Density capacitance

J. D. Wiggins-Camacho, K. J. Stevenson, Effect of nitrogen concentration on capacitance, density of states, electronic conductivity, and morphology of N-doped carbon nanotube electrodes,/. Phys. Chem. C, vol. 113, p.19082-19090, 2009. 

Fig. 9.27 shows the variation of capacitance as a function of the surface area from which it may be concluded that in principle it is possible to obtain double-layer supercapacitors having specific capacitance of the order of 100 F/g so that values of practical capacitance density as high as 30 F/g can be predicted. 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

To optimize the device volumetric capacitance density, once the DLC geometric parameters such as the cell size, the electrode thickness, and width have been fixed, the development efforts must be concentrated on the research of the carbon performance. Typical commercial carbons [18] have a capacitance density in the range of 50F/cm3. Their capacitance specific density is in the range of 100 F/g. Among the best-performing carbons available, there are those derived from metal carbide (carbide derived carbon [CDC]) [19,20], They may reach a capacitance density of 130-140F/g. At that point, to avoid confusion, it is worth mentioning the difference between carbon or electrode capacitance and DLC capacitance. The later is exactly four times smaller because of the series connection of two electrodes whose volume is half of the total electrode volume. 

Many investigations have been performed on carbon nanotube (CNT) use in DLC electrodes [23-25], Today it is well established that CNTs offer a poor surface accessibility for the ions with a resulting low-capacitance density. Ongoing studies show promise in the use of CNTs in small proportion as an additional material to enhance the electronic conductivity and the mechanical properties of the electrode. The CNTs are also used as a support for high-capacitive polymeric redox material in order to increase their weak conductivity [26],... 

For given current frequency and intensity measurement conditions, the carbon capacitance density in the aqueous electrolytes is about twice that in an organic solvent while the series resistance is at least 10 times smaller [14],... 

For example, supercapacitor capacitance density in Kuraray product information for BP20 activated carbon for supercapacitor. http //www.kuraraychemical.com/Products/SC/capacitor.htm... 

P 5 are the potential at the different planes, C s are the capacitance density of the plane layers. 

The capacitance density and energy density at 70°, 25°, and —25°C were estimated based on the experimental results where practical charge voltages were taken into... 

Where /ds is the drain current fV, the channel width Z, the channel length fox, the gate oxide thickness p, the channel carrier mobility C, the capacitance density of the gate oxide Fqs, the gate voltage and Vj is the threshold voltage. 

Thickness and, correspondingly, capacitance variation was less than 2%. The absence of impurity peaks in XPS spectra of silica-coated specimens clearly demonstrates the achieved purity. Yield, defined as the percentage of functioning vs. total measured capacitors, was 100%. Breakdown field strength was in the range 1.1-5.4 MV/cm and leakage current was about lO -lO A/cm at 0.5 MV/cm. Capacitance density was 23-350 nF/cm dependent on thin film thickness and materials. No breakdown was observed after 20 cycles between 0-40 V. Time dependent dielectric breakdown (TDDB) was 185 s at 40 V for ten of the patterned capacitors. 

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. 

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. 

On the other hand, there are applications shown in Figure 27.1 that are not effectively met by CSD. For example, integrated capacitors for dynamic random access memory (DRAM) node elements require a much higher capacitance density, extremely small lateral dimensions, and three-dimensional architectures. For... 

Note that here Cox is given in units of Fcm-2 (capacitance density), tox=df (film thickness) of the oxide. Together with Equation 1.9 for the extension of the space charge layer, we get an expression for (J)ox in terms of the charge NA in the scl ... 

Capacitance density for interdigital capacitors in Fodel -Technology. 

Using standard alumina, the substrate itself can be used as the capacitor dielectrics. However, because of the considerable thickness of substrates (250 pm or more) and the relatively low permittivity of about 10, the capacitance density is very low (e.g., 0.34 pF/mm d = 250 pm). 

Methods to increase the capacitance density with high-K materials in LTCC (a) multilayer, (b) hlgh-K layer, (c) high-K inserts (paste or tape), (d) high-K print with paste. 

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