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improved circuit performance. The ideal solution would be to increase the physical thickness without increasing the electrical oxide thickness. The oxide was assumed to have a constant trap concentration. The excess energy of the tunneling electron is released by means of phonon emission. A thorough investigation of modeling and simulation of tunneling mechanisms can be found in the thesis of Gehring . From this the trap occupancy function can be calculated which is used to compute the tunneling current . These leakage currents are becoming a significant factor to portable device manufacturers because of their undesirable effect on battery run time for the consumer. Leakage in a high- voltage system can be fatal to a human in contact with the leak, as when a person accidentally grounds a high-voltage power line. Figure.7 gives an example of a highly degraded dielectric with traps randomly distributed across the oxide.
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As the wave function penetrates the barrier and can even extend to the other side, quantum mechanics predict a non-zero probability for an electron to be on the other side. The thinner the gate, the larger the tunneling current and the higher the leakage power. Negative Bias Temperature Up:. This "depletion" region acts very much like a thicker oxide, in that it reduces inversion charge (thus reducing inversion capacitance) with resulting degradation in drive current. The tunneling rate of a specific trap is determined by all capture and emission times to and from the trap. A common approach to model the tunneling current is the Tsu-Esaki formula 67 (5.1) where is the electron mass in silicon and the electron mass in the dielectric . The model for the simulation of silc in highly degraded devices is based on inelastic, phonon-assisted tunneling 79 with the tunneling-rate proposed by Herrmann and Schenk . Although the interaction between neighboring traps is of importance in highly degraded dielectrics (Section for less degraded devices this approach can be used 72,. Inelastic Phonon-Assisted Tunneling The defect-assisted tunneling process of an electron from the cathode to the anode via a trap is considered as a two-step process. In addition the filling of oxide traps with carriers, leading to space charge in the oxide and therefore to a shift of the threshold voltage, is accounted for. The primary source of leakage occurs inside transistors, but electrons can also leak between interconnects. For example, magnetic lines of flux will not be entirely confined within the core of a power transformer ; another circuit may couple to the transformer and receive some leaked energy at the frequency of the electric mains, which will cause audible hum.
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