Brar, Samoska, Kroemer and English [J. Vac. Sci. Technol. B 12, 1242 (1994)] characterized heavily tellurium (Te) doped GaSb/AlSb multiquantum-well infrared photodetector (QWIP) structures, in which electrons spill from the Γ ground subband into L-valley subbands and escape across an indirect AlSb X-point barrier. Two issues that work left unresolved define this problem. First, inserting 1–2 monolayers of AlSb at the center of a 3.9 nm GaSb well ('center loading') shifted the intersubband absorption peak from roughly 5 to roughly 8 μm, but the measured ground-state shift was only about half of an ideal envelope-function prediction and the first monolayer produced a smaller shift than the second; islandlike nucleation of the inserted AlSb and structural asymmetry of the wells were proposed as explanations but not demonstrated, so the actual growth-induced morphology and its quantitative effect on the confined states remained undetermined. Second, the approximately 170 meV thermionic activation energy extracted from dark-current Arrhenius analysis rested on a three-dimensional thermionic-emission model acknowledged to be imperfectly applicable to these two-dimensional multi-valley subbands, and on uncertain band offsets and effective masses, leaving the barrier-escape physics without a reliable quantitative description. Both questions remain open.

Background

Quantum-well infrared photodetectors (QWIPs) detect infrared radiation through intersubband absorption: photon-induced transitions between quantized conduction-band states of a doped semiconductor quantum well (a thin narrow-gap layer sandwiched between wider-gap barrier layers). Because the conduction-band minimum of GaAs lies at the Γ point (the center of the Brillouin zone, the crystal-momentum space of the band structure) and is there spherical and nearly parabolic, intersubband absorption in conventional n-type GaAs/AlGaAs wells couples only to light polarized along the growth direction, so normal-incidence (surface-illuminated) detection is forbidden and coupling gratings or 45° facets are needed (reviewed by Levine, 1993). GaSb offers a route around this selection rule: the conduction-band valleys of GaSb at the L points (Brillouin-zone boundary points along the ⟨111⟩ directions) lie only about 90–100 meV above the Γ minimum, and each of the four L valleys is an ellipsoid with strongly anisotropic effective mass, so intersubband transitions between quantized L-derived states do absorb normal-incidence light (Brown and Eglash, 1990; Zhang, Baruch and Wang, 1993). In GaSb wells with AlSb barriers grown by molecular beam epitaxy (MBE, ultrahigh-vacuum layer-by-layer epitaxial growth), heavy n-type tellurium (Te) doping leaves the wells so electron-rich that carriers spill from the first Γ subband into the L subband: Samoska, Brar and Kroemer (1993) measured strong normal-incidence intersubband absorption in heavily doped GaSb–AlSb superlattices (periodic stacks of many wells and barriers) with of order 101210^{12} electrons per well in the L subband. The escape barrier in this system is unusual: AlSb is an indirect-gap semiconductor whose lowest conduction minimum is at the X point of the Brillouin zone (the zone-boundary point along the ⟨100⟩ directions), roughly 400 meV above the GaSb Γ minimum, so the barrier seen by L-subband electrons is an indirect X-point barrier rather than a direct Γ-point one.

The 1994 paper of Brar, Samoska, Kroemer and English reported a consolidated electrical and optical characterization of such heavily doped GaSb–AlSb multiquantum-well (MQW) detector structures. Hall-effect data analyzed with a two-band conduction model (a decomposition of the measured Hall response into a high-mobility Γ-electron and a lower-mobility L-electron contribution) indicated at least 101210^{12} cm−2^{-2} in the L subband at the 80 K operating temperature. Temperature-dependent dark current showed a tunneling regime below about 100 K (escape through the barrier, weakly temperature-dependent) and a thermionic regime above (escape by thermal excitation over the barrier); an Arrhenius plot of J/T2J/T^{2} (dark-current density over temperature squared, the Richardson-type construction for thermionic emission) yielded an activation energy of about 170 meV, interpreted as the separation between the Fermi level extrapolated to 0 K and the top of the AlSb X-point barrier. Photoluminescence (PL, optically detected recombination radiation) showed that heavy Te doping did not strongly degrade the radiative quality of the GaSb wells. To push the intersubband transition to longer wavelengths, the authors implemented 'center loading', a specific case of the potential-inserted quantum well proposed by Sakaki and co-workers: depositing 1–2 monolayers (ML; single atomic planes, here about 0.3 nm each) of AlSb at the center of a GaSb well before completing it. In an ideal symmetric well the node-less ground-state wave function has maximum amplitude at the well center while the first excited state has a node there, so a central insertion raises the ground state while leaving the excited state almost unchanged, red-shifting the intersubband transition. In 3.9 nm wells, two inserted ML shifted the measured absorption peak from roughly 5 to roughly 8 μm — but the shift was only about half of what a simple envelope-function (effective-mass) calculation predicted, the first monolayer shifted the spectra less than the second, and the absorption and PL shifts behaved differently. The authors attributed the discrepancy tentatively to islandlike nucleation of the first AlSb monolayer (so that an exciton, the correlated electron–hole pair created in PL, averages over less than a full inserted monolayer) and to a structural asymmetry of the well that displaces the excited state's node from the insertion plane; these were offered as possibilities under investigation, not demonstrated. At the same time, the thermionic analysis rested on a three-dimensional thermionic-emission model acknowledged to be imperfectly applicable to emission from two-dimensional subbands across an indirect barrier, and on band offsets and effective masses that were uncertain, so the 170 meV activation energy (well below the roughly 265 meV L-subband-to-barrier separation estimated from the envelope-function calculation and a then-current offset of about 400 meV) could not be tied reliably to the band structure. Both issues were left open by that work.

Problem Statement

Give a quantitatively reliable, microscopically grounded account of the confined states and of vertical carrier escape (escape perpendicular to the well plane, across the barriers) in heavily n-doped GaSb wells with AlSb (or AlGaSb) barriers — the structures of Brar, Samoska, Kroemer and English (1994) — by resolving the two issues that work left open.

(a) Center-loading morphology and level shifts. Determine the actual growth-induced morphology of center-loaded GaSb wells — the effective coverage and conformation of the 1–2 monolayer AlSb insertion layer and any structural asymmetry of the wells — and quantitatively explain the measured layer-by-layer level shifts: the shortfall of the observed ground-state shift to roughly half of ideal envelope-function predictions for a symmetric full insertion, the smaller spectral shift produced by the first monolayer than by the second, and the difference between the intersubband-absorption and photoluminescence shifts. Because morphology and band-parameter effects are degenerate in these observables, the morphology must not be established through effective coverage, asymmetry, or offset parameters left free to reproduce the very shifts to be explained.

(b) Barrier escape. Construct a quantitative description of vertical carrier escape from these structures — the thermionic regime above about 100 K with its approximately 170 meV activation energy, and its crossover to the tunneling regime below — valid for wells whose electrons occupy both Γ and L subbands with sheet density of order 101210^{12} cm−2^{-2} and escape across an indirect X-point AlSb barrier, such that the extracted activation energy is connected to the band structure with defensible band offsets and effective masses.

The two parts share one scientific objective — a validated microscopic understanding of these heavily doped multi-valley wells — and are coupled: the escape interpretation depends on the very subband energies that the morphology question determines.

References

  1. B. Brar, L. Samoska, H. Kroemer, 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 (1994). DOI: 10.1116/1.587055, https://doi.org/10.1116/1.587055
  2. L. A. Samoska, B. Brar, H. Kroemer, 'Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices', Applied Physics Letters 62, 2539 (1993). DOI: 10.1063/1.109289, https://doi.org/10.1063/1.109289
  3. L. A. Samoska, B. Brar, H. Kroemer, 'Normal-incidence quantum-well infrared photodetectors utilizing ellipsoidal valley intersubband transitions in n-type GaSb-AlSb multiquantum wells', Proceedings of SPIE 2021, 149 (1993). DOI: 10.1117/12.164938, https://doi.org/10.1117/12.164938
  4. E. R. Brown, S. J. Eglash, 'Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells', Physical Review B 41, 7559 (1990). DOI: 10.1103/physrevb.41.7559, https://doi.org/10.1103/PhysRevB.41.7559
  5. Y. Zhang, N. Baruch, W. I. Wang, 'Normal incidence infrared photodetectors using intersubband transitions in GaSb L-valley quantum wells', Applied Physics Letters 63, 1068 (1993). DOI: 10.1063/1.109835, https://doi.org/10.1063/1.109835
  6. H. Sakaki, H. Sugawara, J. Motohisa, T. Noda, 'Intersubband Transition and Electron Transport in Potential-Inserted Quantum Well Structures and their Potentials for Infrared Photodetector', in E. Rosencher, B. Vinter, B. F. Levine (eds.), 'Intersubband Transitions in Quantum Wells', NATO ASI Series B, Vol. 288, pp. 65–72, Springer (1992). DOI: 10.1007/978-1-4615-3346-7_6, https://doi.org/10.1007/978-1-4615-3346-7_6
  7. H. Xie, W. I. Wang, J. R. Meyer, 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 (1994). DOI: 10.1063/1.112789, https://doi.org/10.1063/1.112789
  8. Y. Abramovich, J. Poplawski, E. Ehrenfreund, D. Gershoni, B. Brar, H. Kroemer, 'Intersubband L-valley and heavy-hole transitions in undoped GaSb/AlSb superlattices', Physical Review B 50, 8922 (1994). DOI: 10.1103/physrevb.50.8922, https://doi.org/10.1103/physrevb.50.8922
  9. J. R. Meyer, I. Vurgaftman, C. A. Hoffman, 'Intersubband all-optical limiter based on thermally induced intervalley transfer', Journal of Applied Physics 81, 7662 (1997). DOI: 10.1063/1.365344, https://doi.org/10.1063/1.365344
  10. C. Ghezzi, B. Cioce, R. Magnanini, A. Parisini, 'In-plane electrical transport in n-type selectively doped GaSb/AlGaSb multiquantum wells', Journal of Applied Physics 90, 5166 (2001). DOI: 10.1063/1.1407310, https://doi.org/10.1063/1.1407310
  11. T. Guettler, O. Krebs, I. L. Dias, J. C. Harmand, F. Devaux, P. Voisin, 'Potential-inserted InGaAs - AlGaInAs shallow quantum wells for electro-optical modulation at 1.55 μm', Semiconductor Science and Technology 12, 729 (1997). DOI: 10.1088/0268-1242/12/6/014, https://doi.org/10.1088/0268-1242/12/6/014
  12. T. Wang, F. Kieseling, A. Forchel, 'Transition from direct to indirect band structure induced by the AlSb layer inserted in the GaSb/AlSb quantum well', Physical Review B 58, 3594 (1998). DOI: 10.1103/physrevb.58.3594, https://doi.org/10.1103/physrevb.58.3594
  13. R. Ferrini, G. Guizzetti, M. Patrini, S. Franchi, 'Optical study of intersubband transitions in GaSb/AlGaSb systems for QWIPs', Optical Materials 17, 351 (2001). DOI: 10.1016/S0925-3467(01)00101-X, https://doi.org/10.1016/S0925-3467(01)00101-X
  14. J.-M. Jancu, F. Bassani, P. Voisin, 'Normal-incidence intersubband absorption in AlGaSb quantum wells', Journal of Applied Physics 92, 641 (2002). DOI: 10.1063/1.1482424, https://doi.org/10.1063/1.1482424
  15. J. M. Jancu, P. Senellart, E. Peter, V. Berger, F. Chevrier, A. Joullie, C. Alibert, O. Krebs, 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
  16. I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, 'Band parameters for III–V compound semiconductors and their alloys', Journal of Applied Physics 89, 5815 (2001). DOI: 10.1063/1.1368156, https://doi.org/10.1063/1.1368156
  17. B. F. Levine, 'Quantum-well infrared photodetectors', Journal of Applied Physics 74, R1 (1993). DOI: 10.1063/1.354252, https://doi.org/10.1063/1.354252
  18. H. Kroemer, 'The family (InAs, GaSb, AlSb) and its heterostructures: a selective review', Physica E 20, 196 (2004). DOI: 10.1016/j.physe.2003.08.003, https://doi.org/10.1016/j.physe.2003.08.003
  19. R. Mohammad, Ş. Katırcıoğlu, 'The electronic band structure of AlN, AlSb, AlAs and their ternary alloys with In', International Journal of Modern Physics B 20, 3199 (2006). DOI: 10.1142/S0217979206035394, https://doi.org/10.1142/S0217979206035394
  20. A. Giani, F. Pascal-Delannoy, J. Podlecki, G. Bougnot, 'Electrical characteristics of GaIn(As)Sb layers grown by metal organic vapor phase epitaxy', Materials Science and Engineering B 41, 201 (1996). DOI: 10.1016/S0921-5107(96)01662-5, https://doi.org/10.1016/S0921-5107(96)01662-5
  21. M. Behet, P. Schneider, D. Moulin, K. Heime, J. Woitok, J. Tümmler, J. Hermans, J. Geurts, 'Low pressure metalorganic vapor phase epitaxy and characterization of (Al,Ga)Sb/GaSb heterostructures', Journal of Crystal Growth 167, 415 (1996). DOI: 10.1016/0022-0248(96)00260-6, https://doi.org/10.1016/0022-0248(96)00260-6
  22. D. Doppalapudi, T. D. Moustakas, 'Epitaxial growth and structure of III-V nitride thin films', Handbook of Thin Films, 57 (2002). DOI: 10.1016/B978-012512908-4/50052-7, https://doi.org/10.1016/B978-012512908-4/50052-7
  23. X. Wei, W. Wang, J. Fang, R. He, 'Mid-infrared optical absorption in InAs/AlSb/GaSb based quantum well system', Physica E 117, 113801 (2020). DOI: 10.1016/j.physe.2019.113801, https://doi.org/10.1016/j.physe.2019.113801