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Thermal conductivity tensors of the cladding and active layers of interband cascade lasers Chuanle Zhou, Boya Cui, I. Vurgaftman, C. L. Canedy, C. S. Kim, M. Kim, W. W. Bewley, C. D. Merritt, J. Abell, J. R. Meyer, and M. Grayson Citation: Applied Physics Letters 105, 261905 (2014); doi: 10.1063/1.4905279 View online: http://dx.doi.org/10.1063/1.4905279 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/26?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Type-I interband cascade lasers near 3.2μm Appl. Phys. Lett. 106, 041117 (2015); 10.1063/1.4907326 Thermally activated leakage current in high-performance short-wavelength quantum cascade lasers J. Appl. Phys. 113, 134506 (2013); 10.1063/1.4798358 Microprobe photoluminescence assessment of the wall-plug efficiency in interband cascade lasers J. Appl. Phys. 104, 046101 (2008); 10.1063/1.2968209 Influence of InAs, AlAs δ layers on the optical, electronic, and thermal characteristics of strain-compensated Ga In As ∕ Al In As quantum-cascade lasers Appl. Phys. Lett. 91, 161111 (2007); 10.1063/1.2798061 Thermal modeling of Ga In As ∕ Al In As quantum cascade lasers J. Appl. Phys. 100, 043109 (2006); 10.1063/1.2222074
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APPLIED PHYSICS LETTERS 105, 261905 (2014)
Thermal conductivity tensors of the cladding and active layers of interband cascade lasers Chuanle Zhou,1 Boya Cui,1 I. Vurgaftman,2 C. L. Canedy,2 C. S. Kim,2 M. Kim,3 W. W. Bewley,2 C. D. Merritt,2 J. Abell,2 J. R. Meyer,2 and M. Grayson1,a) 1
Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60208, USA Code 5613, Naval Research Laboratory, Washington, DC 20375, USA 3 Sotera Defense Solutions, Inc., Crofton, Maryland 21114, USA 2
(Received 2 December 2014; accepted 16 December 2014; published online 30 December 2014) The cross-plane and in-plane thermal conductivities of the W-active stages and InAs/AlSb superlattice optical cladding layer of an interband cascade laser (ICL) were characterized for temperatures ranging from 15 K to 324 K. The in-plane thermal conductivity of the active layer is somewhat larger than the cross-plane value at temperatures above about 30 K, while the thermal conductivity tensor becomes nearly isotropic at the lowest temperatures studied. These results will improve ICL C 2014 performance simulations and guide the optimization of thermal management. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4905279] While interband cascade lasers (ICLs)1 emitting in the midwave infrared typically operate at room temperature, their continuous wave (cw) performance degrades rapidly once the injection current becomes high enough to heat the ridge.2 Thermal management is therefore critical, and the magnitude of the heating is quite sensitive to the thermal impedance of each functional layer in the ICL. The primary contributors to the thermal resistance are the W-active stages and the short-period InAs/AlSb superlattice (SL) optical cladding layers. It follows that a more accurate knowledge of how the thermal conductivity tensors of those two regions vary with temperature would improve the accuracy of ICL simulations and guide the optimization of the device performance. Although we previously measured the cross-plane3 and in-plane thermal conductivities of these most relevant ICL regions at room temperature,4 it is the temperature dependence that is critical for proper thermal management and no temperature dependent data were obtained at that time. In the present work, we have used the 2-wire 3x method5–7 to measure the in-plane and cross-plane thermal conductivities at a series of temperatures ranging from 15 K to 324 K. Furthermore, we apply our recently developed error analysis technique for the 3x method to all data collected here, to provide the best estimate of the fidelity of these measurements.8 Measurements were performed on both a W-active sample and an InAs/AlSb SL cladding sample. The active sample comprised 20 repeats of a typical ICL stage (e.g., see Fig. 3 of Ref. 1) consisting of the InAs/GaInSb/InAs/AlSb “W” electron and hole active quantum wells, the GaSb/ AlSb/GaSb/AlSb hole injector, and the InAs/AlSb electron injector with 6 quantum wells having chirped InAs thicknesses. The total thickness of the 20 stages was 0.78 lm. The sample also contained a 20-nm-thick nþ-InAs cap layer on top and a 63 nm InAs/AlSb SL transition layer that were grown on the n-GaSb substrate and 400 nm GaSb buffer a)
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0003-6951/2014/105(26)/261905/3/$30.00
layer. This structure is shown schematically as the inset of Figure 1. The cladding sample consisted of a 7-lm-thick (8 ML n-InAs/8 ML AlSb) SL layer and a 500 nm GaSb buffer layer grown on the n-GaSb substrate, as shown in the inset of Figure 2. For the sample processing, half of the W-active sample was left intact, while the other half was etched to a depth of 1 lm. The etch to that depth removed the cap, active, and transition layers, along with 0.14 lm of the GaSb buffer layer. Similarly, half of the cladding sample was left unetched, whereas the other half was etched to a depth of 7 lm. Then, plasma enhanced chemical vapor deposition (PECVD) was used to deposit a 70-nm-thick SiNx layer over the full area of both sample surfaces. Wide and narrow metal filaments were then deposited on both the etched and unetched halves of the samples. The width of the wide filaments should be much larger than the thickness of the measured thin film so the heat flow is mostly in the cross-plane direction for the cross-plane thermal conductivity characterization, whereas the width of the narrow filaments needs to be comparable to the thickness of the layer of interest to induce a large in-plane component of the heat flow for the in-plane thermal conductivity measurement. The thickness of the filaments are typically 200–300 nm, which can be neither very small to increase the roughness of the filament nor very large to dissipate heat at the side. The 4-point resistance of the filaments is 20–40 X, comparable independent of the filament width. Therefore, 200-nm-thick Au filaments of width W1 ¼ 30 lm and W2 ¼ 1.8 lm, patterned with photolithography and e-beam lithography, respectively, were deposited on the W-active sample, while 300-nm-thick Ni filaments of widths W1 ¼ 80 lm and W2 ¼ 7 lm, both patterned with photolithography, were deposited on the cladding sample. We used standard lock-in techniques to measure the samples residing in an Oxford variable temperature insert (VTI) helium gas flow cryostat, at temperatures ranging from 324 K down to 15 K. The temperature coefficients of the filaments were measured by slowly sweeping at a rate of
105, 261905-1
C 2014 AIP Publishing LLC V
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261905-2
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Appl. Phys. Lett. 105, 261905 (2014)
FIG. 1. Cross-plane jyy (crosses) and in-plane jxx (dots) thermal conductivity of the 20-stage W-active layer. The gray crosses and dots are cross-plane and in-plane thermal conductivities reported previously for a 0.46 lm-thick W-active layer measured at the room temperature.4 The dashed lines are polynomial fittings of the data.
FIG. 2. Cross-plane jyy (crosses) and in-plane jxx (dots) thermal conductivity of InAs/AlSb cladding layer. The gray crosses and dots are cross-plane and in-plane thermal conductivity of the same layer reported previously for room temperature.4 The dashed lines are polynomial fittings of the data.
less than 2 /h, so as to insure that the filament and cryostat calibration thermometers were at the same temperature. The cross-plane thermal conductivity jyy of the thin film was measured from the differential 3x voltage between the wide filaments on the etched and unetched sides, according to the standard 3x method5–7 with error analysis.8 The GaSb buffer layer was assumed to have the same thermal conductivity as the GaSb substrate. The cross-plane thermal conductivity of the W-active layer (red crosses in Fig. 1) is 25% higher than for a 0.46-lm-thick W-active sample (gray cross in Fig. 1) that was measured by some of the present authors in a prior publication.4 The cross-plane thermal conductivity of the cladding layer (blue crosses in Fig. 2) matches our previous measurement at 300 K (Ref. 4) (gray cross in Fig. 2). The uncertainty of the temperature coefficient dominates the error in the cross-plane characterization, hence the need for the extreme slow thermal calibration protocol described above. We next used 3x voltage of the narrow filaments to fit the in-plane thermal conductivity jxx. First, the thermal conductivity tensor of the SiNx layer was fitted from the narrow filament on the etched side. Next, the cross-plane thermal conductivity of the W-active layer, the best fit thermal conductivities of the SiNx layer, and the isotropic GaSb substrate thermal conductivity were employed, along with an estimated thermal conductivity tensor for the W-active layer, to fit the voltage of the narrow filament on the unetched side. The resulting fits indicate that the in-plane thermal conductivity of the active stages is somewhat larger at temperatures above about 30 K, but that the thermal conductivity tensor approaches near isotropy at the lowest temperatures studied. The in-plane thermal conductivity of this thick W-active layer (red dots in Fig. 1) is more reliable than that of the thinner W-active layer measured previously at room temperature (gray dot in Fig. 1), because the narrow filament width of the present sample is more similar to the thickness of the W-active layer which harbors a larger inplane component of the heat flow. The error of the in-plane thermal conductivity results primarily from the uncertainties
in both the width of the filament and the cross-plane thermal conductivity.8 To allow for easy interpolation of the temperature dependent thermal conductivities and for easy extrapolation to higher and lower temperatures outside of the measured range, we fitted the measured temperature dependence to a Taylor expanded expression9,10 log10 j ¼ log10 jm B log10
T Tm
2
þ C log10
T Tm
3 (1)
to obtain the dashed lines in Figures 1 and 2. For the crossplane thermal conductivity of the W-active layer, the maximum thermal conductivity is jm ¼ 1.73 W/mK at Tm ¼ 121 K, with B ¼ 0.396 and C ¼ 0.229. For the in-plane thermal conductivity of that layer, the maximum is jm ¼ 6.55 W/mK at Tm ¼ 93.4 K, with B ¼ 1.19 and C ¼ 1.11. For the cross-plane thermal conductivity of the cladding layer, the maximum is jm ¼ 3.50 W/mK at Tm ¼ 109 K, with B ¼ 0.712 and C ¼ 0.196. For the in-plane thermal conductivity of that layer, the maximum thermal conductivity is jm ¼ 9.17 W/mK at Tm ¼ 109 K, with B ¼ 1.036 and C ¼ 0.010. One can now make some generalized observations about these results. The measured values of the cross-plane thermal conductivities are near the lower end of the range measured in other III–V semiconductor superlattices.11 The thermal conductivities in Figures 1 and 2 are more than one order of magnitude lower than for bulk semiconductors (InAs, GaSb, etc.), and approximately a factor of 2–3 below the lowest values reported for ternary alloys.3,4,11 This might be expected given their quaternary nature which results in a greater variety of interdiffusion alloy scattering at each interface, as well as given their disparity in constituent atomic masses from the lightest Al (atomic weight of 27.0) to the heaviest Sb (atomic weight of 121.8), enhancing the phonon scattering for interdiffused species. At room temperature, the precise sequence of the layers appears to have a relatively
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minor effect on the magnitude of the thermal conductivity, although the range of layer thickness variation is limited (with well thicknesses between 1.7 and 4.0 nm and barrier thicknesses between 1.2 and 2.3 nm). The thermal conductivities determined in this work are in reasonable agreement with the thermal-impedance area product deduced experimentally (and modeled using prior heat-transport simulations).4 In conclusion, we have measured the in-plane and cross-plane thermal conductivity tensors of typical W-active and cladding layers for interband cascade lasers. The characterization is more accurate than for a thinner active layer that was studied previously.4 The present measurements were carried out over a broad range of temperatures rather than only room temperature, and the present data at 300 K are consistent with the previous result. The characterization indicates a slight increase of the thermal conductivities down to 77 K, followed by a more rapid drop at lower temperatures. The in-plane thermal conductivities are consistently about a factor of 2.5–3.0 larger than the cross-plane thermal conductivities from room temperature down to 77 K. The temperature-dependent thermal conductivities were fit to an analytical power-law expression, so the full thermal conductivity tensors can be interpolated accurately for any given temperature. These data will improve the accuracy of future ICL performance simulations and guide the structural design and processing strategy for optimal thermal management. The work at Northwestern was supported by AFOSR Grant Nos. FA-9550-09-1-0237 and FA-9550-12-1-0169, the
Appl. Phys. Lett. 105, 261905 (2014)
Initiative for Sustainability and Energy at Northwestern (ISEN), and NSF MRSEC Grant No. DMR-1121262. Work at NRL was supported by ONR. 1
I. Vurgaftman, W. W. Bewley, C. L. Canedy, C. S. Kim, M. Kim, J. R. Lindle, C. D. Merritt, J. Abell, and J. R. Meyer, “Mid-IR type-II interband cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1435 (2011). 2 C. L. Canedy, J. Abell, C. D. Merritt, W. W. Bewley, C. S. Kim, I. Vurgaftman, J. R. Meyer, and M. Kim, “Pulsed and CW performance of 7stage interband cascade lasers,” Opt. Express 22, 7702 (2014). 3 T. Borca-Tasciuc, D. Achimov, W. L. Liu, G. Chen, H.-W. Ren, C.-H. Lin, and S. S. Pei, “Thermal conductivity of InAs/AlSb superlattices,” Microscale Thermophys. Eng. 5, 225 (2001). 4 C. Zhou, I. Vurgaftman, C. L. Canedy, C. S. Kim, M. Kim, W. W. Bewley, C. D. Merritt, J. Abell, J. R. Meyer, and M. Grayson, “Thermal conductivity tensors of the cladding and active layers of antimonide infrared lasers and detectors,” Opt. Mater. Express 3, 1632 (2013). 5 T. Borca-Tasciuc, A. R. Kumar, and G. Chen, “Data reduction in 3x method for thin-film thermal conductivity determination,” Rev. Sci. Instrum. 72, 2139 (2001). 6 D. G. Cahill, “Thermal conductivity measurement from 30 to 750 K: The 3x method,” Rev. Sci. Instrum. 61, 802 (1990); S.-M. Lee and D. G. Cahill, “Heat transport in thin dielectric films,” J. Appl. Phys. 81, 2590 (1997). 7 D. G. Cahill, M. Katiyar, and J. R. Abelson, “Thermal conductivity of aSi:H thin films,” Phys. Rev. B 50, 6077 (1994). 8 C. Zhou, G. Koblmuller, M. Bichler, G. Abstreiter, and M. Grayson, “Thermal conductivity tensor of semiconductor layers using two-wire 3x method,” Proc. SPIE 8631, 863129 (2013). 9 C. Zhou and M. Grayson, “Thermal distribution in high power optical devices with power-law thermal conductivity,” Proc. SPIE 8268, 82680V (2012). 10 C. Zhou, B.-M. Nguyen, M. Razeghi, and M. Grayson, “Thermal conductivity of InAs/GaSb Superlattice,” J. Electron. Mater. 41, 2322 (2012). 11 A. Sood, J. A. Rowlette, C. G. Caneau, E. Bozorg-Grayeli, M. Asheghi, and K. E. Goodson, “Thermal conduction in lattice-matched superlattices of InGaAs/InAlAs,” Appl. Phys. Lett. 105, 051909 (2014).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.105.125.19 On: Fri, 30 Jan 2015 16:32:38
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.105.125.19 On: Fri, 30 Jan 2015 16:32:38
APPLIED PHYSICS LETTERS 105, 261905 (2014)
Thermal conductivity tensors of the cladding and active layers of interband cascade lasers Chuanle Zhou,1 Boya Cui,1 I. Vurgaftman,2 C. L. Canedy,2 C. S. Kim,2 M. Kim,3 W. W. Bewley,2 C. D. Merritt,2 J. Abell,2 J. R. Meyer,2 and M. Grayson1,a) 1
Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60208, USA Code 5613, Naval Research Laboratory, Washington, DC 20375, USA 3 Sotera Defense Solutions, Inc., Crofton, Maryland 21114, USA 2
(Received 2 December 2014; accepted 16 December 2014; published online 30 December 2014) The cross-plane and in-plane thermal conductivities of the W-active stages and InAs/AlSb superlattice optical cladding layer of an interband cascade laser (ICL) were characterized for temperatures ranging from 15 K to 324 K. The in-plane thermal conductivity of the active layer is somewhat larger than the cross-plane value at temperatures above about 30 K, while the thermal conductivity tensor becomes nearly isotropic at the lowest temperatures studied. These results will improve ICL C 2014 performance simulations and guide the optimization of thermal management. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4905279] While interband cascade lasers (ICLs)1 emitting in the midwave infrared typically operate at room temperature, their continuous wave (cw) performance degrades rapidly once the injection current becomes high enough to heat the ridge.2 Thermal management is therefore critical, and the magnitude of the heating is quite sensitive to the thermal impedance of each functional layer in the ICL. The primary contributors to the thermal resistance are the W-active stages and the short-period InAs/AlSb superlattice (SL) optical cladding layers. It follows that a more accurate knowledge of how the thermal conductivity tensors of those two regions vary with temperature would improve the accuracy of ICL simulations and guide the optimization of the device performance. Although we previously measured the cross-plane3 and in-plane thermal conductivities of these most relevant ICL regions at room temperature,4 it is the temperature dependence that is critical for proper thermal management and no temperature dependent data were obtained at that time. In the present work, we have used the 2-wire 3x method5–7 to measure the in-plane and cross-plane thermal conductivities at a series of temperatures ranging from 15 K to 324 K. Furthermore, we apply our recently developed error analysis technique for the 3x method to all data collected here, to provide the best estimate of the fidelity of these measurements.8 Measurements were performed on both a W-active sample and an InAs/AlSb SL cladding sample. The active sample comprised 20 repeats of a typical ICL stage (e.g., see Fig. 3 of Ref. 1) consisting of the InAs/GaInSb/InAs/AlSb “W” electron and hole active quantum wells, the GaSb/ AlSb/GaSb/AlSb hole injector, and the InAs/AlSb electron injector with 6 quantum wells having chirped InAs thicknesses. The total thickness of the 20 stages was 0.78 lm. The sample also contained a 20-nm-thick nþ-InAs cap layer on top and a 63 nm InAs/AlSb SL transition layer that were grown on the n-GaSb substrate and 400 nm GaSb buffer a)
Electronic mail: [email protected]
0003-6951/2014/105(26)/261905/3/$30.00
layer. This structure is shown schematically as the inset of Figure 1. The cladding sample consisted of a 7-lm-thick (8 ML n-InAs/8 ML AlSb) SL layer and a 500 nm GaSb buffer layer grown on the n-GaSb substrate, as shown in the inset of Figure 2. For the sample processing, half of the W-active sample was left intact, while the other half was etched to a depth of 1 lm. The etch to that depth removed the cap, active, and transition layers, along with 0.14 lm of the GaSb buffer layer. Similarly, half of the cladding sample was left unetched, whereas the other half was etched to a depth of 7 lm. Then, plasma enhanced chemical vapor deposition (PECVD) was used to deposit a 70-nm-thick SiNx layer over the full area of both sample surfaces. Wide and narrow metal filaments were then deposited on both the etched and unetched halves of the samples. The width of the wide filaments should be much larger than the thickness of the measured thin film so the heat flow is mostly in the cross-plane direction for the cross-plane thermal conductivity characterization, whereas the width of the narrow filaments needs to be comparable to the thickness of the layer of interest to induce a large in-plane component of the heat flow for the in-plane thermal conductivity measurement. The thickness of the filaments are typically 200–300 nm, which can be neither very small to increase the roughness of the filament nor very large to dissipate heat at the side. The 4-point resistance of the filaments is 20–40 X, comparable independent of the filament width. Therefore, 200-nm-thick Au filaments of width W1 ¼ 30 lm and W2 ¼ 1.8 lm, patterned with photolithography and e-beam lithography, respectively, were deposited on the W-active sample, while 300-nm-thick Ni filaments of widths W1 ¼ 80 lm and W2 ¼ 7 lm, both patterned with photolithography, were deposited on the cladding sample. We used standard lock-in techniques to measure the samples residing in an Oxford variable temperature insert (VTI) helium gas flow cryostat, at temperatures ranging from 324 K down to 15 K. The temperature coefficients of the filaments were measured by slowly sweeping at a rate of
105, 261905-1
C 2014 AIP Publishing LLC V
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261905-2
Zhou et al.
Appl. Phys. Lett. 105, 261905 (2014)
FIG. 1. Cross-plane jyy (crosses) and in-plane jxx (dots) thermal conductivity of the 20-stage W-active layer. The gray crosses and dots are cross-plane and in-plane thermal conductivities reported previously for a 0.46 lm-thick W-active layer measured at the room temperature.4 The dashed lines are polynomial fittings of the data.
FIG. 2. Cross-plane jyy (crosses) and in-plane jxx (dots) thermal conductivity of InAs/AlSb cladding layer. The gray crosses and dots are cross-plane and in-plane thermal conductivity of the same layer reported previously for room temperature.4 The dashed lines are polynomial fittings of the data.
less than 2 /h, so as to insure that the filament and cryostat calibration thermometers were at the same temperature. The cross-plane thermal conductivity jyy of the thin film was measured from the differential 3x voltage between the wide filaments on the etched and unetched sides, according to the standard 3x method5–7 with error analysis.8 The GaSb buffer layer was assumed to have the same thermal conductivity as the GaSb substrate. The cross-plane thermal conductivity of the W-active layer (red crosses in Fig. 1) is 25% higher than for a 0.46-lm-thick W-active sample (gray cross in Fig. 1) that was measured by some of the present authors in a prior publication.4 The cross-plane thermal conductivity of the cladding layer (blue crosses in Fig. 2) matches our previous measurement at 300 K (Ref. 4) (gray cross in Fig. 2). The uncertainty of the temperature coefficient dominates the error in the cross-plane characterization, hence the need for the extreme slow thermal calibration protocol described above. We next used 3x voltage of the narrow filaments to fit the in-plane thermal conductivity jxx. First, the thermal conductivity tensor of the SiNx layer was fitted from the narrow filament on the etched side. Next, the cross-plane thermal conductivity of the W-active layer, the best fit thermal conductivities of the SiNx layer, and the isotropic GaSb substrate thermal conductivity were employed, along with an estimated thermal conductivity tensor for the W-active layer, to fit the voltage of the narrow filament on the unetched side. The resulting fits indicate that the in-plane thermal conductivity of the active stages is somewhat larger at temperatures above about 30 K, but that the thermal conductivity tensor approaches near isotropy at the lowest temperatures studied. The in-plane thermal conductivity of this thick W-active layer (red dots in Fig. 1) is more reliable than that of the thinner W-active layer measured previously at room temperature (gray dot in Fig. 1), because the narrow filament width of the present sample is more similar to the thickness of the W-active layer which harbors a larger inplane component of the heat flow. The error of the in-plane thermal conductivity results primarily from the uncertainties
in both the width of the filament and the cross-plane thermal conductivity.8 To allow for easy interpolation of the temperature dependent thermal conductivities and for easy extrapolation to higher and lower temperatures outside of the measured range, we fitted the measured temperature dependence to a Taylor expanded expression9,10 log10 j ¼ log10 jm B log10
T Tm
2
þ C log10
T Tm
3 (1)
to obtain the dashed lines in Figures 1 and 2. For the crossplane thermal conductivity of the W-active layer, the maximum thermal conductivity is jm ¼ 1.73 W/mK at Tm ¼ 121 K, with B ¼ 0.396 and C ¼ 0.229. For the in-plane thermal conductivity of that layer, the maximum is jm ¼ 6.55 W/mK at Tm ¼ 93.4 K, with B ¼ 1.19 and C ¼ 1.11. For the cross-plane thermal conductivity of the cladding layer, the maximum is jm ¼ 3.50 W/mK at Tm ¼ 109 K, with B ¼ 0.712 and C ¼ 0.196. For the in-plane thermal conductivity of that layer, the maximum thermal conductivity is jm ¼ 9.17 W/mK at Tm ¼ 109 K, with B ¼ 1.036 and C ¼ 0.010. One can now make some generalized observations about these results. The measured values of the cross-plane thermal conductivities are near the lower end of the range measured in other III–V semiconductor superlattices.11 The thermal conductivities in Figures 1 and 2 are more than one order of magnitude lower than for bulk semiconductors (InAs, GaSb, etc.), and approximately a factor of 2–3 below the lowest values reported for ternary alloys.3,4,11 This might be expected given their quaternary nature which results in a greater variety of interdiffusion alloy scattering at each interface, as well as given their disparity in constituent atomic masses from the lightest Al (atomic weight of 27.0) to the heaviest Sb (atomic weight of 121.8), enhancing the phonon scattering for interdiffused species. At room temperature, the precise sequence of the layers appears to have a relatively
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.105.125.19 On: Fri, 30 Jan 2015 16:32:38
261905-3
Zhou et al.
minor effect on the magnitude of the thermal conductivity, although the range of layer thickness variation is limited (with well thicknesses between 1.7 and 4.0 nm and barrier thicknesses between 1.2 and 2.3 nm). The thermal conductivities determined in this work are in reasonable agreement with the thermal-impedance area product deduced experimentally (and modeled using prior heat-transport simulations).4 In conclusion, we have measured the in-plane and cross-plane thermal conductivity tensors of typical W-active and cladding layers for interband cascade lasers. The characterization is more accurate than for a thinner active layer that was studied previously.4 The present measurements were carried out over a broad range of temperatures rather than only room temperature, and the present data at 300 K are consistent with the previous result. The characterization indicates a slight increase of the thermal conductivities down to 77 K, followed by a more rapid drop at lower temperatures. The in-plane thermal conductivities are consistently about a factor of 2.5–3.0 larger than the cross-plane thermal conductivities from room temperature down to 77 K. The temperature-dependent thermal conductivities were fit to an analytical power-law expression, so the full thermal conductivity tensors can be interpolated accurately for any given temperature. These data will improve the accuracy of future ICL performance simulations and guide the structural design and processing strategy for optimal thermal management. The work at Northwestern was supported by AFOSR Grant Nos. FA-9550-09-1-0237 and FA-9550-12-1-0169, the
Appl. Phys. Lett. 105, 261905 (2014)
Initiative for Sustainability and Energy at Northwestern (ISEN), and NSF MRSEC Grant No. DMR-1121262. Work at NRL was supported by ONR. 1
I. Vurgaftman, W. W. Bewley, C. L. Canedy, C. S. Kim, M. Kim, J. R. Lindle, C. D. Merritt, J. Abell, and J. R. Meyer, “Mid-IR type-II interband cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1435 (2011). 2 C. L. Canedy, J. Abell, C. D. Merritt, W. W. Bewley, C. S. Kim, I. Vurgaftman, J. R. Meyer, and M. Kim, “Pulsed and CW performance of 7stage interband cascade lasers,” Opt. Express 22, 7702 (2014). 3 T. Borca-Tasciuc, D. Achimov, W. L. Liu, G. Chen, H.-W. Ren, C.-H. Lin, and S. S. Pei, “Thermal conductivity of InAs/AlSb superlattices,” Microscale Thermophys. Eng. 5, 225 (2001). 4 C. Zhou, I. Vurgaftman, C. L. Canedy, C. S. Kim, M. Kim, W. W. Bewley, C. D. Merritt, J. Abell, J. R. Meyer, and M. Grayson, “Thermal conductivity tensors of the cladding and active layers of antimonide infrared lasers and detectors,” Opt. Mater. Express 3, 1632 (2013). 5 T. Borca-Tasciuc, A. R. Kumar, and G. Chen, “Data reduction in 3x method for thin-film thermal conductivity determination,” Rev. Sci. Instrum. 72, 2139 (2001). 6 D. G. Cahill, “Thermal conductivity measurement from 30 to 750 K: The 3x method,” Rev. Sci. Instrum. 61, 802 (1990); S.-M. Lee and D. G. Cahill, “Heat transport in thin dielectric films,” J. Appl. Phys. 81, 2590 (1997). 7 D. G. Cahill, M. Katiyar, and J. R. Abelson, “Thermal conductivity of aSi:H thin films,” Phys. Rev. B 50, 6077 (1994). 8 C. Zhou, G. Koblmuller, M. Bichler, G. Abstreiter, and M. Grayson, “Thermal conductivity tensor of semiconductor layers using two-wire 3x method,” Proc. SPIE 8631, 863129 (2013). 9 C. Zhou and M. Grayson, “Thermal distribution in high power optical devices with power-law thermal conductivity,” Proc. SPIE 8268, 82680V (2012). 10 C. Zhou, B.-M. Nguyen, M. Razeghi, and M. Grayson, “Thermal conductivity of InAs/GaSb Superlattice,” J. Electron. Mater. 41, 2322 (2012). 11 A. Sood, J. A. Rowlette, C. G. Caneau, E. Bozorg-Grayeli, M. Asheghi, and K. E. Goodson, “Thermal conduction in lattice-matched superlattices of InGaAs/InAlAs,” Appl. Phys. Lett. 105, 051909 (2014).
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