Planar capacitor

It is of interest primarily for very uniform ultra-thin films and coatings (0.002-5 mils) in applications such as electrical resistors, thermistors, thermocouples, stator cores, connectors, fast-sensing probes, photo cells, memory units, dropwise steam condensers for recovery of sea water, pellicles for beam splitters in optical instruments, windows for nuclear radiation counters, panels for micrometeorite detection, dielectric supports for planar capacitors, encapsulation of reactive powders, and supports in x-ray and optical work. Any significant growth would depend upon a major breakthrough in process techniques and a consequent lowering in price. 

In order to incorporate both tendencies, Lazare, Sundheim, and Gregor developed an improved model, where the elastic and electrostatic interactions were included. In this model, the resin was regarded as a set of charged planar capacitors, with the plates interconnected by elastic springs (Figure 7.24) [126], The balance between forces is attained when the elastic forces provided by the polymeric resin stabilize the dissolution propensity. 

Lee, B.L, Wang, X., and Hu, M., Nanocrystal barium titanate via low temperature ambient pressure conditions, U.S. Patent application in process, June 2002. Wang, X., Lee, B.L, Hu, M., and Payzant, A., J. Mater. Sci. Lett., 22, 557, 2003. Gould Electronics, TCC embedded planar capacitor technology, available at www.gould.com. 

As discussed above the key to any biosensor is in the transduction mechanism. The mechanism of the capacitive affinity sensor is shown in Figure 2. The sensor consists of a planar capacitor composed of interdigi-tated metal fingers on an insulating substrate. This structure is then coated with a thin layer of a passivation material. The role of the passivation material is to protect the metal structure from deterioration from contact with the solution. A sample of the analyte or an analog retaining the ability to bind an antibody to the analyte is covalently bound to the... 

The electrochemical stability of PtO-OTS in aqueous saline solution was tested by measuring cyclic voltammograms of PtO and PtO-OTS electrodes in 0.1-M KCl, pH 6.8 (Figure 4). The electrode capacitances that correspond to the cyclic voltammograms are shown in Figure 5. These capacitances were measured at 1000 Hz. The OTS layer can be described as a planar capacitor in series with the PtO and double-layer capacitances. Formation of the OTS layer decreased the capacitance however, the PtO beneath the OTS layer was still reduced when the potential was swept below 0.3 V. This observation again is evidence that the OTS layer on PtO is somewhat porous. The onset potential of PtO reduction in aqueous solution is pH-dependent. 

All these dipoles are conservative ones with respect to the entity number, the basic quantity in this case of capacitive dipoles. The interesting feature is that the separability is linked to the symmetry between energies-per-entity (here efforts) When the dipole is inseparable, both efforts are equal in magnitude but opposed in direction (for vectors) or value (for scalars). The converse is not true such symmetry may be found in peculiar cases for separable dipoles. For instance, the two potential values Vi and V2 of a capacitor may be equal in magnitude and opposite however, this happens only in case of equal pole capacitances. This is a frequent case in electrodynamics when the two capacitor plates are strictly identical, as in the case of planar capacitor, but this is not general as nonidentical shapes or geometries can also be found. Note that, in physical chemistry, this never happens, because it would correspond to identical partners in a chemical reaction of to identical phases in an interface ... 

According to the Helmholtz model, the double layer is analogous to a planar capacitor, whose capacity can be calculated by the equation ... 

Free-standing films can be produced of parylene. These ultrathin (250A-3 microns) films, called pellicles, are used as beam splitters in optical instruments, windows for nuclear radiation measuring devices, dielectric supports for planar capacitors, and for extremely fast-responding, low-mass thermistors and thermocouples. 

A is the area of the formed planar capacitor L x W D]j is the dielectric constant of the capacitor material t is the thickness between the capacitor plates K is a conversion constant = 8.854 x l(T Farads/cm... 

An electron prisin , known as an analyser or monochromator, is created by tlie field between the plates of a capacitor. The plates may be planar, simple curved, spherical, or toroidal as shown in Figure Bl.6.2. The trajectory of an electron entering the gap between the plates is curved as the electron is attracted to the positively biased (iimer) plate and... 

The sphere-plane capacitor model gives a useful approximate expression for the function f(Rlz). Equation [13] shows that in the region 0 < z/R < I, which is typical in SPFM imaging, / can be approximated by a 1/z dependence. The planar lever adds a nearly constant term. Thus for the range 0 < z < f , we have the following approximate function... 

Hence, Tct is seen to increase with pore density and pore radius. However, a problem appears at a porous substrate when thin films are to be deposited during metallization to form interconnections, thin-film capacitors, etc.335 Sputtered material falls deep into the pores, which affects the planarity of the deposited layer and the electrical resistivity of the oxide layer underneath.335 To cope with this effect, the porous oxide should be padded by inorganic (A1203 and Si02) or organic (polyimide, negative photoresist) layers. 

The acceptance of chemical mechanical planarization (CMP) as a manufacturable process for state-of-the-art interconnect technology has made it possible to rely on CMP technology for numerous semiconductor manufacturing process applications. These applications include shallow trench isolation (STI), deep trench capacitors, local tungsten interconnects, inter-level-dielectric (ILD) planarization, and copper damascene. In this chapter. 

The surfaces being considered are not planar, and therefore instead of Helmholtz-Perrin parallel-plate condensers, one has concentric-sphere capacitors Gouy-Chapman regions show radial instead of planar symmetry. All such points complicate the mathematics, but lead to few new truths. Hence, such details will be ignored in this very simple account of the dominating role of double layers in colloid chemistry. 

Figure 5.5 SEM picture of a planar STO capacitor (gap width 2 pm) (from [15])...

Figure 5.8 Typical planar resonators being used as building blocks for filters lumped element (a), microstrip (b), folded microstrip with integrated capacitors (c), coplanar (d), and 2-D microstrip resonator. Omitting the capacitive gap in the folded microstrip design (c) leads to a ring resonator (square if circular shaped), which also represents a quite commonly used microstrip resonator design.

Often, the total capacitance is defined to be Q/V, which in the present example has the same value as the differential capacitance. This is true even for geometries other than planar parallel plates, as for example, in cases of capacitors having concentric cylindrical plates or concentric spherical plates. It is only in the realm of space charge where we must be concerned with differences between the total capacitance and the differential capacitance. The space charge situation will be discussed later. 

For capacitors on copper foil substrates, yield of initial samples was an impressive 83-90%. Capacitance density ranged from 20-242 nF/cm this is approximately 50-100 times higher than that of laminated planar epoxyglass capacitors. 

Among other process tq)plications are the use of CMP to improve shallow trench isolation. Bird s beak planarization, and stacked or trench capacitor. 

Applications that have received attention, and the material properties that enable them, are shown in Figure 27.1. These applications are reviewed in detail in Waser and Ramesh. Decoupling capacitors and filters on semiconductor chips, packages, and polymer substrates (e.g., embedded passives ) utilize planar or low aspect ratio oxide films. These films, with thicknesses of 0.1 to 1 J,m, are readily prepared by CSD. Because capacitance density is a key consideration, high-permittivity materials are of interest. These needs may be met by morpho-tropic phase boundary PZT materials, BST, and BTZ (BaTi03-BaZr03) solid solutions. Phase shifters (for phase array antennas) and tunable resonator and filter applications are also enabled by these materials because their effective permittivity exhibits a dependence on the direct current (DC) bias voltage, an effect called tunability. 

The principle of duality concerns the transformation between two apparently different circuits, which have similar properties when current and voltage are interchanged. Duality transformations are applicable to planar circuits only, and involve a topological conversion capacitor and inductor interchange, resistance and conductance interchange, and voltage source and current source interchange. 

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