Anomalous Auger Recombination in PbSe

Using first-principles approaches we find that the Auger recombination in PbSe is anomalous in three distinct ways. First, the direct Auger coefficient is 4 orders of magnitude lower than that of other semiconductors with similar band gaps, a result that can be attributed to the lack of involvement of a heavy-hole band. Second, phonon-assisted indirect Auger recombination prevails, contrary to the common belief that direct Auger is dominant in narrow-gap semiconductors. Third, an unexpectedly weak temperature dependence of the Auger coefficient is observed, which we can now attribute to the indirect nature of the Auger process. The widely accepted explanation of this behavior in terms of an unusual temperature dependence of the band gap is only a secondary effect. Our results elucidate the mechanisms underlying the anomalous Auger recombination in IV-VI semiconductors in general, which is critical for understanding and engineering carrier transport.

Figure 1

Comparison of the band structure of PbSe calculated using the SCAN and HSE functionals (a) without SOC and (b) with SOC. The green and blue symbols show the projected orbital character of the bands for the case with the HSE functional. The energy values are referenced to the VBM. The band gap of the SCAN band structure is scissors-shifted to match the HSE gap. The inset in (a) shows the primitive cell of PbSe, and the inset in (b) depicts the corresponding Brillouin zone and high-symmetry $\mathbf{k}$ points.

Figure 2

Calculated direct Auger coefficient (with and without SOC) as a function of band gap for (a) the eeh and (b) the hhe process. A temperature of 300 K and a carrier density of ${10}^{18}{\mathrm{cm}}^{-3}$ are assumed. The insets schematically show the eeh and hhe direct Auger processes. The light-blue solid (open) circles represent electrons (holes). The black dashed lines indicate the location of the experimental band gap of PbSe at room temperature.

Figure 3

(a) Calculated Auger coefficients as a function of carrier density at 300 K. (b) Calculated Auger coefficients as a function of temperature at a fixed carrier density of ${10}^{17}{\mathrm{cm}}^{-3}$. Experimental data [14, 28] are included for comparison.

Figure 4

Schematic of (a) intravalley and (b) intervalley Auger events in PbSe. ${\mathbf{k}}_1$ through ${\mathbf{k}}_4$ label the momenta of the four states involved in an Auger event. (c) Momentum transfer ($\mathbf{\Delta }\mathbf{k}={\mathbf{k}}_1-{\mathbf{k}}_2$) of all possible Auger events projected onto different planes [($k_x$, $k_y$), ($k_x$, $k_z$), and ($k_y$, $k_z$)] in reciprocal space. The dashed circles are intended to help visualize the slight anisotropy. We note that since the carrier occupation is evaluated on a discrete $\mathbf{k}$-point grid, the momentum transfer is not continuous.