Sketches of the voltage at the structure (a) and distributions of the electric field in the base (b). The electric-field profile is shown at , at the moment when the voltage of stationary breakdown is reached, and at the moment when the front is triggered. and are the effective threshold of impact ionization and maximum electric field. The dashed line in panel (b) shows the electric-field profile for the traveling front . Typically and , so that . For simplicity we assume that during the period neglecting the displacement current through the structure and the respective voltage drop over the load resistance .
Positions of the process-induced levels in the energy gap. The ionized and neutral states of the sulfur impurity correspond to level ( transition) and level ( transition), respectively. The ionized state of the double sulfur complex corresponds to ( transition) level. The neutral state of this double complex corresponds to a shallow level not shown here. and denote the bottom of the conductance band and the top of the valence band, respectively.
Thermal emission rate for electrons bound on , , and levels as a function of temperature calculated according to Eq. (2).
Occupation of , , and levels in equilibrium (solid lines) and the actual occupation at the moment of triggering after the waiting time in the depleted region (dashed lines). The actual occupation of center (dashed line) is of the order of 0.5 for .
The sketch illustrates the field-enhanced emission of bound electron from charged deep-level center to the conductance band in external electric field . The binding energy is counted from the bottom of the conductance band . The potential of the positively charged deep center is depicted by the solid line. The dashed line corresponds to a neutral center whose potential does not have the Coulomb component. The electron escapes to the conductance band thermally in the regime of the Pool-Frenkel effect (arrow 1, low electric field) due to the phonon-assisted tunneling (arrow 2, intermediate field) or by direct tunneling (arrow 3, strong electric field). In the case of phonon-assisted tunneling (arrow 2) electron tunnels under the potential barrier at the energy .
Field dependence of the emission rate for , , and levels in the regime of direct tunneling at low temperatures according to Eq. (9).
Emission rates for and levels in the regime of the phonon-assisted tunneling. The panel (a) shows the field dependence of the ionization rates at . The upper and lower groups of curves correspond to the and levels, respectively. The panel (b) shows the temperature dependence of the level emission rate at . Curves 1, 2, 3, and 4 are calculated according to Eq. (7) for the local phonon energies , 600, 800, and , respectively.
Emission rate for the midgap level in the regime of the phonon-assisted tunneling. The panel (a) shows the field dependence at . The panel (b) shows the temperature dependence at . Curves 1, 2, 3, 4 are calculated according to Eq. (7) for the local phonon energies , 600, 800, and , respectively.
The total emission rate from and levels of the solitary process-induced center normalized by the concentration of solitary centers at (solid line). The dashed line shows the emission rate for levels of the double complex normalized by the respective concentration of such complexes. The shown temperature interval corresponds to the phonon-assisted tunneling regime. The calculation is done for .
Parameters of PI defects according to Refs. 21 and 22.
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