Device simulations of two-dimensional structures with a huge lateral extension indicate that the combination of lateral current flow and a vertical reduction of space-charge region are necessary for the filament formation during the shortcircuit operation of IGBTs and the turn-off of diodes. The shape of the electric-field distribution is introduced as new criterion to estimate the rising branch of the short-circuit destruction curve in the I c -V ce SOA-diagram. The impact of the stray inductance L stray and the gate resistor R G on the short-circuit destruction limit are experimentally investigated. The presented results allow a deeper understanding of the different electrical short-circuit failure mechanisms (turn-on, quasi-stationary state, turn-off) and their relation to one another.
A way of calculating the electron correlation energy for the ground state of large organic molecules is presented. It is demonstrated that various contributions to the correlation energy may be described by simple analytic expressions. In the case of interatomic correlations, they depend only on the bond length, its kind (e.g., σ or π bond) and the atoms involved in the bonding. Intraatomic correlations for a given atom are shown to be determined by its total charge and the fraction of p electrons. The method is developed by starting from semiempirical (self-consistent field) calculations and building correlations into it. It is straightforward and simple to apply. Moreover, it provides considerable physical insight into the phenomenon of electron correlations. A number of tests of its accuracy are presented by considering small molecules for which a comparison with other calculations can be made. An overall satisfactory agreement is found.
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