Measurement of stresses generated in cured polyimide films

Abstract

We have measured "in situ" the stresses generated in polyimide films produced from the ethyl ester of benzophenone tetracarbolic acid and methylene dianiline during the curing cycle. The room temperature stress in a fully cured film (to 400 ·C) is approximately 70 MPa. The stresses at ro~m temperature vary with the cure temperature and are due to coefficient of thermal expansion mlsmatch between film and substrate. The in situ measurements show that the glass transition temperature is the same as the maximum cure temperature that the film experiences. The stress measurements were made using an x-ray double crystal lattice curvature technique.

Anisotropic Thermal Expansion Behavior of Thin Films of Polymethylsilsesquioxane, a Spin-on-Glass Dielectric for High-Performance Integrated Circuits

“…From this result, the Poisson's ratio ν F of the 400 °C cured film is estimated to be 0.36. This value for ν F is comparable to those of aromatic polyimides. , In general, Poisson's ratio varies in the range 0.15−0.5; , higher modulus and harder materials exhibit smaller Poisson's ratios. , Assuming other PMSSQ films have the same ν F value (0.36), the Young's modulus is estimated from the biaxial modulus data to be 8.1 GPa for the 400 °C cured film, 5.3 GPa for the 300 °C cured film, and 3.8 GPa for the 250 °C cured film (Table ). It here is noted that the Young's modulus value of the 400 °C cured film is comparable to that (7.1 GPa) of PHSSQ films …”

“…A PMSSQ film cured at 500 °C was recently reported to have a modulus of 5.8 GPa and a density of 1.3 g/cm 3 , as measured by nanoindentation . This value for the modulus is comparable to those of semirigid or rigid polyimides . From this result, the Poisson's ratio ν F of the 400 °C cured film is estimated to be 0.36.…”

“…The film stress σ F on a substrate with known TEC is a function of two unknowns, α ∥ ( F ) and E F /(1 − ν F ) that are the in-plane TEC and biaxial modulus of the film, respectively: 8,10,11 E F and ν F are the Young's modulus and Poisson's ratio of the film, respectively. These unknowns can be determined independently by measuring the slope of the film stress−temperature plot of the film on two substrates with different TECs. ,, Taking this into account, we chose Si(100) and GaAs(100) substrates which have different TECs: ,, Si(100) substrate, α S = 2.8 ppm/°C and [ E S /(1 − ν S )] = 180.5 GPa; GaAs(100) substrate, α S = 5.8 ppm/°C and [ E S /(1 − ν S )] = 123.9 GPa. The film stresses σ F,1 and σ F,2 of the two substrates can be expressed by the equations 8,10,11 where α S i is the TEC of the substrate i , and T i and T f are the initial and final temperatures of the film, respectively.…”

“…The film stresses σ F,1 and σ F,2 of the two substrates can be expressed by the equations 8,10,11 where α S i is the TEC of the substrate i , and T i and T f are the initial and final temperatures of the film, respectively. In general, the residual stress of a polymer film monotonically increases or decreases with temperature during a heating or cooling run; ,, in the case of PMSSQ films, the residual stress monotonically varies with temperature once the precursor films are thermally cured at a chosen temperature. The linear slopes of stress−temperature profiles measured during heating or cooling runscan be expressed according to the following equations, which have been rewritten from eqs 3a and 3b above …”

“…In multilayer IC devices, the dielectric material is commonly interfaced to itself as well as to other device component materials such as silicon, silicon nitride, silicon oxide, ceramic, copper, aluminum, chromium, tungsten, and capping metals. − At such interfaces, high residual stress is often generated, causing problems for the reliability of the devices such as curl, bend, displacement, crack, and delamination. ,− The residual stress at a given interface is primarily dependent on the mismatch of the thermal expansion coefficients ( α 's) and mechanical properties (i.e., Young's modulus E and Poisson's ratio ν ) of the interfaced layers, as well as on the thermal history of the layers. ,, Therefore, mismatches between the properties of the interfaced layers need to be minimized in order to prevent stress-associated reliability problems. ,,, …”