Short-circuited sample dielectric

The measurement of properties such as the resistivity or dielectric constant of PS requires some kind of contact with the PS layer. Evaporation of a metal onto the PS film-covered silicon sample produces a metal/PS/Si sandwich, which behaves like an MIS structure with an imperfect insulator. Such sandwich structures usually exhibit a rectifying behavior, which has to be taken into account when determining the resistivity [Si3, Bel4]. This can be circumvented by four-terminal measurements of free-standing PS films, but for such contacts the applied electric field has to be limited to rather small values to avoid undesirable heating effects. An electrolytic contact can also be used to probe PS films, but the interpretation of the results is more complicated, because it is difficult to distinguish between ionic and electronic contributions to the measured conductivity. The electrolyte in the porous matrix may short-circuit the silicon filaments, and wetting of PS in-... 

When a dielectric is subjected to an ever-increasing electric field, at some point a short circuit develops across it. Dielectric breakdown is defined as the voltage gradient or electric field sufficient to cause the short circuit. This phenomenon depends on many factors, such as sample thickness, temperature, electrode composition and shape, and porosity. 

Experimentally the process of local breakdown ranges from an inconspicuous repassivation to an explosion-Kke dissolution or vaporization of large parts of the sample. This depends on the electrical and chemical energy stored in the system. The passive film represents the dielectric medium of a capacitor, which is short-circuited by the local breakdown. The electric energy stored on the capacitor heats the breakdown channel, eventually up to temperatures where metal vaporization or plasma formation occurs. At these increased temperatures a very fast reaction of the less noble metals with water or the adjoining metal leads to a destruction of the sample. 

The boundary conditions for these piezoelectric equations are important (a) The condition mechanically free stipulates specifically that boundaries of a piezoelectric sample (e.g., a piezoelectric vibrator) can move, i.e., the vibrator vibrates with a variable strain and zero (or constant) stress. Under this condition, the coefficients in these equations carry a superscript T e.g., is the dielectric constant at constant stress, (b) The condition mechanically clamped stipulates specifically that the boundaries of a vibrator cannot move. This condition means that, when the frequency of the applied voltage is much higher than the resonance frequency of the vibrator, the strain is constant (or zero), while the stress varies. In this case, the coefficients in these equations carry a superscript S e.g., is the dielectric constant at constant strain, (c) The condition of electrical short circuit implies specifically that the electric field = 0 (or a constant), while the electric displacement D 0 inside the vibrator. This is the case when the two electrodes on the surface of the crystal sample are electrically connected (or the electric potential on the entire surface of the sample is constant). Under this condition, the coefficients in these equations carry a superscript E e.g., sfj (or c ) is the elastic compliance (or stiffness) coefficient at constant electric field, (d) The condition of electrical open circuit corresponds to the case when aU the free charges are kept on the electrodes of the sample (electrically insulated) and the internal electric field / 0, while = 0 in the sample, hi this case, the coefficients in these equations carry a superscript D e.g., sjj (or c ) is the elastic compliance (or stiffness) coefficient at constant polarization. 

Figure 2 c) represents the state when the sample is still in the sample holder, but the equilibrium is restored by moving the short circuit piston. At the correct position of the piston the wave-front is restored to the state demonstrated in Figure 2 a). The position of the short circuit piston will be at a new Xj position after the detector signals turn into the initial positions on the standing wave. The difference between position Xi and Xo (Ax) is used to calculate the dielectric constant e (Equation 14). The standing wave ratio is equivalent to the... 

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