Direct Time-Domain View of Auger Recombination in a Semiconductor

The radiationless recombination of electron-hole pairs in semiconductors is detrimental to optoelectronic technologies. A prominent mechanism is Auger recombination, in which nonradiative recombination occurs efficiently by transferring the released energy-momentum to a third charge carrier. Here we use femtosecond photoemission to directly detect Auger electrons as they scatter into energy and momentum spaces from Auger recombination in a model semiconductor, GaSb. The Auger rate is modulated by a coherent phonon mode at 2 THz, confirming phonon participation in momentum conservation. The commonly assumed Auger rate constant is found not to be a constant, but rather decreases by 4 orders of magnitude as hot electrons cool down by $\sim 90\mathrm{meV}$. These findings provide quantitative guidance in understanding Auger recombination and in designing materials for efficient optoelectronics.

Figure 1

Direct detection of $e\text{−}e\text{−}h$ Auger recombination by 2PPE. Top: Detection of Auger recombination from the (a) DAR or (b) PAAR mechanism by TR-2PPE. Following excitation by the pump ($h{\nu }_1$) to initiate the Auger process, the probe ($h{\nu }_2$) ionizes the Auger or CBM electron. The difference between DAR and PAAR is the participation of a phonon (red wavy line) for momentum conservation ($\mathrm{\Delta }k$) in the latter. (c) Pseudocolor (intensity) plot of TR-2PPE spectra ($h{\nu }_1=1.19$ and $h{\nu }_2=4.51\mathrm{eV}$) at an excitation density of $1.3\times {10}^{18}{\mathrm{cm}}^{-3}$; (d) kinetic profiles from horizontal cuts of the 2D plot at $0.79\pm 0.1$ (CBM) and $1.36\pm 0.05\mathrm{eV}$ (Auger); (e) TR-2PPE spectra at selected pump-probe delays ($\mathrm{\Delta }t=0.6–6\mathrm{ps}$); (f) parallel momentum-resolved TR-2PPE for the Auger (blue) and CBM (red) electrons at $\mathrm{\Delta }t=2\mathrm{ps}$. Also shown is data for CBM at $\mathrm{\Delta }t=24\mathrm{ps}$ (gray dots).

Figure 2

Direct evidence for PAAR. (a) A high resolution expanded view of TR-2PPE spectra ($h{\nu }_1=1.19$, $h{\nu }_2=4.51\mathrm{eV}$; excitation $\text{density}=1.5\times {10}^{18}{\mathrm{cm}}^{-3}$) in the high energy Auger electron window at short times showing the oscillatory behavior; (b) a comparison of kinetic profiles of Auger electron intensity (blue) and CBM electron intensity (red), with oscillatory behavior only for the former; (c) Fourier transform (black curve) of the kinetic profile of Auger electrons and the calculated density-of-states (DOS, right axis) distribution of phonons in GaSb from Ref. [34].

Figure 3

Energy dependent Auger rates. Upper: Auger recombination rate constant (crosses, normalized to the average values at $\mathrm{\Delta }t=10–20\mathrm{ps}$) as a function of $\mathrm{\Delta }t$. The two sets of data are obtained with high (red) and low (orange) time resolutions. Also shown is the change in the quasi-Fermi level ($E_{\text{Fermi}}^{*}$, right axis) of the electron distribution near CBM as a function of $\mathrm{\Delta }t$. Lower: relative Auger rate as a function of the average energy of CBM electrons (dots, referenced to CBM). The dashed curve is an exponential fit with $X$ offset of $0.145\pm 0.005\mathrm{eV}$.

Figure 4

Intervalley scattering and rate-limited Auger recombination. (a)–(c) Increasing time after initial photoexcitation.