It depends on whether you want the word to come across as specific, in which case you would capitalize, versus a general word, in which case you don't capitalize. To explain what I mean, consider if I referred to "the Queen," versus "the queen." The former suggests that I am referring to a specific queen, with a specific title and ...
You mention a 'semicolon' but then (correctly) use a colon.
A colon is nearly always preceded by a complete sentence; what follows the colon may or may not be a complete sentence, and it may be a mere list or even a single word.
British usage: no capital letter after a colon unless it is to start a proper noun or acronym.
American usage: a capital letter if ...
If the paper s to be published in a journal or similar academic publication, there is probably a specified style guide to be followed. If there is, follow it strictly. If not, follow the same rules as othe papers in the same field recently published. If there is a specific style guide normally used in the relevant field, follow it. This applies to all style ...
Follow the same capitalization rules in academic writing as you would normally follow when writing in English.
Capitalize the first word of a sentence
Capitalize names and other proper nouns
Don’t capitalize after a colon (usually)
Capitalize the first word of a quote (sometimes)
Capitalize days, months, and holidays, but not seasons
When in doubt, Check with reviewers or publishers, who sometimes have standards for such things. Generally speaking though, both forms are acceptable. I.e., this:
A Caption For Us To Consider
is no better or worse that this:
A Caption for Us to Consider
I tend to prefer the second (as a matter of taste), but I've seen both used. If the place you're ...