Creep curve of silicon wafers

Isomae, Seiichi; Nanba, M.; Tamaki, Y.; Maki, M.

doi:10.1063/1.89261

Cited by 30 publications

(14 citation statements)

References 7 publications

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“…Observations of viscous flow in films include that in SiO 2 /Si, 19,20 Pd-Si/Si, 21 Mo-Si/Si, 22 amorphous Si/crystalline Si, 9,10 and polyimide/Ge; 23 observations of viscous flow in substrates include that in Si/Ge 24,25 and Si 3 N 4 /Si. 26,27 In the presence of viscous flow, stress relaxation occurs and both the residual stresses and the curvature in the system are modified. 9,10,[19][20][21][22][23][24][25][26][27] While rigorous analytical solutions have been obtained for elastic systems, 4,5,16,17 analyses for viscous flow systems are few in number, elementary, and often limited to the case of viscous flow in a thin film constrained by a rigid substrate.…”

Section: Introductionmentioning

confidence: 99%

“…26,27 In the presence of viscous flow, stress relaxation occurs and both the residual stresses and the curvature in the system are modified. 9,10,[19][20][21][22][23][24][25][26][27] While rigorous analytical solutions have been obtained for elastic systems, 4,5,16,17 analyses for viscous flow systems are few in number, elementary, and often limited to the case of viscous flow in a thin film constrained by a rigid substrate. 21,22,24,27 In this case, the film thickness is ignored in the analyses and an analytical model describing how viscous flow in substrates relaxes residual stresses in films has not yet been developed.…”

Section: Introductionmentioning

confidence: 99%

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Effects of viscous flow on residual stresses in film/substrate systems

Hsueh¹,

Lee

2002

Journal of Applied Physics

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An analytical model is developed to analyze the effects of viscous flow on residual stresses in film/substrate systems. This is achieved by utilizing the analogy between the governing field equation of elasticity and the Laplace transform with respect to time of the viscoelastic field equation. While viscous flow can occur in either the film or the substrate, analyses of how viscous flow in the substrate relaxes residual stresses in the film have not been performed. Also, the film thickness is often ignored in analyzing stress relaxation due to viscous flow in the film. The above two issues are studied in the present analysis. For the case of viscous flow in the film, the stress relaxation rate decreases with increasing film thickness. Conversely, for the case of viscous flow in the substrate, the stress relaxation rate increases with increasing film thickness. Compared to viscous flow in the film, viscous flow in the substrate results in slower stress relaxation in the system.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effects of viscous flow on residual stresses in film/substrate systems

Hsueh¹,

Lee

2002

Journal of Applied Physics

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“…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.…”

Section: Introductionmentioning

confidence: 99%

The viscosity of germanium during substrate relaxation upon thermal anneal

et al. 1997

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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.

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“…[3][4][5] However, when temperature is sufficiently high, viscous flow can occur, and stress relaxation has been observed in various film/substrate systems. [6][7][8][9][10][11] While both the Maxwell and the Kelvin models have been developed to describe viscoelasticity, analyses of viscoelastic stress relaxation in film/substrate systems are often based on the Maxwell model. [12][13][14][15][16][17][18][19] Using the Maxwell model, solutions for stress relaxation in the system require solving partial differential equations, and the film thickness is often ignored in order to obtain closed-form solutions.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic stress relaxation in film/substrate systems—Kelvin model

Lee

Hsueh

2003

Journal of Applied Physics

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Although the Maxwell model was widely applied to analyze viscoelastic behavior of film/substrate systems, Rafferty et al. [Appl. Phys. Lett. 54, 151 (1989)] found that the structural relaxation of silicon oxide films on silicon wafers during thermal annealing could be explained by the Kelvin model but not the Maxwell model. This result motivated us to investigate the relaxation of residual stresses due to viscoelastic deformation in a film/substrate system using the Kelvin model. The system can be a viscoelastic film on an elastic substrate or an elastic film on a viscoelastic substrate. The viscoelastic solutions of both cases can be obtained from the elastic solution using the Laplace transform. The stress relaxation rate increases with decreasing film-to-substrate thickness ratio for a viscoelastic film deposited on an elastic substrate. However, it shows the opposite trend for an elastic film deposited on a viscoelastic substrate. The present results are compared with those obtained from the Maxwell model.

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Creep curve of silicon wafers

Cited by 30 publications

References 7 publications

Effects of viscous flow on residual stresses in film/substrate systems

Effects of viscous flow on residual stresses in film/substrate systems

The viscosity of germanium during substrate relaxation upon thermal anneal

Viscoelastic stress relaxation in film/substrate systems—Kelvin model

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