Relaxation in Sub-Micron Si- 1-x Ge x Strain-Layer Mesas
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RELAXATION IN SUB-MICRON
Sil.xGex STRAIN-LAYER
MESAS
DAWEI LUO, DAVID J. HOWARD and DAVID C. PAINE Brown University, Division of Engineering, Providence, RI 02912
ABSTRACT Finite element modelling of strain-layer mesa structures shows that edge effects can contribute to the relaxation of in-plane misfit stress. Calculations were performed for a 200 nm thick layer of Si9OGelO grown epitaxially on an Si substrate which was patterned into 400-nm-high mesas ranging in diameter from 0.6 to 7 gm. These calculations were experimentally investigated using plan-view TEM to study relaxation in patterned and unpattemed material. This composition and film thickness exceeds the critical thickness predicted using simple strain energy considerations. In one experiment, an initially defect-free 200-nm-thick Si9oGelO layer was annealed at 960'C for I hr to create a nearly fully relaxed layer which was then lithographically patterned into an array of sub-micron mesas. The wafer was then annealed for a second time and changes in the character of the pre-existing dislocations were studied.
INTRODUCTION In the absence of kinetic constraints to dislocation nucleation and glide, the onset of misfit relaxation in biaxiall strained epitaxial thin films can be reasonably well predicted using the theory of Matthews . However, the technological implementation of strained-layer structures will, in general, require lithographic patterning. When this is the case biaxial stress conditions do not apply in the region immediately adjacent to a free edge or if the lateral dimensions of the patterned features are small relative to the thickness of the thin film. Under these conditions simple force balance requirements demand that the plane stress be zero at the free film surface which is created when an edge is introduced by lithographic patterning and subsequent etching. Thus, in the near edge region, the in-plane film stress is replaced by interface shear forces as shown schematically in Fig. 1. Furthermore, if the etch depth is greater than the thin film thickness, then the rigid substrate assumption is also no longer valid since the Si-pillar portion of the mesa shares part of the elastic strain. These ideas have been discussed, in part, in a recent review by Hu 2. We have used finite element (FE) analysis techniques to qualitatively determine the magnitude of the edge effect for features with lateral dimensions ranging from 0.6 to 7 4m. The experimental confirmation of FE-based conclusions is complicated by our inability to directly measure strain in sub-micron features. Indirect experimental evidence can, in principle, be obtained by establishing the conditions for the introduction of dislocations for strain relief in films that exceed the critical thickness. This is an unreliable approach since defect nucleation kinetics clearly dominate in structures that are laterally small in size since the probability of either inclusion of a threading dislocation 3 or homogeneous nucleation of one is unlikely in the mesa volume. Consequently, it is di
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