A universal curve of energy-dissipation range vs normalized electron energy is proposed, which includes the average atomic number Z of the material being bombarded in the energy normalization factor. Range-energy expressions of the form R=kEBα, derived from the Bohr-Bethe energy-loss relation, are valid over limited energy ranges, but the exponent α differs for materials of greatly different atomic numbers over the same energy range. For the aluminum-silicon dioxide-silicon system used here, RG = 4.0 EB(keV)1.75 μg/cm2 has been found accurate for 5 <EB <25 keV. Using this value of range, and taking the steady-state electron-beam-induced current through a thin insulating layer of SiO2 as a measure of the energy dissipation in that layer, an energy-dissipation (depth-dose) function has been determined which should be valid for 10 <Z <15. Using this normalized expression, λ(y) = 0.60 + 6.21y − 12.40y2 + 5.69y3 and the range RG, the energy dissipated at any depth may be determined, and hence the carrier-pair generation in semiconductors, light generation in phosphors, etc., may be predicted. An expression relating the depth-dose function to the applied voltage drop across the oxide provided an independent check on the experimental measurements and the assumptions used in reducing the data. The ratio of (mobility × lifetime) to the (mean electron excitation energy in the oxide) was found to be (μτ/EA) = (2.97 ± 0.06) × 10−13(cm/V)2 using the energy-dissipation formulation, and (μτ/EA) = (3.00 ± 0.05) × 10−13(cm/V)2 using the check expression, where the errors quoted are root-mean-square deviations computed for 12 or more points.

Electrons with a mean energy of a f e w electron volts

A simple theoretical calculation is given in which the energy distribution of low-energy secondary electrons emitted from metals is derived. The main feature of the calculation is an energy-dependent electron mean free path. The theory predicts that the peak of the energy distribution occurs at a value of the secondary electron energy equal to φ/3, where φ is the metal work function.

A simple theory conce~ning the reflection of electrons from solid targets is derived, based on the following assumptIOns: (1) the pnmary cause of electron reflection from a solid material is Rutherford scattering through angle.s g~eater than 90°; (2) ~he ener~y loss of electrons penetrating a solid target is given by the Thomson-Wh~ddmgton .law, 0: a m?dlfied version of it; (3) no multiple scattering is allowed. An expression for the ~efle?tl~n coeffiClen~ r IS denved.that agrees surprisingly well with experimental data, in view of the above slmphfymg assumptIOns. In partlcular, the correct variation of r with atomic number Z is obtained ~nd the observed value of the fractional escape energy is calculated in the limit as Z ---> 0 where the theor; IS most acc~rate: A critical. discussion of the simplifying assumptions is given, and the r~nge of validity of the. t~eory IS e~tlmated. ThiS theory leads to a better understanding of the related phenomena of secondary emiSSIOn at pnmary electron energies between 2 and 50 kev.

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