You have a color FAX? Not highly compatible because most FAXes are black only.
In any case, for a typical scanner, the three colors would be integrated on the same piece of silicon. If one color is out, the whole sensor is bad. If they were seperate, alignment of the colors would be a nightmare. As it is, minor alignment issues are sorted out by the calibration program which figures out if any of the colors needs to be offset by a few pixels (each color feeds the pixel stream out serially and in parrellel to each other)
Unless you have a particularly valuable FAX, its time for a complete replacement. If you can wait a couple of months, Black Friday is approaching, that's usually the best time to get a new 4in1 printer/scanner/fax/copier.
However, if you have one color missing from scans, it may not be the sensor but could be the flex cable that connects it to the main circuit board. These are constantly moving when in use and would naturally be a place to look. Flex cables usually have a one piece connector and can be unclipped from the board. Just try to reconnect it.
OTOH if what you are getting at is how do they discern R from G from B. The simple answer is optical filters. Be it in bulk over the entire array or in micro form built right into the pixel.
In micro form, I think the color filtering is achieved by manipulating the thickness of a refracting silicon oxide layer so that all but the desired colors bounce out. It may also be done by manipulating the depth of the active region of the CCD in the Si Substrate. I would need to do a little more research to be precise but I am confident it's done with already available semiconductor processing steps like patterning, deposition and etching one or more layers of the CCD cell structure. It is not a seperate bulk filter that can be removed in any modern case.
See video middle of this link below. There really isn't much difference between a linear CCD found in a scanner and some specialty cameras and a regular CCD array sensor found in a camera. Even a CMOS sensor would need similar filtering at the pixel level. What I am not clear on is if Physically speaking its a filtering (rejecting unwanted wavelengths) or selective sensitiviy (the pixel active area only sees the color it needs to). Certainly the band gap of a junction can be manipulated so that only specific energies can excite it although Si is usually only sensitive to IR like this. I believe its a combination of the two strategies.
http://www.petapixel.com/tag/ccd/
More later