Quantitative analysis of strengthening mechanisms in thin Cu films: Effects of film thickness, grain size, and passivation

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Abstract
Thermal stresses in thin Cu films on silicon substrates were examined as a function of film thickness and presence of a silicon nitride passivation layer. At room temperature, tensile stresses increased with decreasing film thickness in qualitative agreement with a dislocation constraint model. However, in order to predict the stress levels, grain-size strengthening, which is shown to follow a Hall–Petch relation, must be superimposed. An alternative explanation is strain-hardening due to the increase in dislocation density, which was measured by x-ray diffraction. At 600 °C, the passivation increases the stress by an order of magnitude; this leads to a substantially different shape of the stress-temperature curves, which now resemble those of aluminum with only a native oxide layer. The effect of passivation is shown to be very sensitive to the deposition and test conditions.