It’s unclear what you’re trying to do and whether or not what you’re proposing is the best way to do it.
Are you looking for a SAM that is covalently bound or not? SAMs that are covalently bound are easier to get good coverage with, but they degrade the conductivity of the material. Good covalent SAMs include just about any benzene diazonium salt. Good noncovalent SAMs are probably limited to functionalized pyrenes or other PAHs. There is a smattering of other self-assembling adsorbates (including graphene-binding peptides) that might be of interest to you. Typically deposition of all of the above is done in solution phase, not vapor phase. TMDs are more amenable to noncovalent SAMs, but I’m less familiar with the state of the art there.
Also, what do you mean by bind TEA? Covalently will be difficult; maybe a dative bond with an organoboron, or else forming a bond to make a charged ammonium. The other option is non-covalently through an acid-base interaction. This is probably your best bet: to use a fairly acidic carboxyl group to protonate the TEA and rely on the electrostatic interaction of the ammonium with the carboxylate.
BUT: it also sounds like you want to electrostatically dope graphene with TEA, which is usually a physisorptive interaction, so no acid-base. Moreover, you say you want to p-dope one side and (presumably) use TEA to n-dope the other side. Folks have done somewhat similar stuff in the past; look up “Janus membrane” for an idea of what’s been done. Like I said, it’s unclear what you’re after, so it’s hard to give good advice.