Verlag des Forschungszentrums Jülich
JUEL-3600
In order to obtain the dependences of the strains and stresses from the parameters
mentioned above systematic FEM calculations have been made for an infinite array of
parallel lines with va-riations of the geometries and the elastic constants. The
calculations show that cooling from eleva-ted processing temperatures, e.g.
passivation temperature, results in high tensile strains in the 1-direction (parallel
to the lines). These elastic strains are equal [Delta][alpha][Delta]T and are higher than the strains
in the 2-direction (perpendicular to the lines and parallel to the substrate surface)
and in the 3-direction (perpendicular to the lines and to the substrate surface). The
elastic strains in the 2- and 3-directions strongly depend on the aspect ratio A
(line thickness divided by the line width). Con-formal lines with a small aspect
ratio (A<1) have tensile strains in the 2- and compressive strains in the 3-direction
while at high aspect ratios (A>1) both strains change their sign.
Using x-ray diffraction strain-measurements during thermal cycling have been made
on three samples with arrays of parallel AlSi(0.5wt%)Cu(0.5wt%)-lines covered with
different passivations (TEOS, SiNx, USG/PSG/USG). All lines had an aspect ratio of
0.6 (1.2 µm thick, 2.0 µm wide). The strains in the 1- and in the 3-direction show
hysteresis during the thermal cycling between room temperature and 400°C. There is
no hysteresis of strain in the 2-direction. The strains differ from the FEM-results
made with the assumption that no plasticity of the lines can occur. Using the
derived equations mentioned above the type and the amount of the metal plasticity
which took place during thermal cycling can be determined directly from the
experimental data. The metal lines showed no voiding during thermal cycling within
the experimental error. Plastic flow took place from the 3-direction to the
1- and 2-direction during cooling down and vice versa upon hea-ting.
Eppler, Ingo
Elastische und plastisches Verhalten passivierter Leiterbahnen in integrierten Schaltkreisen: FEM-rechnungen und röntgenographische Spannnungsmessungen
145 S., 1998
Passivated metal lines commonly used in integrated circuits show thermally
induced stresses and strains due to the difference Da of the thermal expansion
coefficients of the lines on the one hand and the underlying Si-substrate and the
surrounding ceramic passivation on the other hand. These stresses depend on various
parameters such as the geometry and the elastic constants of both, line and
passivation, and - for the case of an array of parallel lines - on the repetition
distance of the lines. They can cause voidage and plastic flow of the lines and thus
failure of the integrated circuits. Combining the theory of eigenstrains and
calculations made with the finite element me-thod (FEM) one can derive equations
which connect the magnitude of voidage and plastic shear deformation with experimental
strain data measured by x-ray diffraction.
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