The viscosity of germanium during substrate relaxation upon thermal anneal
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The viscosity of germanium during substrate relaxation upon thermal anneal Sara E. Rosenberg, Cynthia G. Madras, Peter Y. Wong,a) and Ioannis N. Miaoulis Thermal Analysis of Materials Processing Laboratory, Mechanical Engineering Department, Tufts University, Medford, Massachusetts 02155 (Received 9 November 1995; accepted 11 March 1997)
Thin-film heterostructures experience structural relaxation when subjected to post-deposition thermal heat treatment. The rate of relaxation, elastic effects, and inelastic effects on the stress and deformation of the structure are determined by the physical properties of the materials, in particular, the solid-phase viscosity. During relaxation, movement of defects causes an increase of viscosity with time at a constant rate as these defects are annihilated. Experimental anneals have been performed on structures with polycrystalline silicon films on (111) germanium substrates, in which the substrate relaxes during thermal annealing. A numerical analysis of the experimental results has determined values for the viscosity and viscosity rate of (111) germanium wafers. In addition, four zones of the relaxation process have been identified, and results indicate that the increasing viscosity with time has a larger effect at lower furnace ramp-up rates.
I. INTRODUCTION
Intrinsic stresses develop as films are deposited due to energetic deposition and lattice mismatch between the materials. In addition, as the structure cools to room temperature, thermal (extrinsic) stresses develop as the temperature changes due to a difference in coefficients of thermal expansion between the film and substrate. When combined, these extrinsic and intrinsic stresses are of a high enough magnitude to cause buckling, peeling, delamination, and ultimately failure of the minute devices. In order to minimize these stresses, thin-film structures can undergo a post-deposition heat treatment. When the temperature is raised to ,60% of the material’s melting temperature,1 inelastic flow is activated, and the material undergoes structural relaxation, reducing stresses throughout the structure. The stress in the soft material will decrease due to relaxation, and the stress in the adjoining harder material will also be reduced. In the case of a hard (high melting point) film on a soft (lower melting point) substrate, the structure will curve more during annealing.2,3 The substrate, when stress relaxation occurs, has less resistance to bending induced by the highly stressed film that tends to expand. In the reversed case of a soft film on a hard substrate, the film will relax and provide less bending force, reducing the induced moment and curvature of the thinfilm structure.4,5 Both cases are examples where no densification of the film will occur during annealing. The amount of and time for relaxation is a function of solid-phase viscosity of the relaxing material. a)
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