The incident beam electrons themselves do not directly generate all of the x-rays entering the x-ray detector.  Backscattered electrons, plus in the TEM forward scattered electrons, also generate signals from the media surrounding the specimen.

In both instruments, unless special precautions are put in place, an operator must consider a spectrum in the light of which elements could be generated from the microscope itself.  Typical microscope materials that may be found in a spectrum are - Copper, Iron, Nickel, Cobalt and Aluminium, depending upon the particular instrument being used. 

The most common features designed to help in this respect are carbon coated aluminium inserts or cover plates, even beryllium parts are used in some cases.  

In the TEM the inserts are placed in the upper and lower objective pole piece and the specimen holder.

In the SEM the instrument may be fitted with a carbon coated aluminium plate on the base of the final lens or operated with the backscattered electron detector between the specimen and the final lens.  Be aware that a specimen containing heavy elements will backscatter more than one containing light elements and the higher level of backscatter will produce a higher level of x-rays from the instrument itself.  Your enemy in this case are SE3 and SE5 production sites!

Also take a look at the section semsigs.htm if you are interested in SEM?