Hi,
wheter a FET is ON or OF is independent of current. It is a question of V_GS.
For sure with a limited V_GS there is a limited current. --> The datasheet will tell you.
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The current diagram is useless. It just tells, that the current goes form 0A to -9A relatively fast but from -9A to 0A relatively slow. Nobody knows why. Wheter this is good or not. No timing information..
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You say the specifications of a gate driver is in picture2. But picture shows only a couple of columns with (random) values.
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We are not here to solve your riddles.
Give complete and detailed informations. Ask dedicated questions.
Then soon you will get satisfying answers.
Klaus