Moscow: Izd. Nauka; 1981. 44. Abramovitz M, Stegun I: Handbook on Special Functions. Moscow: Izd. Nauka; 1979. 45. Landau LD, Lifshitz EM: Quantum Mechanics. Moscow: Izd. Nauka; 1989. 46. Bethe H: Intermediate Quantum Mechanics. New York: Basic Books Inc; 1971. 47. Berestetski VB, Lifshitz EM, Pitaevski LP: Relativistic Quantum Theory. Moscow: Izd. PSI-7977 nmr Nauka; 1971. 48. Fock VA: Zur Theorie des Wasserstoffatoms. Z Phys 1935, 98:145–154.CrossRef Competing interests The authors

declare that they have no competing interests. Authors’ contributions KD gave the main idea of the manuscript, did the calculations, and drafted the manuscript. SM provided theoretical guidance, did the calculations, and drafted the manuscript. BV performed the theoretical analysis of the results and drafted the manuscript. All authors read and approved the final manuscript.”
“Background Infrared detector technology is one of most important opto-electric devices. It has been developed from bulk material to the quantum well structure [1, 2]. The 3 ~ 5 μm middle-wavelength-infrared (MWIR) region is of particular interest in the fields of scientific research, aerial reconnaissance, and missile tracking. The dominant detector in this wavelength field is still HgCdTe (MCT) due to its high quantum efficiency and lower thermal generation rate. However, due to the high density of defect in the MCT material,

it is difficult to reduce the dark current of the MCT device [3]. The quantum Rolziracetam well infrared photodetector (QWIP) is fabricated from a GaAs-based

selleck kinase inhibitor material, which is expected to have lower dark current due to the mature process on both the material and device for GaAs [4, 5]. GaAs-based InGaAs/AlGaAs QWIP working in the MWIR region is studied [6–9]. Low dark current of a few pA was measured in MWIR QWIP based on InGaAs/AlGaAs-strained quantum well grown on GaAs substrates [10]. Recently, a 28% quantum efficiency and a detectivity D* = 7 × 1011 Jones at 77 K were reported in a InGaAs/AlGaAs QWIP working below 4.1 μm [11]. Nevertheless, the huge difference of the growth window for the InGaAs and AlGaAs materials and the easy desorption of the In atom make such Selleck BB-94 multiple quantum well system hard to fabricate [12]. Generally, the typical growth temperature of AlGaAs barrier should be higher than 600°C, and the In atom in the InGaAs quantum well starts the desorption at around 520°C [13–15]. This intrinsic property makes the In composition in the InGaAs quantum well quite unstable when increasing the temperature to grow the followed AlGaAs barrier. Besides, the high mobility of In atoms at the substrate made the surface morphology of InGaAs layer very sensitive to the growth parameters [16]. These problems would make the precise peak wavelength control difficult since the absorption peak wavelength is very sensitive to the structural characteristics of QWIP, such as the In composition and its profiles in the quantum well [17, 18].