Near‐Field Thermal Profiling and 3D Anisotropic Thermal Analysis of Quantum Cascade Lasers

The development of a scanning near‐field optical microscopy (SNOM) method with high temperature and spatial resolution to probe the thermal behavior of quantum cascade lasers (QCLs) is reported. Specifically, thermal profiling of InGaAs/InAlAs/InP buried heterostructure (BH) mounted epi‐layer side down QCLs is performed. The findings are verified by 3D anisotropic thermal analysis of QCLs with anisotropic thermal conductivities in the superlattice active region. Good agreement is observed between the simulated and the measured time constants. Within this design, various realistic device configurations, such as overhanging the laser chip on the submount and placing different dielectric coatings on the front facet, are considered. Analytical studies of the steady‐state thermal performance of QCL arrays compared to an isolated QCL are demonstrated for high‐power requirements with minimal thermal damage and future application in spectroscopic devices.


Introduction
Quantum cascade lasers (QCLs) are unipolar light sources wherein intersubband transitions of electrons occur in repeated layers of superlattices composed of semiconductor gain media. [1] The emission wavelength of QCLs is determined by the superlattice layer thickness and the material composition. Therefore, it can be tuned over a wide range in a given material system. [2] The typical operation wavelength of QCLs is in the mid-infrared (3.5-24 μm) and terahertz (1.2-4.9 THz). [3,4] Because the vibrational modes of many chemical compounds lie in the wavelength range of 3 to 15 μm, mid-infrared QCLs have found various applications in biological and chemical warfare agent detection [5,6] and pollutant detection, [7] and noninvasive medical diagnostics. [5] They can also be used in optical wireless communication: [8] the "terahertz gap" appears due to the absence of radiation sources in this frequency range, and THz QCLs fill the terahertz gap and have been used in imaging and spectroscopy. [9][10][11] However, the low thermal conductivity of QCL's multilayer superlattice gain medium and the ample operational electrical power cause significant self-heating in QCLs, [12,13] which, over time, results in a rise in lasing threshold current, [6] a decrease in output power, [14] and even device failure. [15] Therefore, to better understand QCL's failure mechanism, thermal analysis and monitoring are necessary for designing QCLs with optimal performance. Techniques for temperature monitoring include microphotoluminescence, [16] Raman spectroscopy, [17] thermoreflectance spectroscopy, [18] lock-in IR Thermography, [19] and infrared scanning near field optical microscopy (IR-SNOM). [20] For example, Raman spectroscopy as a non-contact thermometer was used to study output facet heating in an uncoated high-power continuous-wave QCL emitting at 8.5 μm. [17] A comparison of the spatial and temperature resolutions of these techniques can be found in Ref. [21] In this work, we report on developing an IR-SNOM technique with high temperature and spatial resolutions, both achieved by opening a subwavelength aperture at the tip of an IR fiber optic probe. We apply this technique to study the time constants in InP/InAlAs/InGaAs buried heterostructure (BH) mounted epi-layer side down QCLs--a geometry reported to have the best thermal performance by Pieŕscínska et al. [22] To verify the experimental findings, we develop an anisotropic 3D model to study steady-state and DOI: 10.1002/pssa.202200453 The development of a scanning near-field optical microscopy (SNOM) method with high temperature and spatial resolution to probe the thermal behavior of quantum cascade lasers (QCLs) is reported. Specifically, thermal profiling of InGaAs/InAlAs/InP buried heterostructure (BH) mounted epi-layer side down QCLs is performed. The findings are verified by 3D anisotropic thermal analysis of QCLs with anisotropic thermal conductivities in the superlattice active region. Good agreement is observed between the simulated and the measured time constants. Within this design, various realistic device configurations, such as overhanging the laser chip on the submount and placing different dielectric coatings on the front facet, are considered. Analytical studies of the steady-state thermal performance of QCL arrays compared to an isolated QCL are demonstrated for high-power requirements with minimal thermal damage and future application in spectroscopic devices. transient heat transfer in these QCLs. Furthermore, we consider various realistic device structures, such as the laser chip overhanging the submount, with different dielectric coatings placed on the front facet of the active region. Lastly, we consider temperature distribution across QCL arrays for beam-combining applications.

Results and Discussion
In our heat transfer simulations, we used the 3D structure of the BH-mounted epi-layer side down QCL, as shown in Figure 1a. The width, length, and total thickness of the QCL under consideration are 300, 100, and 209.3 μm, respectively. The relatively short cavity length of 100 μm was chosen to reduce simulation time without affecting simulation outcomes. The active region is labeled as "core", consisting of InGaAs/AlInAs superlattice, and is a trapezoidal-shaped ridge waveguide with upper and lower widths of 5.5 and 4.5 μm, respectively. The thickness and length of the core are 1.7 and 100 μm, respectively. InP is used as both cladding and substrate, and copper is used as a heatsink. To extract heat from the core, multiple layers of titanium, gold, nickel, and platinum are placed below the core.
To study the steady-state thermal behavior of QCL during operation, we perform 3D anisotropic heat transfer analysis using the finite element method (COMSOL Multiphysics) to determine temperature distribution T by solving the heat equation where k, ρ, and C p are the thermal conductivity, density, and specific heat capacity of the material, and Q is the internally generated thermal power density that is a function of driving current. Note that the time derivative in Equation (1) is zero in the steady state. In our analysis, a heat source with power density Q ¼ 2.2 Â 10 14 W m À3 is placed inside the core. [16] For the InGaAs/AlInAs superlattice, anisotropic thermal conductivities are considered, with in-plane values and a much lower cross-plane value K z ¼ 1 Wm À1 K À1 due to multiple superlattice interfaces in the z-direction. Isotropic thermal conductivities are used for all other layers. Lastly, thermally insulating boundaries are used for the top and side surfaces. An isothermal boundary held at 293.15 K is used at the bottom of the structure where the heat sink terminates. Values of thermal constants used in this work can be found in Ref. [23] Although the laser core should be aligned with the submount (Figure 1a), in practice, a precise alignment is impossible due to manufacturing variations in epi-down soldering. Because the "underhanging" condition in which the laser chip is embedded within the submount should be avoided and the precise position of the edge of the submount may not be well defined due to www.advancedsciencenews.com www.pss-a.com rounding or chipping, the laser core typically overhangs the submount by 20 to 30 μm, as shown in Figure 1b. Figure 1c shows that a large amount of heat flows from the core to the InP substrate, with a peak temperature of 366 K inside the core for the ideal case without overhanging (Figure 1a). In the practical case, i.e., with the laser chip overhanging on the submount (Figure 1b), the peak temperature increases with increasing overhanging distance due to the misalignment between the laser chip and the metal heat sink, as shown in Figure 1d. The inset of Figure 1d shows the contour surface temperature (in transparent view) with a 30 μm overhanging distance, where the red line represents the outline of the contour surface, indicating that the heat flows from the core in both vertical and lateral directions.
To verify the simulated temperature distribution, we employ the IR-SNOM apparatus ( Figure 2) with high spatial and temporal resolutions by utilizing a subwavelength aperture at the apex of the tapered optical fiber that collects the thermal signal.
The QCL current driver has a rise time (defined as the time from 10% maximum current to 90% maximum current) of 2.6 μs and a fall time of 3.7 μs (defined as the time from 90% maximum current to 10% maximum current). To detect the wide infrared  www.advancedsciencenews.com www.pss-a.com spectral range (3-30 μm), a silver halide optical fiber is used to collect signals from QCL. [20,24] The silver halide fiber is created by first immersing an optical fiber in a KCN solution to taper to a sharp point, then by coating the sides with silver such that signals from the fiber's sides are blocked. Finally, the fiber tip is lightly polished against a fine-grain polishing paper to open an aperture. The modulation of the IR signal is achieved either by an optical chopper or by pulsed QCL. The thermal signal generated by the QCL is measured through the IR optical fiber, and the collected signal is focused on the mercury-cadmium-telluride (MCT) detector. Since the QCL is operated in pulsed mode, a pulsed signal from the function generator is used as the lock-in amplifier's reference signal. To generate a 2D thermal map, the signal after the lock-in amplifier is passed through an analog-to-digital converter (ADC) and is subsequently mapped to the XY position data. A detailed description of the measurement setup is provided in our previous work. [21,25] The QCL under test has a threshold current of 660 mA and a lasing wavelength of 8.3 μm at 25°C. Because both the optical and thermal signals from the QCL are in the wavelength range of 2-10 μm, it is crucial to separate the thermal signal from the optical one. To do so, one can intentionally suppress the optical signal by either operating the QCL below the lasing threshold or mechanically roughening the rear facet of the QCL. Because the contribution of the subthreshold electroluminescence to the overall measured IR signal is minimal far below the threshold, [25] we operate the QCL at 100 mA, far below its threshold current of 660 mA.
The measured time-dependent thermal signal is presented in Figure 3a. The repetition rate of the driving pulse (5 kHz) and the small aperture size of the fiber probe (<20 μm) enable the fiber tip to collect a localized signal of Joule heating inside the core, which is responsible for the initial rise of the thermal signal. Here, the power of the thermal signal is computed by multiplying the driving current by the voltage drop across the QCL measured by an oscilloscope.
The thermal signal is converted to temperature according to Stefan-Boltzmann law where σ is the Stefan-Boltzmann constant. The temperature in the pulse-off state is set to 293 K, and the temperature in the pulse-on state is set to 366 K, which is based on thermal simulation results. As shown in Figure 3a, the measured temperature where C p ¼ 0.443 J K À1 is the total heat capacity of the QCL core, P(t) is the power dissipated in the QCL as a function of time (blue line in Figure 3a), T s is the set temperature in the pulse-off state (293 K), t is time, T is the temperature at the front facet (red line in Figure 3a), and τ is the time constant. Fitting to the measured temperature curve yields a time constant of τ ¼ 2.7 μs. Note that this time constant is calculated with the knowledge of the current rise/fall behavior of the QCL driver, so the time constant only describes the thermal component. Furthermore, for far below threshold driving currents such as the 100 mA used in our measurements, the rising edge of the IR signal fits the basic thermal model very well. [25] Therefore, the contribution from subthreshold emission, which would be most apparent in the rising part of the pulse, is further confirmed to be negligible.
To verify the extracted time constant, transient simulations are performed with the same simulation conditions as the steadystate simulations described earlier ( Figure 3b) and a time constant of 0.7 μs, which is on the same order of magnitude as the measured one, is obtained. The discrepancy between the measured and simulated time constant values is likely due to the slight difference in material compositions and QCL's geometry. Figure 3c shows the experimentally obtained 2D thermal image at the front facet of the QCL operated with a pulse rate of 40 kHz and a driving current of 100 mA, in agreement with the simulated steady-state temperature distribution of Figure 3d.
In terms of optical cavity design, anti-reflection coatings are used on the facets of the laser core to engineer the output power [26] and tune the emission wavelength. [27,28] In the case without overhanging, Figure 4a shows that the dielectric coating helps reduce the front facet temperature due to the higher thermal conductivity of the coating materials compared to air. Still, the effect diminishes as the coating thickness increases. Here, we consider common coatings including Ge, ZnS, ZnSe, Al 2 O 3 , and SiO 2 . Ge provides the best thermal performance of all considered materials due to its highest thermal conductivity. With Ge coating, while the peak temperature does not change significantly as long as Ge is thicker than 0.1 μm, the facet reflectivity varies periodically with the coating thickness. [29] Because facet reflectivity affects a cavity mode's Q factor, the dielectric coating thickness can be used to tune QCL's output power level and single-mode operation range. [28] In the case of overhanging, Figure 4b-f shows the peak temperature, which is always located at the center of the core, as a function of coating thickness and overhanging distance. As expected, a longer overhanging distance corresponds to an increased peak temperature, as the laser core becomes more misaligned with the heat sink.
In applications where high laser power is needed, although increasing the QCL core width can increase output power, its thermal performance will significantly degrade, especially under continuous-wave (CW) current injection due to more severe selfheating. To this end, QCL arrays were introduced to satisfy the high-power requirement with minimal thermal damage. Several laser cores are placed equal-distance apart for efficient heat extraction. [30][31][32] However, because of thermal cross-talk, suboptimal beam quality in QCL arrays at high output power can prevent their CW operation. [31] We thus analyze the thermal Figure 5. a) Schematic diagram of a QCL array with two cores. b) Temperature distribution of a five-core QCL array with 1.5 μm distance between cores (DBC). c) Peak temperature inside the QCL array as a function of DBC between central cores (green line) and an isolated QCL (red line). d) The temperature difference between core 1 and 3 as a function of DBC.
www.advancedsciencenews.com www.pss-a.com behavior of QCL arrays and compare their performance with an isolated QCL. A schematic diagram of a QCL array with two cores is shown in Figure 5a, with a total length and width of 100 and 300 μm, respectively. The distance between cores is denoted as DBC. Similar to the isolated QCL analysis, a heat source with 2.2 Â 10 14 W m À3 power density is placed inside each core. All simulation conditions are the same as those in the isolated QCL, except that no coating is placed on the facets. The temperature distribution of a five-core QCL array with a DBC of 1.5 μm is plotted in Figure 5b, depicting significant thermal crosstalk due to the small 1.5 μm spacing between cores and that the center core (core 3) is most heated. To reduce thermal crosstalk while minimally increasing the device footprint, instead of uniformly increasing DBC, [33] we only increase DBC between central cores (cores 2, 3, and 4) while keeping DBC at 1.5 μm between outer cores (cores 1 and 2, and cores 4 and 5), which also circumvent the nonuniform heating. Figure 5c shows that the peak temperature, which resides in core 3, decreases as a function of DBC between central cores. In comparison, the red line in Figure 5c indicates the peak temperature in the isolated QCL when the laser chip does not overhang on the submount. We observe that even at 15.5 μm DBC between central cores, the peak temperature of the array is 20 degrees higher than that in an isolated QCL. Figure 5d shows the temperature difference between the center (core 3) and edge (core 1) cores, ΔT peak13 . By increasing DBC, the temperature difference between core 3 (most heated) and core 1 (least heated) decreases as the overall temperature drops inside the structure.

Conclusion
In conclusion, our experimental and theoretical work shows the thermal time constant of the core in the microsecond range. By analyzing the effect of front facet dielectric coating, laser core width, and overhanging distance, we provide guidelines for future QCL design for optimal thermal performance. For example, using Ge coating and a short overhanging distance leads to good thermal performance. Lastly, to achieve high output power without significant self-heating, the study of the steady-state temperature distribution in QCL arrays provides an understanding of the means to achieve high output power without substantial self-heating.