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Energetic carriers in semiconductors thermalize by impact-ionization, which generates electron–hole pairs (EHPs), and by energy losses to phonons. The average EHP creation energy is typically about three times the energy gap. In 1960, Shockley derived a simple equation for the average EHP creation energy with a single free parameter that fits experimental values for a wide range of materials, but the underlying assumptions, as stated, have been widely criticized as lacking justification. Modified expressions derived by improved approximations have been proposed but do not fare better. Here, we revisit the foundations of Shockley's equation and provide a robust justification for the kinetic-energy component as a model averaging procedure and then apply a similar procedure to the phonon component of the equation. The phonon result retains Shockley's form, but the interpretation and justification are now on par with those of the kinetic-energy term. The single-parameter fit to the data remains unchanged, i.e., the present analysis accounts for the exceptional applicability of Shockley's equation. [ABSTRACT FROM AUTHOR]

We report on the measurement and analysis of energetic heavy ion radiation effects on the mechanical properties of silicon carbide (SiC) crystals, by exploiting a vertical stack of micromachined vibrating SiC thin diaphragms integrated in a three-dimensional (3D) fashion. The diaphragms are 1 mm × 1 mm in lateral dimensions and 2 μm in thickness, vibrating at their multiple flexural modes in the range of 200 to 800 kHz. Upon 10.25 MeV oxygen ion irradiation, the 4 devices in the 3D stack exhibit saliently different changes in their multimode resonance frequencies. The device that is intended to capture most ions shows the largest frequency downshifts (∼6.6%–11.3%), corresponding to the extracted tension release from 382 MPa to 306 MPa, which can be explained by the maximum displacement damage in this device. The design of 3D integration not only scientifically enables probing different radiation effects in multiple devices simultaneously with clear controls but also economically evades very expensive, repetitive tests on individual devices, thus proving to be a powerful platform for analyzing and understanding radiation damage in micro/nanoelectromechanical systems and other micro/nanosystems. [ABSTRACT FROM AUTHOR]