What is avalanche in MOSFET? (avalanche capability)

Owing to the stray inductance of the circuit, the surge voltage of the MOSFET is superimposed on the voltage between drain and source at turn-off, and the drain-source voltage may break down if it exceeds the maximum rating of the device.
However, MOSFETs do not break even at voltage exceeding V_DSS (rated voltage) when energy and drain current are within certain limits and temperature is under the rated channel temperature T_ch. This is called avalanche capability. The allowable energy is called avalanche energy (E_AS) and the current is called avalanche current (I_AR).
Fig. 1 shows a MOSFET avalanche measurement circuit and Fig. 2 shows a MOSFET equivalent circuit for considering avalanche. The thinned area in Fig. 2 is part of the parasitic element. Fig. 3 shows the voltage and current waveforms of this measurement circuit. In Fig. 1, an inductance L is inserted into the circuit for measurement purposes instead of a stray inductance.
The voltage V_DD is applied externally and the MOSFET is controlled by the gate voltage V_GS. When the gate voltage is lowered at t₀ and the MOSFET is turned off, the I_D that was flowing when it was turned on does not immediately become zero and tries to continue flowing due to the influence of the inductance. As a result, the drain voltage V_DS of the MOSFET rises and even exceeds the maximum drain-to-source voltage rating of V_DSS, as shown in Fig. 3. Ultimately, the parasitic diode D₁ in Fig. 2 enters avalanche break down and drain-to-source voltage V_DS becomes BV_DSS . If the current I_AS is large at this time, the parasitic NPN transistor TR₁ will turn on and a large current will flow, possibly destroying the MOSFET. Some MOSFETs allow the drain-to-source voltage V_DS to momentarily exceed V_DSS within acceptable limits.