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Abstract
We present a highly diagonal “split-well resonant-phonon” (SWRP) active region design for GaAs/Al0.3Ga0.7As terahertz quantum cascade lasers (THz-QCLs). Negative differential resistance is observed at room temperature, which indicates the suppression of thermally activated leakage channels. The overlap between the doped region and the active level states is reduced relative to that of the split-well direct-phonon (SWDP) design. The energy gap between the lower laser level (LLL) and the injector is kept at 36 meV, enabling a fast depopulation of the LLL. Within this work, we investigated the temperature performance and potential of this structure.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Quantum cascade lasers (QCLs) were first demonstrated in 1994 [1], and since then proved to have many applications in a variety of fields, including, among others, communication [2], medicine [3,4], security [5], chemical analysis of proteins [6], and high-resolution measurements [7]. Particularly, mid-IR QCLs demonstrated high output power and continuous wave (CW) operation [8]. However, terahertz (THz) QCLs are the ones that have especially awakened curiosity among the scientific communities. Working in the THz region allows several applications otherwise unreached in quantum technologies, and in the last few years significant progress was achieved in THz-QCLs’ performance [9–16]. Although THz-QCLs have a lot of potential, since they were first demonstrated in 2002 [17], their use has been restricted due to lack of portability. The requirements for cooling THz-QCLs prevent the laser from being a compact and portable system, confining THz-QCLs to the laboratory environment. Therefore, raising the maximum operating temperature (Tmax) is the main goal in the field.
Since 2012 [18], there was relatively little progress in the temperature performance of these devices, until 2019 [19]. After this, a new Tmax of ${\sim} $250 K was achieved and demonstrated [13], enabling the launch of the first portable THz-QCL. Although portable, this device, still required thermoelectric cooling, and the Tmax was reached in pulsed operation. Moreover, up to date, other groups did not report similar Tmax values, indicating how big of a challenge this represents.
To keep improving the temperature performance of THz-QCLs, we need to better understand the physics and obstacles that were overcome over the years to reach the developments that led to the Tmax ${\sim} $250 K [13].
The main mechanism that limits the operation temperature of standard vertical-transition THz-QCLs, is the thermally activated longitudinal optical (LO) phonon scattering from the upper laser level (ULL) to the lower laser level (LLL) [20]. The main strategy used to minimize the thermally activated LO phonon scattering is designing highly diagonal structures [21,22]. Other mechanisms limiting THz-QCLs are thermally activated leakage of charged carriers into the continuum [22], and into excited bound states [23,24]. High barriers (30% Al) combined with thin wells proved to push the excited and continuum states to higher energies and suppress these leakage paths [23,25].
Carefully engineered devices showed clear negative differential resistance (NDR) behavior in the current voltage (I-V) curves all the way up to room temperature [23,25,26]. A clear NDR region means that the electron transport occurs only within the laseŕs active subbands, meaning all thermally activated leakage paths for electrons were suppressed. This way, a clean n-level system was obtained, n being the number of active subbands [23,25,26]. Taking this into account, the strategy has been to design THz-QCLs with as close as possible to clean n-level system, especially at elevated temperatures. This strategy of achieving a clean n-level system, led to the highest recorded Tmax [13] and this is the strategy used in this research.
As indicated, NDR at room temperature was observed not only in the two well (TW) design from Ref. [13], but also in designs from Refs. [23,25,26]. Despite this, QCLs from Refs. [23,25,26] did not show any improvement in their temperature performance. This was attributed to various reasons. Specifically in the split-well direct-phonon (SWDP) design [26], the effects that interface roughness (IFR) scattering [27–34] and that the doping profile engineering [35–40] have on the structures are still being investigated. Further research should be done in the different schemes to understand which conditions have to be altered to achieve an improvement on the temperature performance.
As mentioned before, in previous works, a SWDP scheme, supporting a clean 3-level system, was studied [16,26,32,35]. The design includes a thin intrawell barrier, that pushes the excited states to higher energies. Similar variations of it have been proposed since, such as the integration of a mini-step potential barrier [41]. By adjusting the thin intrawell barrier thickness the energy separation between LLL and the ground state can be tuned to match the exact LO-phonon scattering energy (36 meV) [26].
In this experimental work, we study a novel highly diagonal split-well resonant-phonon (SWRP) scheme (oscillator strength of f∼0.22), based on the same design principles as the SWDP design previously described. In this design we keep the advantages of the SWDP designs described before with the added advantage of a reduced overlap between doped region and active laser states. The large overlap of the doping profile with the active laser states in direct-phonon schemes results in enhanced gain broadening and is assumed to prevent significant improvements of the temperature performance of direct-phonon schemes [26,35]. Moreover, due to the high diagonality of the design, thermally activated LO-phonon scattering from the ULL to the LLL was significantly reduced in our SWRP structure. In highly diagonal schemes, leakages both to excited states and to the continuum are more likely because of the longer ULL lifetime. However, we accomplished a clean-n level system, meaning we were able to entirely overcome these leakage paths. This is verified by the NDR signature in the I-V curves presented below. Designs similar to this were earlier demonstrated, however, only with vertical transition [42].
In our SWRP design, we keep the energy separation between the LLL and the injector at 36 meV, allowing the fastest depopulation of the LLL [43,44]. Schemes such as the one described in Ref. [13] proved to achieve a high Tmax with a larger separation than 36 meV. A larger separation could potentially diminish the thermal backfilling, but in our design making a larger separation would be very challenging, as it would mean further thinning the already very thin intrawell barrier. Also, it was shown in former research that thermal backfilling should still not be a dominant limiting mechanism [45].
As can be seen in Fig. 1, the structure is based on four subbands in each module (all other levels are considered parasitic). The LLL is a doublet (levels 2 and 3 in the scheme) where the resonant tunnelling is very strong with an anticrossing of ${\sim} $4.7 meV. The depopulation of the doublet into the injector level (level 1 in the scheme) displays a resonant phonon scattering scheme [46]. The ULL (level 4 in the scheme) is aligned with the injector of the former module where resonant tunneling occurs with an anticrossing of ${\sim} $2.06 meV (Table 2). The radiative transition occurs between the ULL and the LLL doublet (levels 2 and 3 in the scheme). Level 6 in the scheme, the relevant excited state, is ∼121 meV above the ULL as can be seen in Fig. 1 and in Table 1. The first excited state (level 5 in scheme) is lower and closer to the ULL but there is no overlap between the two, as they are separated by two potential barriers. Even the ULL of the following module (not shown) is at a lower energy than level 5, indicating negligible intermodule leakage.
Fig. 1. Band diagram of one period of the SWRP THz-QCLs with Al0.3Ga0.7As barriers, corresponding to energy levels of Device VB0846 with doping level of ∼3 × 1010 cm−2. More details regarding the design and device parameters can be found in Table 1 and Table 2.
Table 1. Main nominal design parameters and device data.
Table 2. Device parameters and performance.
The thin intrawell barrier allows an energy gap between the LLL and injector of 36 meV (Table 1). The design is a highly diagonal GaAs/Al0.3Ga0.7As SWRP THz-QCL with an oscillator strength ƒ∼0.22 of the radiative transition. The barriers were designed with 30% Al as this was the composition utilized in previous works with good results [13,23,25,26]. The doping is 2.31 × 1016 cm−3 in the quantum wells by the sides of the thin barrier, an integral value of ${\sim} $ 3 × 1010 cm−2 per module. Due to the decreased overlap between the doped region and the active laser states, farther improvement of the laser’s performance could be expected by optimizing the doping profile and its spatial location [47]. In total there are 266 periods in the device, a total thickness of ${\sim} $10 $\mu m$, and it was designed to lase at 15.0 meV (∼ 3.6 THz). The metal-metal waveguide was made of 100 Å Ta / 2500 Å Au (Table 1) [48]. The top contact layer was removed, and the bottom contact is 50 nm thick GaAs with doping of 5 × 1018 cm−3. The device was fabricated by dry etching. The MBE wafer is labeled VB0846, more details regarding the design, more fabrication details and device parameters can be found in Tables 1 and 2. The MBE growth conditions must be highly precise for this design to achieve the alignment of levels before described. As explained, in this scheme, not only the injector must be aligned with the ULL but also the two LLLs must be aligned. The intrawell barrier that determines the energy difference between the LLL-doublet and the injector is very thin. Any fluctuations in the thickness of this layer could affect the alignment obtained. Also, if we were to increase the doping density, possible band bending may affect further the delicate subband alignment. The challenges to precisely grow the scheme may also be the reason behind the lasing output power instability that this structure suffers from as described below.
2. Results and discussion
Pulsed light-current density (L-I) measurements and spectrum of device VB0846 are shown in Fig. 2. A lasing frequency of ∼4 THz (∼16.5 meV) was observed (Table 2). The maximum operating temperature was found to be ∼131 K. With the same barrier composition, and similar lasing frequency of ∼4 THz, design VB0843 from Ref. [32] reached a Tmax of ∼120 K (a detailed comparison of both these devices can be found in Tables 1 and 2). If it weren’t for the lasing output power instability issues (as described in Ref. [32]) we would expect even higher values of Tmax in both these designs and even farther improvement of Tmax in the SWRP design. A comparison to either design VB0837 from Ref. [26] or VB0847 from Ref. [32] would be irrelevant, as different composition barriers affect the performance of the QCL [32]. Moreover, both these lasers lased at ∼ 2.4 THz and ∼2.6 THz, respectively, as opposed to ∼ 4 THz in the SWRP design, and this also would lead to different laser performance.
Fig. 2. Pulsed light–current (L-I) measurements of Device VB0846 with its lasing spectra as inset. More details on this structure can be found in Table 1, Table 2, and Fig. 1.
As can be seen from the plot, the curves are not smooth. We attribute the noisy curves to the lasing output power instability of the laser. Such instability in split-well designs was attributed to the lack of leakages [32]. Not only fluctuations in the L-I curve can be seen (Fig. 2), but also, a fast drop of the output power close to Tmax. Other QCL designs (not based on a split-well) in the same measurement batch showed a smooth L-I curve. Hence, we can assume there is no problem in the measurement procedure but rather an inherent limitation in these designs. If we further observe Fig. 2, we can see that for curves plotted for temperatures higher than ∼89 K, the plot goes backwards on the current density axis. The loop seen in the graphs is a direct result of the NDR, meaning there is still lasing when there is NDR. The Jth is measured at the beginning of the loop when the lasing starts. At Jth, the light output starts to increase and then goes backwards when reaching NDR because the current density decreases. The fast drop in the output power occurs at temperatures over 109 K. These issues will be further addressed in the analysis of the maximum current density (${J_{max}}$) curve.
The I-V curves in Fig. 3 shows a clean NDR signature up to room temperature. This indicates that no leakage channels were activated even at room temperature and that the active laser levels are isolated. There are no significant fluctuations in the I-V curves like the ones reported in SWDP designs [32]. However, despite the observation of NDR, lasing was demonstrated only up to ∼131 K.
Fig. 3. Current voltage (I-V) curves of Device VB0846 at low, around maximum operating, and room temperatures. The maximum operating (lasing) temperature (~131 K) is indicated.
In Fig. 4(a) we present the threshold current versus temperature of the device. As shown, ${J_{th}}$ rises exponentially and its behavior can be well characterized by the standard model of ${J_{th}} = {J_{1 + }}{J_0}{e^{\frac{T}{T_0}}}$. The exponential rise is also an indication of the suppression of leakage to continuum [22]. Jth at low temperatures in the SWRP design is very close to Jth of device VB0843 [32] (Table 2), indicating the similarities between both these devices at low temperatures, particularly regarding the different broadening mechanisms and lateral leakage magnitudes.
Fig. 4. (a) Threshold current versus temperature of device VB0846. (b) Activation energy extracted from the laser’s maximum output power (Pmax) vs. temperature data, for device VB0846.
The curve shows a T0 of ∼ 237 K. For comparison, in the design from VB0843 [32] T0 was ∼ 234 K (Table 2). In both these devices T0 is similar because the thermally activated leakage channel from the ULL to the LLL behaves in a like manner, as they have same lasing frequency of ∼4 THz. Likewise, in the TW design of Ref. [13] where the lasing frequency was also ∼4 THz, T0 was ∼260 K. In design VB0837 [26] the value of T0 is higher due to its lower lasing frequency (∼2.43 THz), meaning the activation energy of the non-radiative ULL to LLL transition is higher.
Additionally, even though Jth at low temperatures in the SWRP design is like Jth of device VB0843 (Ref. [32]), Jmax is higher in the SWRP by ∼100 A/cm2 (Table 2). This large difference in the dynamic range of the devices should lead to a much higher improvement of Tmax than the ∼11 K improvement we observed. The fact that the difference in Tmax is not that big between both schemes is another prove of the noticeable effect the output power instability has on these designs, and the challenge that reaching an ideal alignment represents.
To identify the physical mechanism limiting the temperature performance of our THz-QCL design we use the method of Ref. [20] to analyze the light output power (${P_{out}}$) vs temperature data. The activation energy, (${E_a})$, was extracted by the best fit to the data using Arrhenius plots using the formula $\textrm{ ln}\;\left( {1 - \frac{{{P_{out}}(\textrm{T} )}}{{{P_{out}}\;\textrm{max}}}} \right) \approx \ln (a )- \frac{{{E_a}}}{{KT}}$, where a is a constant. Although the curves presented in previous works had a better fit and were smoother, this is the best fit for the current design. The experimental curve and activation energy are shown in Fig. 4(b). The activation energy extracted from Fig. 4(b) is ∼19 meV (as expected from the measured optical transition, Table 1), indicating the thermally activated LO-phonon relaxation from the ULL to the LLL. Thermally activated leakage channels through excited states are sufficiently suppressed according to this result.
In Fig. 5, ${J_{max}}$ as a function of temperature is plotted all the way up to room temperature. The analysis of the measured ${J_{max}}$ versus temperature in clean n-level systems is a powerful tool that helps us understand the dynamics of the current [26,35]. Assuming the resonant tunneling of the LLL doublet is very strong and does not limit ${J_{max}}$, we can relate to our system as an effective three-level system and describe it by the Kazarinov-Suris formula [26,49]:
Fig. 5. Maximum current density versus temperature of Device VB0846. The three regions defined in the text and maximum operating temperatures –Tmax, (black arrow), are marked on the graph.
As we can see from the plot (Fig. 5), the graph is not monotonic, and we can identify three different regions that correspond to: the strong coupling regime under lasing conditions (Region 1 in Fig. 5), the strong coupling regime under non-lasing conditions (Region 2 in Fig. 5) and the weak coupling regime (Region 3 in Fig. 5).
Region 1 in the graph, corresponds to the strong coupling regime under lasing conditions. Here, ${J_{max}} \sim \frac{1}{\tau } \approx \frac{1}{{{\tau _{st}}}}$ ($\frac{1}{{{\tau _{st}}}}$ being the stimulated emission rate), meaning that the maximum current density decreases while the temperature increases because the transport is strongly limited by the ULL lifetime [50]. The sudden drop observed indicates the termination of lasing immediately and was also seen in device VB0843 [32]. This behavior is attributed to the instability of the output power of the laser [32].
Region 2 in the graph, corresponds to the strong coupling regime under non-lasing conditions. This region starts at around ${\sim} $115 K. According to this result, if lasing is achieved above this temperature, it is strongly unstable. In this region, ${J_{max}}$ will start to increase because the dominant process is the non-radiative scattering rate, which increases as the temperature increases ${J_{max}} \sim \frac{1}{\tau } \approx \frac{1}{{{\tau _{nr}}}}$. Due to this behavior, there is a significant raise of the ${J_{max}}$ as presented in the figure. The nonradiative lifetime ${\tau _{nr}}$ will now affect the ULL lifetime. This behavior will continue until the current is limited by the resonant tunneling between the injector and the ULL, at around ${\sim} $190 K. Similar behavior was observed for device VB0843 from Ref. [32] that has the same lasing frequency of ∼ 4 THz. However, compared to the SWDP in Ref. [26], the increase of Jmax in this region is of a much higher magnitude. The reason behind it, is the faster non-radiative thermally activated scattering from the ULL to the LLL in the SWRP due to its larger lasing frequency.
Above ${\sim} $190 K is the “weak” coupling regime (Region 3 in the graph). ${J_{max}}$ will start to decrease again with the temperature since ${J_{max}} \sim {\tau _\parallel }$ and the dephasing time between the injector and ULL (i.e., ${\tau _\parallel }$) declines as the temperature increases. As can be seen from the curves, the transport enters this region at a relatively early stage, meaning this structure is governed by dephasing at temperatures above ${\sim} $190 K. Similar behavior was also observed in simulations [15].
3. Conclusion
In conclusion, we experimentally demonstrated a SWRP scheme for THz-QCLs. The overlap between the doped region and the active laser states in this design is reduced relative to that of the SWDP design. The SWRP scheme allows efficient isolation of the carriers from the continuum and excited states, meaning it supports a clean 4-level system. We suggest further investigation of this design, by comparing design parameters with other designs supporting clean n-level systems. Considering these systems are not limited by thermal leakage, detailed comparison should be the key for further improvement. We believe that this design should serve an excellent platform to study the temperature performance of the THz-QCLs.
Funding
Israel Ministry of Science and Technology; Israel Science Foundation (ISF).
Acknowledgments
The authors would like to acknowledge the Israel Science Foundation (ISF) and the Israel Ministry of Science and Technology for their grants. The data of this research was taken at Massachusetts Institute of Technology (MIT). This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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