Dislocation and kink motion study in the bulk SiGe alloy single crystals

ELSEVIER

Dislocation

Materials Science and Engineering A234-236 (1997) 735-738

and kink motion study in the bulk SiGe alloy single crystals

N.V. Abrosimov a,b, V. Alex b, D.V. Dyachenko-Dekov a, Yu. L. Iunin a,*, V.I. Nikitenko a, V.I. Orlov a, S.N. Rossolenko apb,W. Schriider b a Institute

of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, b Institute of Crystal Growth, Rudower Chaussee 6, 12489 Berlin, Germany

Russia

Received 6 February 1997; received in revised form 8 April 1997

Abstract The individual dislocation mobility in bulk single SiGe crystals has been studied both with conventional and intermittent loading (IL) techniques. A model is used connecting the experimental data on dislocation paths with values of kink displacements under IL. The experimental data are compared with two models describing the interaction of a dislocation with point defects. It is shown that with small Ge concentration Cottrell atmosphere determines the dynamical drag of the dislocation giving rise to threshold immobilisation. With higher Ge content the specific mode of kink drift along the dislocation line (the motion in the field of random forces) takes place. 0 1997 Elsevier Science S.A. Keywords:

Dislocation; Dislocation kink; SiGe alloys; Point defects

1. Introduction The fundamental aspects of the dislocation mobility in the Peierls relief have been studied mostly using Si and Ge single crystals with deepest potential relief. It appears that even in these materials impurities play a key role in the dislocation mobility at low stresses.The manifestations of point defect influence are of great variety. Impurities serve as obstacles for the kink motion [l], their redistribution near the dislocation core lowers the dislocation energy and leads to the dislocation immobilization [2]. The fluctuations of point defect density along the dislocation might determine the specific nonlinear mode of the one-dimensional kink motion-drift in the field of random forces [3,4]. To study kink pair evolution on dislocations the intermittent loading (IL) technique has been developed [5]. The method allows to study kinetics of kink relaxation after short pulse loading application. The IL data obtained with Si samples differ significantly from the ones obtained with Ge. The immobilization of dislocations in Si with pulse separation increase has been * Corresponding author. Tel.: + 709 657 644014498; fax: + 709 657 64111; e-mail: [email protected] 0921-5093/97/$17.00 0 1997 Elsevier Science S.A. All rights reserved. PII SO92

1-5093(97)00270-O

explained qualitatively [6] as a consequence of the dynamical drag of a dislocation by mobile point defects. In Ge the dynamical drag obviously is not a factor and experimental data could be described in the frameworks of theory considering sublinear kink drift through the point defect fluctuations [7]. The probable cause of dislocation immobilization in Si are electrically inactive light impurities, in particular oxygen atoms [8]. To eliminate the influence of uncontrolled interstitial impurities it may be useful to dope Si with substitution impurity with much higher concentration. Recently the progress in crystal growth has allowed one to get the bulk Si, -xGex single crystals with x up to several atomic percent and low as-grown dislocation density. Ge is the main impurity in this material. It is interesting to study the influence of Ge content on the kink mobility characteristics in SiGe alloys and learn the details of the interaction of dislocation and point defects in them. This research is also important because of the growing interest to the quality and performance of the strained-layered heterostructures, considered as a perspective material for different device applications. The velocities of dislocations were measured not only in SiGe films [9,10], but also in the bulk samples [11,12].

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2. Experimental

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details.

(ill)-, (lOO)- and (IlO)-Si,-,Ge, (O
3. Results and discussion Fig. 1 shows the stress dependence of the average velocity of individual 60” dislocations in bulk SiGe single crystals with Ge content 2 and 5.5 at%. One can see the alignment of plots at high stresses. The data can be described in this region with empirical equation v= v~.(z/Z())m, where z0 = 1 MPa, m = 1.6. The sharp decrease in dislocation mobility is observed with approaching some low threshold of stress. The threshold value increases with Ge content. Fig. 2 presents the plots of mean dislocation glide distances I versus relative pulse separation obtained with SiGe samples containing 2 (curve 1) and 5.5 at%

10

100 7,MPa

Fig. bulk

1. The stress dependence of average 60’ dislocation SiGe samples with a Ge content of 2 and 5.5 at’%.

velocity

in

Ge (curve 2). One can see qualitative distinction between plots. The first dependence is S-shaped with inflection point and is similar to the one observed in silicon samples [6]. The shape of dependence Z(t,) in Si was explained qualitatively in [6] as a result of interaction of dislocations with Cottrell atmosphere leading to the dynamical starting stress 7, = (c, - CJ. u/(ab)

(1)

Here c1 and c2 are the concentrations of point defects in adjacent valleys of the potential relief, u is the energy of short-range interaction of a dislocation with a point defect, a is the kink height, b is the magnitude of the Burger’s vector. The value of AC = (cl - CJ depends on the point defects mobility and the dislocation velocity value V

AC= c,,.[exp(a/Vt,)

- I] z c,a/Vt,

(2)

1.0

0.8

3. 0.6 0.4 0.2 0.0 0.0

0.5

1.0

1.5 fp / ti

2.0

2.5

3.0

Fig. 2. The normalised dislocation displacement vs. relative pulse separation in bulk SiGe single crystals with different Ge content: (1) 2 at% Ge, t, = 20 ms, t,jt, = 0.X; (2) 5.5 at% Ge, t, = 30 ms, 2,/t, = 0.83. z, = 15 MPa.

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Here t, is the characteristic time of the point defect displacement for one lattice parameter, c,, is the average concentration of point defects in the crystal. It was supposed also that t, > t, = a/vSt, where I’,, is a mean dislocation velocity under conventional static loading with rSst= zi. We may conclude from Fig. 1 that z, increase with Ge content. By assuming that value of u does not change significantly with Ge doping it turns out that AC also increases. On the other hand, dependence for the crystal containing 5.5 at% Ge (Fig. 2, curve 2) is similar to the one observed with pure Ge samples [7] where the entrainment of point defects by the dislocation becomes insignificant. It follows that t, increases, i.e. the diffusivity of point defects interacting with dislocation decreases with Ge content. To describe the data presented with curve 2 in Fig. 2 let us consider the kink pair evolution under IL. During the pulse stress action, in addition to thermodynamically equilibrium kinks, extra kink pairs form and spread along the dislocation line. As the pulse separation goes on they become unstable and collapse to the formation centres under the action of the forces caused by the mutual attraction of kinks and the interaction of the dislocation and kink with point defects. In accordance with the Hirth and Lothe theory [14], the dislocation velocity V is proportional to the kink velocity i+: (3)

V=L7.lZ.v,

With small external stresses the density of kinks n is close to thermodynamically equilibrium value n,. When the directed drift motion of kinks prevails over the chaotic diffusion, we can estimate the average kink velocity during the cycle of IL with (xi + x,)/(ti + t,), where xi and xp < 0 are the kink drift displacements during the pulse loading and the ‘pause’, respectively. We receive for the loading duration IZ(ti + tp) the dislocation displacement under IL I = V C (tj + tP) = The dislocation a . n,(q + x,)i(t; + tp> c (4 + tp). displacement

under

static

loading

I,, =

V,;

c,~ =

a en. vk*t,,. Assuming that kink velocity under pulse loading x,/t, = vk, we receive: l/lc~,= 1 +

(4)

X,/Xi

According to the theory [3] the interaction of a dislocation with manifold point defects leads to the existence of critical shear stress r, separating two different modes of the dislocation kink motion. With r > rCr the conventional linear drift takes place: x = v,t Vk = (D/kT)

. (T - T&b

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1

J

0

20

40

60

80

100

120

140

z, MPa Fig. 3. The determination 60” dislocation velocity x =

of rc from the stress dependence in bulk SiGe with a Ge content

of average of 5.5 at%.

x&/t,)”

(6)

with s = T/To I 1, x,, = kT/z,ab, To= (Cl + cJu2/ (2kTa2b), t, = xi/D, and r, z r0 + T,; r, is described with Eq. (1). To check the validity of Eq. (5), we replotted data for SiGe samples with Ge content 5.5 at% with linear axis (Fig. 3). One can see that at stresses above 40 MPa the dislocation velocity is well described with Eq. (3) with vk being determined by Eq. (5) with r, = 25 MPa. Both pulse ri and ‘pause’ rp = 0 stresses are less than zC, so kink drift is nonlinear during all the pulse loading cycle. Using Eq. (6) for kink displacements both during the pulse xi and pause xp and substituting them into Eq. (4) we receive l/l,, = 1 -

K(t&)“p

(7)

with 6, = TJz~, K= (tO/ti)“-‘p, bj = (zi - z,)/+ The curve 2 in Fig. 2 shows the result of fitting of the experimental data with Eq. (7). One can see that the theory and experiment are in good agreement. The fitting parameters allow us to estimate also the kink diffusivity with Eq. (6) and the kink migration enthalpy with expression [14]: W,,, = kT ln(2v,bz/ D) z 1.6 eV. Here vD is the Debye frequency. The estimation value is in reasonable agreement with the ones obtained for dislocation kinks in pure Si [5,15]. The model, Eqs. (4) and (7), relates immediately the microscopic kink displacements and experimentally observable macroscopic dislocation path lengths. This opens up new avenues for the investigation of different modes of dislocation kink dynamics.

(5)

Here r is the effective stress acting on the kink, k is Boltzmann’s constant, and D is the kink diffusivity. With t < r, the sublinear dependence of the kink path length on time takes place with the drift in the field of random forces:

References [l]

V. Celli, M. Kabler, T. Ninomiya, (1963) 58. [2] B.V. Petukhov, Sov. Phys. Solid [3] B.V. Petukhov, Sov. Phys. Solid

R. Thomson, State 24 (1982) State 30 (1988)

Phys. Rev. 248. 1669.

131

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[4] V.M. Vinokur, J. de Physique (Paris) 47 (1986) 1425. [5] B.Y. Farber, Y.L. Iunin, V.I. Nikitenko, Phys. Stat. Sol (a) 97 (1986) 469. [6] Y.L. Iunin, V.I. Nikitenko, V.I. Orlov, B.V. Petukhov, Proc. 10th Int. Conf. ICSMA-IO, Sendai, Japan, Aug. 21-26,1994, Jpn. Inst. Metals, 1994, p. 101. [7] Y.L. lunin, V.I. Nikitenko, V.I. Orlov, B.V. Petukhov, Solid State Phenomena 32/33 (1993) 333. [8] M. Imai, K. Sumino, Phil. Mag. A 47 (1983) 599. [9] R. Hull, J.C. Bean, Crit. Rev. Solid State Mater. Sci. 17 (1992) 507.

and Engineering

A234-236

(1997)

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[lo] K. Kerstin, S.G. Roberts, Phil. Mag. Lett. 74 (1996) 67. [l l] Y.L. Iunin, V.I. Nikitenko, V.I. Orlov, N.V. Abrosimov, S.N. Rossolenko, W. Schroder, Solid State Phenomena 47/48 (1996) 425. [12] I. Yonenaga, K. Sumino, Appl. Phys. Lett. 69 (1996) 1264. [13] N.V. Abrosimov, S.N. Rossolenko, V. Alex, A. Gerhardt, W. Schriider, J. Crystal Growth 166 (1996) 657. [l4] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982. [15] F. Louchet, Phil.Mag. A 43 (1981) 1289.