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Mechanical Strength and Dislocation Velocities in GeSi Alloys
Ichiro Yonenaga, Koji Sumino
To cite this version:
Ichiro Yonenaga, Koji Sumino. Mechanical Strength and Dislocation Velocities in GeSi Alloys. Journal de Physique III, EDP Sciences, 1997, 7 (12), pp.2367-2374. �10.1051/jp3:1997264�. �jpa-00249725�
Mechanical Strength and Dislocation Velocities in Gesi Alloys
Ichiro Yonenaga (~,*) and Koji Sumino (~)
(~ Institute for Materials Research, Tohoku University, Sendai 980-77, Japan (~) Nippon Steel Corporation, Futtsu 293, Japan
(Received 3 October 1996, revised 21 January 1997, accepted 27 May 1997)
PACS 62.20.-x Mechanical properties of solids
PACS.61.72.Lk Linear defects. dislocations, disclinations PACS.61.72.-y Defects and impurities in crystals, microstructure
Abstract. The mechanical strength and dislocation velocities m single crystal Gei-~Si~
alloys grown by the Czochralski method were investigated by compressive deformation and by
the etch pit technique, respectively. In the temperature range 450- 700 °C and the stress range 3-20 MPa, the dislocation velocity in the Gesi with x = 0.004-0.022 decreases monotonically
with an increase in the Si content, reaching about a half of that m Ge at x = 0.022, and can be
expressed as a function of the stress and the temperature as expressed by the empirical equation known m other semiconductors. The yield stress of the Gesi alloy increases with increasing Si
content from x
= 0 to 0.4 and is temperature-insensitive at high temperatures, showing that the
flow stress of alloy semiconductor has an athermal component which is absent in elemental or
compound semiconductors The hardening mechanism in alloy semiconductors is discussed.
1. Introduction
Gesi alloy semiconductor is of interest in view of its variable band gap and lattice parameter
according to the alloy composition. Gesi alloys for opto electronic applications are usually pre- pared as thin films on crystalline substrates by various epitaxial techniques. Above the critical
thickness, introduction of misfit dislocations is unavoidable in such hetero epitaxial structures.
Dislocations affect electrical and /or optical properties of the films and limit their applications.
Very little is known on the dynamic properties of dislocations in alloy semiconductors except the generation of misfit dislocations related to the mismatch at the film/substrate interface.
A few groups measured the velocity of misfit and threading dislocations in Si- or Ge-rich Gesi films grown by molecular beam epitaxy [1-5j. The elemental process controlling dislocation
motion in a Gesi system have often been assumed to be similar to those m Si or Ge, in which dislocation phenomena are well understood [6,7] Little attention has been paid to the unique properties of dislocations that appear due to alloying. The present authors found that the flow stresses of GaASP and InASP alloy semiconductors have an athermal component that is
absent
m compound semiconductors of GaAs, GaP, InAs and InP [8,9]. Since the mechanical behaviour of Si and Ge is well understood on the basis of dynamic properties of dislocations
(*) Author for correspondence (e-mail. yonenagafiimr.tohoku ac.jp)
© Les iditions de Physique 1997
2368 JOURNAL DE PHYSIQUE III N°12
in these crystals [7], it is of interest to investigate the mechanical behaviour of the Gesi alloy
and to extract the unique dislocation process that is brought about by alloying.
The obstacle to conducting such investigations has been the difficulty m growing bulk Gesi crystals of a size suitable for mechanical tests or dislocation velocity measurements. Only one
set of data is available on yield strength of dilute Si-rich Gesi alloys at elevated temperatures (1°).
Recently, we succeeded in growing Gesi bulk crystals by the Czochralski technique ii lj. This has made it possible to investigate the dislocation velocities and t'he mechanical properties of
Gesi alloys to compare them with those of elemental Si and Ge crystals. Even now, the compo- sition range of the alloys available for dislocation velocity measurements is narrower than that of the alloys available for mechanical property measurements due to the necessities of the larger
size specimens with the lower density of grown-in dislocations for the former measurements.
This paper reports the velocities of dislocations in Gei-xsi~ with x
= 0.004-0.022 and the mechanical behaviour in Gei-xsi~ with z
= 0-0.4, respectively.
2. Experiment
Bulk crystals of Gei-xsi~ with z ranging from 0 to 1 were grown by the Czochralski technique.
Single crystals of low Si content and partly single crystal material near the seed crystal for intermediate Si content were obtained. With an increase in Si content the crystals changed
from single material to polycrystal in the middle part of the boule, which may relate to the
occurrence of constitutional supercooling. The composition of each specimen was estimated
by energy dispersive x-ray analysis. The density of native dislocations in the crystals was determined by the etch pit technique. The details of the growth technique and characterization of the obtained crystals are described elsewhere [11j.
The dynamic behaviour of dislocations was investigated in the specimens prepared from
single crystals with Si contents up to z = 0.022 of low native dislocation density 103 cm~~.
Rectangular specimens of 2 x3 x15 mm3 in size with the long axis along the I 10j direction and side surfaces parallel to the (I I I) and (I I I) planes were finished by chemical polishing with
a reagent of SHN03°IHF at 30-40 °C. The specimen was stressed at elevated temperature by three-point bending in a vacuum. The bending axis was parallel to 1 1 §j direction.
Dislocations were generated from a scratch drawn on the (1 1 1) surface along the long axis at room temperature with a diamond stylus. Displacements of dislocations due to stressing were
measured by the etch pit technique with the Billig etchant [12] at 80 °C.
The mechanical properties were investigated on the specimens prepared from single crys-
talline boules and from the single crystalline part of the ploycrystallized boules, near the seed,
with Si contents up to z = 0.4 of native dislocation density 103-10~ cm~~. Rectangular speci-
mens of 2.7 x 2.7 x 10.7 mm~ in size
were finished by the chemical polishing. The compression
axis was parallel to 1 2 ii with the side surfaces parallel to (1 1 1) and (5 I I). Compression
tests were conducted under a constant strain rate using an Instron-type machine at elevated
temperatures. The hardness for the Gei-xsi~ alloys from x
= 0 to 1 was obtained using a
Knoop indentor with 25 g load for 10 s. Specimens of Si rich were prepared from the top part of grown crystals close to the seed crystal which were single crystal but not large enough to
study the mechanical strength.
The dislocation velocity and the mechanical properties of crystals of high purity Ge and Si with grown-in dislocation densities of about 10~ cm~~
were compared with those of the alloys.
600°C
~
E soo°c
(
<~ 450°c
o Ge
v Gej~Si~ x=0004
. Q016
A 0.022
SHEAR STRESS, MPa
Fig i. Velocities of 60° dislocations m Gesi with various Si contents at 450, 500, 550 and 600 °C
as dependent on the shear stress together with those m Ge.
3. Results
3.I. DisLocATioN VELOCITY. Dislocations were generated preferentially from a scratch drawn on the sdrface. It is known in some impurity-doped semiconductors, such as O doped
Si [13,14] and In doped GaAs [15], that a critical stress is needed to generate dislocations from
a scratch. Such critical stress was not detected in the present work. The magnitude of the critical stress in the Gesi alloys investigated may be lower than the lowest stress applied m the experiment, i.e. 3 MPa. This implies that no significant pinning of dislocations takes place in the Gei-xsix alloys with z
= 0.004-0.022.
The velocity was measured as a function of the temperature in the range 450 -700 °C and of the resolved shear stress in the range 3 -20 MPa. Figure 1 shows the velocities of 60°
dislocations at various temperatures plotted against the shear stress in Gei-xsi~ with various contents from z
= 0.004 to 0.022 together with that in pure Ge. As seen in Figure 1, the
logarithm of the velocity of dislocations is linear with the respect to the logarithm of the stress at all temperatures and with approximately the same slope, and the velocity of dislocations in
Gesi decreases monotonically with an increase in the Si content and reaches about a half of that in pure Ge at z
= 0.022.
2370 JOURNAL DE PHYSIQUE III N°12
Table I Magnitudes of vo, m and Q for 60° dislocations in Gei-xsi~ and pure Ge.
CrYstal Vo till/S) m Qlev)
Ge 2.9 x 10~ 1.7 1.62 ~ 0.05
Gei-xsi~ (z
= 0.004) 3.8 x 10~ 1.7 1.65 (z = 0.016) 4.6 x 10~ 1.7 1.68
= 4.2 x 10~ 1.7 1.68
As in other semiconductors, the velocity v of 60° dislocations in the Gei-xsi~ alloys with
z = 0.004 to 0.022 can well be expressed as a function of the stress r and the temperature T
by the empirical equation:
v = vo(r/ro)~°exp(-Q /kBT) (1)
where To
" 1 MPa and kB is the Boltzmann constant. The experimentally determined magni-
tudes of vo, m and Q m Gesi and Ge are given in Table I. The magnitudes of the parameters
m and Q in equation (I) in the alloy are same as those in Ge or only slightly different. This may be due to rather small Si contents in the alloys investigated.
3.2. MECHANICAL STRENGTH. Stress-strain behaviour was measured at various temper-
atures under a shear strain rate of 1.8 x 10~~ s~~. At temperatures lower than 600 °C the
stress-strain curves of all the specimens were characterized by a remarkable stress drop, fol- lowed by an increase in the stress with strain. Such a notable stress drop after the upper yield point is common for various semiconductors, such as Si, Ge, GaAs, InP etc. at relatively low
temperatures.
On the contrary, at a high temperature of 900 °C, no stress drop is seen in the stress-strain
curves of the Gesi alloys with z
= 0.01, 0.10, 0.25 and 0.40 as seen in Figure 2. Stress-strain
curves of Ge and Si are also shown for comparison sake Ge shows no stress drop attributed
to the high mobility of dislocations at this temperature [7]. An ~important fact in Figure 2 is that the Gesi alloys with z larger than 0.10 exhibit much higher levels of yield and flow
stresses in comparison with Ge and Si. The stress-strain curve of the Gesi alloy with z
= 0 10
shows many fine serrations, i.e. repeated peaks each followed by an abrupt drop in the stress, in the deformation stage after yielding when deformation is conducted under a low strain rate 1.8 x 10~~ s~~ at 900 °C. The phenomenon is known as the Portevin-Lechateher phenomenon
and is interpreted as being caused by repeated locking and release processes of dislocations due to the interaction with impurities as observed in highly impurity doped Si [16] and GaAs [17j.
The lower yield stresses for Gesi alloys with z
= 0.01, 0.10 and 0.40 and also those of Si and Ge are plotted against the reciprocal temperature in Figure 3 for the deformation under
a shear strain rate of1.8 x 10~~ s~~. The yield stresses in Si and Ge depend linearly on
the reciprocal temperature in the whole temperature range investigated. The same holds in a temperature range of 500 -700 °C for the alloy of z
= 0.01 and in a range of 550-600 °C for the alloy of x
= 0.10. In such temperature ranges the yield stresses of the alloys are close to that of Ge. On the other hand, the temperature dependencies of the yield stresses of the alloys
become much weaker in a high temperature range. This temperature range expands toward the low temperature side with an increase in the magnitude of z. Thus, the yield stresses of
alloys for concentrated alloys are nearly constant with respect to the temperature and much
higher than that of Ge. In Figure 3, a peak can be recognised in the yield stress of Gesi alloy
with x
= 0.10 deformed under a shear strain rate of1.8 x 10~~ s~~ Siethoff observed the temperature dependence of lower yield stress of Si doped with Ge up to 1.6 at.$l similar to
x=04
i~ ~~~~~
$
~ib
jj x=0J
~
5i ,~_--~
0 5 lo 15
SHEAR STRAIN, %
Fig. 2. Stress-strain curves of Gei-~Si~ alloys with x
= 0.01, 0.10, 0.25 and 0.40 at 900 °C under
a strain rate of1.8 x 10~~ s~~ together with those of Si and Ge. Fine line shows that of Gei-~Si~
with x
= 0.10 deformed under a strain rate of 1.8 x 10~~ s~~.
Ui4
§j x=ool
i
t=!dxio-'s"'
ad I-o 1.2 !4
10~/T, K~
Fig 3. Yield stresses of the Gesi alloys plotted against the reciprocal temperature for deformation under a strain rate of1 8 x 10~~ s~~ and 18 x 10~~ s~~
2372 JOURNAL DE PHYSIQUE III N°12
l
[
k ,
~ ~,
$
,
~~
w i,
~
©~ ' d
(2
'
~k ~
(
o 05 io~
Si content
Fig. 4. Yield stresses ry of the Gesi alloy plotted against Si content for deformation at 900 °C
under a strain rate of18 x 10~~ s~~ together with Knoop hardness Hk
that of Si [10j. This may be attributed to rather low Ge content and also to the fact that the deformation temperature was too low to render the temperature-independent yield stress
appreciable in their Gesi alloys.
Figure 4 shows the dependence of yield stress of Gesi under a shear strain rate of 1.8 x 10~~ s~~ at 900 °C
on the Si content x. The yield stress increases with increasing
Si content in the composition range investigated. The maximum of yield stress is presumed
to exist in the range z = 0.5-1.0. Such a composition dependence differs significantly from the result that the hardness of Gesi alloys using a Knoop indentor with 25 g load for 10 s at the room temperature increases monotonically with increasing Si content up to z = 1. The
present result is similar to the results previously reported by Wang and Alexander [18].
4. Discussion
Alloying effects in the mechanical strength of the Gesi alloy are pronounced at high tempera-
tures. This may account for the fact that the hardness of the Gesi alloy at room temperature
shows no alloying effect. The velocity of isolated dislocations in the Gei-xsi~ alloys with
z = 0-0.022 is observed to be a little lower in the temperature range 450-700 °C than in Ge crystals. This may account for the rather small difference in the yield stresses of the alloys with such contents and of Ge observed in such a temperature range. However, the difference in the dislocation velocity among the Gesi alloys with various Si contents seems to not account for the drastic change in the mechanical strength of the alloys at higl~ temperatures as discussed in next.
It is well accepted that the flow stress of a crystal in any deformation stage consists of two
components [19). One is the effective stress that is needed to mole dislocations at a certain
velocity against the intrinsic resistance of the crystal lattice ma a thermally activated process.
The other is the stress that is needed to overcome any resistance not thermally surmountable and depends weakly on temperature. This stress component is called athermal stress. If we
have to assume that alloying results in a drastic increase of the Peierls potential and brings
about the reduction of dislocation velocity, we expect higher upper yield stress and bigger
amount of the yield drop after the upper yield point in the Gesi alloy than in the Ge on
the basis of consideration of the dislocation dynamics of yield point phenomena in various semiconductors [7). Furthermore, the strengthening effect related to alloying should diminish
as the temperature is increased. Neither is in agreement with the experimental results in this work.
The data in Figure 3 can be interpreted to show that the yield stress of the alloy of any composition consists of two components [19) One decreases rapidly with an increase in the temperature in a similar manner as in Ge (or Si) and the other is almost independent of the temperature and increases with an increase in z. The former is the effective stress and the latter the athermal stress. It is reasonable to suppose that the athermal stress is related to the
alloying effect.
There are a few possible origins for athermal stress related to alloying, as discussed in the
cases of GaASP and InASP [8,9). The first is short-range order observed m most III-V ternary
alloys. Motion of a dislocation destroys the short-range order and produces an interface of positive energy along its slip plane. Thus, an extra stress of athermal nature is needed to move a dislocation through a crystal with short-range order [20]. Ordered structures have been observed in SiGe thin layers grown on substrates by molecular beam epitaxy or metal
organic chemical vapour deposition by many research groups [21-23]. However, it is considered difficult to detect ordered structure as reported by Stenkamp and Jhger in Gesi alloys grown by the vertical Bridgman method [24]
The second is long-range stress related to the local fluctuation of the alloy composition in
a crystal. Since the bond lengths of Si and Ge differ by about 4$l, local fluctuations of the alloy composition in a crystal, causing small regions enriched with Si or Ge, may introduce
a long-range stress field that cannot be surmounted by dislocations via a thermally activated process.
The third is related to the immobilisation of dislocations due to the dynamic development
of a solute atmosphere around them during deformation at high temperatures. An extra stress is needed to release the dislocations from solute atmosphere. In fact, the Portevin-Lechatelier
phenomenon which is interpreted as being caused by the repeated pinning and release process of dislocations was shown in Figure 2. Though the release process of a dislocation from its
solute atmosphere is a thermally activated one, the development of a solute atmosphere around
a dislocation is more enhanced at higher temperature. Thus, the contribution of these effects
to the flow stress compensates each other and may become temperature insensitive, apparently
looking like an athermal stress as discussed in highly impurity doped GaAs [17).
We think that local fluctuation of alloy composition and dynamic development of solute atmosphere around dislocations are the causes for the strengthening of bulk Gesi alloys at elevated temperatures.
5. Conclusion
The mechanical strength and the dislocation velocities in single crystal Gei-xsix alloys grown by the Czochralski method were investigated by the compressive deformation and by the etch pit technique, respectively.
The dislocation velocity in Gei-xsi~ with z
= 0.004-0 022, which reaches about a half of that in Ge at z
= 0.022, can be expressed by the empirical equation known in other
