Constraint Effects on Cohesive Failures in Low-k Dielectric Thin Films
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Constraint Effects on Cohesive Failures in Low-k Dielectric Thin Films Ting Y. Tsui, Andrew J. McKerrow, and Joost J. Vlassak Silicon Technology Development, Texas Instruments Inc, Dallas, TX 75246, U.S.A. Division of Engineering and Applied Sciences, Harvard University, Cambridge MA 02138 ABSTRACT One of the most common forms of cohesive failure observed in brittle thin films subjected to a tensile residual stress is channel cracking, a fracture mode in which through-film cracks propagate in the film. The crack growth rate depends on intrinsic film properties, residual stress, the presence of reactive species in the environment, and the precise film stack. In this paper, we investigate the effect of various buffer layers sandwiched between a brittle carbon-doped-silicate (CDS) film and a silicon substrate on channel cracking of the CDS film. The results show that channel cracking is enhanced if the buffer layer is more compliant than the silicon substrate. Crack velocity increases with increasing buffer layer thickness and decreasing buffer layer stiffness. This is caused by a reduction of the constraint imposed by the substrate on the film and a commensurate increase in energy release rate. The degree of constraint is characterized experimentally as a function of buffer layer thickness and stiffness, and compared to the results of a simple shear lag model that was proposed previously. INTRODUCTION To reduce device size and power consumption, advanced electronic devices are often made of thin-film composite structures that contain very brittle materials. Films with a residual tensile stress may be subject to delamination or cohesive fracture [1-6]. One common cohesive failure mode is channel cracking, where through-film cracks propagate in the film [6]. The energy 4
10
10
Constraint factor, Z
8
E film − Esubstrate
Crack Growth Velocity (microns/sec)
α=
E film + Esubstrate Film
6
Substrate 4
Compliant Films on Stiff Substrates
Stiff Films on Compliant Substrates
2
0
1000 100 10
-0.5
0 Alpha, α
0.5
1
FIG. 1. Plot of the constraint factor (Z) as a function of Dundurs parameters, α and β = α/4 [7].
Reaction Controlled Regime
1 0.1 0.01 0.001 0.0001 10
-1
Diffusion Controlled Regime
-5
0.8
1.2
1.6
2
2.4
2.8
3.2
Strain Energy Release Rate (J/m^2)
FIG 2. Plot of CDS crack growth rate as a function of energy release rate.
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release rate, G, for a channel crack can be calculated using the following equation:
G=Z
π σ 2h 2 E
,
(
(1)
where h, σ, and E = E 1 − ν 2
) represent the film thickness, residual stress, and plane-strain
elastic modulus, respectively. Z is a constant that depends on the elastic mismatch between film and substrate and on the precise geometry. The effect of elastic mismatch on the energy release rate has been calculated by Beuth [7] for films on half spaces and by Vlassak [5] for films on substrates of finite thickness. The factor Z can be expressed as a function of the plane-strain Dundurs parameters [5, 7-8]
α=
E f − Es E f + Es
β=
,
μ f (1
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