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phys. stat. sol. (a), 1–8 (2004) / DOI 10.1002/pssa.200306819
Defects in silicon plastically deformed at room temperature
H. S. Leipner *; 1 , Z. Wang 2 ,H.Gu 1 , V. V. Mikhnovich Jr. 1 , V. Bondarenko 3 ,
R. Krause-Rehberg 3 , J.-L. Demenet 4 , and J. Rabier 4
1 Interdisziplinåres Zentrum fçr Materialwissenschaften, Hoher Weg 8, Martin-Luther-Universitåt,
06120 Halle, Germany
2 Department of Physics, Wuhan University, Wuhan 430072, P.R. China
3 Fachbereich Physik, Friedemann-Bach-Platz 6, Martin-Luther-Universitåt, 06108 Halle, Germany
4 Laboratoire de M tallurgie Physique, UMR 6630, Universit
86962 Futuroscope-Chasseneuil Cedex, France
de Poitiers, SP2MI, BP 30179,
Received 12 August 2003, revised 10 March 2004, accepted 7 April 2004
Published online 11 June 2004
PACS 61.72.Ji, 61.72.Lk, 62.20.Fe, 78.70.Bj
Positron trapping in silicon deformed under high-stress conditions at room temperature is compared to
that in Si plastically deformed at higher temperatures. After room temperature deformation, thermally
rather stable vacancy clusters appear. No evidence for positron capture in dislocations is found. In
contrast, after high-temperature deformation, positrons are trapped in rather large vacancy clusters and
in dislocations acting as combined positron traps. The specific features of positron trapping in silicon
plastically deformed at room temperature are related to the dislocation core structure and to the inhomogeneous
distribution of defects.
1 Introduction
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Plastic deformation of semiconductors in the low temperature/high stress region is of particular interest
due to the anticipated change in the character of dislocation core structure and dislocation motion.
It is well accepted that at high temperatures dislocations are dissociated in the glide set and move via
the thermal activation and migration of double kinks [1]. However, the calculation of Duesbery and
JoÕs [2] demonstrated for silicon that the motion of perfect dislocations in the shuffle set has a lower
activation energy at very high stresses and low temperatures. The transition from the motion of dissociated
glide set dislocations to the predominance of undissociated shuffle set dislocations is expected
at a stress of about 0:01 G (G shear modulus). It is, however, very difficult to extend plastic deformation
experiments to the range of high stresses and low temperatures due to the brittleness of semiconductors.
One approach is the uniaxial compression under confining pressure. In the case of silicon, it
is possible to go to deformation at room temperature by applying a hydrostatic pressure of several
GPa to the sample [3].
Experimental investigations of elemental and III–V semiconductors plastically deformed at elevated
temperatures have shown that a high number of vacancies and vacancy clusters is formed [4]. The
dragging of jogs at screw dislocations is recognized as one of the main sources of vacancies produced
during deformation. Jogs are formed as the result of cutting of dislocations belonging to different slip
systems or cross slip of screw dislocations.
* Corresponding author: e-mail: leipner@cmat.uni-halle.de, Phone: +49 345 55 25 453, Fax: +49 345 55 27 212
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2 H. S. Leipner et al.: Defects in silicon plastically deformed at room temperature
It is an open question how the different dislocation structure formed during high-stress deformation at
room temperature influences point defect generation. Aim of this paper is to compare the defect population
found by means of positron annihilation after plastic deformation at high and low temperatures.
2 Experimental details
Float-zone silicon single crystals with phosphorus doping were used for dynamic deformation experiments
in single and multiple slip orientations. The compression axes were ½123Š and ½110Š. The first
type of sample was deformed at room temperature in an anisotropic multi-anvil apparatus under a
confining pressure of 5 GPa. The confining pressure is necessary in order to avoid brittle fracture of
the sample. In this experimental set up the uniaxial stress is built up as a consequence of the application
of the confining pressure. The strain rate can be estimated to be of the order of 5 10 5 s 1 .
This resulted in a deformation of 16%. The uniaxial stress is unknown during the test and can only be
estimated from post mortem observations by transmission electron microscopy (TEM). The second
type of samples was deformed with a constant strain rate of 2:2 10 5 s 1 under a maximum stress
of 50 MPa up to a strain of 7%. The deformation temperature was 800 C. A pair of identical specimens
with a thickness of 1 mm was prepared from the middle of each deformed bar. Conventional
positron lifetime measurements were carried out with a fast–fast spectrometer. The resolution of the
spectrometer (FWHM) was 260 ps. A closed-cycle He cryostat was used for measurements in the
temperature range 15 to 600 K. In order to study the thermal stability of defects, isochronal annealing
experiments up to 1300 C were carried out in vacuum. The annealing time was 30 min.
3 Results and discussion
3.1 Microstructure after room temperature and high-temperature deformation
Deformation microstructures obtained after deformation under high confining pressures in silicon have
been already discussed in several papers [3, 5, 6]. Dislocations resulting from plastic deformation
under a confining pressure of 5 GPa in a temperature range from room temperature to 150 C show
specific features, which are very different from those of dislocations obtained in experiments conducted
at higher temperatures and large strains [1, 7, 8]. Indeed, large stresses favor usually the occurrence
of dissociated dislocations (connected with the occurrence of intrinsic stacking faults) or dislocation
segments showing large dissociation widths (so-called noses). Consequently, the dislocations
formed in these conventional deformation experiments belong to the glide set. This is not the case at
room temperature. Although high stresses are also obtained (1 to 1.5 GPa deduced from measurements
of the dislocation curvature), perfect dislocations – at the resolution of the TEM weak beam
technique – are found to build the deformation substructure. This shows that dislocations with different
core structures are nucleated under conditions where dissociated glide set dislocations would result
in the formation of extended stacking faults and twinning. Such features are consistent with perfect
dislocations moving in the shuffle set, as expected from the extrapolation of the calculations of Duesbery
and JoÕs at higher stresses [2, 9]. Apart from being undissociated, these dislocations exhibit
Peierls valleys different from the usual h110i ones observed in Si deformed in conventional tests.
Indeed, the dislocations are found to lie in screw, h112i/30 , and h123i/41 orientations (indicating the
direction and the angle between the dislocation line and the Burgers vector). The occurrence of the
h112i/30 Peierls valleys is consistent with the minimization of the number of dangling bonds induced
by a perfect dislocation in the shuffle set, which corresponds likely to a low core energy [5]. The
other direction with a low core energy (h123i/41 ) could be consistent with dislocation directions
which allow for dangling bond reconstructions, i.e. a regular density of kinks on a h112i dislocation
where reconstruction could be possible [10].
As far as room temperature deformed samples are concerned, the deformation microstructure is
very heterogeneous, although a deformation as high as 20% could be possible. Regions of very high
dislocation densities are separated by regions almost free of dislocations. This can be understood
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phys. stat. sol. (a) (2004) / www.pss-a.com 3
Fig. 1 Perfect dislocation half loops with an
a=2½101Š Burgers vector nucleated at crack edges
after deformation at room temperature under 5 GPa.
Dislocations are elongated along the ½321Š direction
of the ð111Þ slip plane. TEM weak beam dark field
image with a (g ¼ 202; 4:1g) diffraction condition (g
is the diffraction vector). The foil plane is ð101Þ.
Fig. 2 Microcrack associated with a large density
of perfect dislocations with an a=2½101Š Burgers vector
on a ð111Þ slip plane showing Peierls valleys
along screw and h123i/41 orientations after deformation
at 5 GPa and room temperature. Weak beam
dark field image with a (g ¼ 220; 5g) condition,
ð111Þ foil plane.
through the formation of numerous cracks. Isolated dislocations appear to be created at surface edges
of micro-cracks, which act as favorable locations for dislocation nucleation. The cracks are likely to
be formed in the early stages of the deformation–pressurization process. When the pressure increases,
their extension is stopped and the applied stress provide the driving force for nucleation of dislocations
from lateral surfaces of cracks. Figure 1 shows such an example, where dislocation half loops
with an a=2½101Š Burgers vector (a is the lattice constant), lying in the ð111Þ plane, are seen to be
nucleated from lateral surfaces of a crack. Several nucleation centers are efficient on both sides of the
crack. The elongation of dislocation half loops along the ½321Š direction bear witness of a strong
Peierls stress along this direction. Other areas (see Fig. 2) give evidence that a large density of dislocations
close to the cracks can be achieved. Furthermore, the occurrence of other types of Peierls
valleys usually encountered is also demonstrated in this micrograph.
The dislocation structure of silicon deformed at medium and high temperatures has been extensively
studied and is well known. Dislocations are mainly generated at the sample surfaces [1] and
their distribution within the sample is rather homogeneous. Depending on the stress level and the
cooling rate after deformation, the dislocations are more or less well aligned in h110i Peierls valleys.
The dislocations are found in the glide set and are dissociated. The dissociation width of the partial
dislocations can be very high under high-stress conditions [1, 7, 8]. Main dislocation slip occurs for a
½123Š deformation axis in a single slip system, but a certain amount of dislocations is also formed in
auxiliary slip systems. For a ½110Š orientation, four equivalent slip systems are activated. The interaction
of dislocations belonging to different slip systems leads to the formation of dislocation tangles
and barriers, which block further dislocation glide. Moreover, kinks and jogs are formed during dislocation
cutting. The latter defects on the dislocation line may not be able to follow the glide motion of
the dislocation. The motion of such segments is only possible non-conservatively, i. e. by the emission
of vacancies or interstitials. This process is known as jog dragging. Particularly, screw dislocations
play an important role in point defect generation, as the intersection of screws always produces nonglissile
jogs. The vacancies formed during jog dragging immediately agglomerate to stable clusters,
which are left behind the dislocations [11].
3.2 Positron lifetime measurements of deformed silicon
Figure 3 shows the average positron lifetime t measured as a function of the temperature in samples
deformed at 20 and 800 C, respectively. A distinct increase in the average positron lifetime is ob-
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4 H. S. Leipner et al.: Defects in silicon plastically deformed at room temperature
Average positron lifetime (ps)
320
300
280
260
240
T def = 800 ˚C
T def = 20 ˚C
0 100 200 300 400 500
Sample temperature (K)
Fig. 3 (online colour at: www.interscience.wiley.
com) Average positron lifetime measured as a function
of the sample temperature in as-deformed samples. The
deformation temperature Tdef was 800 and 20 C, respectively.
tained in comparison to as-grown Si material with a positron bulk lifetime of 216 ps. In both types of
sample, the lifetime increases with the reduction of the sample temperature. Over the whole temperature
range measured, t is lower for the sample deformed at room temperature. One reason for this
may be the lower strain of this sample, which is related to a lower defect density. The increase in t
towards lower temperature can be interpreted by the presence of extended open-volume defects and
the corresponding diffusion-limited trapping. Another possibility is the presence of charged vacancies.
Distinct differences in the course of the two curves are found at sample temperatures below 100 K.
While the average lifetime of the sample deformed at room temperature continues to increase in this
range, a drop in t occurs for the other sample type. Such a drop is a well-known indication for the
presence of shallow positron traps. At low temperatures, positrons may be captured in such shallow
traps having a defect-specific positron lifetime close to the bulk value. In plastically deformed material,
the main candidates to have the character of a shallow positron trap are dislocations, especially
regular dislocation segments with a rather small open volume [12].
No evidence for the presence of shallow positron traps is found after room temperature deformation.
It is not clear at the moment, if this is due to the change in the character of the dislocation core
deduced from TEM observations or a result of the inhomogeneous distribution of dislocations.
The result of the decomposition of the positron lifetime spectra is shown in Fig. 4. The spectra of
the sample deformed at 800 C can be decomposed into three lifetime components. The long-lived
lifetime component t3 amounts to about 500 ps, the shorter defect-related lifetime t2 to about 280 ps.
The corresponding intensities of these components are shown in the upper panel of Fig. 4a. Above
100 K, the lifetimes are almost independent of the sample temperature. Below 100 K, the decomposition
becomes unstable, which is expressed by the large errors shown in the figure. The instability is
due to the appearance of shallow positron traps in this temperature range.
The lifetime t3 is related to vacancy clusters. However, no clear statement about the size of the
clusters can be made. If the experimental value of 500 ps is compared with recent theoretical calculations
[13], it can be deduced that the clusters should be certainly much larger than V18. The positron
lifetime for larger vacancy clusters tends to saturate around 500 ps that the sensitivity of the positron
lifetime to the size of vacancy agglomerates is lost.
The lifetime component t2 is due to a monovacancy-type defect. It can be assumed that isolated
monovacancies are not stable above room temperature, as it is known from electron irradiation experiments
[15]. It is concluded that monovacancies are incorporated in the dislocation core, where they are
thermally rather stable. Positron trapping to such dislocation-bound vacancies can be explained by a
two-stage process: Positrons are first captured in the regular dislocation line, acting as a shallow positron
trap. In a cascade transition, they are then captured by the vacancies in the dislocation core [16].
The spectra of the sample deformed at room temperature can only be reliably decomposed into two
lifetime components (Fig. 4b). The shorter lifetime t1 practically coincides with the bulk lifetime tb
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phys. stat. sol. (a) (2004) / www.pss-a.com 5
Intensity (%)
Positron lifetime (ps)
100
80
60
40
20
0
600
500
400
300
200
100
0
0 100 200 300 400 500
Sample temperature (K)
I 2
I 3
τ 3
τ 2
τ 1
a)
Intensity (%)
Positron lifetime (ps)
0
0 100 200 300 400 500
Sample temperature (K)
Fig. 4 (online colour at: www.interscience.wiley.com) Decomposition of lifetime spectra. The lifetime components
ti and the corresponding intensities Ii (i ¼ 1; 2; 3) are shown as a function of the sample temperature.
(a) Three-component decomposition for the sample deformed at 800 C. (b) Two-component decomposition of the
lifetime spectra for the room-temperature-deformed sample.
of 216 ps. The longer lifetime t2 amounts to about 460 ps. No straightforward interpretation of these
two components seems to be possible. A simple two-state trapping (one positron trap and positron
annihilation in the bulk) would result in a reduced bulk lifetime t1 ¼ 1=ðtb þ jÞ distinctly shorter
than tb. j is the trapping rate of the positron trap. One possibility would be that t1 obtained in the
two-component decomposition is a mixed component of a short reduced bulk lifetime and a defectrelated
lifetime (e. g. around 300 ps) which cannot be further resolved. We prefer another interpretation
which is in accordance with the results of transmission electron microcopy. As demonstrated in
Section 3.1, there are regions of a very high dislocation density near cracks besides regions with a
very low dislocation density. The two positron lifetime components obtained can be interpreted by
positron trapping related to this inhomogeneous defect distribution. The defect-rich zone near the
cracks give rise to the defect-related component t2 and likely to a very short reduced bulk lifetime,
which cannot be resolved in the spectrometer. The regions almost free of defects simply provide the
bulk lifetime, t1 ¼ tb.
The experimental long-lived component t2 of 460 ps in the sample deformed at room temperature
is by about 40 ps lower that the void-related component in the sample deformed at high temperature.
It is rather close to the theoretical value of 450 ps for V18, which should be a stable configuration
according to the magic-number sequence of vacancy agglomerates in Si [13].
3.3 Annealing experiments
The thermal stability of defects formed during plastic deformation has been studied in isochronal
annealing experiments. Figure 5 shows the course of the average positron lifetime as a function of the
annealing temperature for the samples deformed at 800 and 20 C, respectively. The result of the
high-temperature deformation resembles very much earlier findings [14]. A distinct annealing stage
occurs above 700 C. A pronounced maximum occurs at 600 C. This maximum has been interpreted
by the re-arrangement of the dislocation network during annealing. The interaction of dislocations
gives rise to the formation of new vacancies, which cluster to stable agglomerates. Above 600 C, the
stability limit of the clusters is reached, and they start to decay.
100
80
60
40
20
0
600
500
400
300
200
100
I 2
τ 2
τ 1
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b)

6 H. S. Leipner et al.: Defects in silicon plastically deformed at room temperature
Average positron lifetime (ps)
Average positron lifetime (ps)
320
300
280
260
240
320
300
280
260
240
T def = 800 ˚C
T def = 20 ˚C
T meas = 20 K
T meas = 100 K
T meas = 300 K
T meas = 35 K
T meas = 300 K
0 200 400 600 800 1000 1200
Annealing temperature (˚C)
Fig. 5 (online colour at: www.interscience.wiley.
com) Average positron lifetime measured for the samples
deformed at Tdef ¼ 800 C (upper panel) and 20 C
(lower panel) as a function of the annealing temperature.
The measurements have been carried out at different
sample temperatures Tmeas. The lines are drawn to guide
the eye.
The run of the annealing curve of the room-temperature-deformed sample cannot be interpreted by
one single process. Obviously, several maxima, which may be due to a series of clustering and decay
reactions, appear. TEM investigations which may give more insight into the re-ordering of the dislocations
during annealing are currently carried out.
Intensity (%)
Positron lifetime (ps)
100
80
60
40
20
0
600
500
400
300
200
100
T meas = 300 K
I 2
I 3
0
0 200 400 600 800 1000 1200
Annealing temperature (˚C)
τ 3
τ 2
τ 1
a)
Intensity (%)
Positron lifetime (ps)
100
80
60
40
20
0
600
500
400
300
200
100
T meas = 35 K
τ 2
τ 1
0
0 200 400 600 800 1000 1200
Annealing temperature (˚C)
Fig. 6 (online colour at: www.interscience.wiley.com) Positron lifetime components and intensities for the sample
deformed at 800 C (a) and the sample deformed at 20 C (b) as a function of the annealing temperature. For
the high-temperature deformation, the lifetime t3 disappears after annealing at 800 C and only a two-component
decomposition is possible for higher temperatures. The sample temperature during the measurement Tmeas was
300 K in (a) and 35 K in (b). The dashed line represents the mean value of the long-lived component at low
annealing temperatures in the room-temperature-deformed sample.
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I 2
b)

phys. stat. sol. (a) (2004) / www.pss-a.com 7
In the course of the annealing treatment, the average positron lifetime has been always measured as
a function of the sample temperature. t is plotted for two or three characteristic sample temperatures
in Fig. 5. The influence of shallow positron traps is manifested in the sample deformed at 800 Cin
the differences of the average positron lifetime measured at high and low sample temperatures, reflecting
the decrease or saturation of t at low sample temperatures. In the sample deformed at room
temperature, t measured at low sample temperatures is always higher than that at room temperature.
This is due to the influence of diffusion-limited positron trapping to extended defects. The temperature
dependence of diffusion-limited trapping is the reason for the increase in t at low sample temperatures
in this sample (Fig. 3). The run of the average lifetime versus sample temperature does not
change in principle after annealing. The elevated average positron lifetime at the highest annealing
temperature indicates that some defects still remain in both sample types.
The individual positron lifetime components and their intensities are given as a function of the
annealing temperature in Fig. 6 as the result of the decomposition of the spectra. All lifetimes are
independent of the sample temperature during measurement. The lifetime t3 related to vacancy clusters
in the sample deformed at 800 C disappeared after annealing at 800 C. One can conclude that
only dislocations and dislocation-bound vacancies remain at higher annealing temperatures.
From the two-component decomposition of the spectra measured in the sample deformed at room
temperature, it can be seen that thermally very stable vacancy clusters are formed. t2 stays constant at
460 ps below annealing temperatures of 800 C. It increases from 480 ps at 800 C to 530 ps after
annealing at 1225 C. No change occurs during annealing in the shorter positron lifetime component t1.
4 Summary
Two types of positron trapping centers related to larger vacancy clusters (defect-related positron lifetime
of 500 ps) and dislocation-bound vacancies (positron lifetime of 280 ps) are introduced during
deformation at 800 C. The vacancies bound to dislocations act as deep positron traps, while regular
dislocation segments are active as shallow positron traps. After additional annealing at 800 C, the
positron traps related to vacancy clusters disappear, and dislocation-bound vacancies remain.
Regular dislocation segments (i. e. shallow positron traps) have a significant influence on positron
trapping at low temperatures only in samples deformed at high temperatures.
The only positron trapping centers observed in the samples deformed at room temperature are
related to vacancy clusters. The defect-related positron lifetime amounts to 460 ps, which is much
smaller than in high-temperature deformed Si. In contrast to high-temperature deformation, a voidrelated
positron lifetime remains even after annealing above 1200 C. Table 1 summarizes the positron
lifetimes measured in both types of sample.
The different void-related lifetimes found after deformation at 20 and 800 C may be interpreted by
different sizes of the voids. The smaller size after room temperature deformation may be related in
turn to a lower mobility of dislocations in the glide set, provided dislocation jog dragging is the
dominating mechanism of vacancy supply.
We have previously assumed that the increase in the density of voids upon annealing as a result of
dislocation rearrangement is responsible for the maximum in the average lifetime around the anneal-
Table 1 Defect-related positron lifetimes related to vacancy clusters tvoid and dislocation-bound vacancies
tdv measured in silicon plastically deformed at a temperature Tdef ¼ 20 C and at 800 C, respectively.
Additionally, the positron lifetimes measured after annealing at 1225 C are given.
Tdef/ C 20 800
tvoid/ps 460 500 as deformed
530 – after 1225 C annealing
tdv/ps – 280 as deformed
– 280 after 1225 C annealing
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8 H. S. Leipner et al.: Defects in silicon plastically deformed at room temperature
ing temperature of 600 C. However, this simple interpretation seems to fail with the complicated
annealing behavior of the sample deformed at room temperature.
A different core structure may be responsible for the findings that dislocations in high-temperaturedeformed
silicon act as combined traps (i. e. regular dislocation lines as shallow positron traps and
dislocation-bound vacancies as deep traps), while no dislocation-related trapping is found in the sample
deformed at room temperature.
The specific lifetime components in the room-temperature-deformed sample can be interpreted by
an inhomogeneous distribution of positron traps: i) regions of a very high density of traps near cracks
and ii) regions almost free of positron traps.
Acknowledgements The work was supported by the Deutsche Forschungsgemeinschaft and by the French–German
PROCOPE program.
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