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Energy loss and equilibrium charge distribution of nitrogen ions transmitted through thin silicon crystals
Nuclear Instruments and Methods in Physics Research B80/81 (1993) 33-36 North-Holland
HON B
Besam Intencttons with Materials iAtoms
Energy loss and equilibrium charge distribution of nitrogen ions transmitted through thin silicon crystals G.G . Bentini
l,
M . Bianconi and R. Nipoti
CNR - Istituto LAMEL, Via Castagnoli 1, 1-40126Bologna, Italy
Transmission experiments of 1 .0-1 .8 MeV N ` ions through thin Si crystals in random, (100) and (110) alignment geometries were performed . An electromagnetic analyser was used to simultaneously measure the charge distribution and the energy of the transmitted beams . The emerging ions had charge values ranging from 0 to 4 and equal average energy. Stopping power data were collected in both random and channe ing geometries using samples with thickness ranging from 0 .2 to 0 .5 g. :n . The mean and the effective charge values of the transmitted ions were found to agree with the charge and the effective charge values calculated by the model of Brandt and Kitagawa [Phys. Rev. B25 (1982) 5631) . 1. Introduction A renewed interest in stopping power and straggling measurements in the MeV region has been stimulated by the advent of high-energy ion implantation. This energy region corresponds to the so-called intermediate region for many ions like those used in standard implantation processes such as N. O and B . In this region, where the ion velocity (u) is higher than the Bohr velocity, uo , but lower than T.Z13 uo, where Z is the projectile atomic number, the theories fail in describing the energy loss process [1]. In the intermediate region the ar.Jastic (i.e . electronic) stopping power dominates over the elastic (i.e . nuclear) one . The interaction between the ion and th° medium electrons depends on the ion charge value (q) which dynamically changes inside the crystal because of the continuous exchange process of the electrons with the medium . The statistical nature of the phenomenon produces ions having a charge distribution F(q) characterized by a mean value q = EQgF(q). As the ion charge distribution can be measured only outside the sample, the corresponding average value will be indicated by q* . This value should be compared with the effective charge of the ions, Zeff, as computed by the scaling rule Zeff = (SP/S,)1/2, where S P and S H are the projectile -tnd the hydrogen electronic stopping power, respectively [2] . Usually the experiments performed with solid targets show tnat Zeff differs from q*. Assuming q = q *, Zeff values higher than q * have been attributed either to zr increased interaction due Present address: Addetto Scientifico, Ambasciata d'italia, Calle Lagasca 98, 28006 Madrid, Spain .
to close collisions [3] or to the energy lost in the charge exchange process [4] . Zeff values lower than q* have been attributed to an Auger process taking place at the exit surface of the sample [5]; in this case it should be
q
In this work transmission of 1 .0-1 .8 MeV N' ions through thin Si samples in random and channeling geometries were studied . The use of an electromagnetic analyser allowed ii .c si-nultaneous determination of q* and the energy loss (i .e. Zeff) of the transmitted ions. The discussion of the experimental data will give a contribution to some basic questions still open . In particular (a) relationship between the energy lost by an ion and its charge state ; (b) relationship between 3, q* and Ztff ; (c) effect of the electronic density on the previous points (i .e . comparison between random and channeling experiments). 2 . Experimental The experiments were carried out by the 2 MV Van de Graaff facility of the Laboratori Nazionali di Legnaro (INFN, Padova, Italy). He's and N + beams were selected by the analyzing magnet, collimated and delivered onto the samples . An electromagnetic analyser (EMA) was placed about 3 m behind the sample chamber and aligned with the axis along the direction of the primary beam. Its acceptance angle, 0, was 0 .005°. The EMA magnetic field (B) was constant while the perpendicular electric field (E) could be varied. The filter axis was always kept at zero potential . It is important to point out that when u = E/B, all the ions travel along the axis of the filter, whereas for u * EIB the ions spread
0168-583X/93/$06.00 0 1993 - Elsevier Science Publishers B.V . All rights reserved
1ü. isASIC INTERACTIONS (a)
34
G. G. Bentini et al. / Transmission of Niora through thin Si crystals
over different trajectorizs depending or. their charge state . Two surface barrier detectors were used as counters. One was placed on-axis to measure the ratio of the total charged fraction (Eq ,nFq ) to the neutral fraction (Fn ). The other was placed off-axis and allowed the measurement of both the energy and the relative charged fraction ratio (Fq ,r/FI). The output of each detector was delivered to a multichannel analyser working in the MCS mode and synchronized with the EMA variable electric field . In the experimental spectra, the yield of each channel represented the number of ion collected at the corresponding voltage. The x-scale calibration (energy to voltage) was performed by using direct monoenergetic beams. In the case of N ions the energy could be determined with a maximum error of about 1% and a rms energy resolution ranging from 0.8 to 3 keV depending on the energy and the charge state values. The samples for the transmission experiments were thin (0.2-0 .5 wm) self-supported Si single crystals, prepared by the "boron diffusion technique" developed at the Physics Institute of the Aarhus University. The thickness of the samples was determined by He' Rutherford backscattering spectrometry (RBS) measurements, where the tabulated stopping power data for He in ref. [6] were used . The thickness homogeneity of the Si samples, inside the beam area (0.3 x 0.3 mm), has been evaluated by the RBS spectra to be about 1% . 3. Results and discussion Fig . 1 shows some significative spectra collected off-axis (figs . la-1c) and on-axis (figs. Id-If). In both cases the spectra obtained in random, (100) and (110) geometries are shown, as indicated inside the figures . The off-axis spectra correspond to a primary N + beam of 1 .8 MeV transmitted through a 0.45 Run silicon sample ; the peaks are due to different charge states, as labeled in fig. l a. For every off-axis spectrum it was possibl-- to find at least one or more charge states having the energy distribution well separated from the others In this case the mean value of the energy distribution of the ions could be determined. As for the sp-ctra on-axis the primary beam had energy equal to 1 .2 MeV. The constant background was produced by the neutral fraction (q = 0) of the transmitted beam, which was unaffected by the variable electric field, while the peak was generated by the overlap of the charged components in the analysed beam. Both the on-axis and off-axis spectra were necessary to obtain the charge state distribution. Fig . 2 shows the mean energy (Eoa ) of the transmitted ions with different charge state versus the primary beam energy (E;n) for the (100) geometry and two different sample thicknesses. It can be seen that, within
3 , 2 i
~
Rand .
(a)
:Ja . 1n r-rr~TT. =
:
(b)
-
1: 3 .0
3 .5
4 .0
1 .5
Electric Field (KV/ein) Fig . 1 . Typical EMA spectra obtained for N ions transmitted through a 0 .45 Wm Si crystal along different orientations as indicated inside the figures. The spectra (a)-(c) were collected off-axis; spectra (d)-(f) were collected on-axis . The energy of the pri- y beam was 1 .8 and t .2 MeV for the former and the latter :.pectra, respectively. The peaks in the off-axis spectra correspond to different charge states as ipdicated in (a). the experimental errors, the transmitted ions had the same energy independently of the charge state . Similar figures could be drawn for the random geometry and
Fig . 2. Mean energy of the transmitted N ions versus the primary beam energy for different emerging charge states. The data were obtained with two samples of different thickness (100) oriented.
G. G. Bentini et al. / Transmission of N tons through thin Si crystals
35
0.5 0 .4
0 .2
0 .0 1 0 .6
E (MeV)
Fig. 3 . Experimental random and channeling stopping power for N in Si versus the ion energy . The continuous lines are the fits of the present data. the dashed line is the fit of the random data of ref. [FJ.
for all the sample thicknesses between 0.2-0 .5 p.m. These results demonstrate that in all the random and (100) experiments the statistical equilibrium in the charge exchange process between the ion and the medium was reached. Mean energy values were also computed for the peaks collected in the (110) orientation, but care must be taken in using them . In fact, the large spread of the energy distribution (see fig . lc) could indicate that, in spite of the very low acceptance angle, the EMA collected ions which travelled along very different trajectories inside the channel [7j. Fig . 3 shows the experimental random and channeling stopping power dE/dx of nitrogen in silicon versus the average ion energy, as obtained by samples of different thickness. The plotted data are calculated by assuming E=(Ei +E, )/2 and dE/dx=AE/Ax, where AE=(Ei -E..,) is the energy loss and Ax is the sample thickness. The main source of error in the stopping power measurements is the determination of the sample thickness. As this was obtained by RBS, the thickness values are affected by the uncertainties of the tabulated :;topping data (10%). The continuous curves are the fits of the nresent data, whereas the dashed curve is the fit of the random data of ref. [81. The agreement between the measurements performed with different detection systems is satisfactory . The (100) channeling data of r ,f. [bl, not shown in the figure, obtained for an acceptance angle 0 = t/rr were close to the random values, where t#, is the critical angle for axial channeling . In the present measurements the <100) channeling data show a significant reduction in the energy loss, since only hyperchanneled (0 ~ 0,) trajectories were selected . The (110) data are similar
1
~~---C 0 .8
1 .(
sa
0 -
E_t (MeV)
i
1 .2
Fig. 4. Charge di-iribution of N ions transmitted in random (open symbols) and (106) (full symbols) alignment versus the emerging energy. For every charge state a single curve can be drawn for both the random and the channeling data. Close to each line the corresponding charge value is reported. to those of ref. [8], but, as already discussed, they cannot be considered conclusive . The evaluation of the charge state distribution was complicated by the overlap among the peaks, especially at the lower energies . In order to overcome this p~oblem a Monte Carlo programme wan written to simulate the spectrum obtained for a given energy and charge distribution entering the EMA . Fig . 4 shows the charge state distribution, F(q*), of N ions transmitted in random and (100) alignment versus the transmitted energy, Eom . In the case of the (110) orientation the overlap among the peaks was too large to obtain
E (~~1eV )
Fig . 5. Effective and average charge of N ions transmitted through St. Random (open symbols) and (100) (full symbols) dnio arc shown. The effective and the average charge as calculated by the mode; of ûtaudt and Kuagawa [2,3J are reported by the dashed and continuous line, respeethelv. Ia . BASIC INTERACTIONS (a)
36
G.G. Bentini et al. / Transmission of Nions through thin Si crystals
straightforward information . It must be remarked that negative charges were never detected . As the experimental error on F(q*), accounting for sample to sample reproducibility, was estimated to be about ±0 .025, for every charge state a single curve can be drawn for both the random and the channeling data. Hence, the measured charge distribution is a function of the ion velocity only and it is independent of the electronic density of the crossed medium . This is a further confirmation that the statistical equilibrium in the charge exchange process was reached . In fig . 5 the average charge q* as obtained from the data of fig. 4 is plotted versus the output energy. The effective charge Zett, as obtained by the random stopping values scaled on the H stopping values of ref. [9], is shown for comparison. Our results are consistent with the calculation of the effective charge (dashed line) and the mean charge inside the samples (solid line) reported in ref. [2] based on the theory proposed by Brandt and Mtagawa [3]. In this picture q* is well rcp-esented by q, suggesting that any charge exchange effect (such as Auger de-excitation) took place at the exit surface of the sample . The quite good agreement of the Zett with the model supports tire thesis that close collisions increase the ion-medium interaction. 4 . Conclusion The use of a detection system suitable for the simultaneous measurement of both the energy and the charge state of ions transmitted through thin crystals provided information on the relationships between the stopping power, the charge and the effective charge of ions in the condensed matter. In particular, it has been evidenced that, once the :statistical equilibrium in the charge exchange process is reached, the energy lost by each transmitted ion is
independent of its emerging charge state. Furthermore, the charge state distribution of the transmitted particles depends only on their velocity and it is independent of the electronic density of the medium . As in the experimental conditions of this paper the average ion charge outside the sample is well represented by an analytical description of the average ion charge inside the sample [3], it can be assumed that any important effect, changing the charge state distribution takes place at the exit sample surf.ce. As for the Zoff measurement, the agreement with the model of Brandt and Kitagawa [3] is quite satisfactory. Acknowledgements This work was financially suppo-tc.d by the CEE Contract no . SCI *-0326-C. The authors thank Dr. F. Malaguti for the Si samples . References [1] A . Cruz, Radiat. Eff. 88 (1986) 159 . [2] J .F . Ziegler, J.P. Biersack and U . Limnark, The Stopping and Range of Ions in Salids, vol. 1 (Pergaman, New York, 1985). [31 W. Brandt and M . Kitagawa, Phys . Rev. B25 (1982) 5631 . (4] A. Arnau, M. Penalba, P .M. Echenique, F. Flores and R.H. Ritchie, Phys. Rev. Lett. 8 (1990) 1024. [5] H.D. Betz, Rev. Mod. Phys. 44 (1972) 465. [6] J .F. Ziegler, Helium: Stopping Powers and Ranges in All Elements (Pergamon, New York, 1977). [71 S. Datz, B.R. Appleton and C.D. Moak, in Channeling, Theory, Observation and Application, ed . D.V. Morgan (Wiley. London, 1973) p. 159. [8] G .G . Bentini, M. Bianconi, R. Nipoti, F. Malaguti and E. Verondini, Nucl. Instr . and Meth . B53 (1991) 1 . (91 A. Carnera, G . Delta Mea, A .V. Drigo, S . Lo Russo, P. Mazzoldi and G .G. Bentini, Phys. Rev. B17 (1978) 3492 .
HON B
Besam Intencttons with Materials iAtoms
Energy loss and equilibrium charge distribution of nitrogen ions transmitted through thin silicon crystals G.G . Bentini
l,
M . Bianconi and R. Nipoti
CNR - Istituto LAMEL, Via Castagnoli 1, 1-40126Bologna, Italy
Transmission experiments of 1 .0-1 .8 MeV N ` ions through thin Si crystals in random, (100) and (110) alignment geometries were performed . An electromagnetic analyser was used to simultaneously measure the charge distribution and the energy of the transmitted beams . The emerging ions had charge values ranging from 0 to 4 and equal average energy. Stopping power data were collected in both random and channe ing geometries using samples with thickness ranging from 0 .2 to 0 .5 g. :n . The mean and the effective charge values of the transmitted ions were found to agree with the charge and the effective charge values calculated by the model of Brandt and Kitagawa [Phys. Rev. B25 (1982) 5631) . 1. Introduction A renewed interest in stopping power and straggling measurements in the MeV region has been stimulated by the advent of high-energy ion implantation. This energy region corresponds to the so-called intermediate region for many ions like those used in standard implantation processes such as N. O and B . In this region, where the ion velocity (u) is higher than the Bohr velocity, uo , but lower than T.Z13 uo, where Z is the projectile atomic number, the theories fail in describing the energy loss process [1]. In the intermediate region the ar.Jastic (i.e . electronic) stopping power dominates over the elastic (i.e . nuclear) one . The interaction between the ion and th° medium electrons depends on the ion charge value (q) which dynamically changes inside the crystal because of the continuous exchange process of the electrons with the medium . The statistical nature of the phenomenon produces ions having a charge distribution F(q) characterized by a mean value q = EQgF(q). As the ion charge distribution can be measured only outside the sample, the corresponding average value will be indicated by q* . This value should be compared with the effective charge of the ions, Zeff, as computed by the scaling rule Zeff = (SP/S,)1/2, where S P and S H are the projectile -tnd the hydrogen electronic stopping power, respectively [2] . Usually the experiments performed with solid targets show tnat Zeff differs from q*. Assuming q = q *, Zeff values higher than q * have been attributed either to zr increased interaction due Present address: Addetto Scientifico, Ambasciata d'italia, Calle Lagasca 98, 28006 Madrid, Spain .
to close collisions [3] or to the energy lost in the charge exchange process [4] . Zeff values lower than q* have been attributed to an Auger process taking place at the exit surface of the sample [5]; in this case it should be
q
In this work transmission of 1 .0-1 .8 MeV N' ions through thin Si samples in random and channeling geometries were studied . The use of an electromagnetic analyser allowed ii .c si-nultaneous determination of q* and the energy loss (i .e. Zeff) of the transmitted ions. The discussion of the experimental data will give a contribution to some basic questions still open . In particular (a) relationship between the energy lost by an ion and its charge state ; (b) relationship between 3, q* and Ztff ; (c) effect of the electronic density on the previous points (i .e . comparison between random and channeling experiments). 2 . Experimental The experiments were carried out by the 2 MV Van de Graaff facility of the Laboratori Nazionali di Legnaro (INFN, Padova, Italy). He's and N + beams were selected by the analyzing magnet, collimated and delivered onto the samples . An electromagnetic analyser (EMA) was placed about 3 m behind the sample chamber and aligned with the axis along the direction of the primary beam. Its acceptance angle, 0, was 0 .005°. The EMA magnetic field (B) was constant while the perpendicular electric field (E) could be varied. The filter axis was always kept at zero potential . It is important to point out that when u = E/B, all the ions travel along the axis of the filter, whereas for u * EIB the ions spread
0168-583X/93/$06.00 0 1993 - Elsevier Science Publishers B.V . All rights reserved
1ü. isASIC INTERACTIONS (a)
34
G. G. Bentini et al. / Transmission of Niora through thin Si crystals
over different trajectorizs depending or. their charge state . Two surface barrier detectors were used as counters. One was placed on-axis to measure the ratio of the total charged fraction (Eq ,nFq ) to the neutral fraction (Fn ). The other was placed off-axis and allowed the measurement of both the energy and the relative charged fraction ratio (Fq ,r/FI). The output of each detector was delivered to a multichannel analyser working in the MCS mode and synchronized with the EMA variable electric field . In the experimental spectra, the yield of each channel represented the number of ion collected at the corresponding voltage. The x-scale calibration (energy to voltage) was performed by using direct monoenergetic beams. In the case of N ions the energy could be determined with a maximum error of about 1% and a rms energy resolution ranging from 0.8 to 3 keV depending on the energy and the charge state values. The samples for the transmission experiments were thin (0.2-0 .5 wm) self-supported Si single crystals, prepared by the "boron diffusion technique" developed at the Physics Institute of the Aarhus University. The thickness of the samples was determined by He' Rutherford backscattering spectrometry (RBS) measurements, where the tabulated stopping power data for He in ref. [6] were used . The thickness homogeneity of the Si samples, inside the beam area (0.3 x 0.3 mm), has been evaluated by the RBS spectra to be about 1% . 3. Results and discussion Fig . 1 shows some significative spectra collected off-axis (figs . la-1c) and on-axis (figs. Id-If). In both cases the spectra obtained in random, (100) and (110) geometries are shown, as indicated inside the figures . The off-axis spectra correspond to a primary N + beam of 1 .8 MeV transmitted through a 0.45 Run silicon sample ; the peaks are due to different charge states, as labeled in fig. l a. For every off-axis spectrum it was possibl-- to find at least one or more charge states having the energy distribution well separated from the others In this case the mean value of the energy distribution of the ions could be determined. As for the sp-ctra on-axis the primary beam had energy equal to 1 .2 MeV. The constant background was produced by the neutral fraction (q = 0) of the transmitted beam, which was unaffected by the variable electric field, while the peak was generated by the overlap of the charged components in the analysed beam. Both the on-axis and off-axis spectra were necessary to obtain the charge state distribution. Fig . 2 shows the mean energy (Eoa ) of the transmitted ions with different charge state versus the primary beam energy (E;n) for the (100) geometry and two different sample thicknesses. It can be seen that, within
3 , 2 i
~
Rand .
(a)
:Ja . 1n r-rr~TT. =
:
(b)
-
1: 3 .0
3 .5
4 .0
1 .5
Electric Field (KV/ein) Fig . 1 . Typical EMA spectra obtained for N ions transmitted through a 0 .45 Wm Si crystal along different orientations as indicated inside the figures. The spectra (a)-(c) were collected off-axis; spectra (d)-(f) were collected on-axis . The energy of the pri- y beam was 1 .8 and t .2 MeV for the former and the latter :.pectra, respectively. The peaks in the off-axis spectra correspond to different charge states as ipdicated in (a). the experimental errors, the transmitted ions had the same energy independently of the charge state . Similar figures could be drawn for the random geometry and
Fig . 2. Mean energy of the transmitted N ions versus the primary beam energy for different emerging charge states. The data were obtained with two samples of different thickness (100) oriented.
G. G. Bentini et al. / Transmission of N tons through thin Si crystals
35
0.5 0 .4
0 .2
0 .0 1 0 .6
E (MeV)
Fig. 3 . Experimental random and channeling stopping power for N in Si versus the ion energy . The continuous lines are the fits of the present data. the dashed line is the fit of the random data of ref. [FJ.
for all the sample thicknesses between 0.2-0 .5 p.m. These results demonstrate that in all the random and (100) experiments the statistical equilibrium in the charge exchange process between the ion and the medium was reached. Mean energy values were also computed for the peaks collected in the (110) orientation, but care must be taken in using them . In fact, the large spread of the energy distribution (see fig . lc) could indicate that, in spite of the very low acceptance angle, the EMA collected ions which travelled along very different trajectories inside the channel [7j. Fig . 3 shows the experimental random and channeling stopping power dE/dx of nitrogen in silicon versus the average ion energy, as obtained by samples of different thickness. The plotted data are calculated by assuming E=(Ei +E, )/2 and dE/dx=AE/Ax, where AE=(Ei -E..,) is the energy loss and Ax is the sample thickness. The main source of error in the stopping power measurements is the determination of the sample thickness. As this was obtained by RBS, the thickness values are affected by the uncertainties of the tabulated :;topping data (10%). The continuous curves are the fits of the nresent data, whereas the dashed curve is the fit of the random data of ref. [81. The agreement between the measurements performed with different detection systems is satisfactory . The (100) channeling data of r ,f. [bl, not shown in the figure, obtained for an acceptance angle 0 = t/rr were close to the random values, where t#, is the critical angle for axial channeling . In the present measurements the <100) channeling data show a significant reduction in the energy loss, since only hyperchanneled (0 ~ 0,) trajectories were selected . The (110) data are similar
1
~~---C 0 .8
1 .(
sa
0 -
E_t (MeV)
i
1 .2
Fig. 4. Charge di-iribution of N ions transmitted in random (open symbols) and (106) (full symbols) alignment versus the emerging energy. For every charge state a single curve can be drawn for both the random and the channeling data. Close to each line the corresponding charge value is reported. to those of ref. [8], but, as already discussed, they cannot be considered conclusive . The evaluation of the charge state distribution was complicated by the overlap among the peaks, especially at the lower energies . In order to overcome this p~oblem a Monte Carlo programme wan written to simulate the spectrum obtained for a given energy and charge distribution entering the EMA . Fig . 4 shows the charge state distribution, F(q*), of N ions transmitted in random and (100) alignment versus the transmitted energy, Eom . In the case of the (110) orientation the overlap among the peaks was too large to obtain
E (~~1eV )
Fig . 5. Effective and average charge of N ions transmitted through St. Random (open symbols) and (100) (full symbols) dnio arc shown. The effective and the average charge as calculated by the mode; of ûtaudt and Kuagawa [2,3J are reported by the dashed and continuous line, respeethelv. Ia . BASIC INTERACTIONS (a)
36
G.G. Bentini et al. / Transmission of Nions through thin Si crystals
straightforward information . It must be remarked that negative charges were never detected . As the experimental error on F(q*), accounting for sample to sample reproducibility, was estimated to be about ±0 .025, for every charge state a single curve can be drawn for both the random and the channeling data. Hence, the measured charge distribution is a function of the ion velocity only and it is independent of the electronic density of the crossed medium . This is a further confirmation that the statistical equilibrium in the charge exchange process was reached . In fig . 5 the average charge q* as obtained from the data of fig. 4 is plotted versus the output energy. The effective charge Zett, as obtained by the random stopping values scaled on the H stopping values of ref. [9], is shown for comparison. Our results are consistent with the calculation of the effective charge (dashed line) and the mean charge inside the samples (solid line) reported in ref. [2] based on the theory proposed by Brandt and Mtagawa [3]. In this picture q* is well rcp-esented by q, suggesting that any charge exchange effect (such as Auger de-excitation) took place at the exit surface of the sample . The quite good agreement of the Zett with the model supports tire thesis that close collisions increase the ion-medium interaction. 4 . Conclusion The use of a detection system suitable for the simultaneous measurement of both the energy and the charge state of ions transmitted through thin crystals provided information on the relationships between the stopping power, the charge and the effective charge of ions in the condensed matter. In particular, it has been evidenced that, once the :statistical equilibrium in the charge exchange process is reached, the energy lost by each transmitted ion is
independent of its emerging charge state. Furthermore, the charge state distribution of the transmitted particles depends only on their velocity and it is independent of the electronic density of the medium . As in the experimental conditions of this paper the average ion charge outside the sample is well represented by an analytical description of the average ion charge inside the sample [3], it can be assumed that any important effect, changing the charge state distribution takes place at the exit sample surf.ce. As for the Zoff measurement, the agreement with the model of Brandt and Kitagawa [3] is quite satisfactory. Acknowledgements This work was financially suppo-tc.d by the CEE Contract no . SCI *-0326-C. The authors thank Dr. F. Malaguti for the Si samples . References [1] A . Cruz, Radiat. Eff. 88 (1986) 159 . [2] J .F . Ziegler, J.P. Biersack and U . Limnark, The Stopping and Range of Ions in Salids, vol. 1 (Pergaman, New York, 1985). [31 W. Brandt and M . Kitagawa, Phys . Rev. B25 (1982) 5631 . (4] A. Arnau, M. Penalba, P .M. Echenique, F. Flores and R.H. Ritchie, Phys. Rev. Lett. 8 (1990) 1024. [5] H.D. Betz, Rev. Mod. Phys. 44 (1972) 465. [6] J .F. Ziegler, Helium: Stopping Powers and Ranges in All Elements (Pergamon, New York, 1977). [71 S. Datz, B.R. Appleton and C.D. Moak, in Channeling, Theory, Observation and Application, ed . D.V. Morgan (Wiley. London, 1973) p. 159. [8] G .G . Bentini, M. Bianconi, R. Nipoti, F. Malaguti and E. Verondini, Nucl. Instr . and Meth . B53 (1991) 1 . (91 A. Carnera, G . Delta Mea, A .V. Drigo, S . Lo Russo, P. Mazzoldi and G .G. Bentini, Phys. Rev. B17 (1978) 3492 .