Reduction of the Auger rate in semiconductor quantum dots

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Abstract
We propose the use of quantum dots in semiconductor lasers to reduce the Auger rate, the dominant process limiting the performance of today’s semiconductor lasers in the thermal infrared. We will see that many Auger processes cannot occur in quantum dots that are surrounded by a very large potential energy barrier because continuum energy states are not available as final states. We present many possible materials that can be used for these quantum dots and barriers. We also derive an analytical expression for the Auger rate in a quantum sphere, in which there are two electrons and two holes, in terms of Slater integrals, reduced matrix elements, and Racah coefficients of total-angular-momentum quantum numbers. We note that the total angular momentum must be conserved for Auger processes in a quantum dot, unlike the linear momentum conservation law required in the bulk. We present a practical example of a 150-Å-radius InSb quantum dot surrounded by CdTe barriers, whose room-temperature band gap is at 4.8 μm (258 meV), and whose room-temperature Auger lifetime is calculated as 135 ns, which is at least two orders of magnitude better than the Auger lifetime in other low-temperature semiconductor lasers. We present partial Auger rates and tabulate them in a Grotrian diagram labeled by the bound states involved. We calculate and discuss the temperature dependence of quantum-dot Auger rates. In calculating the (nonparabolic) band structure and energy states, we use a multiband envelope-function approximation in eight-band k⋅p theory, which also included some of the effects of higher-order bands. Single and multiparticle eigenstates are chosen to diagonalize the total angular momentum. We include valence-band mixing in calculating our single-particle quantum-dot states.

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