As an aside, the whole "8 hour half-life" is astonishingly high, to me. Caffeine is nice, but it doesn't seem to have that strong an effect on me, and certainly nothing I notice 5-8 hours after. I drink quite a lot of caffeine these days, but even at times when I went off caffeine for a few weeks, I didn't get effect durations any longer than 1-3 hours.
I have the genes that extend caffeine half-life. If I drink an American large coffee, I get anxious. I can drink a whole pot or two of green tea and feel a nice lift in mood.
As others have mentioned, any coffee after noon and I can't fall asleep until around 2am. I avoid caffeine most days except for the occasional morning kombucha.
[1] https://www.reddit.com/r/nootropics/wiki/faq#wiki_l-theanine
Might have something to do with the strength of the tea, though.
Metabolism of drugs like caffeine is genetically quite variable and is quite an issue for pharmaceutical companies.
short summary: 200mg at 7 a.m., and going to bed at 11 p.m. had following effect: "Compared to placebo, sleep efficiency and total sleep time were significantly reduced."
The effects are 6 hours for me, less than 1 hour for my father (who smokes), and can last over 18 hours for my wife and mother-in-law.
I haven't seen the studies on caffiene half-life, but I suspect the variation is very high.
I personally take it early morning and after a siesta.
Green tea is less of a problem (then again, the way I prepare it, it contains much less caffeine).