Mid-IR stimulated emission in Hg(Cd)Te/CdHgTe quantum well structures up to 200 K due to suppressed Auger recombination

Compact coherent sources in the mid-IR and far-IR spectral regions are of great interest for spectroscopy applications, such as medicine and environmental monitoring. Development of these devices is one of the most topical problems in modern semiconductor physics. It is well known that HgCdTe compounds hold the leading position as a material of choice for mid-IR and far-IR semiconductor detectors [1] due to direct band gap and variable band gap energy E_g, which ranges from 1.5 eV down to 0 eV by varying Cd content. As for emitting properties of HgCdTe structures, physicists have actively investigated interband lasing in HgCdTe since middle 60 s [2]. However, room temperature lasing has only been achieved in the near-IR range (2.2 μm wavelength [3]), and at longer wavelengths the critical temperature T_max, at which stimulated emission (SE) could be obtained, decreased rapidly: T_max was ∼190 K for 2.6 μm lasing [4], while 5.3 μm laser operated at temperature as low as 45 K [5]. It is well established that the observed strong thermal quenching of interband lasing from narrow gap materials is related to activation of nonradiative Auger recombination processes [5–7].

Auger recombination is a three-particle process, in which an electron–hole pair recombines and transfers energy to the third carrier [8]. During Auger process, the total kinetic energy of initial system has to exceed certain threshold value to meet the energy and momentum conservation laws [9]; this threshold energy depends strongly on the dispersion law of the charge carriers involved. Higher symmetry of electron and hole dispersion (which may be expressed as closer values of electron and hole effective masses for parabolic dispersion) generally translates into higher Auger recombination threshold. In the extreme case of symmetric hyperbolic Dirac dispersion law, principles of energy and momentum conservation cannot be fulfilled at all and thus Auger threshold energy tends to infinity [10]. To the certain extent, similar band dispersion may be realized in narrow band HgTe/CdHgTe quantum wells (QWs) [11], in contrast to either bulk HgCdTe alloys or Cd-rich HgCdTe QWs. Therefore, HgTe/CdHgTe QWs are expected to establish a high energy threshold for Auger recombination, which provides a basis for creation of long-wavelength emitters [12]. Such HgTe/CdHgTe QWs for mid- and far-IR optoelectronics may be nowadays readily fabricated due to significant progress in the molecular beam epitaxy (MBE) of HgCdTe heterostructures [13], and SE at wavelengths up to 20 μm has been demonstrated in optically pumped HgCdTe/CdHgTe QW heterostructures [14, 15]. However, critical temperature T_max of SE generation is yet to be improved.

In this work, we investigated critical temperature of SE generation in the series of four HgCdTe QW structures and compared the experimental results with calculated threshold energies of Auger recombination. In our structures, we only varied the QW thickness while Cd content in the QW and barrier layers was kept constant (at ∼10% and ∼65%, respectively). Next, for each structure we examined an optimized QWs design employing binary HgTe (adjusting the QW thickness to retain bandgap energies). Finally, we computed Auger threshold energies in the optimized structures and evaluated relative increment in threshold energy related to transition from HgCdTe QWs to HgTe QWs.

The structures studied were MBE grown on semi-insulating GaAs (013) substrate with ZnTe and CdTe buffers with in situ ellipsometric control of layer thickness and Cd content in it giving raw data such as presented in the figure 1 (inset). We further refined this raw data via ex situ structure characterization by measuring spectra of interband photoluminescence (PL) in a wide temperature range, from which the dependence of band gap energy E_g on temperature was extracted. QW thickness and Cd content were identified by comparing this dependence with calculations within 8 × 8 Kane model, as in [16]. Table 1 shows the QW parameters for the structures studied. Hereafter we consider SE and Auger recombination by the example of the model structure #2, and discussion can be directly applied to any other structure in the investigated series.

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The structures were designed to effectively confine guided modes near the QWs array, for which the QWs were incorporated into thick (several microns) wide-gap HgCdTe waveguide layers, see figure 1.

Measurements of PL and SE spectra were performed in a closed-cycle optical helium cryostat (Advanced Research Systems DE-202) with an 8–300 K operating temperature range. The cryostat was optically coupled with a BrukerVertex 80v Fourier spectrometer operating in the step-scan mode. Test samples had a typical size of 8 × 8 mm and were chipped from a 3" grown structure. Due to the specific growth direction (013), naturally cleaved facets do not form a Fabry–Perot resonator, so we studied single-pass SE. We observed SE in the optimal geometry—from the cleaved facet. A near-IR optical parametric oscillator was used as an excitation source to optically excite structures (10 Hz repetition rate, 10 ns pulse duration, output wavelength range: 1.94–2.36 μm, pulse energy 20–30 mJ). Pumping radiation covered samples completely in all experiments. The scattered radiation of the excitation laser was cut off by an InAs filter limiting the spectrometer range to 450–2700 cm⁻¹. Emitted radiation was detected by a Kolmar Technologies D317 MCT photodetector.

We measured emission spectra over a wide temperature range for each structure in the series. Figure 2 represents the evolution of the emission spectrum with temperature in the structure #2. SE could only be obtained up to some certain temperature T_max (for the structure #2, T_max = 160 K), above which we observed only a low intensity, broadband spontaneous emission spectrum at any excitation power. The exact T_max values for each structure are presented in figure 3.

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One can see from the figure 3 that the critical temperature of SE generation decreases from 200 K (17.2 meV) for sample #4 (the widest band gap) to 80 K (6.9 meV) for sample #1 (the narrowest one). Since temperature quenching of SE is related to activation of non-radiative Auger processes, we calculated band spectra and corresponding E_th energies for each sample studied. Band spectra were calculated within 4-band 8 × 8 Kane model, as described in [17]. E_th values were calculated by finding the constrained extremum of the total kinetic energy of the carriers involved in the Auger process (calculation technique is discussed in [18]). We only considered CHCC processes (which involve a hole and two electrons) since CHHH processes (with an electron and two holes) feature several times higher threshold energies. In figure 3, the decrease in T_max observed as we move towards narrow gap QWs correlates with E_th decrease from 24.6 meV to 14.9 meV. The graph shows that the critical temperature of SE generation corresponds to or exceeds the E_th/2; the same ratio was observed in [19].

Figure 4 shows the calculated band diagram for the structure #2 (solid lines). Note that valence V1 subband has additional local maxima at k ≠ 0 some 20 meV below the valence band top, the electronic states in these maxima being directly responsible for CCHC Auger recombination in our QWs (green arrows in figure 4 indicate corresponding carrier transitions). The energy offset of the discussed side maxima relative to the valence band Γ-point is in excellent agreement with calculated threshold energy (∼19 meV, see table 2).

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As it was demonstrated in [20], the side maxima could be suppressed by a move from wide HgCdTe-based QWs to narrow HgTe QWs with the same bandgap. Thus, one can increase Auger recombination threshold energy by implementation of pure HgTe QWs. We designed a series of the optimized structures with binary HgTe QWs for the same band gap energies (see table 2). The band spectrum of the optimized structure #2^* is also shown in figure 4 (dash dot lines). Hole dispersion curve in the optimized QW lies lower and provides threshold energy E_th ^* higher than E_th in the (initial) HgCdTe QW. Table 2 combines parameters of the structures studied, parameters of the optimized structures with binary QWs (asterisk marked), threshold energies E_th and E_th ^* for all the structures, and relative E_th increment. This increment is expressed as a percentage and is calculated by the formula (E_th ^*/E_th − 1) × 100%.

Figure 5 demonstrates E_th and E_th ^* values for the structures studied and the optimized structures respectively. The E_th ^* energy in the optimized structures with binary QWs increases significantly reaching 49.6 meV and 41.3 meV for the most wide-band structure #4^* and the most narrow-band structure #1^* respectively. Comparison of the threshold energies E_th and E_th ^* allow us to suggest that the rate of Auger processes in HgTe QWs could be lower than in HgCdTe QWs at the same temperature. It is natural to expect that Auger recombination influence on SE generation in the binary HgTe QWs will be weaker leading to higher critical temperature of SE generation.

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Having calculated Auger threshold energies for both series, we clearly see the advantage of binary HgTe QWs for designing long-wavelength emitters. However, one should also note that the well thickness must be almost twice lower for pure HgTe QWs than for 10% Cd ternary HgCdTe QWs, down to a few nanometers. It may pose certain technological challenges to fabricate such structures, so slightly thicker QWs with a few percent Cd seem to be more convenient and realistic. Therefore, we expect that some intermediate E_th' values (between E_th and E_th ^*) could be achieved. As E_th values tend to decrease in the narrow-gap region, we calculated the relative increase in E_th to understand how important the transition to pure HgTe QWs is for different parts of IR range. Yellow dots in the figure 5 represent the relative increment calculated. It is obvious that relative E_th increment rises as the structure bandgap decreases. While the pair of the structures #4–#4^* (7.2 μm SE wavelength at 10 K) have 101% relative E_th increment, the pair of the structures #1–#1^* (SE at 13.25 μm wavelength) demonstrates almost 180% energy gain. Thus, implementing binary HgTe QWs as pure as possible becomes essential as we move towards long-wave IR region.

In summary, we study the thermal stability of stimulated emission from HgCdTe/CdHgTe QW heterostructures designed for 7–13 μm spectral range. We demonstrate that the critical temperature of SE generation in a series of samples with decreasing band gap directly correlates with the Auger recombination threshold energy. The latter value depends strongly on the electronic band spectra of the QWs under consideration. We compare the QWs studied (which contain typically ∼10% Cd) to optimized HgTe QWs (with the QW width adjusted to retain the band gap energy) in terms of AR threshold, and show that pure HgTe QWs provide at least twofold higher threshold energies. Consequently, one may expect a solid increase in the SE critical temperature once incorporation of residual Cd into Hg(Cd)Te QWs is suppressed. The above enhancement becomes more pronounced with decreasing band gap, which clearly demonstrates the importance of binary HgTe QWs for realization of HgCdTe interband QW based lasers emitting beyond mid-infrared range.

The authors declare that they have no conflict of interest. The study was performed using equipment of the Center 'Physics and technology of micro- and nanostructures' at IPM RAS. The work was supported by the Ministry of Science and Higher Education of the Russian Federation, Grant #075-15-2020-797 (13.1902.21.0024).