- Email: [email protected]
Defect production by MeV cluster impacts
cw
Nuclear Instruments
and Methods in Physics Research B 106 (1995) 43-46
-_
__
Beam Interactions with Materials 6 Atoms
!!I!! ELSEVIER
Defect production by MeV cluster impacts
*,
M. DSbeli a* F. Ames b, R.M. Ender b, M. Suter b, H.A. Synal a, D. Vetterli b a Paul Scherrer Institute c/o ETH-HSnggerberg, b Institute of Particle Physics, ETH-Hanggerberg,
CH-8093 Ziirich, Switzerland CH-8093 Ziirich, Switzerland
Abstract Monocrystalline silicon has been irradiated by MeV carbon and germanium clusters (C”, it = 1, 2, 3, 4, 6, 8 and Ge,, n = 1,2,3) with fluences up to 3 X lOI atoms per cm ‘. The energy has been varied between 0.2 and 4 MeV per atom. The produced defect concentration profiles have been measured by channeling Rutherford backscattering (RBS). While the damage at the end of range of the particles (where the fragments of a cluster have straggled far apart) is independent of the cluster size, the defect concentration in the first few hundred nm below the sample surface depends significantly on the size of the molecule. Up to a size of approximately 6 the swift carbon clusters (for which electronic stopping is clearly dominant) produce fewer defects per incident constituent than single carbon atoms of the same velocity. For larger carbon clusters the defect production per atom is increased. The appreciably slower polyatomic Ge particles, however, show a strong enhancement of the defect production close to the sample surface. This enhancement increases strongly with cluster size, but is reduced for higher energies. From the shape of the defect profile a radius of interaction between the individual fragment tracks of one cluster can be estimated.
1. Introduction There are at least two reasons to investigate MeV cluster beams. First, these experiments might contribute to the basic understanding of the physical processes involved in the ion-solid interaction. By changing the cluster size, the total energy deposited along the first part of the cluster track (where the constituents have not yet straggled far apart) can be changed without considerably affecting either the ratio between electronic and nuclear energy loss or the energy and range distribution of secondary particles (6 electrons and recoil nuclei) produced along the ion path. Secondly, the electronic energy density deposited by clusters can be extremely high and can even exceed the densities reached by the heaviest single atoms at their maximum stopping power [ 11. In the following we describe high dose MeV Ge, and C, cluster irradiation experiments that were conducted to investigate collective effects in the defect production in crystalline silicon.
2. Experimental
procedure
Experiments have been performed at the PSI/ETH Tandem accelerator laboratory at ETH-Honggerberg. More
* Corresponding author, Tel. + 41 1 633 2045, fax + 41 1 633 1067, e-mail doebeli@particle. phys.ethz.ch. 0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00675-3
detailed information on the experimental set-up can be found in Ref. [2]. The primary beam of negative carbon cluster ions is produced in a Cs-sputter ion source. The negative Ge, or C, ion beam is energy and momentum analysed in a 40” electrostatic deflector followed by a 90” dipole magnet and injected into the 6 MV EN Tandem accelerator. Then an energy to charge state ratio is selected with a 15” electrostatic deflector. Thus, only unbroken clusters and possible contaminants with the same mass as the injected particles can pass this energy filter [2]. Square spots of between 2 X 2 mm2 and 3 X 3 mm2 on pieces of (100) silicon wafers have been irradiated at room temperature at a tilt angle of 10” off the main axis. The beam which was focused to approximately 1 mm diameter was raster scanned across a collimator placed 10 cm in front of the target. The beam current was periodically measured in a Faraday cup behind the target. The overall transmission from the ion source to the target is approximately 0.5% depending on the cluster size. The currents obtained for C,(n = 1, 2, 3, 4) have been listed in Ref. [2]. C, and C, yielded currents of approximately 1 nA. For Ge, and Ge, we measured 10 and 1 nA, respectively. For each cluster irradiation, a single atom irradiation with the same fluence and the corresponding energy per atom was done on the same sample for comparison. Huences ranged from 1 X lOi to 3 X lOI atoms per cm* and energies from 0.2 to 4.0 MeV per atom in the cluster. The produced defect profile has been analysed with 2 and 3 MeV 4He channeling Rutherford backscattering (CRBS) along the crystal axis perpendicular to the sample
I. BASIC PROCESSES
M. Dabeli et al./Nucl.
44
Instr. and Meth. in Phys. Rex 3 106 11995) 43-46 14
/
,
II /
1.2
G _/ \
z
/ / IO-
0
v,c
’
0.0
’
0.5
’
’
j
’
’
1.0
Fluence
/
’
1.5
’
2.0
// 41 4 ’ 0__+__”
-
1
j 2.5
10’6cm-2
Fig. 1. Measured defect concentration versus C atom fluence for C, clusters (crosses) and single C atoms (triangles) at an energy of 0.8 MeV per C atom.
surface [3]. The carbon irradiation produced flat defect profiles between the sample surface and the end of range peak [2]. Values for the minimum yield ( x,,,~,> have been obtained by dividing the integrated yield in an energy region corresponding to a depth interval between 100 and 200 nm below the sample surface by the corresponding yield of the random spectrum. Defect concentrations are then expressed by the incremental minimum yield Axmin which is the difference between the x,,, of an irradiated spot and the x,,,~, of an unirradiated area.
3. Results
3. I. C, irradiations Concerning the shape and height of the end of range damage peak, no significant deviations from the single atom case have been measured for any polyatomic particle. This was expected since at the end of range the cluster fragments have straggled far apart so that collective effects are rather improbable. For C, clusters the evolution of the defect concentration with the irradiation fluence has been measured and compared with the case of single C atom irradiation at an energy of 0.8 MeV per C atom (see Fig. 1). The solid lines in Fig. 1 represent a fit to the experimental data of the form Ax,,,
\\. \
/
\
0.8
0.00
/
Fig. 2. Ratio between the saturation defect density of clusters and single C atoms as a function of cluster size at a constant energy of 0.8 MeV per C atom. The dashed line is a tit to the data with the model of Tombrello [8].
of 0.8 MeV per atom and a fluence of lOI atoms per cm2 (see Fig. 2). At this fluence the saturation defect density is almost completely reached so that in principle n, is measured. 3.2. Ge, irradiations In the case of molecular Ge irradiations a very peculiar shape of the damage depth profile has been found. Fig. 3 shows a comparison of the profile obtained with single Ge to those of Ge, and Ge, at an energy of 2.8 MeV per atom and a fluence of 3 X lOI atoms per cm2. In addition to the broad end of range peak a pronounced surface peak appears for the molecular particles. The integrated yield to a depth of 400 nm below the sample surface is plotted versus the size of the molecule in Fig. 4. For Ge, the area and height of the peak decreases monotonically with increasing energy (measurements have been done at 1, 2.8 and 4 MeV per atom at a fluence of 3 X lOI cm-‘).
= na( 1 - epFiFO)
where F is the C atom fluence and n, the saturation value of the incremental minimum yield. For single C atoms no = (3.1 + O.l)lO-’ and F, = (2.5 f 0.2)10’5 cm-’ are found while in the case of C, clusters n, = (2.3 + O.l)lO-’ and F, = (2.2 + 0.3)10i5 cm-’ are obtained. The ratio between the defect concentration produced with clusters to that for single C atom irradiation has been measured as a function of cluster size at a constant energy
Depth
/
pm
Fig. 3. Channeling RBS spectra of Ge,(n = 1, 2, 3) irradiated silicon. In all cases the energy was 2.8 MeV per atom and the total fluence 3 X 10’” atoms per cm2.
45
M. Diibeli et al. / Nucl. Insrr. and Meth. in Phys. Res. B 106 (1995) 43-46
two) with the theoretical simple models [4,5].
values obtained
with relatively
4.1. Ge, irradiations
Fig. 4. Integrated RBS yield from the sample surface to 400 nm depth as a function of the molecular size n for the channeling spectra shown in Fig. 3. The yield is normalized to the case of Ge, . The solid line is a linear fit to the data.
For all energies and particle types used the sample surface can be amorphised to a degree where the RBS surface yield in the channeling direction reaches the random level. The amorphisation behavior at an energy of 2.8 MeV per atom is shown in Fig. 5 for Ge, Ge, and Ge,.
4. Interpretation C and Ge ions with an energy of about 1 MeV are in two completely different regimes of energy loss. While the C ions deposit 99% of their energy into the electronic system of the target, the Ge ions lose about 50% of their energy to recoiling target atoms. The atomic displacement cross sections which can be extracted from the measurement of xmin as a function of the irradiation fluence (cf. Figs. 1 and 5) agree reasonably well (within a factor of
For a single 1 MeV Ge particle the atomic displacement cross section is of the order of lo-” cm*. This corresponds to about 5 atomic displacements per nm track length. Interaction between point defects is highly probable at such a high density of displaced atoms and can lead to defect clustering and local collapse of the crystal lattice which causes the complete amorphisation of the material observed at elevated fluences. Hence, it is not unexpected that the damage production depends in a non-linear way on the density of primary displaced atoms and thus on the cluster size. The linear increase of the number of stable defects produced per incident atom as a function of n (cf. Fig. 4) is actually a quadratic increase of the number of defects produced per Ge, molecule. In the most simple approximation the density of primary atomic displacements produced by one cluster in the surface near region is proportional to the cluster size (deviations from this assumption are discussed e.g. in Ref. [6]). Thus, the density of remaining stable defects depends in a quadratic way on the number of primarily displaced atoms along the track which points toward a binary interaction between the mobile primary point defects which leads to stable complex defects (e.g. divacancy formation). Since the average distance between two cluster constituents can be estimated [2] the depth to which the enhanced surface peak extends can be translated into a radius ri of interaction between individual fragment tracks. This is schematically displayed in Fig. 6. Independent of
Depth 0.6
t luence
/
1o14
atoms
/ ~“m 0.4
0.2
0.0
cm-2
Fig. 5. Channeling RBS yield from the sample surface (normalized to the random yield) as a function of the irradiation fluence for 2.8 MeV per atom Ge,, Ge, and Ge,. The irradiation fluence is given in number of single Ge atoms Per cm’. The solid lines are drawn to guide the eye.
Fig. 6. Schematic description of how a track interaction radius can he extracted from the surface Peak width.
1. BASIC PROCESSES
46
M. Diibeli et al./Nucl.
Instr. and Meth. in Phys. Rex B 106 (1995) 43-46
the particle energy a value of ri = 1 nm is found for Ge, irradiations. 4.2. C, irradiations For a 1 MeV C ion the atomic displacement cross section is approximately lo-” cm2 [2]. This corresponds to the displacement of only one Si atom per 20 nm ion track length. For a displacement energy of 20 eV an incident C ion has to come closer than 0.02 nm to a Si atom to eject it from its lattice site. Since the initial distance between the cluster constituents is about 10 times larger than this and increases rapidly along the ion path by mutual Coulomb repulsion and angular straggling (at a depth of 150 nm the average distance between two C atoms is more than 2 nm [2]> it is very improbable that the primary nuclear scattering process is subject to collective interaction with more than one cluster constituent. Therefore, the observed reduction of the saturation defect density for small clusters must be the consequence of a different annealing behavior of the primarily produced defects. On the one hand this can be due to the increased total deposited energy density along the cluster track. On the other hand the larger density of primarily displaced atoms per track length (which in this case is in a good approximation proportional to the cluster size) might lead to different defect kinetics (annihilation of Frenkel pairs, clustering of defects, etc.). For cluster sizes larger than approximately six enhanced defect production sets in and the saturation defect density lies above the level for single atom irradiation. This can again be due to some threshold effect in the density of primary displaced atoms along the cluster track (as in the case of Ge) or it could be caused by the very high density of electronic energy deposition. The electronic energy loss of a single 0.8 MeV carbon atom in Si is approximately 1 keV per nm and thus 8 keV per nm for a C,. However, since the range of secondary particles (S electrons) is much smaller for these carbon ions than for fast heavy ions of comparable stopping power the effective volume density of the deposited energy around the center of the cluster track could be extremely high. The shape of the curve displayed in Fig. 2 has a striking resemblance to the defect density produced by GeV heavy ions in metals [7] if the abscissa is expressed in units of the electronic stopping power of the clusters (as stated above dE/dx = n X 1 keV/nm). Tombrello has recently published a model [8] which describes how the defect production cross section by nuclear stopping is modified by electronic energy loss in metals. The reduction of the defect production at low and intermediate values of electronic energy loss is explained by excited
and ‘softened’ bonds along the track which allow for enhanced self-annealing of defects. The increased defect production at high electronic energy loss is caused by recoiling target atoms which pass through these regions of softened bonds. In its most simple version the model has essentially only two parameters: M is the number of target atoms constituting the region of softened bonds which can be broken by the recoil and (dE/dx), is a characteristic value of the electronic stopping power. With M = 5 and (d E/d x), = 6.9 keV/nm we obtain an excellent fit to our data (dashed curve in Fig. 2). Despite the quality of the tit the following inconsistency has to be mentioned: while Tombrello’s model yields a formula for the defect production cross section we fitted it to the defect saturation density.
5. Conclusions We measured defect density profiles in Si after MeV C, and Ge, irradiation. In the case of Ge, strongly enhanced defect production in the surface region is observed, probably related to the high density of displaced atoms along the part of the track where the cluster fragments are still closer than 1 nm. In the case of C, enhanced defect annealing is observed for small clusters and increased defect production for cluster sizes larger than six. This behavior is well described by a recent model by Tombrello for defect production by heavy ions in metals.
Acknowledgement The authors would like to thank Tom Tombrello for his stimulating interest in our work and his help in interpreting the data.
References [l] H. Dammak, A. Dunlop, D. Lesueur, A. Bnmelle, S. DellaNegra and Y. Le Beyec, Phys. Rev. Lett. in press. [2] M. DBheli, R.M. Ender, U.S. Fischer, M. Suter, H.A. Synal and D. Vetterli, Nucl. Instr. and Meth. B 94 (1994) 388. [3] W.K. Chu, J.W. Mayer and M.A. Nicolet, in: Backscattering Spectrometry (Academic Press, New York, 1978). [4] G.W. Kinchin and R.S. Pease, Rep. Prog. Phys. 18 (1955) 1. [5] J.F. Ziegler, J.P. Biersack and U. Littmark, in: The Stopping and Range of Ions in Solids (Pergamon, New York, 1985). [6] P. Sigmund, J. Phys. (Paris) Coil. C2 50 (1989) C2-175. [7] A. Dunlop, D. Lesueur, P. Legrand, H. Dammak and J. Dural, Nucl. Instr. and Meth. B 90 (1994) 330. [8] T.A. Tombrello, Nucl. In&r. and Meth. B 95 (1995) 501.
Nuclear Instruments
and Methods in Physics Research B 106 (1995) 43-46
-_
__
Beam Interactions with Materials 6 Atoms
!!I!! ELSEVIER
Defect production by MeV cluster impacts
*,
M. DSbeli a* F. Ames b, R.M. Ender b, M. Suter b, H.A. Synal a, D. Vetterli b a Paul Scherrer Institute c/o ETH-HSnggerberg, b Institute of Particle Physics, ETH-Hanggerberg,
CH-8093 Ziirich, Switzerland CH-8093 Ziirich, Switzerland
Abstract Monocrystalline silicon has been irradiated by MeV carbon and germanium clusters (C”, it = 1, 2, 3, 4, 6, 8 and Ge,, n = 1,2,3) with fluences up to 3 X lOI atoms per cm ‘. The energy has been varied between 0.2 and 4 MeV per atom. The produced defect concentration profiles have been measured by channeling Rutherford backscattering (RBS). While the damage at the end of range of the particles (where the fragments of a cluster have straggled far apart) is independent of the cluster size, the defect concentration in the first few hundred nm below the sample surface depends significantly on the size of the molecule. Up to a size of approximately 6 the swift carbon clusters (for which electronic stopping is clearly dominant) produce fewer defects per incident constituent than single carbon atoms of the same velocity. For larger carbon clusters the defect production per atom is increased. The appreciably slower polyatomic Ge particles, however, show a strong enhancement of the defect production close to the sample surface. This enhancement increases strongly with cluster size, but is reduced for higher energies. From the shape of the defect profile a radius of interaction between the individual fragment tracks of one cluster can be estimated.
1. Introduction There are at least two reasons to investigate MeV cluster beams. First, these experiments might contribute to the basic understanding of the physical processes involved in the ion-solid interaction. By changing the cluster size, the total energy deposited along the first part of the cluster track (where the constituents have not yet straggled far apart) can be changed without considerably affecting either the ratio between electronic and nuclear energy loss or the energy and range distribution of secondary particles (6 electrons and recoil nuclei) produced along the ion path. Secondly, the electronic energy density deposited by clusters can be extremely high and can even exceed the densities reached by the heaviest single atoms at their maximum stopping power [ 11. In the following we describe high dose MeV Ge, and C, cluster irradiation experiments that were conducted to investigate collective effects in the defect production in crystalline silicon.
2. Experimental
procedure
Experiments have been performed at the PSI/ETH Tandem accelerator laboratory at ETH-Honggerberg. More
* Corresponding author, Tel. + 41 1 633 2045, fax + 41 1 633 1067, e-mail doebeli@particle. phys.ethz.ch. 0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00675-3
detailed information on the experimental set-up can be found in Ref. [2]. The primary beam of negative carbon cluster ions is produced in a Cs-sputter ion source. The negative Ge, or C, ion beam is energy and momentum analysed in a 40” electrostatic deflector followed by a 90” dipole magnet and injected into the 6 MV EN Tandem accelerator. Then an energy to charge state ratio is selected with a 15” electrostatic deflector. Thus, only unbroken clusters and possible contaminants with the same mass as the injected particles can pass this energy filter [2]. Square spots of between 2 X 2 mm2 and 3 X 3 mm2 on pieces of (100) silicon wafers have been irradiated at room temperature at a tilt angle of 10” off the main axis. The beam which was focused to approximately 1 mm diameter was raster scanned across a collimator placed 10 cm in front of the target. The beam current was periodically measured in a Faraday cup behind the target. The overall transmission from the ion source to the target is approximately 0.5% depending on the cluster size. The currents obtained for C,(n = 1, 2, 3, 4) have been listed in Ref. [2]. C, and C, yielded currents of approximately 1 nA. For Ge, and Ge, we measured 10 and 1 nA, respectively. For each cluster irradiation, a single atom irradiation with the same fluence and the corresponding energy per atom was done on the same sample for comparison. Huences ranged from 1 X lOi to 3 X lOI atoms per cm* and energies from 0.2 to 4.0 MeV per atom in the cluster. The produced defect profile has been analysed with 2 and 3 MeV 4He channeling Rutherford backscattering (CRBS) along the crystal axis perpendicular to the sample
I. BASIC PROCESSES
M. Dabeli et al./Nucl.
44
Instr. and Meth. in Phys. Rex 3 106 11995) 43-46 14
/
,
II /
1.2
G _/ \
z
/ / IO-
0
v,c
’
0.0
’
0.5
’
’
j
’
’
1.0
Fluence
/
’
1.5
’
2.0
// 41 4 ’ 0__+__”
-
1
j 2.5
10’6cm-2
Fig. 1. Measured defect concentration versus C atom fluence for C, clusters (crosses) and single C atoms (triangles) at an energy of 0.8 MeV per C atom.
surface [3]. The carbon irradiation produced flat defect profiles between the sample surface and the end of range peak [2]. Values for the minimum yield ( x,,,~,> have been obtained by dividing the integrated yield in an energy region corresponding to a depth interval between 100 and 200 nm below the sample surface by the corresponding yield of the random spectrum. Defect concentrations are then expressed by the incremental minimum yield Axmin which is the difference between the x,,, of an irradiated spot and the x,,,~, of an unirradiated area.
3. Results
3. I. C, irradiations Concerning the shape and height of the end of range damage peak, no significant deviations from the single atom case have been measured for any polyatomic particle. This was expected since at the end of range the cluster fragments have straggled far apart so that collective effects are rather improbable. For C, clusters the evolution of the defect concentration with the irradiation fluence has been measured and compared with the case of single C atom irradiation at an energy of 0.8 MeV per C atom (see Fig. 1). The solid lines in Fig. 1 represent a fit to the experimental data of the form Ax,,,
\\. \
/
\
0.8
0.00
/
Fig. 2. Ratio between the saturation defect density of clusters and single C atoms as a function of cluster size at a constant energy of 0.8 MeV per C atom. The dashed line is a tit to the data with the model of Tombrello [8].
of 0.8 MeV per atom and a fluence of lOI atoms per cm2 (see Fig. 2). At this fluence the saturation defect density is almost completely reached so that in principle n, is measured. 3.2. Ge, irradiations In the case of molecular Ge irradiations a very peculiar shape of the damage depth profile has been found. Fig. 3 shows a comparison of the profile obtained with single Ge to those of Ge, and Ge, at an energy of 2.8 MeV per atom and a fluence of 3 X lOI atoms per cm2. In addition to the broad end of range peak a pronounced surface peak appears for the molecular particles. The integrated yield to a depth of 400 nm below the sample surface is plotted versus the size of the molecule in Fig. 4. For Ge, the area and height of the peak decreases monotonically with increasing energy (measurements have been done at 1, 2.8 and 4 MeV per atom at a fluence of 3 X lOI cm-‘).
= na( 1 - epFiFO)
where F is the C atom fluence and n, the saturation value of the incremental minimum yield. For single C atoms no = (3.1 + O.l)lO-’ and F, = (2.5 f 0.2)10’5 cm-’ are found while in the case of C, clusters n, = (2.3 + O.l)lO-’ and F, = (2.2 + 0.3)10i5 cm-’ are obtained. The ratio between the defect concentration produced with clusters to that for single C atom irradiation has been measured as a function of cluster size at a constant energy
Depth
/
pm
Fig. 3. Channeling RBS spectra of Ge,(n = 1, 2, 3) irradiated silicon. In all cases the energy was 2.8 MeV per atom and the total fluence 3 X 10’” atoms per cm2.
45
M. Diibeli et al. / Nucl. Insrr. and Meth. in Phys. Res. B 106 (1995) 43-46
two) with the theoretical simple models [4,5].
values obtained
with relatively
4.1. Ge, irradiations
Fig. 4. Integrated RBS yield from the sample surface to 400 nm depth as a function of the molecular size n for the channeling spectra shown in Fig. 3. The yield is normalized to the case of Ge, . The solid line is a linear fit to the data.
For all energies and particle types used the sample surface can be amorphised to a degree where the RBS surface yield in the channeling direction reaches the random level. The amorphisation behavior at an energy of 2.8 MeV per atom is shown in Fig. 5 for Ge, Ge, and Ge,.
4. Interpretation C and Ge ions with an energy of about 1 MeV are in two completely different regimes of energy loss. While the C ions deposit 99% of their energy into the electronic system of the target, the Ge ions lose about 50% of their energy to recoiling target atoms. The atomic displacement cross sections which can be extracted from the measurement of xmin as a function of the irradiation fluence (cf. Figs. 1 and 5) agree reasonably well (within a factor of
For a single 1 MeV Ge particle the atomic displacement cross section is of the order of lo-” cm*. This corresponds to about 5 atomic displacements per nm track length. Interaction between point defects is highly probable at such a high density of displaced atoms and can lead to defect clustering and local collapse of the crystal lattice which causes the complete amorphisation of the material observed at elevated fluences. Hence, it is not unexpected that the damage production depends in a non-linear way on the density of primary displaced atoms and thus on the cluster size. The linear increase of the number of stable defects produced per incident atom as a function of n (cf. Fig. 4) is actually a quadratic increase of the number of defects produced per Ge, molecule. In the most simple approximation the density of primary atomic displacements produced by one cluster in the surface near region is proportional to the cluster size (deviations from this assumption are discussed e.g. in Ref. [6]). Thus, the density of remaining stable defects depends in a quadratic way on the number of primarily displaced atoms along the track which points toward a binary interaction between the mobile primary point defects which leads to stable complex defects (e.g. divacancy formation). Since the average distance between two cluster constituents can be estimated [2] the depth to which the enhanced surface peak extends can be translated into a radius ri of interaction between individual fragment tracks. This is schematically displayed in Fig. 6. Independent of
Depth 0.6
t luence
/
1o14
atoms
/ ~“m 0.4
0.2
0.0
cm-2
Fig. 5. Channeling RBS yield from the sample surface (normalized to the random yield) as a function of the irradiation fluence for 2.8 MeV per atom Ge,, Ge, and Ge,. The irradiation fluence is given in number of single Ge atoms Per cm’. The solid lines are drawn to guide the eye.
Fig. 6. Schematic description of how a track interaction radius can he extracted from the surface Peak width.
1. BASIC PROCESSES
46
M. Diibeli et al./Nucl.
Instr. and Meth. in Phys. Rex B 106 (1995) 43-46
the particle energy a value of ri = 1 nm is found for Ge, irradiations. 4.2. C, irradiations For a 1 MeV C ion the atomic displacement cross section is approximately lo-” cm2 [2]. This corresponds to the displacement of only one Si atom per 20 nm ion track length. For a displacement energy of 20 eV an incident C ion has to come closer than 0.02 nm to a Si atom to eject it from its lattice site. Since the initial distance between the cluster constituents is about 10 times larger than this and increases rapidly along the ion path by mutual Coulomb repulsion and angular straggling (at a depth of 150 nm the average distance between two C atoms is more than 2 nm [2]> it is very improbable that the primary nuclear scattering process is subject to collective interaction with more than one cluster constituent. Therefore, the observed reduction of the saturation defect density for small clusters must be the consequence of a different annealing behavior of the primarily produced defects. On the one hand this can be due to the increased total deposited energy density along the cluster track. On the other hand the larger density of primarily displaced atoms per track length (which in this case is in a good approximation proportional to the cluster size) might lead to different defect kinetics (annihilation of Frenkel pairs, clustering of defects, etc.). For cluster sizes larger than approximately six enhanced defect production sets in and the saturation defect density lies above the level for single atom irradiation. This can again be due to some threshold effect in the density of primary displaced atoms along the cluster track (as in the case of Ge) or it could be caused by the very high density of electronic energy deposition. The electronic energy loss of a single 0.8 MeV carbon atom in Si is approximately 1 keV per nm and thus 8 keV per nm for a C,. However, since the range of secondary particles (S electrons) is much smaller for these carbon ions than for fast heavy ions of comparable stopping power the effective volume density of the deposited energy around the center of the cluster track could be extremely high. The shape of the curve displayed in Fig. 2 has a striking resemblance to the defect density produced by GeV heavy ions in metals [7] if the abscissa is expressed in units of the electronic stopping power of the clusters (as stated above dE/dx = n X 1 keV/nm). Tombrello has recently published a model [8] which describes how the defect production cross section by nuclear stopping is modified by electronic energy loss in metals. The reduction of the defect production at low and intermediate values of electronic energy loss is explained by excited
and ‘softened’ bonds along the track which allow for enhanced self-annealing of defects. The increased defect production at high electronic energy loss is caused by recoiling target atoms which pass through these regions of softened bonds. In its most simple version the model has essentially only two parameters: M is the number of target atoms constituting the region of softened bonds which can be broken by the recoil and (dE/dx), is a characteristic value of the electronic stopping power. With M = 5 and (d E/d x), = 6.9 keV/nm we obtain an excellent fit to our data (dashed curve in Fig. 2). Despite the quality of the tit the following inconsistency has to be mentioned: while Tombrello’s model yields a formula for the defect production cross section we fitted it to the defect saturation density.
5. Conclusions We measured defect density profiles in Si after MeV C, and Ge, irradiation. In the case of Ge, strongly enhanced defect production in the surface region is observed, probably related to the high density of displaced atoms along the part of the track where the cluster fragments are still closer than 1 nm. In the case of C, enhanced defect annealing is observed for small clusters and increased defect production for cluster sizes larger than six. This behavior is well described by a recent model by Tombrello for defect production by heavy ions in metals.
Acknowledgement The authors would like to thank Tom Tombrello for his stimulating interest in our work and his help in interpreting the data.
References [l] H. Dammak, A. Dunlop, D. Lesueur, A. Bnmelle, S. DellaNegra and Y. Le Beyec, Phys. Rev. Lett. in press. [2] M. DBheli, R.M. Ender, U.S. Fischer, M. Suter, H.A. Synal and D. Vetterli, Nucl. Instr. and Meth. B 94 (1994) 388. [3] W.K. Chu, J.W. Mayer and M.A. Nicolet, in: Backscattering Spectrometry (Academic Press, New York, 1978). [4] G.W. Kinchin and R.S. Pease, Rep. Prog. Phys. 18 (1955) 1. [5] J.F. Ziegler, J.P. Biersack and U. Littmark, in: The Stopping and Range of Ions in Solids (Pergamon, New York, 1985). [6] P. Sigmund, J. Phys. (Paris) Coil. C2 50 (1989) C2-175. [7] A. Dunlop, D. Lesueur, P. Legrand, H. Dammak and J. Dural, Nucl. Instr. and Meth. B 90 (1994) 330. [8] T.A. Tombrello, Nucl. In&r. and Meth. B 95 (1995) 501.