Energy level spectroscopy of InSb quantum wells using quantum-well LED emission

We have investigated the low-temperature optical properties of InSb quantum-well (QW) light-emitting diodes, with different barrier compositions, as a function of well width. Three devices were studied: QW1 had a 20 nm undoped InSb quantum well with a barrier composition of ${\text{Al}}_{0.143}{\text{In}}_{0.857}\text{Sb}$, QW2 had a 40 nm undoped InSb well with a barrier composition of ${\text{Al}}_{0.077}{\text{In}}_{0.923}\text{Sb}$, and QW3 had a 100 nm undoped InSb well with a barrier composition of ${\text{Al}}_{0.025}{\text{In}}_{0.975}\text{Sb}$. For QW1, the signature of two transitions (CB1-HH1 and CB1-HH2) can be seen in the measured spectrum, whereas for QW2 and QW3 the signature of a large number of transitions is present in the measured spectra. In particular transitions to HH2 can be seen, the first time this has been observed in AlInSb/InSb heterostructures. To identify the transitions that contribute to the measured spectra, the spectra have been simulated using an eight-band $\mathbf{k}.\mathbf{p}$ calculation of the band structure together with a first-order time-dependent perturbation method (Fermi golden rule) calculation of spectral emittance, taking into account broadening. In general there is good agreement between the measured and simulated spectra. For QW2 we attribute the main peak in the experimental spectrum to the CB2-HH1 transition, which has the highest overall contribution to the emission spectrum of QW2 compared with all the other interband transitions. This transition normally falls into the category of “forbidden transitions,” and in order to understand this behavior we have investigated the momentum matrix elements, which determine the selection rules of the problem.

Figure 1

Schematic cross section showing the structure of the QW LEDs. $L$ is the quantum-well thickness.

Figure 2

Real-space energy diagrams of conduction-band, heavy-hole band, and light-hole band edges as functions of transverse direction $z$ for quantum wells of sizes 20 (QW1), 40 (QW2), and 100 (QW3) nm, under zero and finite net biases across the wells. The band edges are represented by thick lines; in particular, the thick line in the hole subband represents the light-hole band edge. The bottoms of the conduction and hole subbands resulting from the size quantization in the QWs are shown as horizontal lines in the wells. The threshold energies of the transitions are designated with arrows and associated labels.

Figure 3

Measured (at 15 K) and simulated spectral emittance from LED sample QW1 (20 nm). The upper subplot shows the experimentally measured and theoretically simulated spectral emittance for QW1. The threshold energies of the relevant interband transitions are designated with arrows and associated labels. The lower subplot shows the simulated spectral emittance due to spontaneous emission from the well together with the signal due to the relevant interband transitions.

Figure 4

Measured (at 15 K) and simulated spectral emittance from LED sample QW2 (40 nm). The upper figure shows the experimentally measured and theoretically simulated spectral emittance for QW2. The threshold energies of the relevant interband transitions are designated with arrows and associated labels. The lower figure shows the simulated spectral emittance due to spontaneous emission from the well together with the signal due to the relevant interband transitions.

Figure 5

Measured (at 25 K) and simulated spectral emittance from LED sample QW3 (100 nm). The upper figure shows the experimentally measured and theoretically simulated spectral emittance for QW3. The threshold energies of the relevant interband transitions are designated with arrows and associated labels. The lower figure shows the simulated spectral emittance due to spontaneous emission from the well together with the signal due to the relevant interband transitions.

Figure 6

Simulated emission spectra for QW1 (at 15 K) as a function of homogeneous and inhomogeneous broadenings. Spectral emittance line shape as a function of homogeneous and inhomogeneous broadenings for the 20 nm well simulated for effective temperature and injected carrier density. The peak height of the data resulting from simulation with homogenous broadening and inhomogeneous broadening has been normalized, and the results of the other simulations have been scaled with respect to it.

Figure 7

(Color online) Momentum matrix elements as functions of transition energies obtained from the simulations for QW2 (40 nm wide) for zero net bias and finite net bias.