Besides capacitive parasitics as Coss, Crss and Ciss, parasitic inductances as LS, LG and the inductance sharing both gate path and power path define fast-switching behaviour. What do you look for first?
Unwanted turn-on seems caused most by Crss, combined with the dV/dT ratio of the voltage over the power device. (when the transistor is off, the current through the inductors Ls, Lg is zero, and cannot contribute.)
Excessive overvoltage is caused by the energy in the inductances. Please note that reducing is not always feasible. I mean, when large currents need to be carried (eg 100 Amps), you need thick wires and large devices, this leads to current loops with large area, and this in combination with the already large current, leads to high parasitic energy.
I think that to go further than these generalities, you need to go in detail on the schematic diagram of the circuit you want to realize, and make calculations on the impact of Crss together with dV/dT and see what it does, and likewise for the overvoltage make calculations on the parasitic inductances and Ls and Lg and the dI/dT (Ls is the biggest concern, the gate current being much smaller means Lg will store less energy. Also, it is more easy to keep Lg small, because of its smaller current.)
thank you for your valuable comments. I agree with you that reduction of parasitic inductances becomes tougher at high currents and thus larger setups. However, I think this can be handled by placing many semiconductors in parallel as already done in power modules. What`s not yet done - at least not on a large scale - is equipping every half-bridge made of two chips with an individual ceramic capacitor in order to shrink the area enclosed by the power current loop.
I am not that much with you when it comes to the role and the impact of LG. You argue that the gate current is low and thus the energy is low compared to the energy stored in the power loop's parasitic inductance. That's true. However, the gate circuit properties are amplified to the power branch - MOSFETs, JFETs, IGBTs and BJTs are used due to their ability to control high energy levels by low energy levels. Resonances of the semiconductor inputs directly affect the output - thus the whole system.