We study the interplay of elastic and plastic strain relaxation of SiGe/Si(001). We show that the formation of crosshatch patterns is the result of a strain relaxation process that essentially consists of four subsequent stages: (i) elastic strain relaxation by surface ripple formation; (ii) nucleation of dislocations at the rim of the substrate followed by dislocation glide and deposition of a misfit dislocation at the interface; (iii) a locally enhanced growth rate at the strain relaxed surface above the misfit dislocations that results in ridge formation. These ridges then form a crosshatch pattern that relax strain elastically. (iv) Preferred nucleation and multiplication of dislocations in the troughs of the crosshatch pattern due to strain concentration. The preferred formation of dislocations again results in locally enhanced growth rates in the trough and thus leads to smoothing of the growth surface.

Topics
Mechanical stress
1.
A. G.
Cullis,
D. J.
Robbins,
A. J.
Pidduck
, and
P. W.
Smith,
J. Cryst. Growth
123
,
333
(
1992
).
Google Scholar
 
2.
D.
Dutartre,
P.
Warren,
F.
Chollet,
F.
Gisbert,
M.
Bérenguer
, and
I.
Berbézier,
J. Cryst. Growth
142
,
78
(
1994
).
Google Scholar
 
3.
M. A. Grinfeld, Dokl. Akad. Nauk SSR 290, 1358 (1986).
4.
D. J.
Srolovitz,
Acta Metall.
37
,
621
(
1989
).
Google Scholar
 
5.
S.
Christiansen,
M.
Albrecht,
H. P.
Strunk,
P. O.
Hansson
, and
E.
Bauser,
Appl. Phys. Lett.
64
,
3617
(
1995
).
Google Scholar
 
6.
F.
Jonsdottir
and
L. B.
Freund,
Mater. Res. Soc. Symp. Proc.
317
,
309
(
1994
).
Google Scholar
 
7.
D. E.
Jesson,
S. J.
Pennycook,
J.-M.
Baribeau
, and
D. C.
Houghton,
Phys. Rev. Lett.
71
,
1744
(
1993
).
Google Scholar
 
8.
E. A.
Fitzgerald,
Y.-H.
Xie,
D.
Monroe,
P. J.
Silverman,
J. M.
Kuo,
A. R.
Kortan,
F. A.
Thiel
, and
B. E.
Weir,
J. Vac. Sci. Technol. B
10
,
1807
(
1992
).
Google Scholar
 
9.
K. H.
Chang
and
H.
Ming Liaw,
Mater. Res. Soc. Symp. Proc.
280
,
719
(
1993
).
Google Scholar
 
10.
S. E.
Harvey,
J. E.
Angelo
, and
W. W.
Gerberich,
Mater. Res. Soc. Symp. Proc.
308
,
433
(
1993
).
Google Scholar
 
11.
W. Dorsch, S. Christiansen, M. Albrecht, H. P. Strunk, P. O. Hansson, and E. Bauser, Surf. Sci. 331–333, 896 (1995).
12.
The layer thickness has been determined of cross-sectional samples. Therefore, we used parts of the sample, where first dislocations have formed, assuming that the equilibrium position of dislocations during this stage of growth corresponds to the chemical interface.
13.
S. Christiansen, M. Albrecht, J. Michler, and H. P. Strunk (unpublished).
14.
A rough criterion for preferred dislocation nucleation at troughs based on an energetic assessment for the critical layer thickness is given by Matthews et al. (Ref. 15): The critical thickness of a continuous layer hc is essentially given by the critical radius rc of a dislocation half-loop (hc⩾rc). The critical radius depends on the shear stress T according to rc∝1/T. If the shear stresses at the trough is enhanced by a factor S(λ/A) (compared to that of a two-dimensional strained layer) the critical thickness is reduced by rc2D/S(λ/A), while the strained layer thickness is reduced to dr=d−A. Thus dislocation nucleation is preferred if S>rc/(d−A).
15.
J. W.
Matthews,
S.
Mader
, and
T. B.
Light,
J. Appl. Phys.
41
,
3800
(
1970
).
Google Scholar
 
16.
This contrast is due to strain relaxation at surface steps, which can easily be seen by the asymmetric contrast behavior of steps at the center of the trough in Fig. 3 marked with t: the contrast of steps is dark at one side of the trough and bright at the other side of the trough. The line where the contrast changes from dark to bright is exactly the center of the trough.
17.
M. Albrecht, S. Christiansen, and H. P. Strunk, Phys. Status Solidi 150, 453 (1995).
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© 1995 American Institute of Physics.
1995
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