How to design ultra low-power opamp?
There is nothing special about ultra-low power OTAs/OpAmps. Of course you can use a few tricks to improve the power consumption, but also standard textbook circuits can be designed to work with low power consumption.

The ultimate limits are speed and leakage currents which depend on the given technology. Usually 40uA is not considered ultra-low power, as such designs consume typically less than 1uA in total.

A few ideas to get you started:
Low power implies low speed, therefore you need to consider the load, which is usually capacitive. For a given bandwidth a certain transconductance will be required to drive the capacitance. A relationship like GBW = (gm/(2*pi*C) will result.

Say we have an ultra-low power design and we want to drive 200fF and achieve a GBW of 1MHz. A gm of 1e6 * 2*pi *200e-15 ~ 1.3uS will be required. To keep things simple we use a telescopic OTA where (nearly) all the current can be used to generate a transconductance.

For ULP designs we aim at an gm/Id ratio of at least 20. Since we have two transistors in the input stage we will need twice the current which results in 1.3uS / (10uS/uA) = 130nA.

If we wanted to drive 1pF (=5*200fF) or we wanted to achieve a GBW of 5MHz (=5*1MHz) then 5 times the current would be required. The transistors will also introduce parasitic capacitances so a higher current will be required.