Thermal bimorph

To solve for the temperature distribution T(x) along the length of the beam, we set the anchored end of the beam at x = 0 to the temperature of the substrate, Tsub- The other end of the beam that is released has the longest thermal path to the substrate, so it will get the hottest. Since the temperature is maximum at x=L, the derivative of the temperature distribution will be zero. In equilibrium, dTldt = 0, so that equation (5.16) becomes 

We can use this temperature distribution to find the deflection of a bimorph actuator. In one dimension the change in length of a cantilever beam would be 

For a bimorph actuator comprised of two layers with different coefficients of thermal expansion, y and yj, the temperature change causes a strain mismatch between the layers, leading to curvature of the bimorph  

The curvature of the bimorph causes a deflection. If we simplify the analysis by considering two layers that only differ in their coefficients of thermal expansion, taking E = E2 = E and Vi = V2 = v, and convert the strain to stress using the modulus of elasticity for a beam. 

We can then use Stoney s formula to convert the stress into bending of the bimorph beam, similar to the bending of a substrate due to strain mismatch from a deposited film. Here the Young s modulus E, Poisson s ratio v, and the film thickness are for the substrate, and the strain oy is for the deposited film with a thickness tf. 

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The IR filter is realized by a PS layer with a modulation of porosity, which constitutes an interference filter as described in detail in the next section. The 30 pm thick porous layer is then released from the substrate by electropolishing, which is easily done in situ by increasing the etching current density above JPS. This process is commonly applied to form free-standing PS membranes and PS tubes [Tj 1], The internal strain between the Si3N4 layer used for masking and the porous layer lifts the filter up to its rest position, as shown in Fig. 10.10. The filter is suspended at two microactuator arms, which work as thermal bimorph actua-... 

Thermal bimorph actuators consist of deformable microstructures that curl into and out of the substrate plane. 

Thermomechanical Valves, Figure 7 Schematic of a normally closed thermal bimorph-actuated valve... 

A thermal bimorph actuator is comprised of two materials with different coefficients of thermal expansion that are bonded together, as shown in Figure 5.12. As the materials heat up they expand at different rates, causing the actuator to deflect toward the side that expands the least. 

When silicon is in contact with a metal, a low-temperature liquid eutectic can be formed, far below the melting temperature of either silicon or the metal. For example, the eutectic temperature for silicon and gold occurs around 370°C for 30% silicon. In contrast, the melting point for pure gold is 1064°C, and the melting point for pure silicon is 1410°C [5]. Aluminum and silicon can form a eutectic around 577°C at around 12% silicon. In designing thermal actuators, such as gold/silicon thermal bimorph actuators or suspended heaters with metal wires and contacts, the metal should not be used in the proximity of any silicon that is heated unless the temperature is kept below the eutectic point. 

The thermal flux from the enzyme/substrate reaction crosses the aqueous layer and rapidly diffuses through the 200 Angstrom thick aluminum coating on the top layer of the bimorph. Modelling of the heat transport within the film, to be published elsewhere, shows that the thermal transport process may be treated as a semi-infinite solid ... 

A structure composed of two active layers and one or more passive layers. Typically the active layers work through either thermal expansion, hygrothermal expansion, or piezoelectric expansion via an externally applied electrical field. Bimorphs are used in the latter case to amplify... 

Electrothermal or Thermal Actuation Motion is generated by differential thermal expansion in materials such as sDicon or metals, while heat is typically injected into the actuator by means of Joule heat dissipation. Some actuator components expand more than others due to different cross-sections and therefore electrical resistance. Typical microactuator configurations include in-plane bimorph elements (Fig. 2a), out-of-plane bimorph plates, in-plane Chevron, or bent-beam elements (Fig. 2b) [3]. These types of actuators exhibit larger force capabiUties (in mN range), can achieve displacements of 100 pm or less but generally consume a lot of power (hundreds of mW), and have low bandwidth (Hz to KHz). Common methods of fabrication for electrothermal microactuators include surface micromachining... 

Tomonari et al. [11] have used thermal isolation comb regions to minimize the thermal conduction loss from the membrane in their microvalve. As shown in Fig. 10a, they used a Si — Ni bimorph as the microactuator. They fabricated thermal isolation comb regions on either side of the silicon bimorph by etching Si or filling the structure with polyimide resin. Because of the low-heat conductivity of the polyimide resin, this structure can effectively protect from heat loss. Figure 10b shows their microvalve. 

Thermomechanical Valves, Fig. 10 A Si — Ni bimorph-actuated microvalve with thermal isolation comb regions, (a) Thermal isolation comb regions (b) photograph of the microvalve... 

The developed bimorph beam model of IPMC was validated using the finite element method (FEM) and the used software was MSC/NASTRAN. As the software does not directly support the electromechanical coupling, the thermal analogy technique as described in [Lim et al. (2005) Taleghani and Campbell (1999)] was used. The simulated versus measured force-displacement relationship of an IPMC actuator is shown in Fig. 2.39. The relative errors for A = 0 between the calculated values and the measured data for 2V and 3V are 2.8% and 3.7%, respectively. The equivalent Young s moduli estimated from the equivalent beam model and the equivalent bimorph beam model are 1.01 GPa and 1.133-1.158 GPa, respectively, which are very close. However, the values from the equivalent beam model... 

Piezoelectric scanners Piezoelectrics are materials whose dimensions deform in response to an applied electric field. If the voltages that are applied to a piezoelectric are precisely controlled, extremely precise movements can be performed. The geometry of piezoelectric positioning devices used in STM includes bars, bimorphs, or tubes tubular scanners are the most commonly used. They operate at a high resonant frequency, enabling high scan rates. Thermal isolation of the piezoelectric elements is necessary since these ceramics are also sensitive to... 

For all numerical analyses, a commercial finite element analysis program, MSC/ NASTRAN [29], was used in conjunction with the equivalent bimorph beam model. A thermal analogy technique proposed by Taleghani and Campbell [30] was used to implement the electromechanical coupling effect into the finite element model. In the thermal analogy technique, the electromechanical coupling coefficient (dj/) is converted into the thermal expansion coefficient a/ as follows ... 

Thermal actuation makes use of the thermal expansion of solids as they are heated, or the differences in the rates of thermal expansion between different materials as in a bimorph actuator. Relative to electrostatic... 

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