Resolving the band alignment of InAs/InAsSb mid-wave-infrared type-II superlattices

TL;DR

This study targets the band alignment of InAs/InAsSb type-II superlattices, crucial for mid-infrared detectors, by combining photoluminescence, photoreflectance, and a $14$-band $k\cdot p$ model. Higher-order optical transitions observed in PR are leveraged, alongside refractive-index calculations, to constrain bowing parameters $b_v$ and $b_g$ and extract a valence-band offset $VBO$ of about $328$ meV for InAs/InAs$_{0.65}$Sb$_{0.35}$. The optimized parameters ($b_v=-0.60$ eV, $b_g=0.80$ eV) yield band-edge energies $E_v\approx416$ meV and $E_g\approx168$ meV at $x=0.35$, and transitions HH1\to CB1, LH1\to CB1, and HH3\to CB1 are identified near $k_z\approx0$. The work demonstrates a powerful, data-driven approach to refine fundamental material parameters in complex heterostructures, with implications for designing high-performance InAs/InAsSb infrared detectors.

Abstract

In this work, three InAs/InAs$_{0.65}$Sb$_{0.35}$ superlattices with different periods were investigated using photoluminescence and photoreflectance measurements and their band structure was simulated using a 14 bulk-band kp model. The structures were studied by analyzing the evolution of the spectral features in temperature and excitation power to determine the origin of optical transitions. After identifying which of these are related to the superlattice mini-bands, a rich collection of observed higher-order optical transitions was compared with refractive-index calculations. This procedure was used to adjust the parameters of the theoretical model, namely the bowing parameters of the InAsSb valence band offset and bandgap. It was also shown that the spectroscopy of the higher-order states combined with numerical modeling of the refractive index is a powerful tool for improvement of the material parameters, presenting a new approach to material studies of advanced semiconductor heterostructures.

Figures (4)

• Figure 1: Optical properties of the InAs/InAs$_{0.65}$Sb$_{0.35}$ superlattices. a) Normalized photoluminescencence spectra of the samples at 10 K (solid line) and 80 K (dashed line) temperature shown in blue, red and black for sample with 5 nm, 6 nm and 8 nm period, respectively. b) Energies of the dominating photoluminescence emission fitted with Varshni equation shown in blue, red and black for samples with 5 nm, 6 nm and 8 nm period, respectively, with the parameters of the fitted function - $\alpha$ and $\beta$. c) Close up of the emission lineshape of 5 nm period sample at 10 K temperature with the red fitted curve comprising of three distinct gaussian peaks with the green, violet and orange colours representing the optical transitions originating from acceptor level, a defect state corresponding to indium vacancy and an unknown confined state. d) Temperature evolution of the photoluminescence signal from the sample with 5 nm period with fitted gaussian peaks colour coded as in the panel c and additional wine colour representing a fundamental transition from the first confined states within the conduction mini-band to the valence mini-band. e) Photoreflectance spectra of the fundamental transitions shown in blue, red and black for the samples with 5 nm, 6 nm and 8 nm period, respectively, with the bandgap energies predicted by fitting the Varshni equation to higher-temperature energies of the dominating photoluminescence emission, presented as dashed lines with colours corresponding to the samples. f) Power-dependent photoluminescence spectra of the sample with 5 nm period at 10 K in logarithmic scale, denoting the defect states within the spectra. g) Temperature evolution of photoluminescence signal from 8 nm period sample showing the maximum of signal intensity at around 80 K.
• Figure 2: Results of the photoreflectance experiment. a,b) Photoreflectance spectra of the sample with 8 nm (panel a)), and 6 nm (panel b) period at 10 K temperature with fitted curves using Equation \ref{['PR resonance']}. c,d) Moduli calculated with the Equation \ref{['PR modulus']} using the parameters from the fitting procedure of the photoreflectance response for sample with 8 nm (panel c)) and 6 nm period (panel d)).
• Figure 3: Comparison between the numerical calculations from 14 bulk band model and the results of photoreflectance measurements. a,b) Optimization maps for $\Delta$ (panel a) and $\Delta_{1}$ (panel b) for the 8 nm superlattice period made by plotting the difference between the resonant energies from the calculated refractive index $\Delta$n and the energies obtained from the photoreflectance spectra $\Delta$R/R. $\Delta$n = n$(E;0)$$-$n$(E;\rho)$ was calculated for a given combination of InAsSb valence band offset b$_{\text{v}}$ and gamma gap b$_{\text{g}}$ bowing parameters, assuming a photoexcited carrier density $\rho$ equal to $2\times 10^{16}$ cm$^{-3}$. c) Comparison between $\Delta$n, calculated with the optimal parameters found in a), i.e., b$_{\text{v}} = -$0.6 eV and b$_{\text{g}} =$0.8 eV, and $\Delta$R/R for different superlattices periods $P$. Each set of parameters {b$_{\text{g}}$, b$_{\text{v}}$} provides a valence band offset (VBO) as shown in panel d) with the conduction (CB), heavy-hole (HH), light-hole (LH) and split-off (SO) band edges. e) Composition dependent Eq.(\ref{['eq:InAsSb_energies']}) for the optimal bowing parameters obtained in this work (b$_{\text{v}} = -$0.6 eV and b$_{\text{g}} =$0.8 eV), and parameters reported in the literature (Vurgaftman et al.Vurgaftman2001 b$_{\text{v}} = 0$ eV and b$_{\text{g}} = 0.67$ eV; Manyk et al.Manyk2018 b$_{\text{v}} =-$0.47 eV and b$_{\text{g}} = 0.72$ eV).
• Figure 4: a) Band structure for the 8 nm period superlattice with the absorption $\Delta\alpha \equiv$$\alpha (\text{E};0) -\alpha (\text{E};\rho)$ resolved in the k-space. $d$ represents the superlattice period. b) Calculated refractive index $\Delta$n in the presence of external carriers with a density $\rho = 2\times 10^{16}$cm$^{-3}$, plotted with a sum of $\Delta\alpha$ corresponding to the states with the highest contribution to the optical resonances. k$_{z}$ and k$_{||}$ refer to directions along and perpendicular (i.e., parallel to the layer plane) to the growth direction $z$, respectively. The remaining superlattice periods were presented in Supplementary material.