Sorry for the delayed response, but I have worked through several iterations to be sure to provide the best possible advice.
If you’re looking to build a low-power solution, I would suggest using the Notecarrier-AL, which we’ve purpose-built for this use case, and which runs in our Airnote.
Using the Notecarrier-AL gives you FULL CONTROL of the circuitry running between the Notecard and the host MCU, which allows you to tailor the power solution to your project. Then from your sketch, you will request the Notecard to completely disable the host MCU, thus maximizing the potential of your battery.
In the example linked below, the host firmware requests for the Notecard to disable the host MCU for a specific period of time using the ATTN
pin, wakeup and report sensor data, then request to be put back to sleep. In order to simulate being routed to the EN pin on a regulator, this example uses the EN pin on the Feather’s MCU.
Several options exist which allow the Notecard to wake up the host MCU when certain events occur (such as incoming messages from the Notehub). There is a nice guide on the developer site that explores these options.
https://dev.blues.io/reference/notecard-walkthrough/low-power-design/
To answer your question exactly as asked:
Each MCU manufacturer publishes its own way of putting its MCU into “deep sleep” mode, such as this for the ESP32. We recommend that you look to your host MCU’s manufacturer for guidance and examples.
https://docs.espressif.com/projects/esp-idf/en/latest/esp32/api-reference/system/sleep_modes.html
Here is a great article written on the topic: