Also for gate resistor calculation, Total resistance = Driver IC internal resistance + Gate Resistor + IGBT internal gate resistance, Is this correct equation????
In general, yes, but from what I know, gate drivers are designed to provide a specified current value - so their resistance should not be an important factor (please correct me if I am wrong).
Then, the resistance of the routing from the gate driver (or from the gate port or pad) to the device, and "internal" resistance of the IGBT gate network, are important factors.
The total resistance (routing and internal gate resistance) will determine the switching speed, impact transient losses, etc.
Digging deeper - internal gate resistance is not a simple thing.
Gate network is a complex multi-layer net distributing the gate signal over a large area.
Calculating its effective resistance is not a trivial task, especially when its layout is not "regular" - having some metal lines going inside the active area, asymmetry, cutouts for the gate pad, etc.
There are EDA tools that can do this effectively.
Also, for a large distributed system like gate network (in IGBT, in MOSFET, etc.), one value of effective resistance does not tell the whole story.
Different points over active area will have different gate resistance - for example, points close to the gate pad or to the entry point of the gate routing will have lower resistance than points far away.
This will lead to non-uniform gate switching, and possibly to a dynamic current crowding, heating, and reliability issues during switching events.
Furthermore, you should pay attention to current density during gate charging or discharging, uniformity of current distribution or current crowding in contacts and vias, etc.
Also, in power MOSFETs using in DC-DC converters, gate resistance may impact the dynamic drain dV/dt effect, where a fast ramp on the drain temporarily opens certain portions of the transistor (Vg higher than Vt) even if its gate voltage is zero, leading to shoot-through current and to efficiency loss and/or heating and reliability issues.
Max