n- and p-type material, see Fig. 4. The vacancy is observed only in p-Ge, the self-interstitial in p-and n-Ge but not in highly doped material. The entire trapping behaviour can be consistently explained when Fermi level-dependent charge states are assigned to the defects, keeping in mind that the shallow acceptor 111In is always negative (or partly neutral in heavily p-doped material). Trapping of the vacancy in the form shown in Fig. 4 becomes understandable if an acceptor state for V at E ¼ EV þ 0:20 eV
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Fig. 4. Fractions of 111In atoms forming complexes with vacancies (squares) and self-interstitials (circles) observed versus carrier concentration in n- and p-type Ge after electron irradiation at 77 K and subsequent warm-up to room temperature.
assume the level close to the conduction band to be an acceptor. In this case, trapping would take place between neutral Is and the In probes. Loss of trapping in n-material would then result from the Coulomb repulsion when I turns negative. Loss of trapping in p-type Ge either from competitive trapping of the neutral Is with the Ga dopants or due to a second gap state of the Is in the lower half of the band gap which might render Is positive in highly doped material also leads to competitive trapping at Ga. The trapping data alone cannot decide between these two options. Recent ab initio calculations [12] indeed place an acceptor level close to the conduction band, which is also in accordance with earlier more indirect evidence [1]. If we accept that interpretation (scenario 2), an interesting question arises as to the origin of the interaction between a neutral I and a negative In atom while, on the other hand, there is practically no interaction between the Is and the donor dopants (Sb). This question is thoroughly discussed in Ref. [13]. 3.3. Kinetic properties of vacancies and self-interstitials
Fig. 5. Electrical levels of vacancy and self-interstitial in Ge as deduced from PAC. For the self-interstitial two options are possible: The acceptor represents the more likely case, see text.
exists, see Fig. 5. This leads to trapping at 111In when V is neutral whereas in the negative state no trapping occurs due to Coulomb repulsion. Obviously, the trapping must be caused by elastic interaction between V and the strongly oversized 111In atom in the Ge matrix. This reasoning becomes unique when the presence of the Ga dopants are simultaneously taken into account; vice versa with similar considerations, one can infer that the Ga doping atoms, being shallow acceptors like the In probes, do not (or very weakly) interact with Vs. Recent ab initio calculations also place an acceptor level for V in that energy region [11]. This is also in accordance with earlier evidence from electrical measurements [1]. For the self-interstitials’ trapping at the probes, the data displayed in Fig. 4 leave two possible scenarios for the interstitials’ charge states. Both need a level close to the conduction band, see Fig. 5. If this level were a donor, trapping might be explained as occurring between positive Is and the probes (Coulomb attraction), loss of trapping in highly doped n-Ge would then result from the neutralisation of I: Loss of trapping in p-type Ge would result from competitive Coulomb trapping at the Ga dopants. A second scenario might
Fig. 6 shows detailed annealing experiments in p-Ge following electron irradiation. Capture of the neutral vacancy and the interstitial (presumably also neutral, see above) occurs in a similar temperature range, 200(10) K for the vacancy and 220(10) K for the interstitial (for 15 min isochronal anneals). From several supporting arguments, we conclude that the capture processes are diffusion limited implying that both defects undergo long range migration with very similar activation energy, about 0.6(1) eV. This finding is somewhat surprising since interstitial migration is often assumed to occur at much lower temperatures. From the annealing behaviour shown in Fig. 6 the binding energy to the In probe can also be extracted: 0.5(1) eV for both I and V: With the given defect identification, the
Fig. 6. Normalised fractions of 111In atoms forming complexes with vacancies (squares) and self-interstitials (circles) observed versus annealing temperature after electron irradiation at 77 K in p-Ge.
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production and thermal annealing of the neutrino recoil can also be understood. The recoil process leads to a vacancy-associated probe (nQ1 ) with a defect stability of only 205 K in contrast to the stability of this same pair occurring in the trapping reaction (about 400 K, see Fig. 6). This fact implies that the mechanisms erasing the pair are different: after recoil, the pair is annihilated by the close-by but not visible antidefect, the self-interstitial; after trapping, however, the pair disappears when the vacancy overcomes the binding to the probe and diffuses away. Both, free interstitial trapping (220 K, see Fig. 6) and pair annihilation by the close-by interstitial are rather close in temperature (the latter about 20 K lower) indicating that the processes are diffusion limited and not determined by barriers since eventual barriers should be quite different.
defect pairs in semiconductors [8,9]. In the present case, the small electric field gradient (quadrupole coupling nQ ¼ 54 MHz) obtained for the Cd–V pair has prompted us to suggest that the Cd probe might assume a positi n in the centre of a divacancy-like configuration (‘‘split-vacancy’’) analogous to the Sn-vacancy configuration in Si unravelled by Watkins [3]. This special configuration might also be involved in defect structures measured by PAC in Si [15–17] where defect frequencies in close analogy to Ge appear (nQ ¼ 29 and 451 MHz). Calculations for both Ge and Si are presently on the way [18] and seem to corroborate the identifications given for the vacancy and self-interstitial in the present work.
3.4. Electrical level of In–V pair
4. Conclusion
Since the probe–defect complexes (In–V, In–I, Cd–V, Cd–I) play such an important role in PAC, further electrical and structural information on these pairs is desirable. For electrical information DLTS is useful, however, even though quite a number of studies on radiation-induced defect–impurity pairs exist, interpretation of the data remained more or less speculative. We have, therefore, used DLTS on radioactive 111In probes as described above. In this study, a level in p-Ge at E ¼ EV þ 0:33 eV decreases in concentration with a half-life of 2.8 d and must, therefore, be related to the 111 In probe [14]. From PAC measured on the same sample, we can assign this level uniquely to the In–V defect, which is the only one appearing in the PAC spectra. Since the Cd–V level, into which the In–V level decays, is not observed in these spectra, we conclude that it must be situated in the upper half of the band gap. Levels associated with I are neither observed in ptype nor in n-type material, one reason might be that these levels are too shallow to be detected.
A combination of several experimental techniques based on radioactive probes has been used to study the fundamental defects, vacancy and self-interstitial in Ge. Identification of the defects could be achieved and a variety of microscopic defect parameters determined. Recently, published results obtained with positron annihilation spectroscopy [19] and X-ray techniques [20] confirm the conclusions of the present paper on the kinetic properties of V and I: Newly developed ab initio calculations of EFGs will allow to draw detailed structural information from the measured PAC parameters by comparison of experiment and theory in the near future [18].
3.5. Structural properties of defect–impurity pairs
References
Since PAC always measures the properties of defect– probe pairs, structural information on the isolated defects is not directly available. Some information on the defect–probe pairs, however, can directly be gained by PAC-like symmetry properties and crystallographic orientation. This information was used in characterising the Cd–V and Cd–I pair. Another major source of information, the strength of the EFG (coupling constant nQ ) has in the past found little application in determining defect structures since it could not be reliably calculated for comparison with experiment. This situation, however, is about to change. Recently, ab initio methods have been used to calculate the geometric structure and resulting field gradients for defects and
Acknowledgements Helpful work by R. Govindaraj in the preparation of this manuscript is gratefully acknowledged.
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[10] H. H.asslein, R. Sielemann, Ch. Zistl, Phys. Rev. Lett. 80 (1998) 2626. [11] A. Fazzio, A. Janotti, A.J.R. da Silva, R. Mota, Phys. Rev. B 61 (2000) R2401. [12] A.J.R. da Silva, A. Janotti, A. Fazzio, R.J. Baierle, Phys. Rev. B 62 (2000) 9903. [13] R. Sielemann, H. H.asslein, Ch. Zistl, Physica B 302–303 (2001) 101. [14] Ch. Zistl, R. Sielemann, H. Haesslein, S. Gall, D. Br.aunig, J. Bollmann, Mater. Sci. Forum 258–263 (1997) 53.
[15] D. Forkel, F. Meyer, W. Witthuhn, H. Wolf, M. Deicher, M. Uhrmacher, Hyperfine Interaction 35 (1987) 715. [16] Th. Wichert, M. Deicher, G. Gruebel, R. Keller, N. Schulz, K. Skudlik, Appl. Phys. A48 (1989) 59. [17] H. Haesslein, et al., Annual Report Hahn-MeitnerInstitut, Bereich Schwerionenphysik, 1990, p. 114. [18] P. Blaha, private communication. [19] A. Polity, F. Rudolf, Phys. Rev. B 59 (1999) 10025. [20] P. Ehrhart, H. Zillgen, J. Appl. Phys. 85 (1999) 3503.
Vacancies and self-interstitials in germanium: a picture derived from radioactive probes R. Sielemanna,*, H. H.assleina, Ch. Zistla, M. Muller . a, L. Stadlera, V.V. Emtsevb a
Hahn-Meitner-Institut Berlin GmbH, Glienicker Strasse 100, 14109 Berlin, Germany b Joffe Institut St. Petersburg, Russia
Abstract Several experimental methods based on radioactive probes have been used and combined to study vacancies and selfinterstitials in Ge. Central to the studies is the perturbed angular correlation spectroscopy. Defects are created and detected by electron irradiation with subsequent trapping at 111In probe atoms and the neutrino-recoil technique. From combination of both types of techniques defect identification is achieved and numerous microscopic defect parameters of the isolated defects and defect–impurity pairs are extracted. Additional information on electrical levels is obtained by applying deep level transient spectroscopy (DLTS) to samples containing radioactive 111In probes (radiotracer-DLTS). r 2001 Elsevier Science B.V. All rights reserved. Keywords: Germanium defects; Perturbed angular correlation; Deep level transient spectroscopy
1. Introduction Though point defects in Ge have attracted intensive research for a long time and numerous results have been obtained, mostly by electrical and capacitance techniques [1,2], no microscopic identification of either vacancy or self-interstitial has yet been accomplished. Thus, a definite assignment of the collected data to the respective defects is still missing and interpretation of the results has remained largely speculative. It is clear, however, that a better knowledge would be of considerable interest not only for Ge itself but also with respect to Si for which a large amount of definite data exist [3]. Recently, another approach to identify and study the intrinsic defects in Ge has been presented. Several experimental techniques based on the radioactive probe nuclei have been employed. Primarily, the perturbed
*Corresponding author. Tel.: +49-30-8062-2725; fax: +4930-8062-2293. E-mail address: [email protected] (R. Sielemann).
angular correlation (PAC) technique has been used which is based on the fact that defects in the immediate vicinity of a radioactive probe atom (111In) can be studied via the induced hyperfine interaction. In this way, structural and electronic defect properties can be obtained. Vacancies and self-interstitials were produced either by electron irradiation or by using the PAC probe itself as primary knock-on atom (PKA) effected by the emission of a neutrino in a preceeding nuclear transmutation. From the combination of both types of experiments, identification of both the vacancy and the selfinterstitial is achieved and numerous defect properties are obtained. A further experimental technique used is DLTS applied to Ge samples doped with radioactive 111 In probes. In this contribution, we will first shortly present the experimental techniques. In the following, we list and discuss the properties of the vacancy and self-interstitial and how these properties were extracted from the various experiments. Finally, we touch recent results obtained by other experimental techniques and mention work in progress which calculates the geometrical structure and electronic properties of the relevant defect–probe pairs.
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2. Experimental techniques 2.1. Perturbed angular correlation spectroscopy (PAC) The PAC method is based on the measurement of the nuclear quadrupole interaction of a radioactive probe nucleus with the charge distribution in its immediate environment. The charge distribution yields information on the probe’s lattice site and defects, which might be situated around it in the form of an electric field gradient (EFG) tensor. The tensor parameters measured are the strength (frequency) nQ ; the asymmetry parameter Z and the crystallographic orientation which yields microscopic information on the probe–defect structure. In addition, the fraction of probes with a certain defect configuration can be determined. The probe nucleus used throughout the experiments is 111In decaying to 111 Cd on which the hyperfine parameters are measured. A recent review of the PAC technique can be found in Ref. [4]. 2.2. Defect production by electron irradiation Vacancies and self-interstitials were produced in two different ways: either by irradiation with 1.2 MeV electrons or by the neutrino recoil technique. In the first case, irradiations of the samples were performed at cryogenic temperatures (in some cases at room temperature) to fluences of typically 5 1016 e/cm2. Following the irradiations, isochronal anneals were performed monitored by PAC to search for trapping at the 111In probes. 2.3. Defect production by neutrino recoil The direct neighbourhood between probe atom and defect is essential for PAC. A full exploitation of this fact is made by a defect production technique which is centered on the probe atom [5]. This is accomplished by using a probe atom which also serves as PKA. Fig. 1 shows the principle: instead of using 111In as parent activity, the precursor 111Sn is used. In the electron capture decay to 111In a high energy neutrino is emitted which leads to a monoenergetic recoil of 29 eV on the 111 In probe. This is an energy close to or above the threshold Td for single Frenkel pair formation in most materials in immediate vicinity of the 111In probe. For Ge Td is known to be about 20 eV. 2.4. Deep level transient spectroscopy (DLTS) on radioactive probes A current weakness of DLTS is the fact that it does not contain information on the chemical nature and microscopic structure of an observed defect. This deficiency makes it difficult to correlate DLTS with
Fig. 1. Partial decay scheme illustrating the neutrino recoil effect. The neutrino emitted in the decay of 111Sn carries an energy of 2.5 MeV leading to 29 eV recoil on the PAC probe 111 In.
structure sensitive methods. In recent developments, it was shown that information on the chemical nature can be added by applying DLTS to radioactive atoms [6]. In the present case, we have used samples like those prepared for PAC with radioactive 111In probes subjected to electron irradiation and isochronal anneals. DLTS spectra were measured on these samples during a period of several days covering the decay of 111In (T1=2 ¼ 2:8 d). One expects that the concentration of deep levels related to 111In should decrease and those related to 111Cd increase as function of time.
2.5. Probe production and recoil implantation All methods described above are based on the incorporation of radioactive probe atoms in Ge [5]. This is done by a recoil implantation technique: A heavy ion beam of high energy (50–100 MeV) produces 111In (or 111Sn) atoms. In this process, the radioactive ions receive recoil energies between 1 and 10 MeV and become well separated from the primary heavy ion beam. The high recoil energies lead to implantation depths of typically 1–5 mm and low probe concentrations: typically between 1013 and 1014 cm3. Following implantation, the Ge samples are annealed at slightly above 6001C to remove the implantation damage and relax the probes to substitutional sites. This process is well monitored and leads to completely unperturbed probe incorporation.
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3. Experimental results and discussion 3.1. Identification of vacancy and self-interstitial Combining the results of the neutrino recoil experiments with those from the trapping experiments, identification of vacancy and self-interstitial is possible. In the recoil experiment, 111Sn was implanted in p- and n-type samples with subsequent annealing of the implantation damage. Following this procedure, the probe is cooled to 4.2 K so that the decay of 111Sn to 111 In takes place at this temperature. The result is shown in Fig. 2. 11% of the probes display an interaction frequency nQ1 ¼ 54 MHz with axial symmetry (Z ¼ 0), showing that a defect is present at the probe. From additional experiments, the orientation of the probe– defect complex can be inferred to be in a /1 1 1S direction. This defect production is restricted to p-Ge, in n-type and intrinsic material no defect production occurs. Isochronal anneals show that the defect is stable to 205 K [7] and then disappears. Since the threshold for Frenkel pair formation is known to be around 20 eV, only one Frenkel pair, one vacancy and one interstitial can be produced. The probe atom as the PKA can either knock a neighbouring atom out of its site and take its position, leaving a vacancy behind (adjacent to the probe), or it may itself end up in an interstitial position. So the defect (54 MHz) connected with nQ1 must be the association of the probe with a vacancy or represents the probe on some type of interstitial site. Theory has until recently not been able to calculate the EFGs pertaining to specific defect situations with sufficient accuracy, this situation, however, is presently changing [8,9]. Remedy of this ambiguity, however, can be obtained by combining the results from neutrino recoil with those from the trapping experiments described in the following.
Fig. 3. PAC spectrum of 111In/111Cd and Fourier transform after electron irradiation in p-Ge measured at 293 K. The spectrum shows both nQ1 and nQ2 :
In these experiments, the 111In-implanted and subsequently annealed samples were electron irradiated (mostly at 77 K). Isochronal annealing was executed and monitored by PAC in a range up to several hundred K. These experiments were performed with p-(Ga), n(Sb) type, and also with high purity material. Depending on doping either one or two defects are trapped at the probes [10]: the already known defect from neutrino recoil (54 MHz) and a second one with nQ2 ¼ 420 MHz (Z ¼ 0 and orientation /1 1 1S), Fig. 3. Since nQ1 ¼ 54 MHz occurs in both the recoil and the trapping experiment, the probe has to occupy a position compatible with both types of defect formation. This leaves only the substitutional site for the probe atom and identifies nQ1 with a monovacancy nearest neighbour to the probe. For nQ2 ; such an identification is not possible since this defect is not produced by neutrino recoil. From extended series of experiments [10], it could be excluded that unintentional impurity trapping is observed. Thus, by exclusion of that possibility one can associate nQ2 with a self-interstitial trapped at the probe in /1 1 1S direction. Additional corroboration of this identification will be discussed below. 3.2. Electrical properties of vacancy and self-interstitial
Fig. 2. PAC spectrum of 111In/111Cd measured at 4.2 K after neutrino recoil in p-Ge. The spectrum shows a defect with nQ1 ¼ 54 MHz.
Given the above identification of vacancy and selfinterstitial microscopic defect parameters can be extracted from the data [10]. The defects’ trapping behaviour was studied as function of the carrier concentration (Fermi level) in n- and p-type material, see Fig. 4. The vacancy is observed only in p-Ge, the self-interstitial in p-and n-Ge but not in highly doped material. The entire trapping behaviour can be consistently explained when Fermi level-dependent charge states are assigned to the defects, keeping in mind that the shallow acceptor 111In is always negative (or partly neutral in heavily p-doped material). Trapping of the vacancy in the form shown in Fig. 4 becomes understandable if an acceptor state for V at E ¼ EV þ 0:20 eV
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Fig. 4. Fractions of 111In atoms forming complexes with vacancies (squares) and self-interstitials (circles) observed versus carrier concentration in n- and p-type Ge after electron irradiation at 77 K and subsequent warm-up to room temperature.
assume the level close to the conduction band to be an acceptor. In this case, trapping would take place between neutral Is and the In probes. Loss of trapping in n-material would then result from the Coulomb repulsion when I turns negative. Loss of trapping in p-type Ge either from competitive trapping of the neutral Is with the Ga dopants or due to a second gap state of the Is in the lower half of the band gap which might render Is positive in highly doped material also leads to competitive trapping at Ga. The trapping data alone cannot decide between these two options. Recent ab initio calculations [12] indeed place an acceptor level close to the conduction band, which is also in accordance with earlier more indirect evidence [1]. If we accept that interpretation (scenario 2), an interesting question arises as to the origin of the interaction between a neutral I and a negative In atom while, on the other hand, there is practically no interaction between the Is and the donor dopants (Sb). This question is thoroughly discussed in Ref. [13]. 3.3. Kinetic properties of vacancies and self-interstitials
Fig. 5. Electrical levels of vacancy and self-interstitial in Ge as deduced from PAC. For the self-interstitial two options are possible: The acceptor represents the more likely case, see text.
exists, see Fig. 5. This leads to trapping at 111In when V is neutral whereas in the negative state no trapping occurs due to Coulomb repulsion. Obviously, the trapping must be caused by elastic interaction between V and the strongly oversized 111In atom in the Ge matrix. This reasoning becomes unique when the presence of the Ga dopants are simultaneously taken into account; vice versa with similar considerations, one can infer that the Ga doping atoms, being shallow acceptors like the In probes, do not (or very weakly) interact with Vs. Recent ab initio calculations also place an acceptor level for V in that energy region [11]. This is also in accordance with earlier evidence from electrical measurements [1]. For the self-interstitials’ trapping at the probes, the data displayed in Fig. 4 leave two possible scenarios for the interstitials’ charge states. Both need a level close to the conduction band, see Fig. 5. If this level were a donor, trapping might be explained as occurring between positive Is and the probes (Coulomb attraction), loss of trapping in highly doped n-Ge would then result from the neutralisation of I: Loss of trapping in p-type Ge would result from competitive Coulomb trapping at the Ga dopants. A second scenario might
Fig. 6 shows detailed annealing experiments in p-Ge following electron irradiation. Capture of the neutral vacancy and the interstitial (presumably also neutral, see above) occurs in a similar temperature range, 200(10) K for the vacancy and 220(10) K for the interstitial (for 15 min isochronal anneals). From several supporting arguments, we conclude that the capture processes are diffusion limited implying that both defects undergo long range migration with very similar activation energy, about 0.6(1) eV. This finding is somewhat surprising since interstitial migration is often assumed to occur at much lower temperatures. From the annealing behaviour shown in Fig. 6 the binding energy to the In probe can also be extracted: 0.5(1) eV for both I and V: With the given defect identification, the
Fig. 6. Normalised fractions of 111In atoms forming complexes with vacancies (squares) and self-interstitials (circles) observed versus annealing temperature after electron irradiation at 77 K in p-Ge.
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production and thermal annealing of the neutrino recoil can also be understood. The recoil process leads to a vacancy-associated probe (nQ1 ) with a defect stability of only 205 K in contrast to the stability of this same pair occurring in the trapping reaction (about 400 K, see Fig. 6). This fact implies that the mechanisms erasing the pair are different: after recoil, the pair is annihilated by the close-by but not visible antidefect, the self-interstitial; after trapping, however, the pair disappears when the vacancy overcomes the binding to the probe and diffuses away. Both, free interstitial trapping (220 K, see Fig. 6) and pair annihilation by the close-by interstitial are rather close in temperature (the latter about 20 K lower) indicating that the processes are diffusion limited and not determined by barriers since eventual barriers should be quite different.
defect pairs in semiconductors [8,9]. In the present case, the small electric field gradient (quadrupole coupling nQ ¼ 54 MHz) obtained for the Cd–V pair has prompted us to suggest that the Cd probe might assume a positi n in the centre of a divacancy-like configuration (‘‘split-vacancy’’) analogous to the Sn-vacancy configuration in Si unravelled by Watkins [3]. This special configuration might also be involved in defect structures measured by PAC in Si [15–17] where defect frequencies in close analogy to Ge appear (nQ ¼ 29 and 451 MHz). Calculations for both Ge and Si are presently on the way [18] and seem to corroborate the identifications given for the vacancy and self-interstitial in the present work.
3.4. Electrical level of In–V pair
4. Conclusion
Since the probe–defect complexes (In–V, In–I, Cd–V, Cd–I) play such an important role in PAC, further electrical and structural information on these pairs is desirable. For electrical information DLTS is useful, however, even though quite a number of studies on radiation-induced defect–impurity pairs exist, interpretation of the data remained more or less speculative. We have, therefore, used DLTS on radioactive 111In probes as described above. In this study, a level in p-Ge at E ¼ EV þ 0:33 eV decreases in concentration with a half-life of 2.8 d and must, therefore, be related to the 111 In probe [14]. From PAC measured on the same sample, we can assign this level uniquely to the In–V defect, which is the only one appearing in the PAC spectra. Since the Cd–V level, into which the In–V level decays, is not observed in these spectra, we conclude that it must be situated in the upper half of the band gap. Levels associated with I are neither observed in ptype nor in n-type material, one reason might be that these levels are too shallow to be detected.
A combination of several experimental techniques based on radioactive probes has been used to study the fundamental defects, vacancy and self-interstitial in Ge. Identification of the defects could be achieved and a variety of microscopic defect parameters determined. Recently, published results obtained with positron annihilation spectroscopy [19] and X-ray techniques [20] confirm the conclusions of the present paper on the kinetic properties of V and I: Newly developed ab initio calculations of EFGs will allow to draw detailed structural information from the measured PAC parameters by comparison of experiment and theory in the near future [18].
3.5. Structural properties of defect–impurity pairs
References
Since PAC always measures the properties of defect– probe pairs, structural information on the isolated defects is not directly available. Some information on the defect–probe pairs, however, can directly be gained by PAC-like symmetry properties and crystallographic orientation. This information was used in characterising the Cd–V and Cd–I pair. Another major source of information, the strength of the EFG (coupling constant nQ ) has in the past found little application in determining defect structures since it could not be reliably calculated for comparison with experiment. This situation, however, is about to change. Recently, ab initio methods have been used to calculate the geometric structure and resulting field gradients for defects and
Acknowledgements Helpful work by R. Govindaraj in the preparation of this manuscript is gratefully acknowledged.
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