The primary electrons in the incident beam lose energy upon entering a material through inelastic scattering or collisions with other electrons. In such a collision the momentum transfer from the incident electron to an atomic electron can be expressed as formula_1, where formula_2 is the distance of closest approach between the electrons, and formula_3 is the incident electron velocity. The energy transferred by the collision is given by formula_4, where formula_5 is the electron mass and formula_6 is the incident electron energy, given by formula_7. By integrating over all values of formula_8 between the lowest binding energy, formula_9 and the incident energy, one obtains the result that the total cross section for collision is inversely proportional to the incident energy formula_6, and proportional to formula_11. Generally, formula_12, so the result is essentially inversely proportional to the binding energy.

By using the same integration approach, but over the range formula_13 to formula_6, one obtains by comparing cross-sections that half of the inelastic collisions of the incident electrons produce electrons with kinetic energy greater than formula_15. These secondary electrons are capable of breaking bonds (with binding energy formula_15) at some distance away from the original collision. Additionally, they can generate additional, lower energy electrons, resulting in an electron cascade. Hence, it is important to recognize the significant contribution of secondary electrons to the spread of the energy deposition.

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Electron energy deposition in matter
Charging
Proximity effect