Using techniques similar to those that were originally developed for miniaturized semicond...

Using techniques similar to those that were originally developed for miniaturized semiconductor electronics, scientists and engineers are creating Micro-Electro-Mechanical Systems (MEMS). An example is an electrothermal actuator that is driven by heating its different parts using an electrical current. The device is used to position 125-µm-diameter optical fibers with submicron resolution and consists of thin and thick silicon arms connected in the shape of a U, as shown in the figure. The arms are not attached to the

Substrate under the device but are free to move, whereas the electrical contacts (marked + and ‒ in the figure) are attached to the substrate and cannot move. The thin arm is 3.0 ∙101 µm wide, and the thick arm is 130 µ.m wide. Both arms are 1800 µ.m long. Electrical current flows through the arms, causing them to heat up. Although the same current flows through both arms, the thin arm has a greater electrical resistance than the thick arm and therefore dissipates more electrical power and gets substantially hotter. When current is made to flow through the beams, the thin beam reaches a temperature of4.0∙102 °C, and the thick beam reaches a temperature of 2.0∙102 °C. Assume that the temperature in each beam is constant along the entire length of that beam (strictly speaking, this is not the case) and that the two arms remain parallel and bend only in the plane of the paper at higher temperatures. How much and in which direction will the tip move? The linear expansion coefficient for silicon is 3.2∙10‒6 °C‒1 .