Determination of Kilovolt Electron Energy Dissipation vs Penetration Distance in Solid Materials

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.