$\mathbf{k}·\mathbf{p}$ model for the energy dispersions and absorption spectra of InAs/GaSb type-II superlattices

We have fitted the $\mathbf{k}·\mathbf{p}$ model derived recently by one of the authors [Klipstein, Phys. Rev. B 81, 235314 (2010)] to experimentally measured photoabsorption spectra at 77 and 300 K for representative InAs/GaSb superlattices with band-gap wavelengths between 4.3 and 10.5 $\mu \mathrm{m}$. The model is able to reproduce the main features of the absorption spectra, including a strong peak from the zone boundary ${\mathrm{HH}}_2\to E_1$ transition. We have also used the same model to predict the band-gap wavelengths of over 30 more superlattices, measured by photoluminescence spectroscopy. The maximum error is 0.6 $\mu \mathrm{m}$, which corresponds to an uncertainty of less than 0.4 ML in layer width. This is comparable with the experimental uncertainty in layer widths, determined by in situ beam-flux measurements in the growth reactor. By eliminating all terms from the Hamiltonian, the energy contribution of which is less than the error due to the uncertainty in layer widths, the number of unknown fitting parameters has been reduced to six: two Luttinger parameters, three interface parameters, and the valence band offset. The remaining four Luttinger parameters are not independent and are determined from the two independent ones. Our set of Luttinger parameters is close to that reported by Lawaetz [Phys. Rev. B 4, 3460 (1971)], with a maximum deviation in any parameter of 0.6. The interface parameters are diagonal and have values of $D_S=3\mathrm{eV}\AA$, $D_X=1.3\mathrm{eV}\AA$, and $D_Z=1.1\mathrm{eV}\AA$ at 77 K. The off-diagonal interface parameters $\alpha$ and $\beta$ are too small to be fitted with any accuracy and have negligible effect on the unpolarized photoabsorption spectra. We also propose values for the room-temperature Luttinger and interface parameters. The fitted unstrained InAs/GaSb band overlap is 0.142 eV.

Figure 1

Example of x-ray diffraction spectrum for a T2SL sample. Inset: Central peak region.

Figure 2

Normalized PL spectrum at 10 K and absorption spectrum at 77 K for sample SLMW02.

Figure 3

Superlattice layer widths used in the $\mathbf{k}·\mathbf{p}$ calculations. Solid: Layer widths determined from the flux measurements. Diamonds are for the MWIR and circles for the LWIR band-gap regions. Open circles: Nominal layer widths of the MWIR samples with InSb-like interfaces, taken from Ref. 35.

Figure 4

Dispersion relation of a 13.8/7.8 InAs/GaSb T2SL with InSb interfaces (superlattice period $=$ 21.6 ML) for several directions in the Brillouin zone.

Figure 5

Calculated absorption spectrum for sample SLMW01 with $\Delta E_0=3$ meV, and with three different values of $\Delta E_1$: 3, 25, and 60 meV.

Figure 6

Calculated absorption spectrum of sample SLMW01 with fitted (solid) and zero (dashed) interface parameters.

Figure 7

Measured (solid line) and calculated (dashed line) absorption spectrum of sample SLMW01, at 77 K.

Figure 8

Measured (solid line) and calculated (dashed line) absorption spectrum of sample SLMW02, at 77 K.

Figure 9

Measured (solid line) and calculated (dashed line) absorption spectrum of sample SLMW03, at 300 K.

Figure 10

Measured (solid line) and calculated (dashed line) absorption spectrum of sample SLLW01, at 77 K.

Figure 11

Deviation of predicted PL wavelengths from the measured PL peak wavelengths. The dashed and dotted lines indicate the effect of an error of $k_{B}T$ in band-gap energy at 77 K.

Figure 12

Deviation of fitted InAs widths from the growth nominal widths. Solid: Nominal width is the width calculated by the flux method. Circles: Nominal layer width is taken from Table VI in Ref. 35.