Relaxation of a Strained Elastic Film on a Viscous Layer
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Relaxation of a Strained Elastic Film on a Viscous Layer R. Huang1 , H. Yin2 , J. Liang3 , K. D. Hobart4 , J. C. Sturm2 , and Z. Suo 3 Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544 2 Department of Electrical Engineering and Center for Photonics & Optoelectronic Materials, Princeton University, Princeton, NJ 08544 3 Department of Mechanical & Aerospace Engineering and Princeton Materials Institute, Princeton University, Princeton, NJ 08544 4 Naval Research Laboratory, Washington, DC 20375
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ABSTRACT Experiments were conducted with SiGe film islands on a layer of borophosphorosilicate glass (BPSG). Initially the SiGe is under compression. Upon annealing, the glass flows and the SiGe islands relax by both inplane expansion and wrinkling. This paper provides a twodimensional (2D) model for inplane expansion. The results from the model are compared with the experiments with small SiGe islands. The effect of winkling, which is ignored in the present model, is discussed qualitatively. INTRODUCTION Various types of compliant substrates have been proposed and fabricated to grow relaxed heteroepitaxial films with low dislocation density for optoelectronic applications [1]. Figure 1 shows the schematic of one fabrication process [2]. A compressively strained SiGe film on a Si wafer is bonded to another Si wafer covered with a layer of borophosphorosilicate glass (BPSG), with SiGe facing BPSG. The SiGe film is very thin to avert threading dislocations. Subsequently remove the Si on top of SiGe, and pattern the SiGe film into islands. At this stage, the SiGe islands remain strained. Upon annealing above the glass transition temperature, the BPSG flows and the SiGe islands relax. The goal is to obtain flat, strain- free islands, on which one can grow epitaxial optoelectronic devices. Large islands are desired; the large an island is, the more devices it can accommodate. SiGe Si Host wafer BPSG
SiGe islands
Si
Si Si Handle wafer
Wafer bonding
Si Remove top Si
Figure 1. Schematic fabrication process
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Si Pattern and anneal
Different relaxation mechanisms have been observed in experiments. A small island relaxes by inplane expansion. A large island wrinkles at the center. Further annealing of the large island gives rise to one of two outcomes. The wrinkles may disappear when inplane expansion arrives, leading to a flat and strain- free island. Alternatively, the wrinkles may cause significant tensile stress at the island surface, leading to fracture. Everything else being equal, a critical island size exists, below which the island relaxes without wrinkle-fracture. Several theoretical studies have followed up the above experiments to model the relaxation process [3-8]. In this paper, we focus on relaxation of small islands, where wrinkling is not significant. We formulate a 2D model for inplane expansion of a strained film island on a viscous layer. Our approach follows that of a one-dimensional analysis by Freund and Nix [3]. The model is valid for films under either
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