With load .. you mean "load current"?
What are you expect it to express?
I mean, for sure V_GS controls the conductivity of a MOSFET, thus it surely has influence on I_D.
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Again: you mean "load current"?
The timing of the plateau depends more on switching voltage than on switching current. But for sure there is some kind of influence.
And the "load current" , or better say the I_D has influence on the level of the plateau. Especially on MOSFETs with low g_m.
Klaus