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First and second breakdown in silicon diodes are studied with a one-dimensional computer program that includes both electronic and thermal processes. Extensive calculations of both static and dynamic current density-voltage characteristics are shown for temperatures from 300 to 600 K. The variations of first and second breakdown voltages with doping density and diode width are presented. Second breakdown voltages are shown to increase initially with temperature due to the decrease in avalanche coefficients and saturation velocities with increased temperature, and then to decrease as thermal injection from the high doping boundary regions drastically reduces the multiplication factor required to reach the breakdown current. It is shown how the temporal rate of temperature increase, as a function of current density, can be used to calculate both current-versus-time and voltage-versus-time curves from static characteristics at several temperatures. A limited comparison is made with experimental data and with other computations.