Limiting capacitance measurement

A solution of brain lipids was brushed across a small hole in a 5-ml. polyethylene pH cup immersed in an electrolyte solution. As observed under low power magnification, the thick lipid film initially formed exhibited intense interference colors. Finally, after thinning, black spots of poor reflectivity suddenly appeared in the film. The black spots grew rapidly and evenutally extended to the limit of the opening (5, 10). The black membranes have a thickness ranging from 60-90 A. under the electron microscope. Optical and electrical capacitance measurements have also demonstrated that the membrane, when in the final black state, corresponds closely to a bimolecular leaflet structure. Hence, these membranous structures are known as bimolecular, black, or bilayer lipid membranes (abbreviated as BLM). The transverse electrical and transport properties of BLM have been studied usually by forming such a structure interposed between two aqueous phases (10, 17). 

Although several methods for making the capacitance measurements have been suggested, we will limit our discussion to the use of the LC oscillator and frequency counter shown in Fig. 2. 

The limitations of capacitance measurements in undoped a-Si H have resulted in a greater emphasis on measurement techniques which use the shift of with a trapped space charge (Eq. (4.18)). An example is the field effect experiment, which is of special interest because it was the first technique used to obtain N E) in a-Si H (Madan, LeComber and Spear 1976). The experimental configuration is shown in Fig. 4.19. A voltage across the dielectric layer induces a space charge Q = C Vj in the a-Si H film, where is the capacitance of the dielectric. The Fermi energy in the a-Si H near the interface... 

The depletion layer profile contains information about the density of states distribution and the built-in potential. The depletion layer width reduces to zero at a forward bias equal to and increases in reverse bias. The voltage dependence of the jimction capacitance is a common method of measuring W V). Eq. (9.9) applies to a semiconductor with a discrete donor level, and 1 is obtained from the intercept of a plot of 1/C versus voltage. The 1/C plot is not linear for a-Si H because of the continuous distribution of gap states-an example is shown in Fig. 4.16. The alternative expression, Eq. (9.10), is also not an accurate fit, but nevertheless the data can be extrapolated reasonably well to give the built-in potential. The main limitation of the capacitance measurement is that the bulk of the sample must be conducting, so that the measurement is difficult for undoped a-Si H. 

One such properly is the capacitance, which is observed whenever a metal-solution interphase is formed. This capacitance, called the double layer capacitance, is a result of the charge separation in the interphase. Since the interphase does not extend more than about 10 nm in a direction perpendicular to the surface (and in concentrated solutions it is limited to 1.0 nm or less), the observed capacitance depends on the structure of this very thin region, called the double layer. If the surface is rough, the double layer will follow its curvature down to atomic dimensions, and the capacitance measured under suitably chosen conditions is proportional to the real surface area of the electrode. 

Our research builds on this limited body of work concerning diffusion at the interface of adhesive joints. We have measured the interfacial diffusion process of acetone into a bonded pressure sensitive adhesive tape bj employing single frequency capacitance measurements and a novel interdigitated electrode sensor design. 

In the following discussion we shall examine some of the various ways in which junction capacitance measurements for an amorphous semiconductor may be interpreted. Experimental results for a-Si H are presented for several representative studies mentioned above. We shall then discuss the limitations of capacitance techniques to deduce densities of states and also mention some of the capacitance profiling techniques that have been used to aid in the interpretation of capacitance measurements. 

Differential capacitance measurements by Niki et for cytochrome C3 from D. vulgaris, strain Miyazaki, were consistent with irreversible, diffusion-limited adsorption for 4-s drop times above a concentration of 10 fiM. The surface excess of cytochrome C3 was calculated to be 0.92 x 10 " mole/cm. Niki etal also investigated the a.c. polarographic behavior of cytochrome C3 at the reversible half-wave potential. The capacitive peak height was frequency independent while the resistive peak height decreased with increasing frequency to a value of zero above 2000 Hz. These results were fit to a Laitinen-Randles equivalent circuit yielding an n value of... 

The converse electrostrictive effect—the stress dependence of the permittivity—is also used in stress sensors [19]. A himorph structure provides superior stress sensitivity and temperature stability. A measuring system with a himorph structure, which subtracts the static capacitances of two dielectric ceramic plates, has been proposed [ 19]. The capacitance changes of the top and bottom plates have opposite signs for uniaxial stress and the same sign for temperature deviation. The response speed is limited by the capacitance measuring frequency to about 1 kHz. Unlike piezoelectric sensors, electrostrictive sensors are effective in the low-frequency range, especially DC. 

A second commercially available pre-screening system is very similar, but uses a capacitive measurement made at each time of the finely spaced row of scanning contacts. The overall function is very similar to that just described, except that the alternative of a true DC measurement of continuity and isolation is not provided. For those customers that do not perform such tests with their existing flying probers, this may not prove a significant limitation. For high reliabihty applications where DC continuity testing is required the utility of this method may be reduced. 

Answer Hoyen, Jr.) The capacitance measured over the frequency range from 40 to lO cps decreased with increasing frequency, approaching a limit at both the high- and low-frequency values. Using an equivalent circuit model as described in the text, the capacitance of the bulk and of the space charge regions for the crystal can be calculated. The dependency is not simple function of the square of the frequency. 

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