The Effect of Intrinsic Passivation Stress on Stress in Encapsulated Interconnect Lines
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Table 1 Temperature-dependent Materials Properties Used in the Model
Aluminum
Silicon
SiNx
Temperature E (GPa) v a (10"6*C) E (GPa) v _a (106/C)
25°C 71.5 0.35 23.6 149.6 0.28 2.6
500'C 38.7 0.35 31.4 149.6 0.28 3.5
E (GPa)
160
160
v at (106/OC)
0.25 2.0
0.25 2.0
Aluminum cy (MPa) 195 160 140 60 10
Temperature (°C) 25 150 200 300 380
Geometry of FEM Model
h 0
C"D
0
0
-o
CL
8-. ,0 0
Figure 1: Geometry of the finite element model. Due to symmetry, only the right half of the line is modeled. The dual symmetry conditions simulate an infinite series of parallel lines. In this paper, the x direction is referred to as longitudinal, the y direction transverse, and the z direction normal.
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particular model should be used only for comparative, rather than predictive, purposes. The temperature-dependent materials properties used in the calculations are shown in Table 1. The properties are assumed to vary linearly with temperature. The model is assumed to be thermalstress-free at the passivation deposition temperature, taken to be 400°C in these calculations, and is cooled to room temperature (25°C) in 25'C temperature steps. The silicon and passivation behave in a purely elastic way throughout the calculation, and the aluminum line is elastic-perfectly plastic. Its temperature-dependent yield strength, derived from curvature vs. temperature measurements of aluminum films 5, is shown in Table 1. Intrinsic Stress In order to compare the stress in a metal line for the case of an intrinsic-stress-free passivation to that for the case of a passivation with a large intrinsic stress, it is necessary to include somehow the initial passivation stress in the calculations. In currently available commercial finite element codes, this can be done in two ways: by applying external loads to produce the desired initial stress, or thermally. There are disadvantages to both techniques. In the former case, the loads must remain in place, or the initial stress will disappear. In addition, since the details of the desired initial stress distribution may not be known a priori,the choice of external loads is somewhat arbitrary. In the case of applying the intrinsic stress thermally, the stress distribution is by definition the thermal stress distribution, which may not be the same as the intrinsic stress distribution. Some commercial codes allow a third option: specifying an initial stress in particular regions can be done directly. Again, the fact that the precise distribution is not known limits implementation of this option for intrinsic passivation stresses. For this work we have chosen to simulate the initial stress in the passivation thermally. Since for a blanket film the thermal and intrinsic stress distributions are certainly the same (equi-biaxial), and since the passivation film is essentially a blanket film deposited on a slightly bumpy substrate, we find this to be a reasonable approximation. In order to induce an initial stress, the passivation is given a different stress-free temperature than the rest of
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