Energy Dissipation of Fast Electrons in Polymethylmethacrylate: Toward a Universal Curve for Electron-Beam Attenuation in Solids between ∼0 eV and Relativistic Energies

Spectroscopy of correlated electron pairs was employed to investigate the energy dissipation process, as well as the transport and the emission of low-energy electrons on a polymethylmethacrylate surface, providing secondary electron spectra causally related to the energy loss of the primary. Two groups are identified in the cascade of slow electrons, corresponding to different stages in the energy dissipation process. The characteristic lengths for attenuation due to collective excitations and momentum relaxation are quantified for both groups and are found to be distinctly different: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>λ</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub><a:mo>=</a:mo><a:mo stretchy="false">(</a:mo><a:mn>12</a:mn><a:mo>±</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>Å</a:mi></a:mrow></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>λ</e:mi><e:mn>2</e:mn></e:msub><e:mo>=</e:mo><e:mo stretchy="false">(</e:mo><e:mn>62</e:mn><e:mo>±</e:mo><e:mn>11</e:mn><e:mo stretchy="false">)</e:mo><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>Å</e:mi></e:math>. The results strongly contradict the commonly employed model of exponential attenuation with the electron inelastic mean free path as characteristic length, but they essentially agree with a theory used for decades in astrophysics and neutron transport, albeit with characteristic lengths expressed in units of angstroms rather than light-years.