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Ultrasonic velocity changes in bulk neutron-disordered silicon
Physica B 263—264 (1999) 152—155
Ultrasonic velocity changes in bulk neutron-disordered silicon M. Coeck , C. Laermans *, E. Peeters Katholieke Universiteit Leuven, Department of Physics, Celestijnenlaan 200 D, B-3001 Heverlee, Belgium SCKzCEN, Dept. BR2, Boeretang 200, B-2400 Mol, Belgium
Abstract Measurements of the changes in ultrasonic velocity were performed on bulk single-crystalline silicon irradiated with fast-neutron doses up to 1.7;10 and 3.2;10 n/cm (E'0.1 MeV). Compared to the unirradiated material, a large additional effect is observed at low temperatures the behavior of which is similar to the predictions of the tunneling model. Together with results previously obtained from attenuation measurements and Raman spectroscopy, this result puts the presence of tunneling states in high coordinated bulk silicon clearly in evidence. 1999 Elsevier Science B.V. All rights reserved. Keywords: Tunneling states; Low temperatures; Neutron irradiation; Disordered silicon
1. Introduction During the past few decades several experiments have shown that glasses exhibit universal properties which differ from those in crystals. Below a few Kelvin this anomalous behavior can be very well described by the tunneling model [1,7], postulating the presence of low-energy excitations called tunneling states (TS). These are atoms or groups of atoms which can have two equilibrium positions and can therefore quantum mechanically tunnel in a double asymmetric potential well. They have a wide distribution of energies and relaxation times and appear with an almost constant density of
* Corresponding author. Tel.: #32-16-327185; fax: #32-16327987; e-mail: [email protected]. Now at SRON, P.O. Box 800, NL-9700 AV Groningen, The Netherlands.
states. It was first believed that these TS could only occur in typical glass-forming amorphous solids having a low average coordination of the individual atoms. Also in partly disordered low-coordinated solids such as neutron-irradiated quartz, TS have been observed [2]. The presence of TS in higher coordinated materials such as silicon or germanium is however controversial. Both affirming [3] and denying [4,8] arguments concerning the presence of TS in these high coordinated materials were reported. In order to contribute to this discussion and to explore the possibility of the presence of these states in topologically higher constrained disordered solids, we have performed low-temperature ultrasonic measurements in bulk neutron-irradiated silicon single crystals. In this paper we present the results obtained from measurements of the changes in ultrasonic (&0.1 GHz) velocity (*v/v) as a function of temperature (0.3—30 K). Our measurements
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 2 1 0 - 1
M. Coeck et al. / Physica B 263—264 (1999) 152—155
show a pronounced difference between the behavior of the irradiated and the unirradiated material. Furthermore, the irradiated material shows a remarkable similarity with the predictions of the tunneling model, putting in evidence the possibility of the introduction of TS in high coordinated materials.
2. Sample description and experimental details Measurements were carried out on bulk, singlecrystalline silicon, one unirradiated sample (labeled Si-0) and two neutron-irradiated ones labeled Si-2 and Si-4. The irradiation with fast (E'0.1 MeV) neutrons up to doses of 1.7 and 3.2;10 n/cm respectively, was carried out at the BR2 reactor of the Belgian Nuclear Research Center (SCKzCEN) in Mol, Belgium.
153
From earlier reported Raman scattering experiments, the neutron irradiation is seen to introduce amorphous regions into the silicon, leading to an amorphous volume fraction of at least 3.7% and 4.1%, respectively [5]. For the performance of ultrasonic measurements on these partly amorphous samples, a piezo-electric LiNbO transducer with a ground frequency of 30 MHz was attached to one end of the sample by means of a very thin layer of DC 200 Si fluid. Measurements of *v/v were performed at frequencies of approximately 160 and 290 MHz, at temperatures between 0.3 and 30 K.
3. Results and discussion Fig. 1 shows the results obtained from measurements of *v/v for the unirradiated silicon and the
Fig. 1. Changes in ultrasonic velocity as a function of temperature for unirradiated crystalline silicon and silicon irradiated with different neutron doses.
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M. Coeck et al. / Physica B 263—264 (1999) 152—155
Fig. 2. Influence of the frequency of the ultrasonic wave on the ultrasonic velocity changes in neutron irradiated silicon.
two irradiated samples Si-2 and Si-4. The curves were obtained for similar frequencies around 290 MHz. The unirradiated sample shows a typical crystalline behavior, while for the irradiated samples an additional effect is observed. This effect involves a logarithmic increase, followed by a maximum and a logarithmic decrease. The influence of the frequency of the ultrasonic wave is presented in Fig. 2. As can be seen from this figure, the logarithmic increase at low temperatures is frequency-independent. These observations are in agreement with the predictions of the tunneling model. Furthermore, the additional effect is more pronounced for higher neutron doses. These results, together with the ones obtained from ultrasonic attenuation measurements performed on Si-4 [6], give evidence for the fact that TS can be introduced in high coordinated materials by means of fast-neutron irradiation. The fact that the logarithmic slope at low temperatures is steeper
Table 1 Tunneling parameters derived from numerical fits on experimental data presented in Figs. 1 and 2 Velocity measurements performed on sample: Neutron dose: (n/cm) (E'0.1 MeV)
Si-2
Si-4
1.7;10
3.2;10
Frequency (MHz) C (&10\) K (&10 K\ s\) Pc (&10 g cm\ s\) c(eV) P (&10 erg\ cm\)
296 3.5 16 5.8 1.8 6.8
288 5 23 8.3 2.2 6.8
for a sample irradiated with a higher dose indicates that the DOS of the TS (P) is higher. From numerical fits, based on the formulas of the tunneling model, the typical tunneling parameters were derived. The results are listed in Table 1.
M. Coeck et al. / Physica B 263—264 (1999) 152—155
Although the measured differences were very small, of the order of 10\, it was possible to obtain a theoretical curve which was very close to the experimental one and the outcome of the fits is consistent for the different experiments. Since it can be directly derived from the slope of the logarithmic increase of *v/v below 2 K, the parameter C is a very reliable value giving information on the DOS of the TS. The value of C is higher for higher neutron doses. The relatively high value of the coupling constant c , compared to values obtained in amorphous solids such as a-SiO , is explained in the framework of the soft potential model where it can be attributed to the high value of the sound velocity in silicon. The fact that the calculated values show no difference in P for Si-2 and Si-4 is because of the fact that the maximum of the curve is difficult to fit, leading to an inaccuracy of K . 4. Conclusion It is shown that, due to neutron irradiation, tunneling states can be introduced in highly coordinated silicon by means of fast-neutron irradiation. The DOS of these TS increases with increasing neutron dose. From Raman scattering experiments it could be concluded that fast-neutron irradiation also induced amorphous regions in silicon. The volume fraction of these regions also
155
increases with increasing neutron dose. Therefore we conclude that the induce TS are related to these amorphous regions, and are probably located in these regions.
Acknowledgements The authors wish to thank B. Ponsard and J. Vermunt of the department BR2 of the Belgian Nuclear Research Center for the irradiation of the silicon samples. They are also grateful to the Belgian FWO for financial support.
References [1] P.W. Anderson, B.I. Halperin, C.M. Varma, Phil. Mag. 25 (1972) 1. [2] V. Keppens, C. Laermans, Phys. Rev. B 51 (1995) 8158. [3] B. Golding, J.E. Graebner, W.H. Haemmerle, in: W.E. Spaer (Ed.), Amorphous and Liquid Semiconductors, Center for Industrial Consultancy and Liaison, University of Edinburgh, Edinburgh, 1977, p. 367. [4] M. von Haumeder, U. Strom, S. Hunklinger, Phys. Rev. Lett. 44 (1980) 84. [5] M. Coeck, C. Laermans, R. Provoost, R.E. Silverans, Mater. Sci. Forum 258—263 (1997) 623. [6] M. Coeck, C. Laermans, E. Peeters, Nucl. Instr. and Meth. B 141 (1998) 585. [7] W.A. Philips, J. Low Temp. Phys. 7 (1972) 351. [8] J.E. Graebner, L.C. Allen, Phys. Rev. B 29 (1984) 5626.
Ultrasonic velocity changes in bulk neutron-disordered silicon M. Coeck , C. Laermans *, E. Peeters Katholieke Universiteit Leuven, Department of Physics, Celestijnenlaan 200 D, B-3001 Heverlee, Belgium SCKzCEN, Dept. BR2, Boeretang 200, B-2400 Mol, Belgium
Abstract Measurements of the changes in ultrasonic velocity were performed on bulk single-crystalline silicon irradiated with fast-neutron doses up to 1.7;10 and 3.2;10 n/cm (E'0.1 MeV). Compared to the unirradiated material, a large additional effect is observed at low temperatures the behavior of which is similar to the predictions of the tunneling model. Together with results previously obtained from attenuation measurements and Raman spectroscopy, this result puts the presence of tunneling states in high coordinated bulk silicon clearly in evidence. 1999 Elsevier Science B.V. All rights reserved. Keywords: Tunneling states; Low temperatures; Neutron irradiation; Disordered silicon
1. Introduction During the past few decades several experiments have shown that glasses exhibit universal properties which differ from those in crystals. Below a few Kelvin this anomalous behavior can be very well described by the tunneling model [1,7], postulating the presence of low-energy excitations called tunneling states (TS). These are atoms or groups of atoms which can have two equilibrium positions and can therefore quantum mechanically tunnel in a double asymmetric potential well. They have a wide distribution of energies and relaxation times and appear with an almost constant density of
* Corresponding author. Tel.: #32-16-327185; fax: #32-16327987; e-mail: [email protected]. Now at SRON, P.O. Box 800, NL-9700 AV Groningen, The Netherlands.
states. It was first believed that these TS could only occur in typical glass-forming amorphous solids having a low average coordination of the individual atoms. Also in partly disordered low-coordinated solids such as neutron-irradiated quartz, TS have been observed [2]. The presence of TS in higher coordinated materials such as silicon or germanium is however controversial. Both affirming [3] and denying [4,8] arguments concerning the presence of TS in these high coordinated materials were reported. In order to contribute to this discussion and to explore the possibility of the presence of these states in topologically higher constrained disordered solids, we have performed low-temperature ultrasonic measurements in bulk neutron-irradiated silicon single crystals. In this paper we present the results obtained from measurements of the changes in ultrasonic (&0.1 GHz) velocity (*v/v) as a function of temperature (0.3—30 K). Our measurements
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 2 1 0 - 1
M. Coeck et al. / Physica B 263—264 (1999) 152—155
show a pronounced difference between the behavior of the irradiated and the unirradiated material. Furthermore, the irradiated material shows a remarkable similarity with the predictions of the tunneling model, putting in evidence the possibility of the introduction of TS in high coordinated materials.
2. Sample description and experimental details Measurements were carried out on bulk, singlecrystalline silicon, one unirradiated sample (labeled Si-0) and two neutron-irradiated ones labeled Si-2 and Si-4. The irradiation with fast (E'0.1 MeV) neutrons up to doses of 1.7 and 3.2;10 n/cm respectively, was carried out at the BR2 reactor of the Belgian Nuclear Research Center (SCKzCEN) in Mol, Belgium.
153
From earlier reported Raman scattering experiments, the neutron irradiation is seen to introduce amorphous regions into the silicon, leading to an amorphous volume fraction of at least 3.7% and 4.1%, respectively [5]. For the performance of ultrasonic measurements on these partly amorphous samples, a piezo-electric LiNbO transducer with a ground frequency of 30 MHz was attached to one end of the sample by means of a very thin layer of DC 200 Si fluid. Measurements of *v/v were performed at frequencies of approximately 160 and 290 MHz, at temperatures between 0.3 and 30 K.
3. Results and discussion Fig. 1 shows the results obtained from measurements of *v/v for the unirradiated silicon and the
Fig. 1. Changes in ultrasonic velocity as a function of temperature for unirradiated crystalline silicon and silicon irradiated with different neutron doses.
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M. Coeck et al. / Physica B 263—264 (1999) 152—155
Fig. 2. Influence of the frequency of the ultrasonic wave on the ultrasonic velocity changes in neutron irradiated silicon.
two irradiated samples Si-2 and Si-4. The curves were obtained for similar frequencies around 290 MHz. The unirradiated sample shows a typical crystalline behavior, while for the irradiated samples an additional effect is observed. This effect involves a logarithmic increase, followed by a maximum and a logarithmic decrease. The influence of the frequency of the ultrasonic wave is presented in Fig. 2. As can be seen from this figure, the logarithmic increase at low temperatures is frequency-independent. These observations are in agreement with the predictions of the tunneling model. Furthermore, the additional effect is more pronounced for higher neutron doses. These results, together with the ones obtained from ultrasonic attenuation measurements performed on Si-4 [6], give evidence for the fact that TS can be introduced in high coordinated materials by means of fast-neutron irradiation. The fact that the logarithmic slope at low temperatures is steeper
Table 1 Tunneling parameters derived from numerical fits on experimental data presented in Figs. 1 and 2 Velocity measurements performed on sample: Neutron dose: (n/cm) (E'0.1 MeV)
Si-2
Si-4
1.7;10
3.2;10
Frequency (MHz) C (&10\) K (&10 K\ s\) Pc (&10 g cm\ s\) c(eV) P (&10 erg\ cm\)
296 3.5 16 5.8 1.8 6.8
288 5 23 8.3 2.2 6.8
for a sample irradiated with a higher dose indicates that the DOS of the TS (P) is higher. From numerical fits, based on the formulas of the tunneling model, the typical tunneling parameters were derived. The results are listed in Table 1.
M. Coeck et al. / Physica B 263—264 (1999) 152—155
Although the measured differences were very small, of the order of 10\, it was possible to obtain a theoretical curve which was very close to the experimental one and the outcome of the fits is consistent for the different experiments. Since it can be directly derived from the slope of the logarithmic increase of *v/v below 2 K, the parameter C is a very reliable value giving information on the DOS of the TS. The value of C is higher for higher neutron doses. The relatively high value of the coupling constant c , compared to values obtained in amorphous solids such as a-SiO , is explained in the framework of the soft potential model where it can be attributed to the high value of the sound velocity in silicon. The fact that the calculated values show no difference in P for Si-2 and Si-4 is because of the fact that the maximum of the curve is difficult to fit, leading to an inaccuracy of K . 4. Conclusion It is shown that, due to neutron irradiation, tunneling states can be introduced in highly coordinated silicon by means of fast-neutron irradiation. The DOS of these TS increases with increasing neutron dose. From Raman scattering experiments it could be concluded that fast-neutron irradiation also induced amorphous regions in silicon. The volume fraction of these regions also
155
increases with increasing neutron dose. Therefore we conclude that the induce TS are related to these amorphous regions, and are probably located in these regions.
Acknowledgements The authors wish to thank B. Ponsard and J. Vermunt of the department BR2 of the Belgian Nuclear Research Center for the irradiation of the silicon samples. They are also grateful to the Belgian FWO for financial support.
References [1] P.W. Anderson, B.I. Halperin, C.M. Varma, Phil. Mag. 25 (1972) 1. [2] V. Keppens, C. Laermans, Phys. Rev. B 51 (1995) 8158. [3] B. Golding, J.E. Graebner, W.H. Haemmerle, in: W.E. Spaer (Ed.), Amorphous and Liquid Semiconductors, Center for Industrial Consultancy and Liaison, University of Edinburgh, Edinburgh, 1977, p. 367. [4] M. von Haumeder, U. Strom, S. Hunklinger, Phys. Rev. Lett. 44 (1980) 84. [5] M. Coeck, C. Laermans, R. Provoost, R.E. Silverans, Mater. Sci. Forum 258—263 (1997) 623. [6] M. Coeck, C. Laermans, E. Peeters, Nucl. Instr. and Meth. B 141 (1998) 585. [7] W.A. Philips, J. Low Temp. Phys. 7 (1972) 351. [8] J.E. Graebner, L.C. Allen, Phys. Rev. B 29 (1984) 5626.