One influence on sleep is light. Basically dim reddish light signals to your brain that it is night, and very bright blue light signals to your brain that it is day. One way to interfere with your sleep is therefore to have bright light, particularly bright blue light, shining directly into your eyes late at night.
Which is exactly what using a laptop, or watching TV, or using an iPhone or iPad does.
This is why Apple has introduced Night Shift, which makes your screen redder as the evening progresses. Unfortunately, it doesn't do anything about screen brightness. And even set to minimum, the built-in brightness setting is still very bright in the night.
There is however a solution that involves combining the built-in brightness with a display accommodation setting.
Ideally you might not have your device in the bedroom at all, but there are lots of scenarios (e.g. listening to audio) where you might want it nearby.
To dim your iPad or iPhone before bed, start with the pull-up brightness control, or with Settings -> Display and Brightness, and set the brightness to the minimum and Auto-Brightness to off.
Next, you need to add a display accommodation to make the screen even dimmer.
Go to Settings -> General -> Accessibility -> Display Accommodations and set Reduce White Point to on, with the reduction set to 100%
You might also want to experiment with changing the colour of the screen, in Settings -> General -> Accessibility -> Display Accommodations -> Color Filters
To dramatically reduce the amount of blue, choose Greyscale.
You can also experiment with other colour change options. (I actually leave my phone in partially-reduced white point and greyscale mode almost all the time, I find it much less distracting than the usual bright candy colours of all the icons.)
Depending on your eyes, you may have to play around a bit with the exact settings. At 0% Brightness and 100% Reduce White Point the screen is only barely visible in a totally dark room, once your eyes are totally night adjusted.
It's unfortunate this all has to be manually done (and undone) each day. It would be nice if Apple added an option to set extra levels of screen dimming in Night Shift.
SIDEBAR: If you take a screenshot in Color Filter mode, it will take an image of the original screen, e.g. even if you are in Greyscale filter mode, the screenshot will still be in full color. I had to use a post-processing image filter to change the screenshot to actual greyscale. END SIDEBAR