Oct 28, 1991 - ATdic T Bell Laboratories, Murray Hill, New Jersey 07974 ... Randall Laboratory ofPhysics, University ofMichigan, Ann Arbor, Michigan 48l09.
VOLUME
67, NUMBER 18
PHYSICAL REVIEW LETTERS
Real-Time X-Ray Diffraction Observation
28 OCTOBER 1991
of a Pin-Slip Mechanism in Ge Sil
Strained Layers
W. Lowe, R. A. MacHarrie, J. C. Bean, and L. Peticolas ATdic T Bell Laboratories, Murray Hill, New Jersey 07974 Randall Laboratory
R. Clarke and W. Dos Passos of Physics, University of Michigan, Ann
Arbor, Michigan
48l09
C. Brizard and B. Rodricks Adi anced Photon Source Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received 16 July 1991)
Steplike behavior of the perpendicular lattice strain in Ge Sil — alloy layers, grown epitaxially on revealed by real-time x-ray scattering during rapid thermal annealing. A cooperative pin-slip mechanism is proposed which accounts for the observed kinetic effects including the coexistence of domains with different states of strain.
Si(001), is
PACS numbers:
61. 10.— i, 64. 70. Kb, 68.35.Rh
When two structurally similar materials are joined to form an interface many of the atoms in each material adjacent to the interface are related by simple lattice translation vectors. If the degree of misfit is small, the number of atoms that are coherent across the interface can be quite large [I]. The role of such coherent or "commensurate" regions was first addressed in a simple 1D model by Frenkel and Kontorova [2] (FK) and later refined to explicitly include the 3D nature of a thin film [3-6]. with discommensurations (misfit dislocations) Such models have been applied to explain the physical characteristics of real systems, especially to treat the crossover between pseudomorphic (i.e. , coherent) growth and structures in which misfit dislocations relieve the elastic strain for film thickness beyond some supposed critical value [7]. At present the key issue of strain relaxation extends kinetics and static models. In beyond single-dislocation the absence of probes operating in real time down to the atomic level very little is known about the dynamic pro-
cess of relaxation. In this Letter we address the kinetics of strained-layer relaxation by studying in real titne the dynamics of Ge, Sil „alloy films grown epitaxially on a silicon (100) substrate. Rather than viewing relaxation as the result of single-dislocation kinetics [8] (nucleation and multiplication), we find that it is necessary to take a more global view of the problem. In particular, we take advantage of the power of real-time x-ray scattering [9] to provide information about the long-range cooperative behavior of the strained layer during the relaxation process. The real-time x-ray-diffraction method used to make is based on angular these measurements dispersive at methods developed for fast structural measurements the X-16B beam line of the National Synchrotron Light Source. Details of the scattering geometry and dispersive optics will be presented elsewhere [10]. A description of the special position-sensitive detector has been published previously
[11].
The incident x-ray beam from the synchrotron was tuned to 7. 316 keV with an energy resolution of dE/E . On beam line X-16B a horizontal focusing collects 3 mrad of radiation from the monochromator synchrotron and focuses it to a 0.5-mm spot in the (horizontal) scattering plane. The beam has a vertical extent at the sample also of 0.5 mm. Therefore the scattering volume is 0.25 mm times the penetration depth of the xray beam. By working in the horizontal plane a continuous angular span of radiation about 250 arcsec wide defines a range of incident wave vectors k;. Since each k; is populated simultaneously, they are all available for diffraction at slightly different angles. All of the diffracted wave vectors kf are collected simultaneously on the detector. Thus a full diffraction scan was collected in parallel, and in this way a profile of the (004) strainedlayer diffraction peak could be recorded every 100 msec. The detector was a charge-coupled-device (CCD) array with all but the top row masked. This row was used to collect the diffracted x rays and the remainder of the rows were used for storage. The temporal resolution is governed by the CCD row transfer rate, source brilliance, and the sample diffraction efficiency. To activate the lattice kinetics the samples were heated using a 2-kW 7 mm quartz-halogen lamp. The lamp was positioned from the face of the sample, just far enough away not to interfere with the incident and diffracted beam wedges. A gold refiector broadly focused the lamp over an area of 15 mm, where the total sample area was 25 mm . The Ge„Si~ —„samples used in this study were grown by molecular-beam epitaxy (MBE) at 550'C [12]. The composition and thickness of the samples are chosen so that they have small dislocation densities, typically 100-200 cm . Ge„Si] — is a model strained-layer system and is well suited for these studies because of the The large body of literature on structural measurements. two sets of samples used in this study span the so-called "metastable" region of composition-thickness values, where the kinetics of strain relaxation has been found
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1991 The American Physical Society
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PHYSICAL REVIEW LETTERS
67, NUMBER 18
previously to play an important role in determining the nature of the epitaxial structure [13,14]. The data presented here were taken from measurements on samples with h~ =2000 A and x =0.2. A sample with x =0. 18 shows similar behavior. Films with h~ 1000 A did not show anomalous behavior of the type described
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here. A schematic illustrating a coherent region of a Ge„Si~ -Si interface is shown in Fig. 1. The Si substrate potential is represented as a periodic array of sinusoidal wells. The Gep ppSip 8p overlayer is elastically strained with b&) bi~i where b~ and bi are the lattice spacings of the epitaxial overlayer measured normal to the film plane and parallel to the interface, respectively. The thermal expansion coe%cients for Si and Ge„Si]— are temperature dependent and differ by approximately 0.5x10 '/K over the temperature range [15], therefore no substantial shear stresses are developed when the film and substrate are at the same temperature. Neither do we expect a significant temperature gradient in the samIn a pseuples during the kinetic measurements. domorphic overlayer b = b, (1+si), where ~i
1
—v
1+v
sJ. ) i
and b is the bulk lattice constant for a Gep2pSipgp alloy, si is the in-plane strain, s~ is the strain along (001), and v is Poisson s ratio. Using these expressions the perpendicular lattice constant, b& =b, (1+@i), is related to b~~ by Poisson's ratio. Therefore as the lattice is compressed in the interface plane, the cell expands along the perpendicular direction by an appropriate amount, tending to conserve the cell volume. the diffraction angle of the (004) By monitoring Ge, Si] „peak, which is a direct measure of b&, both lattice constants b~ and bi are known throughout the heating cycle. Since the x-ray penetration depth is several microns, the Si substrate lattice constant ap is also monitored. In this experiment the tetragonal distortion or strain of the overlayer can be followed in real time during a rapid thermal annealing cycle. In Fig. 2 the lattice con-
[001]
= [010] I
o
~
o
GexSi(| -x)
o
~
~
o
~
o
~ ~
~
o
~
o
o
o
I
o ——
l
~
o
~
bll
o
stant along the growth direction, b~ (plotted as open circles), and ao are plotted versus time. The temperature along the top of the plot was calibrated using the measured thermal expansion of the Si lattice constant ap, shown by the lower curve. The calibration is in agreeatment with readings obtained using thermocouples tached to the front and back of the substrate. Also shown in Fig. 2 for comparison is the calculated 1attice constant of a Geo 2oSio so free-standing film undergoing thermal expansion (curve b). This curve represents the behavior that a GepppSip8p film would have if removed from the substrate. The topmost curve represents the calculated lattice constant (b&) for a pseudomorphic layer. The lattice constant for the pseudomorphic case (bi =an) is
b~
=(b, —ao) 1+v —v +ao, 1
for temperature. The most striking feature of the data in Fig. 2 is the existence of several discontinuities. The first discontinui200 C on heating and the final one at ty appears at =300 C on cooling. On heating, b& starts increasing thermal expansion curve, but along the pseudomorphic then undergoes a transition to a smaller (base-line) value somewhat lower than that at ambient temperature. b& then increases, following the same slope as the pseudomorphic curve. On further heating, b& drops back to its base-line value, increases again, drops back, and so on. A similar behavior, in reverse, is observed on cooling. The strain is double valued in a region around each of the It discontinuities, indicating a coexistence phenomenon. is interesting that during the whole cycle there is practiand all the lattice spacings have been adjusted
=
5.56
5.54— 5.52— 5.50— 5.48— 5.46 5.44— 5.42
FIG. 2. The I
I I
Si|,
ap
I
-Si interface showing the Si surFIG. l. The (l00) Ge, face as a series of identical potential wells.
2514
('C)
Temperature
o ——
Si Substrate
28 OCTOBER 1991
300 ~
I
I
1000 1200 1
I
I
I
400 I
I
200
~
I
(b)
(a) I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
80 120 160 200 240 280 320 Time (sec) lattice constant (b+), plotted as open circles, of 0
40
a Geo. 20Sio&0 strained layer vs time and temperature measured using real-time x-ray diA'raction during rapid thermal annealing. The lattice constant for silicon (measured) is shown by the lowest curve (a) and the two curves above are the calculated lattice constants b~ for (curve b) relaxed Geo poSlosp and (curve c) pseudomorphic Geo. 2oSio. so.
VOLUME
67, NUMBER 18
PHYSICAL REVIEW LETTERS
cally no net change in the perpendicular strain; i.e. , the behavior on heating and cooling is completely reversible. Therefore there is no net relaxation and presumably no increase in misfit dislocation density. Furthermore, on heating we see that the net thermal expansion for b& is negligible. In fact, as we approach the highest temperature (1080 C), the value of b& is close to that of the fully relaxed case (see Fig. 2, curve b), indicating that the effect of the substrate potential is substantially reduced at these temperatures, which are close to the melting point. In the limit of slow heating and cooling ( 0. 1 'C sec ') no transitions are observed in b~. This is strong evidence that the observed behavior is kinetic in origin. A complete understanding of the cooperative kinetics cannot be arrived at from these initial findings; however, several important features of the Ge Si1 —,strained-layer system are prominent and point the way to an explanation of the behavior. To lay a foundation for the understanding of the dynamics of strain relaxation we refer again to the FK model. During rapid heating the Geo2oSiosQ layer expands along the [001] direction (and also in the basal plane) increasing the vertical strain b& —b~~ faster than the basalplane expansion. The Ge02pSiogo basal plane is pinned to the Si lattice by the periodic surface potentials shown in Fig. l. As b& — critical, the Geo 2oSipsp b~~ becomes strained layer can reduce its vertical strain as well as continue its expansion in the [001] direction by unpinning and slipping along the interface. Once this occurs, the strain along [001] is decreased abruptly. A sharp discontinuity in b & accompanied by coexistence clearly indicates that two scattering domains exist concurrently one with less strain (b&) and one with more strain and further that the domains exist for some time (b& ) interval iJ.t. Taking the difference between bi and b& and keeping the cell volume constant, the increase of each basal-plane axis is 0.05% or (5 A)/(10000 A). Therefore the transition of the entire scattering volume (0.5 mm &&0.5 mmx2000 A) from b& to b& occurs at discrete temperatures (T) on a time scale ht(T). Since b& changes by a constant, discrete amount at each discontinuity, one might surmise that coherent regions of typical size 1 pm undergo a sudden expansion by one lattice constant. Evidence for a coherent microstructure on this length scale has been seen in plane-view TEM [16]. Finally, we remark on the unusual dependence of the coexistence, ht, on the rate of temperature change ~T~. This is illustrated in Fig. 3. We see that the faster the rate of heating (or cooling), the shorter is the coexistence, the overall behavior following a power-law dependence. We do not yet fully understand the significance of this, except to point out that it identifies the transitions as being kinetic in origin (dependence on ( T rather than T). In particular, in the lower limit of ~T~, the behavior makes contact with the observation of irreversible relaxation in samples subjected to prolonged heating. Addition-
200
—
~
=
160 =
~ &
~~
Heating Cooling
120— 40
O
8040-
(
—
28 OCTOBER 1991
0 0
,
I
8
12
16
.
I
20
h, t(sec) F'IG. 3. The time dependence of the domain growth with respect to the rate of change in temperature. The squares are for heating and the triangles for cooling. The solid line is a power-law fit to the data.
al work is underway to better understand the temporal behavior of the strain through a molecular-dynamics simulation [17]. In conclusion, evidence is presented for discontinuous strain behavior in Ge Sii — under rapid thermal conditions when the sample is grown in the metastable regime the timeFurthermore, near its critical thickness. show the resolved x-ray-diffraction data unambiguously existence of two concurrent (in time) strain states with a time dependence based on the time rate of change of the Our measurements clearly suggest that temperature. cooperative kinetic mechanisms are active and dominant in interface relaxation processes and that the kinetics of single misPt dislocations may not be representative of such dynamic processes as strained-layer relaxation. The authors acknowledge helpful discussions with R. People, R. Hull, G. Gilmer, B. Orr, and D. V. Lang. B.R. and C. B. were supported by the U. S. Department of Energy, RES-Materials Science, under Contract No. W-31-109-ENG-38. R.C. was supported in part by NSF Grant No. DMR 8805156. The synchrotron studies were done at the National Synchrotron Light Source on the X-168 beam line. The NSLS is supported by the U. S. DOE, Basic Energy Sciences, Materials and Chemical Sciences under Contract No. DE-AC02-76CA0016.
by E. Kasper Rubber, Boca Raton, 1988),
[1] Silicon Molecular Beam Epitaxy. edited
J. C. Vol. l.
and
Bean (Chemical
[2] Y. I. Frenkel and T. Kontorova, Zh. Eksp. Teor. Fiz. 8, 1340 (1938). [3] J. H. van der Merwe, J. Appl. Phys. 34, 117 (1963). [4] J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974); 29, 273 (1975); 32, 265 (1976). [5] J. H. van der Merwe and W. A. Jesser, J. Appl. Phys. 64,
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PH YSICAL REVIEW LETTERS
4968 (1988). [6] J. Y. Tsao and B. W. Dodson, Appl. Phys. Lett. 53, 848
(1988). [7] R. Bruinsma and A. Zangwill, J. Phys. (Paris) 47, 2055
(1986).
(1989).
(1989).
[14] C. G. Tuppen and C. J. Gibbins, Thin Solid Films 183, 133 (1989).
[9] R. Clarke, W. Dos Passos, W. Lowe, B. G. Rodricks, and C. Brizard, Phys. Rev. Lett. 66, 317 (1991). [10] W. Lowe, R. Clarke, and R. MacHarrie (to be published).
[11] B. Rodricks, R. Clarke, R. Smither,
Rev. Sci. Instrum. 60, 2586 (1989). [12] J. C. Bean, T. T. Sheng, L. C. Feldman, A. T. Fiory, and R. T. Lynch, Appl. Phys. Lett. 44, 109 (1984). [13] R. Hull, J. C. Bean, D. J. Werder, and R. E. Leibenguth, Phys. Rev. B 40, 1681
[8] S. S. lyer and F. K. LeGoues, J. Appl. Phys. 65, 4693
28 OCTOBER 1991
and A. Fontaine,
[15] V. V. Zhdanova, M. G. Kakna, and T. Z. Samadashvili, lzv. Akad. Nauk. SSSR Neorg. Mater. 3, 1263 (1967). [16] R. Hull and J. C. Bean, J. Vac. Sci. Technol. A 4, 2580 (1989). [17] B. G. Orr and D. Kessler (unpublished).
