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tried to conceal the title and the body question of the OP
V.V.T
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Outside the context of the title question, the answer to the body question can be "in the saturation mode, the electric field is the greatest at the drain side of the channel because of the oxide interface charge distribution, pinch-off, etc." But the breakdown voltage \$BV_{DSS}\$ parameter of power transistors is more concerned with breaking down the reverse-biased body-drift diode and the consequent avalanche multiplication process resulting in uncontrolled current flowing between the source and drain with the gate and source being short-circuited. Seeing that the avalanche breakdown most often result in total destruction of the transistor (more precisely, an individual cell of millions of identical trenches in the modern power MOSFET), I am going to try and answer the question: "Which is the most likely location for the onset of avalanche breakdown?".

There are different types of power transistors and different breakdown modes, all sharing the fact that their layouts are entirely different from the textbook pictures of lateral long channel MOSFETs with their wedge-shaped inversion layers (greatly oversimplified up to the point of falsely depicting the thing). Closer to the reality is a visualization of Figure 14 MOSFET cross-section with parasitic BJT from Infineon's application note Some key facts about avalanche.

VDMOS.png

As you see in this picture, avalanche most likely starts in a lightly doped drift region, which is not a part of the p-type channel, neither it is the FET drain, but the collector of the parasitic npn transistor just outside the FET p-type channel. In this section 2.2 Failure mechanism of the application note, the latch-up mechanism is discussed which results in the single pulse avalanche. Although in many new technologies latch-up no longer occurs, the repetitive avalanche discussed in the section 4.2 Failure mechanism (page 31 and on) also most likely starts in the parasitic npn transistor collector.

The application note explains the greater electric field in the vicinity of the parasitic BJT by mentioning the technology structure:

If the technology is structured in such a way that the electric field is high in the vicinity of the parasitic NPN bipolar junction transistor (BJT), a significant amount of current will flow through its base resistor, producing a voltage between base and emitter.

The other application note AN-1005, Power MOSFET Avalanche Design Guidelines, is more specific to this end:

Due to the radial field component, the electric field inside the device is most intense at the point where the junction bends.

and you can see in Figure 14 of the Some key facts about avalanche application note that the avalanche multiplication zone is placed closer to the highest curvature of the pn junction line.

As concerns the device fault location, AN-1005 enlightens us that

Typical modern Power MOSFETs have millions of identical trenches, cells or many strips in parallel to form one device, as shown in Figure 9. For Robust designs, then, avalanche current must be shared among many cells/strips evenly. Failure will then occur randomly in a single cell, at a high temperature. In weak designs, the voltage required to reach breakdown electric field is lower for one device region (group of cells) than for others, so critical temperature will be reached more easily causing the device to fail in one specific area.

(AN-1005, page 6, under Figure 8: Power MOSFET Cross Section Under Avalanche).

"Failure will then occur randomly in a single cell".

V.V.T
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