Re: Slew rate rise time
The charging of a capacitor is not "exponential" or "linear", it is given by what charges the cap. For an RC circuit, yes, the charging voltage is exponential, because the current varies exponentially, too.
But for a constant current, the voltage across the cap varies linearly.
That is because the voltage is u=1/C*∫i(t) dt
If the capacitor current is constant, the integral is a first-order function with respect to time, that is a ramp, so the voltage across the cap varies LINEARLY with time.
As I mentioned in the previous post, the internal capacitor is charged by a constant-current source, which acts as an active load. Since the current is constant, the capacitor charges linearly, so the slew rate is "linear." (I don't like this term; what I really mean is that the output voltage of an opamp experiencing slew rate limiting varies linearly with time, not being able to follow the input.)
Settling time is simply another parameter used to characterize opamps. It refers to the time needed for the output to reach the final value within a certain percentage-usually 0.1 or 0.01%. The response can be oscillatory (ringing), so this takes into effect all that and tells you when the output is within the specified percentage of the final value. It is useful for example in A/D signal conditioning, since it tells you when you can start the conversion and be certain that the result will be accurate. Look at the picture.