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, R_G = 4.0 E_B(keV)^1.75 μg/cm² has been found accurate for 5 <E_B <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 R_G, 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/E_A) = (2.97 ± 0.06) × 10⁻¹³(cm/V)² using the energy‐dissipation formulation, and (μτ/E_A) = (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.