Stress analysis in tungsten and Si3N4 coated silicon wafers

A paper by G. Gerald Stoney [Gerald Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proc. R. Soc. Lond. A 82 (1909) 172–175], entitled “The Tension of Metallic Films deposited by Electrolysis,” was presented to the Royal Society of London by the Hon. C. A. Parsons. It was well known at that time that films deposited electrolytically were liable to peel off when exceeding a certain thickness. After examining many thin Steel rules of thickness d which have a thin, t, deposit of Nickel, which curved the Rule to a radius r. Taking the moments about the point b for the steel, Stoney then arrived at the following equation where the integral must be equal to zero;(1) ∫ d 0 ( E / r ) ( b − x ) x d x = 0 so that b = 2 / 3 d he solution of Eq. (1), we obtain the important fact that the neutral plane is at 2/3 the thickness of the rule from film surface. This also implies that the absolute value of the stress on the film side is twice that on the opposite side of the steel rule. The important point is that if the absolute stress in the silicon on the film side is twice that on the opposite side then the position of the neutral plane must be at 2/3 d. The purpose of this paper is to show that the neutral plane in silicon wafers, which have a thin film (~ 3 μm) of tungsten or Si3N4 is indeed at 2/3 the thickness of the wafer.