Man I don't think I'm ever going to really *get* transistors. Strange little bastards.
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I probably need to be corrected on this summary, but for me it helps to focus on "thermal" in the first place: there's *a lot* of electron motion in rest, and you nudge that cloud of electrons/holes *only slightly* using electric fields.
This was when it started to click for me - understanding the thermal aspects, and all those seemingly magic values like 26mv, 800mv, etc