About start up time of LP2997

Satoshi,
Vtt come up instantaneously. Since it's a regulator, the half of VTT come up as soon as VDDQ is turned ON. Historically we learned that it's a better idea to soft start the VDDQ if you have large capacitance at the VTT line to avoid high inrush current. The delay of VTT coming up is in a few nano seconds. (really small)

Satoshi-san,
I have some start up data for LP2998 which is pretty similar to LP2997. If you are interested, I can send you that. In the meanwhile I'm getting some LP2997 Parts soon. I can evaluate them on bench and provide you some data by next Monday.

Satoshi-San,

Here is a similar plot for LP2998 in DDRIII configuration. Time scale is 100usec

Hope this helps. Please suggest this as answer if this is what you are looking for. 

Best