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In one of my classes, we skimmed over lithography, but mostly the optics side of things (the diffraction limit, liquid immersion to increase angle of incidence, etc).

One point that was never covered is how the light actually dopes the silicon, and creating a transistor. I've tried to stumble around on the net but every article is either way over my head, or way too vague.

In short, how does a focused beam of light directed at a compound like silicon lead to a "printed" transistor, for lack of a better term?

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There are multiple steps but the basic process is that you use a photoresist.

At the beginning of a process step, a photoresist is "spun" on to the wafer. It is a very literal thing, they spin the wafer while dripping the polymer onto the surface which spreads out into a thin layer of precise thickness. This is cured and then placed into a photolitographic machine, which projects an image onto the wafer that leaves latent images in the Photoresist (AKA PR).

The PR is developed (some resists are negative and some are positive, which means the exposed areas stay or the exposed areas are eliminated). the development process removes the parts of the PR that are to be removed leaving behind the desired pattern.

The PR can define areas that are etched (removed) or windows through which ions are implanted. Implanting is the process through which the Si is doped.

Once the area is implanted, the remaining PR is removed and the wafer is thermally treated to anneal the implant damage.

In between litho steps are depositions, growths, etches, wet baths, plasma treatments etc.

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To elaborate on the projection (imaging) step:

The original design of a microchip is "drawn" by some other means (e.g. electron microscopy) on a glass plate called reticle. The reticle is imaged on the photoresist with reduction (e.g. 4 times reduction in ASML machines), producing tiny structures. While all steps in making a chip are important, this imaging step is critical in defining the quality and the feature size of the final chip, and also in terms of its complexity and cost.

When technology is mentioned with nanometres, it is about the critical dimension (smallest feature size) created at this step (provided it can be then "processed" chemically. Currently it is around 20 nm (compare to the visible light wavelength of 500 nm and to the silicon atomic diameter of 0.2 nm). Usually the smaller the critical dimension, the faster and more energy-efficient is the chip.

Current photolithography machines use DUV (deep ultraviolet) light of 193 nm wavelength. The next generation machines will be based on EUV light (extreme ultraviolet) with 13.5 nm wavelength and will be using pure mirror-based optics in vacuum (because glass and even air absorb EUV light).

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This webpage (link stolen from an answer to this question) shows the different steps for creating a transistor on a wafer. Very well explained with clear illustrations.

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I think that what you are missing is that the light isn't used directly to dope the silicon, it is used to make a mask which protect the part of the silicon which doesn't have to be doped. The doping itself is done by exposing the unprotected part to some gas which diffuse in the silicon.

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