Phonon-Assisted Auger-Meitner Recombination in Silicon from First Principles

We present a consistent first-principles methodology to study both direct and phonon-assisted Auger-Meitner recombination (AMR) in indirect-gap semiconductors that we apply to investigate the microscopic origin of AMR processes in silicon. Our results are in excellent agreement with experimental measurements and show that phonon-assisted contributions dominate the recombination rate in both $n$-type and $p$-type silicon, demonstrating the critical role of phonons in enabling AMR. We also decompose the overall rates into contributions from specific phonons and electronic valleys to further elucidate the microscopic origins of AMR. Our results highlight potential pathways to modify the AMR rate in silicon via strain engineering.

Figure 1

Quasiparticle band structure of silicon depicting Auger-Meitner recombination processes. (a) Schematic of the direct $eeh$ Auger-Meitner process involving two electrons (solid circles) near the conduction band minimum and a hole (open circle) near the valence band maximum. The blue areas indicate the range of initial carrier states that are included in the calculations. (b) Schematic of the phonon-assisted $hhe$ Auger-Meitner process, where the inclusion of a phonon conserves the overall momentum and allows this process to take place.

Figure 2

AMR coefficient ($C$) as a function of carrier concentration for (a) the $eeh$ process and (b) the $hhe$ process at 300 K. We decompose the total rate (black circles) into contributions from the phonon-assisted (red triangles) and direct (blue diamonds) processes. The curves are generated by our model [Eq. S4] [22]. We also compare our results to experimental measurements [34, 35] and approximate Coulomb-enhancement effects using existing models [11, 36].

Figure 3

AMR coefficient as a function of temperature for (a) the $eeh$ process and (b) the $hhe$ process at a carrier concentration of ${10}^{18}{\mathrm{cm}}^{-3}$. We decompose the total rate (black circles) into contributions from the phonon-assisted (red triangles) and direct (blue diamonds) processes. The curves are generated by our model [Eq. S5] [22]. Experimental data points are also included for comparison, though we note that not all points are at carrier concentrations of exactly ${10}^{18}{\mathrm{cm}}^{-3}$ [34, 35, 40, 41].

Figure 4

Analysis of different contributions to the overall AMR rate. (a) Relative importance of the three different initial valley arrangements for electrons in the $eeh$ process, which are illustrated in (b) with the $f$-type arrangement contributing most strongly. The strength of phonon-assisted AMR for $eeh$ (solid black) and $hhe$ (red dash) processes as a function of phonon energy (c) and wave vector magnitude (d), where the strongest peaks are associated with TA phonons, highlighted in the inset phonon dispersion. (e) The distribution of excited carrier states throughout the first Brillioun zone for the direct and phonon-assisted $eeh$ and phonon-assisted $hhe$ processes, with slices removed to show the internal structure.