The electric fields produced by tDCS aren't strong enough to force neurons to fire, even in brain areas very close to the surface/electrode, though they can adjust the timing of neural activity, so that cells fire slightly sooner/later than they might otherwise. My collaborators and I have collected some nice data from awake, behaving monkeys (which have obvious similarities to humans) demonstrating this.

- DC + behavior: http://packlab.mcgill.ca/Krause%20et%20al%202017.pdf - AC + deeper structures: http://packlab.mcgill.ca/Krause%20et%20al%202019.pdf

There's also a recent preprint replicating our AC results: https://www.biorxiv.org/content/biorxiv/early/2019/07/09/696...