Transport theory for kinetic emission of secondary electrons from solids

Kinetic secondary electron emission from a solid target resulting from incidence of keV electrons or keV and MeV ions is treated theoretically on the basis of ionization cascade theory. The energy and angular distribution and the yield of secondary electrons are calculated for a random target. These quantities are determined from the solutions to a system of Boltzmann transport equations. Input quantities are the cross sections for collisions between the involved particles and the surface barrier of the target. A general power cross section has been utilized in the analytical procedure. It is shown that liberated electrons of low energy move isotropically inside the target in the limit of high primary energy as compared to the instantaneous energy of the liberated electrons. The connection between the spatial distribution of kinetic energy of the liberated electrons and the secondary electron current from a solid is derived. To find the former, existing computations for ion slowing down and experimental and theoretical ones for electron bombardment can be utilized. The energy and angular distribution of the secondary electrons and the secondary electron yield are both expressed as products of the deposited energy at the surface of the target and a factor which depends only on the properties of the escaping secondary electrons. Corrections for energy transport away from the surface by energetic recoil electrons are partly included. Also the contribution from recoiling target atoms at heavy-ion bombardment in the keV region is largely taken into account. The predicted energy and angular distribution agree with absolute spectra for incident electrons, whereas the agreement with absolute spectra for incident protons is less satisfactory. Extrapolation of the energy distribution down to the vacuum level gives a spectrum which shows good agreement with experimental data. The electron- and proton-induced yields from aluminum are evaluated on the basis of existing low-energy-electron stopping-power data. The agreement with existing experimental data is good. Also, experimental yields from electrons, protons, and noble gas ions incident on copper agree within the accuracy of the treatment.