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A thyristor, I know, is a four-layer PNPN structure, with an anode on the first P section, a gate on the second P section, and a cathode on the second N section. This simple structure suggests that any thyristor ought to be possible to turn off, by routing all of the anode current out through the gate, making the cathode current go to zero, thereby unlatching the thyristor.

In a simulator, a two-transistor model of a thyristor as shown below does indeed turn off when a sufficiently low-resistance path to ground is provided.

^{simulate this circuit – Schematic created using CircuitLab}

So my question is this: What makes a GTO thyristor special? Is it just an ordinary thyristor but with specified characteristics for this mode of operation? Or is there some different silicon structure inside of it that makes it work fundamentally differently?

Interesting question!

Let's start with how we typically use a Thyristor. The Cathode will usually be connected to Ground and the Anode to supply via the load:

^{simulate this circuit – Schematic created using CircuitLab}

So the electrons enter at the Cathode and travel to the Anode.

In the drawings below, the Cathode is at the top! So the electrons flow from top to bottom (only in the doping profiles, not in the schematic above)!

After some searching I found these two drawings of the doping profiles of both devices.

This is the doping profile of a "normal" Thyristor, from this site.

And here is the doping profile from a GTO from the Wikipedia page about the GTO.

The main difference that I see is that the GTO has an additional P+ region (highly doped P-region) for the Gate contact. Such a highly doped region is used to make a "better", more low-ohmic contact to that doping region.

According to Wikipedia:

Turn off is accomplished by a "negative voltage" pulse between the gate and cathode terminals. Some of the forward current (about one-third to one-fifth) is "stolen" and used to induce a cathode-gate voltage which in turn causes the forward current to fall and the GTO will switch off (transitioning to the 'blocking' state.)

For me that could explain why the GTO can be turned off while the normal Thyristor cannot. In a normal Thyristor the gate doesn't have such a good contact to the top P region which prevents it from diverting enough of the electrons to make the Thyristor turn off.

In a GTO the contact to that P-region is much better so many more electrons can be removed (via the Gate) from that P-region. Also the voltage of this P-region can be controlled much better through the low-ohmic contact. That also allows the Gate to pull down the voltage of this P-region relative to the Cathode which will bias the Cathode (N+) to Gate (P) junction in reverse and blocking the Cathode current.