1. Introduction

Mid-infrared LEDs have attracted interest for low-cost non-dispersive infrared (NDIR) gas sensors, where their high on/off speed and rapid stabilization time can lead to extended battery times, and their packaging is more compact compared to incandescent sources [1]; and for thermal scene generation, due to their large modulation bandwidth, ability to achieve high apparent temperatures and to be packed together in high resolution surface emitting arrays [2].

W-quantum wells (W-QWs) have made possible low threshold interband cascade lasers (ICLs) with intermediate output powers in the mid infrared. For ICLs, it is highly desirable to use a thin active region per stage to keep threshold low and slope efficiency high. This is typically achieved with a single quantum well per stage; higher gain is typically achieved by cascading devices, a serial current solution, which reduces threshold current while raising threshold voltage. Multi-QWs, a parallel current solution, are generally avoided as a way of increasing gain because they result in degraded hole transport and increased resistance [3,4]. W-QWs are operated at room temperature and owe their success in part to strong electron-hole overlap for a type-II structure leading to a strong dipole moment, to high gain, and to suppressed Auger scattering from the broken gap alignment and compressive strain [5,6,7], which leads to lh-hh splitting, as well as hole confinement and clearing out of valence bands.

While single W-QWs are advantageous for ICLs for reasons discussed above, the lack of a threshold in infrared LEDs makes W-superlattices (W-SL) [5] more attractive. In a laser, carrier density ideally clamps at input powers equal to and greater than threshold [8], whereas in an LED, carrier density keeps climbing with input current. The increased thickness of a superlattice compared to a QW means that the LEDs can operate at lower carrier densities than in a QW for the same input current, which reduces Auger scattering at higher input currents. Recent work has shown that the internal quantum efficiency of W-SLs peaks at nearly 80% and is 3-4 times more efficient than that of InAs/GaSb superlattices [9], a past standard [10]. W-SL cascaded LEDs have also shown superior wallplug efficiencies in the mid-infrared compared to those based on InAs/GaSb superlattices [11]. In this work, we investigate the characteristics that give the W-SLs such superior radiative efficiency compared to other superlattices through ultrafast optical measurements of carrier dynamics. In doing so, we improve on the ultrafast technique used previously to find A, B, and C coefficients in other materials [12–14] by incorporating quasi-continuous wave measurements to reduce assumptions and further constrain the fit parameters [15].

2. Experimental methods

The sample was grown by molecular beam epitaxy in a Veeco Gen-20 reactor using techniques described in Ref. [9]. The W-SL stack was grown on a lightly doped Te:GaSb substrate and consists of GaSb and AlAsSb buffer layers, nominally 0.5 µm thick InAs/Ga_0.7In_0.3Sb/InAs/AlAs_0.27Sb_0.73 superlattice layers surrounded by 30 nm AlAsSb clads, and a 10 nm GaSb cap to prevent oxidation. A thinner absorber was used to ensure uniform excitation, and to make use of data from Ref. [9]. A drawback of the thinner absorber is that signal-to-noise ratio is lower in pump-probe measurements, limiting lifetime measurements to carrier densities above about 10¹⁶ cm^-3. The bandgap energy of the superlattice at the two temperatures was measured by photoluminescence (PL) and the absorption of the superlattice at the wavelength of the pump laser was extracted from power transmission measurements as described in the Supplementary Information. A technique known as the Fermi tail analysis of the sample photoluminescence at low beam intensity provided the background carrier density for the superlattice layers. A description of the Fermi tail fit is contained in the Supplementary Information. The results for these measurements are summarized in Table 1.

Table 1. The SL linear absorption coefficient at the pump wavelength (λ=2.55 µm), bandgap, and background carrier density of the W-SL measured at different temperatures by power transmission and FTIR-photoluminescence measurements, respectively.

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Time-resolved pump-probe techniques utilizing two different probes were used to collect differential transmission ($\Delta T/T$) measurements to investigate the carrier dynamics of the W-SL at $77\; K$ and $300\; K$. The pump used to excite carriers in the measurement was created by the $\lambda = 2.55\; \mu m$ idler output of a Ti:Sapphire-pumped optical parametric amplifier (OPA). This work utilized two different probes to observe the change in carrier density of the W-SL: one an electronically delayed quantum cascade laser ($\Delta \tau \; \sim \; 3.5\; ns$, $\lambda = 9.3\; \mu m$), the other a long-wave infrared (LWIR) output beam from a second OPA ($\Delta \tau \; \sim \; 500\; fs$, $\lambda = 8.6\; \mu m$) pumped by the same Ti:Sapphire laser, and phase-locked to the pump. Note that both probes are below the bandgap of the W-SL, so monitor carriers through free carrier absorption. The nanosecond probe (ns) was originally used to cover the entire W-SL decay but was found to have insufficient time resolution for collecting the decay behavior at high-carrier density. The femtosecond probe (fs), in which the time delay is created by directing the pump beam along a double-pass mechanical mirror, was used to collect the decay behavior at high-carrier density ($> {10^{17}}\; \; c{m^{ - 3}}$).

The pump beam is attenuated by a pair of Teflon polarizers for incident fluences between $500\; nJ/c{m^2}$ and $12,000\; nJ/c{m^2}$ and focused onto the sample housed in a low-vibration, closed-cycle, He-cooled Janis cryostat. The pump and probe come in at small angles on either side of the surface normal and are overlapped such that they are approximately colinear along the thickness of the SL. The pump and probe beams were measured to have ${e^{ - 1}}$ radii of $670\; \mu m$ and $250\; \mu m$, respectively. The probe is smaller than the pump so a uniform carrier density can be sampled. The 1kHz master clock inside the Ti:Sapphire laser triggers the time delay as well as a series of electronics which process the detector signal. The initial excess carrier density ($\Delta n({t = 0} )$) is calculated from the fraction of the initial ultrashort pump pulse absorbed.

The differential transmission decay scans for both probes at $77\; K$ and $300\; K$ at multiple initial carrier densities are shown in Fig. 1. It was found that nonlinear absorption of the pump in the substrate altered probe transmission on long time scales. However, the W-SL differential probe signal was reasonably dominant for both temperatures, and residual slow substrate signal was subtracted out.

 

Fig. 1. Decay scans of the W-SL layers taken with the fs ((a) and (c)) and ns ((b) and (d)) probes with the n-GaSb substrate signal removed for the 300 K data ((a) and (b)) and the 77 K data ((c) and (d)).

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Using the data presented in Fig. 1, the recombination rate, $R({\Delta n} )$, can be calculated from the differential transmission, ($\Delta T/T$), as function of excess carrier density, $\Delta n$, as,

The two datasets from the respective probes are combined to create a total recombination curve for each temperature as shown in Fig. 2. The total recombination rate equation posits that the total recombination curve can be described by the combination of three separate rates, each representing a different recombination mechanism: the Shockley-Read-Hall recombination (R_SRH), the radiative recombination (R_Rad), and the Auger recombination mechanism (R_Auger). Each of the three mechanism rates can be expressed as a function of $\mathrm{\Delta }n$ [16,17],

 

Fig. 2. A and C were used as free parameters to fit the recombination rate data, with B fixed from the direct internal quantum efficiency measurements (Fig. 3). The resulting recombination rate fit is shown in red, with breakdown into contributions from the SRH rate (black), radiative rate (blue), and Auger rate (orange).

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3. Results and Discussion

To determine the SRH, radiative, and Auger recombination coefficients (A, B, and C, respectively), we made use of both ultrafast recombination data in Fig. 2, and direct measurements of the IQE from carriers in/photons out measurements. A potential problem with determining the ABC coefficients solely from a fit of Eq. (2) to carrier-dependent recombination data, as has been done previously [11,12], is that it relies on each process dominating over a particular carrier density range, e.g. SRH dominating at low carrier density, radiative dominating at intermediate densities, and Auger at high carrier density, which may or may not be true, and cannot be known in advance. We have handled this problem by separately determining the B coefficient as a fit parameter to the direct IQE measurements, and the A and C coefficients as fit parameters to the ultrafast recombination rate data at low and high carrier density, using the separately determined B-coefficient. The IQE can be written as

The direct measurements of IQE with a laser pump injecting electron-hole pairs and measuring photons out gives IQE as a function of the current density (IQE(J)). This data was obtained from Ref. [9], which used the same sample. To obtain IQE(Δn), as is needed for the fit using Eq. (3), J and Δn can be connected through the equation,

 

Fig. 3. Internal quantum efficiency as a function of excess carrier density, including measured values (gray, black lines), and single parameter fits (red solid, dotted) varying the radiative B-coefficient in Eq. (3). The error in the measured datapoints is shown as error bars; the error in the 300K dataset is smaller than the width of the line.

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With the B-coefficient determined, the A and C coefficients can be obtained from a fit using Eq. (2) of R(Δn) versus Δn measurements obtained from the ultrafast data. The only assumptions needed are that the combined SRH and radiative processes dominate over Auger at low carrier density and combined radiative and Auger dominate over SRH at high carrier density. Additionally, we depend on a quadratic dependence of the Auger scattering, which is true below saturation. Saturation generally occurs >1 × 10¹⁸ cm^-3 [18] whereas our maximum carrier densities are below this. Experimental data and fits are shown in Fig. 2. Values for A, B, and C at room and low temperature are summarized in Table 2.

Table 2. Extracted A, B, and C coefficients for each temperature. The B coefficient and its error come from the fit to the IQE dataset. The A and C coefficients and their error come from the fit to the pump probe data with B fixed.

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The A (C) coefficient at low temperature may be less reliable, because its associated rate is relatively smaller than the radiative rate even at low (high) carrier density. The A and C coefficients at low temperature may be viewed primarily as upper limits, because if they were any larger, the recombination rate fit would begin to deviate from the measured data, keeping in mind the low uncertainty in the B coefficient from single parameter fits to independent IQE measurements.

From the data and Table 2, what is most striking about the low temperature data is that the radiative recombination dominates over Auger and SRH over most of the interesting carrier density range. This is a result of a relatively large dipole moment [9] compared to InAs/GaSb superlattices stemming from improved electron-hole overlap from the AlSb layers, combined with lower SRH as discussed next, along with strong Auger suppression, also discussed next. This combination is very favorable for a high quantum efficiency infrared LED.

The SRH coefficient in the W-QWs is relatively small. In InAs/GaSb mid-infrared superlattices at 77K, the best mid-infrared SRH lifetimes reported have been close to 100 ns at cryogenic temperatures [12,19], while the SRH lifetime found in the W-SL here is 3x longer. The longer SRH is surprising in that the W-SL has bandgap and band offsets very similar to the InAs/GaSb superlattices, and even contains Ga-containing layers which have been attributed to formation of mid-gap states shortening the SRH lifetime [20]. The total room temperature minority carrier recombination rate of the W-SL, dominated by SRH, is even smaller than that reported for Ga-free mid-infrared InAs/InAsSb superlattices at room temperature [12], where the latter is strongly limited by Auger scattering. The longer minority carrier lifetime may point to promise of W-SLs as a mid-infrared detector material, particularly at higher temperatures.

While A and C coefficients change only modestly going to room temperatures, a 40x drop in the B coefficient at room temperature is the major cause of the observed 10x drop in quantum efficiency of the W-SLs at room temperature (Fig. 3). The observed temperature scaling of the A, B, and C coefficients is in line with expectations from theory [22–24], and comparable to that observed in related materials [15]. Comparing C coefficients, it appears that the Auger coefficient is 2-10x larger than reported for comparable W-QWs at room temperature [21], but >80x smaller than Ga-free mid-infrared InAs/InAsSb [12]. For LEDs, it is important to remember that Auger scattering is a function of the Auger coefficient, but also carrier density squared; for the same current density injection, W-QWs will run at much higher carrier density due to their relative thinness compared to a superlattice. While mid-infrared Ga-free superlattices have the largest dipole moments, and the longest SRH lifetimes at low temperatures (microseconds), it is the relatively poor Auger scattering rate that leads to their limited use as an LED at higher injection and as a detector at room temperature. To further refine measurements of A and C for W-SLs at low temperatures, measurements would have to be repeated with thicker superlattices.

4. Conclusions

Here, we used pump-probe measurements to elucidate the recombination mechanisms of a mid-infrared III-V W-SL, InAs/GaInSb/InAs/AlAsSb, which in previous work had demonstrated a high IQE performance for emission. The W-SL was measured at two temperatures commonly of interest to MWIR LEDs, 77 K and 300 K. Recombination rate data was combined with internal quantum efficiency measurements to obtain SRH, radiative, and Auger coefficients. The radiative rate dominates over a large range of carrier densities at 77 K which has not been seen in similar III-V SLs designed for light emission. The W-SL demonstrated an improved SRH lifetime over previous InAs/GaSb SLs at low temperature and a longer minority carrier lifetime than InAs/InAsSb at room temperature.