Quantitative Measurement of the Effect of Annealing on the Adhesion of Thin Copper Films Using Superlayers
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Mat. Res. Soc. Symp. Proc. Vol. 505 0 1998 Materials Research Society
hours in a nitrogen atmosphere, and cooled to room temperature at 20 0C/min. Tungsten was then sputter-deposited simultaneous on all eight wafers. All film thicknesses were measured with Rutherford backscattering spectroscopy, using a 3.7 MeV ion beam of He++ and are given in Table I. Residual stresses were determined using waferbow measurements and are considered nominal. The as-sputtered copper films have previously been shown to have a grain size of 50-100 nm and indentation hardness of 5-10 GPa [15]. Table I. Sample Thicknesses and Tensile Residual Stresses. Group A Group B Group C Actual Thickness
225 nm
As-sputtered Cu residual stress Annealed Cu
215 MPa 165 MPa
225 nm
385 nm
425 nm
610 nm
235 MPa 225 MPa
165 MPa
590 nm
Group D
1000 nm 1025 nm
240 MPa 220 MPa 230 MPa 265 MPa
150 MPa
90 MPa
75 MPa
residual stress
SuperlayerW
715 nm
635 nm
715 nm
685 nrn
710 nm
720 nm
695 nm
710 nm
l10MPa
65 MPa
thickness SuperlayerW residual stress
365 MPa 180 MPa
315 MPa 310 MPa
290MPa 210 MPa
Mechanics of Delamination Nanoindentation-induced delamination has been studied by a number of researchers [16-18]. The test method consists of driving a spherical-tip conical indenter perpendicularly into and then out of, the film. The methodology of Marshall and Evans [11] is used to characterize the interfacial energy driving delamination, using solutions by Hutchinson and Suo [7] for the buckling stress of an axisymmetric clamped plate. This model assumes that indentation volume results only in radial expansion of the film, inducing a strain-field within the film. Strain energy is calculated as a function of residual-stress, OR, and indentation-induced stress, TI,which is given as
0,
VI Ef
27rha 2 (1- Vf)
In this expression, V1 is the indentation volume, h is the film thickness, a is the radius of the circular delamination and the subscript 'f refers to the elastic constants of the film. Buckling occurs when the sum of indentation and residual stresses exceed the critical buckling stress for the delaminated circular section as given by, 2 9S= Ef
h2
2 12(l- v2) a
In this expression, g 2=14.68 as the buckle occurs over the entire diameter of a clamped circular disk of radius a, referred to as single-buckling, which can only occur after removal of the indenter tip. Annular-buckling is possible when the indenter pins the center down, for which I2=42.67. Standard corrections to gIexist to account for a central hole. The strain energy release rate derived from calculation of the strain energies is
G = haI2(1 - v2) + (1 -- ) h 2Ef
h(
G-Vf)
Ef
- a3)(I -
Vf)
(3)
Ef
where the slope of a/(YB vs. A/AB (radial displacement) is cx=l before buckling, and after onset of buckling decreases to a = 1- [1/{1 + 0.9021(1- vf)}]
(4)
364
It is noted that this analysis is explicitly applicable only to circular delamination of a single film that does not spall or crack upon testing. In the case of a bilayer film, these equations are ac
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