Studies of the Polymer Thin Film Glass Transition Temperature Monitored With the Complex Viscoelastic Cofficients
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speed for microprocessors. Photoresists are primarily composed of flexible polymers. For a moderate molecular mass of a flexible polymer (200 ku), the polymer's coil dimension is approximately 10nm-20nm which is on the order of one-third of the current state-of-the-art line width [1]. For these ultra-thin line widths, the mechanical behavior of these ultra-thin films has been assumed to be similar to the polymer properties observed in the bulk phase. However, recent observations have suggested that these ultra-thin polymer layers (•100nmn) show significant deviation from the assumed bulk behavior [2-4]. These observations indicate a potential limit for the current lithographic technology. The deviation from assumed bulk behavior would seriously derail the planned increases in clock speed of semiconductor microprocessors. In order to continue to decrease the size of the line widths, an accurate assessment of the physical properties of these ultra-thin polymer film behaviors is required. A strategy for developing precise metrology for use in ultra-thin polymer film characterization would involve adapting existing technology to extremely small sample geometries. This paper will detail developments made at NIST for the measurement of complex viscosity (,q*)of ultra-thin polymer films based upon the dual torsional quartz crystal resonator [5, 6]. Nanoscale Measurement of the Complex Viscosity One of the most important properties from a material processing and performance standpoint is that of the complex viscosity: y1*= ?lmeio = 17- il/" [7]. Data about the temperature
and frequency dependence of the complex viscosity has been an effective experimental tool in 175 Mat. Res. Soc. Symp. Proc. Vol. 543 01999 Materials Research Society
developing a fundamental understanding of polymer dynamics. The determination of the complex viscosity for ultra-thin polymer film is useful in two distinct ways: 1) further development of processing conditions for lithography, and 2) the evaluation of fundamental theories of polymer dynamics near confining surfaces. There have been several attempts to measure the viscosity of ultra-thin layers. These include modifying existing techniques such as the atomic force microscope[8, 91, the quartz crystal microbalance [10, 11], and the surface forces apparatus[12-16]. While these three methods provide qualitative information about polymer films, they are fundamentally not designed to provide a quantitative assessment of ultra-thin polymer film complex viscosity. In order to make rigorous comparisons of experimental observations with theoretical predictions, a quantitative approach to the design of an instrument to measure the complex viscosity of the ultra-thin film is required. Bulk complex viscosity or modulus measurements require determining the response of a sample to an imposed deformation [7]. The resulting complex force balance expression that describes this response has many terms. This complicated expression can be greatly simplified by
the application of one of two limiting conditions
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