Theory and Applications of Junctions

Now that we have laid the groundwork for understanding how we can engineer various carrier concentrations and Fermi levels into semiconducting materials, we can explore some of the numerous devices that have become possible using these novel materials. 

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The semiconductor/electrolyte contact has been extensively investigated since the 1970s. A recent review [32] and text books [33, 34] furnish details of the theory and applications of semiconductor electrodes. Below are given only some elements necessary for the discussion. Phenomenologically the liquid junction behaves more or less like a solid-state Schottky diode, with the electrolyte playing the role of the metal layer. 

Temperature measurements are readily made using commercially available instrumentation. Thermocouples of the copper-constantan (T) type are usually chosen as the measurement probes. These can be made sufficiently small to ensure point measurements can be taken. Thermocouple hot junctions less than 1 mm wide can be used to measure temperatures in small containers and crevices, regions likely to retain air in sterilisation processes or into which heat conduction or convection is inefficient. Kemper gives full details of the theory and applications of thermocouple devices. 

Table 2 Characterization of Polystyrene Networks by Swelling Equilibrium Measurements in Toluene, and Application of the Constrained Junction Theory ...

Note. The Debye length (LD), although not introduced into the present simplified discussion, is a parameter frequently referred to in the gas-sensor literature. It was originally introduced into ionic solution theory and later applied to semiconductor theory where it is especially applicable to semi con -ductor/metal and semiconductor/semiconductor junctions. It is a measure of the distance beyond which the disturbance at the junction has effectively no influence on the electron distribution and therefore closely related to d (see Eq. (4.49)). It is a material parameter given by LD = (j kl /e2(, )12 where cQ is the undisturbed electron concentration, essentially the extrinsic electron concentration in the case of doped n-type tin oxide, and the other symbols have their usual meaning.)... 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

The Kramers theory and its extensions have found many applications since the original work by Kramers. Recent application of the non-Markovian theory in the low-friction limit to thermal desorption was described by Nitzan and Carmeli. Another novel application of the Markovian theory is to transition from a nonequilibrium state of a Josephson junction. In what follows we shall briefly review the recent application of the generalized Kramers theory to chemical rate processes. More detailed reviews of the exjjerimental and theoretical status of this field may be found in Hynes. ... 

In spite of well-developed classical theory, the interest to investigation of synchronization phenomena essentially increased within last two decades and this discipline still remains a field of active research, due to several reasons. First, a discovery and analysis of chaotic dynamics in low-dimensional deterministic systems posed a problem of extension of the theory to cover the case of chaotic oscillators as well. Second, a rapid development of computer technologies made a numerical analysis of complex systems, which still cannot be treated analytically, possible. Finally, a further development of synchronization theory is stimulated by new fields of application in physics (e.g., systems of coupled lasers and Josephson junctions), chemistry (oscillatory reactions), and in biology, where synchronization phenomena play an important role on all levels of organization, from cells to physiological subsystems and even organisms. 

It is clear from Eq. (13-105) that a knowledge of e and ci- permits evaluation of the activity coefficient v . Comparison of results obtained by this method with those from other techniques yields excellent agreement. Thus, the applicability of thermodynamic theory to the case of partial equilibrium in a galvanic cell with liquid junction is demonstrated. 

The basic electronic theory of the semiconductor was developed in two papers in the Proc. Royal Society in 1931. It was based on the existence of potential wells in which the electron can reside. With the application of additional voltage, the electron can leave the well and migrate on the surface of the solid. It did not reach a practical stage until the World War of 1939 when the physicist, R. Ohl, at Bell Laboratories tried to use the cat s whiskers as an electronic amplifier. It was found to work in an unreliable manner and was about to be abandoned when a cracked crystal showed excellent but unpredictable results. This was eventually traced to the junction caused by the crack in the crystal. The research team that was formed developed the solid-state diode—composed of two joined crystals. The diode was made of germanium and became known as the semiconductor. 

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