Energy loss of proton,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>particle, and electron beams in hafnium dioxide films

Abstract

The electronic stopping power, $S$, of ${\text{HfO}}_{2}$ films for proton and alpha particle beams has been measured and calculated. The experimental data have been obtained by the Rutherford backscattering technique and cover the range of 120--900 and 120--3000 keV for proton and alpha particle beams, respectively. Theoretical calculations of the energy loss for the same projectiles have been done by means of the dielectric formalism using the Mermin energy loss function---generalized oscillator strength (MELF-GOS) model for a proper description of the ${\text{HfO}}_{2}$ target on the whole momentum-energy excitation spectrum. At low projectile energies, a nonlinear theory based on the extended Friedel sum rule has been employed. The calculations and experimental measurements show good agreement for protons and a quite good one for alpha particles. In particular, the experimental maximums of both stopping curves (around 120 and 800 keV, respectively) are well reproduced. On the basis of this good agreement, we have also calculated the inelastic mean-free path (IMFP) and the stopping power for electrons in ${\text{HfO}}_{2}$ films. Our results predict a minimum value of the IMFP and a maximum value of the $S$ for electrons with energies around 120 and 190 eV, respectively.