Hi. The result of the transient simulation should not be dependent on the time step unless you are using a very large time step and therefore are ending up with too few points in the frequency domain plot. The key to getting consistent result here most likely lies in the accuracy setting (abs. tol.) of the solver. The transient solver often requires a larger accuracy setting than the steady state solver. The default values for the abs. tol. (absolute tolerance) for both the Poisson and drift-diffusion solver are 1e-4. You can try reducing this value to (say) 1e-6 to see if this affects your result. Once you see the result is consistent irrespective of the value of abs. tol., you should have accurate result that will give you accurate bandwidth.
Now regarding the parameters for the transient solver, here are some pointers:
min time step (fs): The minimum time step should be small enough so that you have enough points in your time domain response. This will ensure, (i) you have enough points in your frequency domain response and (ii) your frequency domain response has a large enough span. The limiting factor here is the electron relaxation time in the semiconductor which typically varies from 0.2 to 1 ps. So the minimum allowed value for “min time step” is around (say) 500 fs.
max time step (fs): This option can be used to speed up the simulation when solver gets close to reaching steady state. However, if you are thinking about doing fft then you may need to re-sample the result to get a uniform time grid.
abs lte limit / rel lte limit: These entries determine when the solver will increase the time step to speed up the simulation. If the absolute error (or relative error) is less than this value then the solver increases the size of the time step.