In heavily nn-doped, nonalloy GaSb–AlSb superlattices, electrons spill over from the lowest Γ\Gamma subband into the four tilted LL valleys of the GaSb wells, whose anisotropic ellipsoidal mass tensors let normally incident light excite intersubband transitions — yielding a peak fractional absorption per well of 6.8×10−36.8\times 10^{-3} at λ≈15 μm\lambda\approx 15\,\mu\mathrm{m} (Samoska, Brar and Kroemer, 1993). The quantitative validation of this picture was left open in three linked respects: the Γ\Gamma/LL carrier partitioning was inferred from density-of-states arguments and indirect Hall analysis rather than measured directly; the finite-well model for subband energies and Γ\Gamma–LL separations omitted strain and band nonparabolicity, leaving systematic discrepancies against measured Γ\Gamma-peak positions at narrow wells; and the cause of the decrease of the peak absorption per well at 300 K (relative to 77 K) was unexplained. The problem is therefore open.

Background

Intersubband absorption — optical excitation of an electron between quantized conduction-band levels ("subbands") of a semiconductor quantum well — is the physical basis of quantum-well infrared photodetectors (QWIPs). In a (001)-grown well whose occupied states derive from the parabolic, isotropic Γ\Gamma valley at the Brillouin-zone center, the intersubband electric-dipole matrix element points along the growth axis zz, so light incident normal to the layers (electric field in the plane) cannot drive the transition; practical devices therefore need Brewster-angle or waveguide geometries (light zig-zagging through a polished facet), which complicate two-dimensional detector arrays. Conduction-band minima with anisotropic effective-mass tensors — ellipsoidal constant-energy surfaces tilted with respect to zz — evade this selection rule, because their intersubband dipole acquires a zz component that couples to normally incident light. In GaSb the four LL valleys sit along the ⟨111⟩\langle 111\rangle directions, 54.7∘54.7^\circ from [001], only about 63 meV63\ \mathrm{meV} above the Γ\Gamma minimum in the bulk, with a large (about 1 eV1\ \mathrm{eV}) LL-point conduction-band offset against AlSb. Ting and Chang had computed LL-valley-derived subband states in (001) GaSb/AlSb quantum wells before the experiment in question. Samoska, Brar and Kroemer then demonstrated the physical exploitation of this situation: in 50-period nonalloy GaSb–AlSb superlattices ("nonalloy" meaning alternating binary layers: GaSb wells of 4.0–8.0 nm and 8 nm AlSb barriers, with no ternary-alloy layers) heavily nn-doped (tellurium) so that the per-well electron sheet concentration NsN_s reaches 1.6×1012 cm−21.6\times 10^{12}\ \mathrm{cm}^{-2}, electrons spill over from the lowest Γ\Gamma subband into the higher-energy but far denser LL subbands. Because the two-dimensional density of states (2D DOS) of the four LL valleys (effective DOS mass mDS∗≈1.09 mem_{\mathrm{DS}}^*\approx 1.09\,m_e) exceeds that of the Γ\Gamma subband (mΓ∗≈0.041 mem_\Gamma^*\approx 0.041\,m_e) by a factor of about 27, roughly 96% of carriers beyond the spillover threshold occupy LL-derived subbands, where normal-incidence intersubband absorption is allowed. They measured a peak fractional absorption per well ζp=6.8×10−3\zeta_p=6.8\times 10^{-3} at λ≈15 μm\lambda\approx 15\,\mu\mathrm{m} (E=82 meVE=82\ \mathrm{meV}) at 77 K for the 8.0 nm, Ns=1.6×1012 cm−2N_s=1.6\times 10^{12}\ \mathrm{cm}^{-2} sample (absorption coefficient per unit well thickness α≈8500 cm−1\alpha\approx 8500\ \mathrm{cm}^{-1}); in waveguide geometry the same samples show a Γ\Gamma-valley intersubband peak (at 202 meV202\ \mathrm{meV}) that is absent at normal incidence, confirming the LL-valley origin, and the Γ\Gamma peak disappears entirely for wells narrower than about 4.2 nm, consistent with a size-induced Γ→L\Gamma\to L crossover near 4 nm. A companion normal-incidence photodetector demonstration in LL-valley GaSb wells was reported the same year by Zhang, Baruch and Wang. The quantitative validation of this picture, however, was left with three linked gaps, which together constitute the present problem. First, the Γ\Gamma/LL partitioning was an inference from DOS ratios supported only by Hall measurements — which undercount carriers when the low-mobility LL valleys are populated, owing to two-band conduction with unequal mobilities — not a direct valley-resolved measurement. Second, the finite-well calculation used for the transition energies and the Γ\Gamma–LL separation (yielding ΔEΓL≈24 meV\Delta E_{\Gamma L}\approx 24\ \mathrm{meV} and a spillover threshold NΓ≈4.1×1011 cm−2N_\Gamma\approx 4.1\times 10^{11}\ \mathrm{cm}^{-2} for 8 nm wells) omitted both the strain from the 7% lattice mismatch between the superlattice and its GaAs substrate/AlSb buffer and the conduction-band nonparabolicity (the energy dependence of the very light Γ\Gamma effective mass from coupling to remote bands), and it systematically misplaced the measured Γ\Gamma-peak positions at narrower wells. Third, the peak absorption per well rose from 6.0×10−36.0\times 10^{-3} at 4.2 K to 6.8×10−36.8\times 10^{-3} at 77 K and fell to 5.6×10−35.6\times 10^{-3} at 300 K, and the reason for the 300 K decrease was stated to be unclear from the data.

Problem Statement

The problem is to complete the quantitative validation of the Γ\Gamma–LL carrier-partition picture for normal-incidence far-infrared intersubband absorption in heavily nn-doped, nonalloy GaSb–AlSb quantum-well superlattices. Three linked aspects jointly serve this single objective — establishing how many carriers occupy the Γ\Gamma and LL subbands and how that partitioning controls the normal-incidence absorption: (1) Valley-resolved carrier populations. Provide a quantitative determination of the carrier populations in the Γ\Gamma and LL subbands as functions of the per-well sheet doping (spanning and exceeding the spillover threshold, about 4.1×1011 cm−24.1\times 10^{11}\ \mathrm{cm}^{-2} for 8.0 nm wells in the source paper's model), the GaSb well width (approximately 4–8 nm), and the temperature, together with the concurrently measured normal-incidence LL-valley intersubband absorption strength, so that the claimed connection between LL population and absorption per well can be tested quantitatively, including the density-of-states-based prediction that about 96% of carriers beyond the threshold occupy LL subbands. Because this partition has never been measured directly, the determination must (i) extract the Γ\Gamma/LL partition that the existing transport and optical data support, stating explicitly the analysis basis and its model dependence, and (ii) specify the direct, valley-resolved measurement (samples, geometry, technique, and expected signatures) that would determine the partition independently. (2) Strain- and nonparabolicity-inclusive subband modeling. Replace the simple finite-well calculation with a band-structure treatment that includes the strain state of the structure and conduction-band nonparabolicity, and reconcile the calculated Γ\Gamma- and LL-subband intersubband transition energies with the measured peak positions across the full range of well widths — resolving the systematic discrepancy between calculated and measured Γ\Gamma-peak positions at narrower wells — thereby establishing a reliable Γ\Gamma–LL subband separation and spillover threshold for this system. (3) Temperature dependence of the absorption. Explain quantitatively the measured non-monotonic temperature dependence of the peak fractional absorption per well — 6.0×10−36.0\times 10^{-3} at 4.2 K, 6.8×10−36.8\times 10^{-3} at 77 K, 5.6×10−35.6\times 10^{-3} at 300 K for the 8.0 nm, Ns=1.6×1012 cm−2N_s=1.6\times 10^{12}\ \mathrm{cm}^{-2} sample, with no measurable shift of the peak energy between 4.2 K and 300 K — in particular the decrease at 300 K. The target is the physics of the nonalloy GaSb–AlSb system, not the specific 1993 wafers.

References

  1. L. A. Samoska, B. Brar, and H. Kroemer, 'Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices', Applied Physics Letters 62, 2539-2541 (1993). DOI: 10.1063/1.109289, https://doi.org/10.1063/1.109289
  2. D. Z.-Y. Ting and Yia-Chung Chang, 'L-valley-derived states in (001) GaSb/AlSb quantum wells and superlattices', Physical Review B 38, 3414-3422 (1988). DOI: 10.1103/PhysRevB.38.3414, https://doi.org/10.1103/PhysRevB.38.3414
  3. Y. Zhang, N. Baruch, and W. I. Wang, 'Normal incidence infrared photodetectors using intersubband transitions in GaSb L-valley quantum wells', Applied Physics Letters 63, 1068-1070 (1993). DOI: 10.1063/1.109835, https://doi.org/10.1063/1.109835
  4. B. Brar, L. Samoska, H. Kroemer, and J. H. English, 'Electrical and optical properties of heavily n-doped GaSb-AlSb multiquantum well structures for infrared photodetector applications', Journal of Vacuum Science & Technology B 12, 1242-1245 (1994). DOI: 10.1116/1.587055, https://doi.org/10.1116/1.587055
  5. H. Xie, W. I. Wang, and J. R. Meyer, 'Infrared electroabsorption modulation at normal incidence in asymmetrically stepped AlSb/InAs/GaSb/AlSb quantum wells', Journal of Applied Physics 76, 92-96 (1994). DOI: 10.1063/1.357065, https://doi.org/10.1063/1.357065
  6. H. Xie, W. I. Wang, J. R. Meyer, and L. R. Ram-Mohan, 'Normal incidence second-harmonic generation in L-valley AlSb/GaSb/Ga1-xAlxSb/AlSb stepped quantum wells', Applied Physics Letters 65, 2048-2050 (1994). DOI: 10.1063/1.112789, https://doi.org/10.1063/1.112789
  7. Guoping Ru, Yanlan Zheng, and Aizhen Li, 'Interference oscillations in Fourier-transform infrared spectra of AlSb/GaSb superlattices', Journal of Applied Physics 77, 6496-6499 (1995). DOI: 10.1063/1.359126, https://doi.org/10.1063/1.359126
  8. J. R. Meyer, I. Vurgaftman, and C. A. Hoffman, 'Intersubband all-optical limiter based on thermally induced intervalley transfer', Journal of Applied Physics 81, 7662-7665 (1997). DOI: 10.1063/1.365344, https://doi.org/10.1063/1.365344
  9. R. Ferrini, G. Guizzetti, M. Patrini, A. Bosacchi, S. Franchi, and R. Magnanini, 'Infrared reflectance study of n-type GaSb epitaxial layers', Solid State Communications 104, 747-751 (1997). DOI: 10.1016/S0038-1098(97)00400-6, https://doi.org/10.1016/S0038-1098(97)00400-6
  10. D. C. Smith, E. D. O'Sullivan, L. Rota, A. C. Maciel, and J. F. Ryan, 'Ultrafast optical response and inter-valley scattering in GaSb/AlSb quantum wells', Physica E: Low-dimensional Systems and Nanostructures 2, 156-160 (1998). DOI: 10.1016/S1386-9477(98)00034-4, https://doi.org/10.1016/S1386-9477(98)00034-4
  11. C. Ghezzi, B. Cioce, R. Magnanini, and A. Parisini, 'In-plane electrical transport in n-type selectively doped GaSb/AlGaSb multiquantum wells', Journal of Applied Physics 90, 5166-5170 (2001). DOI: 10.1063/1.1407310, https://doi.org/10.1063/1.1407310
  12. R. Ferrini, G. Guizzetti, M. Patrini, and S. Franchi, 'Optical study of intersubband transitions in GaSb/AlGaSb systems for QWIPs', Optical Materials 17, 351-354 (2001). DOI: 10.1016/S0925-3467(01)00101-X, https://doi.org/10.1016/S0925-3467(01)00101-X
  13. Jean-Marc Jancu, Franco Bassani, and Paul Voisin, 'Normal-incidence intersubband absorption in AlGaSb quantum wells', Journal of Applied Physics 92, 641-643 (2002). DOI: 10.1063/1.1482424, https://doi.org/10.1063/1.1482424
  14. J.-M. Jancu, P. Senellart, E. Peter, V. Berger, F. Chevrier, A. Joullie, C. Alibert, O. Krebs, and P. Voisin, 'Normal-incidence intersubband absorption in AlGaSb quantum wells: enhanced oscillator strength and new functionalities using asymmetry', IEE Proceedings - Optoelectronics 150, 381 (2003). DOI: 10.1049/ip-opt:20030722, https://doi.org/10.1049/ip-opt:20030722
  15. J.-M. Jancu, R. Scholz, G. C. La Rocca, E. A. de Andrada e Silva, and P. Voisin, 'Giant spin splittings in GaSb/AlSb L-valley quantum wells', Physical Review B 70, 121306 (2004). DOI: 10.1103/PhysRevB.70.121306, https://doi.org/10.1103/PhysRevB.70.121306
  16. Hiroaki Yasuda, 'Intervalley scattering in terahertz quantum cascade lasers with GaSb and InGaSb wells', AIP Advances 8, 025125 (2018). DOI: 10.1063/1.5023404, https://doi.org/10.1063/1.5023404