As all the other comments note they aren’t placed on the chip, they’re printed on them using photolithography (a poor name considering they don’t print with stone…).
It should also be noted that when designing the chips the transistors aren’t even placed or drawn (they used to be a long time ago in simpler days). Now you have languages and compilers (hardware description languages and synthesizers) that create the chip design. The designer describes what they want the circuit to do and the computer creates the artwork that will be used to print the circuit on the chip.
BTW we’re way past millions and well into billions of transistors on modern ICs…
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