Multilayer film with small total thickness

4-6 Multilayer film with small total thickness 

As another example of the result obtained in Section 2.4, consider the case of a thin film of total thickness hf which consists of a number N of 

If the expression for curvature k given in (2.51) is evaluated for this case, and if only those terms of first order in Ahi/hg are retained, then it is found that 

In the foregoing development, it is tacitly assumed that the individual layers in the film are added sequentially and that the mismatch strain in each layer depends only on the substrate but not on the order in which the layers are formed. If this is the case, then (2.73) yields the cumulative curvature after Nf layers have been added. However, it is noted that the same reasoning can be applied if the layers are removed sequentially. In the 

614/xm thick tetraethylorthosilane (TEOS) film is deposited on a relatively thick Si wafer. The biaxial stress in the TEOS film, say tteos is estimated from wafer curvature measurements to be — 114 MPa. A 0.6 pm thick silicon nitride film is then deposited on the TEOS film. The average stress in the bilayer film (composite TEOS and silicon nitride layers) is estimated from curvature measurements to be — 190 MPa. (a) If a 0.6 pm thick silicon nitride film is then deposited on a Si wafer, estimate the mismatch stress (Tsin in this film, (b) Suggest an experimental strategy for determining the stress in each film for a two-film stack deposited on a substrate, without relying on the superposition formula given in (2.74). 

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