Spontaneous hot-carrier photon emission rates in silicon: Improved modeling and applications to metal oxide semiconductor devices

The recent publication of controversial experimental evidence on the origin of hot-carrier currents in 4–10 nm tunnel metal oxide semiconductor capacitors renewed the interest in improving hot-carrier luminescence models for silicon devices. This work presents several such improvements, aimed at making possible a physically based analysis of the hot-carrier luminescence effects taking place during tunneling experiments in relatively thick ${\mathrm{SiO}}_2$ layers. To this purpose, silicon band structure and scattering rate calculations have been extended well above 10 eV by considering eight conduction bands, instead of the usual four, so as to allow for a detailed description of the high-energy carriers injected from silicon into silicon dioxide during tunneling experiments. The absolute contributions of the direct and phonon-assisted, interband and intraband transitions of electrons and holes to the total photon emission rate are analyzed, so the results can be directly compared with the experimental data. To the best of our knowledge, it is for the first time that results for valence-to-valence band transitions of holes are presented and compared with those of conduction-to-conduction band transitions of electrons. Results can be directly compared with experimental data. Template results obtained with a variety of carrier distributions (Maxwellian, Gaussian, and Dirac’s delta-like) are shown and implications for device analysis are discussed.