Hello,
Do you know of an IC from ti.com that can do the above?
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The TPS61175 can be operated in a split rail configuration where you tie a separate >3V supply to the IC's Vin and then the 2V input supply to the inductor for the power stage. If you don't have a separate >3V supply, then I suggest using one of our TPS60xxx or REG710 charge pumps to provide that supply. Note that efficiency will not be very good because the TPS61175's internal FET is a bit too resistive for such a low input voltage. You could do that same thing with the TPS40210, a pick a very low Rdson FET to boost efficiency, but you need a >5V supply for that IC.
The TPS43000 can do this in one IC but it is expensive and cumbersome to design.