Analytical Modeling of Alpha-Particle Emission Rate at Wafer-Level

Alpha-particle emissivity at wafer-level has been analytically modeled for material layers contaminated by uranium and/or thorium impurities. Our approach evaluates the number (or the fraction) of escaping alpha particles from any monolayer or multilayer of arbitrary material composition. The global emissivity of the (stacked) material and its corresponding alpha-particle energy spectrum can be also analytically derived. The model has been fully validated with Monte Carlo simulation in terms of alpha-particle emissivity and energy spectra for different layer thicknesses and detection threshold energies. Finally, we propose a general nomogram for silicon material directly giving the alpha-particle emissivity versus the silicon contamination level expressed in ppb of uranium and thorium.