The substrate curvature method

As noted in previous sections, the development of life prediction models for the reliability of patterned features such as periodic lines on substrates inevitably requires knowledge of intrinsic stress and mismatch stress generated during film growth, patterning, passivation and service. In this section, three prominent experimental methods for determining stress in thin films with patterned lines are considered the substrate curvature method, the x-ray diffraction method, and the micro-Raman spectroscopic method. The advantages and limitations of each of these techniques are also briefly addressed. 

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The thickness, density, and residual stress in sintered films can be determined by the methods described above. The X-ray diHfaction method of determining stress is generally more suitable for sintered films since it does not require the removal of the film, as do the substrate curvature methods. The surface roughness can be measured with a profilometer, whereas the adhesion of the film to the substrate can be determined by a pull test, in which a wire is bonded to the film and then pulled with the force needed to remove the film from the substrate. The amount of camber or warpage can also be determined with a profilometer. Grain and pore sizes can also be determined by the same techniques used for bulk ceramics. 

The ease with which the film mismatch stress can be estimated from the change in curvature of a relatively thick substrate subjected to thermal excursion has led to the widespread use of the substrate curvature method for the study of mechanical properties. As reviewed in Section 2.3, substrate... 

A single crystal alloy thin film with composition Sio.ssGeo.is is grown on an initially flat Si(OOl) substrate which is 0.5 mm thick. The lattice parameter of Si at room temperature is asi = 0.5431 nm, while that of Ge is ace = 0.5656 nm. Any dislocations formed as a consequence of epitaxial mismatch between the film and the substrate are known to be 60° dislocations with Burgers vectors in the family represented by (6.18). Assume that the biaxial moduli of Si(OOl) and Ge(OOl) crystals are Mgi(ooi) = 180.5 GPa and MGe(ooi) = 142 GPa, respectively, that the Poisson ratio of the film is i/f R 0.25, that Vq = 6/2, and that 6 w 0.4 nm. Curvature measurements are made continuously using the multibeam optical stress sensor method (see Section 2.3.2) so as to monitor the evolution of internal stress during film deposition. Estimate the substrate curvature at which misfit dislocations are first able to form at the interface between the film and the substrate. 

Advantages in the use of substrate curvature method for the extraction of film properties can be summarized as follows. 

With bending-beam methods, the deflection of the free end of a one-side clamped substrate strip or the central deflection of a two-sided clamped strip is measured, which is produced under the influence of the film stress. The strip or beam length is often ten times its width. The deflection is detected either optically, mechanically or electrically. The sensitivity achievable depends to a large extent on the system of detection. Highest sensitivities are achieved with optical and electrical detectors. The radius of curvature of the substrate beam is calculated from ... 

First, let us examine the change in adhesion with increasing effective radius of curvature due to a difference in roughness of the substrate. The force of adhesion of gold particles (3-8-jLtm diameter) is affected by the method used in finishing glass surfaces, as follows (particles detached by centrifuging [157]) ... 

The issue of film thickness effects on substrate curvature evolution is pursued now by recourse to the energy minimization method which was introduced in Section 2.1 for the derivation of the Stoney formula. All other features of the system introduced in that section are retained in this discussion, which follows the work of Freund et al. (1999). It is assumed that the film material carries an elastic mismatch strain in the form of an isotropic extension em (or contraction if Cm is negative) in the plane of the interface the physical origin of the mismatch strain is immaterial. The mismatch strain is spatially uniform throughout the film material. In this case, em is... 

Methods to measure changes in substrate curvature during stress evolution in a layered material can be broadly classified into the following... 

Many of the limitations of the above techniques are overcome by optical methods which offer the convenience, accuracy and flexibility to measure curvature through remote sensing capabilities. In this section, several different optical techniques for the measurement of substrate curvature are described, and their advantages and limitations are examined. 

Fig. 2.8. Schematic illustration of the scanning laser method for measuring substrate curvature.

The optical method for measuring substrate curvature is generally convenient for in-situ measurement of film deposition stress in CVD and MBE systems, provided that optical access is provided to the substrate and that the specimen is mounted in a manner which facilitates unconstrained curvature evolution in one direction. One of the most common optical methods of... 

A system based on the CGS method offers several advantages for curvature measurements for thin films and layered solids. The measurement provides all the normal and shear components of the curvature tensor. It also provides full field information from the entire area of the substrate—film system. The measurement area could also be scaled as necessary from a few millimeters to hundreds of millimeters so that large wafers and flat panels with thin film deposits are tested. The method involves non-contact measurements which are carried out with an adjustable working distance, and performed in-situ and in real time as, for example, during thermal cycling. 

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