Dielectric thickness

The minimum length l and width id of a resistor are calculated from the given resistance R, the sheet resistance R in ohms per square, dissipated power P, and permissible power dissipation per square inch P by use of the formulas u> = /(P R)/P R and l = u>R/R. The capacitance of film capacitors is given by C = 0.225D(W — 1 )A/t, where C is the capacitance in picofarads. D the dielectric constant. N the number of plates, A die area in square inches, and / the dielectric thickness in inches. 

A variety of transmission line structures can be fabricated in planar layers of conductor and dielectric (Figure 9). The stripline and offset stripline are best suited for multilayer structures. The offset stripline, with two orthogonal signal layers between a pair of reference voltage planes, eliminates one intermediate plane and achieves higher characteristic impedance for a given dielectric thickness than do two stripline layers but increases the possibility for crosstalk between layers. 

Figure 9. Examples of planar transmission line structures. Dimensions are as follows b is dielectric thickness, w is line width, and t is conductor thickness.

In summary, the main advantages of thick-film technology are the high-conductivity conductors and the relatively inexpensive process equipment, whereas the drawbacks are the limited number of layers, the multiple printing and firing steps, the low conductor line resolution, and the limited dielectric thickness. 

Of course, for a given working voltage Uw, the dielectric thickness cannot be reduced indefinitely because the electric field E = Uw/h would eventually attain the breakdown value Eb. In fact, to achieve acceptable reliability the working voltage must be less than the normal breakdown voltage Ehh by a factor ij so that... 

Barrier-layer capacitors are based on the limited reoxidation of a reduced composition. This results, in the simplest case, in a surface layer of high resistivity and a central portion of conductive material so that the effective dielectric thickness is twice the thickness hQ of a single reoxidized layer and there is an apparent gain in permittivity over that of a fully oxidized unit by a factor of h/2ha, where h is the overall dielectric thickness (Fig. 5.51). Alternatively each... 

Discoloration—Metals Thickness Variations and/or Dielectric Thickness Variation... 

Lee, B.I., and Zhang, J., Dielectric thick fihn deposition by particle coating method. Mater. Res. Bull, 36, 1065, 2001. 

Here h is the total bilayer thickness (=4nm), is the dielectric thickness (=2.8nm for lecithin bilayers [93, 94]), and Em is the membrane permittivity (=2eo, where Eq is the vacuum permittivity). For vesicles with some initial tension Ob, the total tension reached during the pulse is simply... 

When designing these high speed interconnection circuits the dimensions of the copper track, the separation between tracks and ground planes, and the dielectric thickness all come into the calculations. 

Capacitive interference, the signal delay caused by the permittivity of insulating layers, the minimum required interlayer dielectric thicknesses, and the power dissipation, can all be decreased by designing polymers with lower values of e. The synthesis of polymers which simultaneously have low values of and outstanding thermal and mechanical properties is therefore crucial for applications in the electronics industry. 

Minimizing dielectric thickness is an alternative to increasing the capacitance of these hlms snbject to the constraint of acceptable leakage currents, effective insulation of the gate, and snfficient dielectric breakdown strength. 

Thick gate dielectric requirements. Typical gate dielectric thicknesses in most printed processes will be several tens to hundreds of nanometers. This is required to avoid concerns with pinholes, etc., in typical highspeed printing processes. 

One issue that complicates efforts to develop a model for the mechanism by which peptide ion channels work is the width of the bilayer that must be spanned by the transmembrane helix. Vodyanoy and Hall (251) measured the dielectric thickness of monoglyceride bilayers and found it to vary from 3.1 to 2.0 nm as the fatty acid chain length went from C22 to C14. The crystal structure (252) of the photosynthetic reaction center indicates a 3.0-3.1-nm hydrophobic zone perpendicular to the membrane that is smaller than might be expected for C18 lipids but is in accord with estimates of dielectric thickness as well as recent physical studies (253). With the assumption that a transmembrane segment must span this thickness to give a stable pore structure, a rise per residue of 1.5 A can be estimated for an a-helix, and 20 amino acid residues would be required. Peptides shorter than 20 residues, such as mastoparan and emerimicin, are capable of ion channel formation,... 

Table 6.3. Device performance, structure, and test parameter table for IEEE 1620 compliance, adapted from [114], Fig. 4. At least two of the specific gate insulator capacitance, relative dielectric constant, and gate dielectric thickness are required. Reprinted with permission from IEEE Standard 1620-2004, IEEE Standard for Test Methods for the Characterization of Organic Transistors and Materials, Copyright 2004 by IEEE.

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