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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 3, Iss. 10 — Oct. 1, 2013
  • pp: 1632–1640
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Thermal conductivity tensors of the cladding and active layers of antimonide infrared lasers and detectors

Chuanle Zhou, I. Vurgaftman, C. L. Canedy, C. S. Kim, M. Kim, W. W. Bewley, C. D. Merritt, J. Abell, J. R. Meyer, A. Hoang, A. Haddadi, M. Razeghi, and M. Grayson  »View Author Affiliations


Optical Materials Express, Vol. 3, Issue 10, pp. 1632-1640 (2013)
http://dx.doi.org/10.1364/OME.3.001632


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Abstract

The in-plane and cross-plane thermal conductivities of the cladding layers and active quantum wells of interband cascade lasers and type-II superlattice infrared detector are measured by the 2-wire 3ω method. The layers investigated include InAs/AlSb superlattice cladding layers, InAs/GaInSb/InAs/AlSb W-active quantum wells, an InAs/GaSb superlattice absorber, an InAs/GaSb/AlSb M-structure, and an AlAsSb digital alloy. The in-plane thermal conductivity of the InAs/AlSb superlattice is 4–5 times higher than the cross-plane value. The isotropic thermal conductivity of the AlAsSb digital alloy matches a theoretical expectation, but it is one order of magnitude lower than the only previously-reported experimental value.

© 2013 OSA

1. Introduction

III–V antimonide infrared (IR) detectors typically operate cryogenically [1

1. S. Abdollahi Pour, E.K. Huang, G. Chen, A. Haddadi, B.M. Nguyen, and M. Razeghi, “High operating temperature midwave infrared photodiodes and focal plane arrays based on Type-II InAs/GaSb superlattices,” Appl. Phys. Lett., 98, 143501 (2011). [CrossRef]

, 2

2. E.K. Huang, M.A. Hoang, G. Chen, S.R. Darvish, A. Haddadi, and M. Razeghi, “Highly selective two-color mid-wave and long-wave infrared detector hybrid based on Type-II superlattices,” Optics Letters , 37, 4744 (2012). [CrossRef] [PubMed]

], whereas the latest generation of midwave IR (mid-IR) lasers operates at room temperature [3

3. D. Caffey, T. Day, C. S. Kim, M. Kim, I. Vurgaftman, W. W. Bewley, J. R. Lindle, C. L. Canedy, J. Abell, and J. R. Meyer, “Performance characteristics of a continuous-wave compact widely tunable external cavity interband cascade lasers,” Optics Letters , 18, 15691 (2010).

, 4

4. 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. Topics Quantum Electron. , 17, 1435 (2011). [CrossRef]

]. However, both performances degrade rapidly with increasing temperature. So to enable optimization, it is important to identify the most critical thermal bottlenecks in the device structures so that the net thermal resistance can be minimized and the heat dissipation can be maximized. T2SLs have also been reported recently as a possible new class of transverse thermoelectric material, in which low thermal conductivity would actually be advantageous [5

5. C. Zhou, S. Birner, Tang Yang, K. Heinselman, and M. Grayson, “Driving perpendicular heat flow: p× n type transverse thermoelectrics for microscale and cryogenic peltier cooling,” Phys. Rev. Lett. 110, 227701 (2013). [CrossRef]

].

In this work, we have measured the in-plane and cross-plane thermal conductivities of a variety of short-period antimonide heterostructure device components using the 2-wire 3ω method [7

7. T. Borca-Tasciuc, A.R. Kumar, and G. Chen, “Data reduction in 3ω method for thin-film thermal conductivity determination,” Rev. Sci. Instrum. , 72, 2139 (2001). [CrossRef]

]. The investigated structures include InAs/AlSb cladding layers and InAs/GaInSb/InAs/AlSb W quantum wells (QWs) of ICLs, the InAs/GaSb LWIR active absorber region and InAs/GaSb/AlSb M-structure of T2SL PDs, InAsSb and an AlAsSb digital alloy insulating layer. While the cross-plane thermal conductivities of InAs/AlSb SLs [6

6. 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 Thermophysical Engineering 5225 (2001). [CrossRef]

], AlAsSb digital alloys [8

8. T. Borca-Tasciuc, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Nosho, L. J. Whitman, H. Lee, R. U. Martinelli, G. W. Turner, M. J. Manfra, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93and Al0.9Ga0.1As0.07Sb0.93alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys. , 92, 4994 (2002). [CrossRef]

], and T2SLs [9

9. C. Zhou, B.-M. Nguyen, M. Razeghi, and M. Grayson, “Thermal conductivity of InAs/GaSb Superlattice,” J. Elect. Mat. , 41, 2322 (2012). [CrossRef]

] have been measured previously, to the best of our knowledge the in-plane thermal conductivities have never been reported.

2. Experiment

The four samples studied in this work, which were grown at NRL and Northwestern by molecular beam epitaxy on GaSb substrates, are specified in Table 1. Sample A is a thin ICL cladding structure, consisting of a 0.5-μm (AlAs)1/(AlSb)12.5 digital alloy buffer layer, followed by a 1-μm InAs/AlSb (24.3/23 Å) SL, and an n-doped 10-nm InAs capping layer. Sample B is a thick ICL cladding structure, consisting of a 7-μm-thick InAs/AlSb SL (24.3/23 Å) on a GaSb substrate. Sample C consists of InAs/GaInSb/InAs/AlSb repeated W-active QWs with total thickness 0.485 μm. Sample D is an InAs/GaSb T2SL structure, comprising a 0.5-μm InAsSb alloy buffer layer followed by a 0.67-μm-thick InAs/GaSb (39.6/21.3 Å) T2SL and 0.2-μm-thick InAs/GaSb/AlSb/GaSb (54.9/9.1/15.2/9.1 Å) M-structure.

Table 1. Thermal conductivity tensor components at 300 K. The data from the present study are listed without references (black). Literature values are cited with references numbers in brackets (grey).

table-icon
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The 3ω method uses metal filaments deposited on the sample as both heaters and thermometers. An AC current I(ω) can heat up the filament by ΔT(2ω), which is proportional to the measured third harmonic voltage V3ω. The sample thermal conductivity can be deduced from the frequency dependent ΔT(2ω). To prepare for the 3ω method measurement, we first etched the layer of interest from half of the sample area. For Samples A (thin ICL cladding) and D (T2SL), both of which contained multiple layers of interest, we etched the samples into several steps, as shown in the inset of Fig. 1(a). Then we used PECVD to deposit dSiNx,f = 60 nm of SiNx as an insulating layer, followed by the deposition of 200-nm-thick Au filaments to serve as both heaters and thermometers. One wide filament of 2b = 30 μm and one narrow filament of 2b = 2 μm were deposited on the film, the buffer layer and the substrate. For the thick cladding sample, one narrow Ni filament of 2b = 4 μm was deposited on both the film and the substrate, as shown in the inset of Fig. 1(b). The PECVD-deposited SiNx has a higher thermal conductivity (1.5–1.9 W/m·K) than a sputtered dielectric layer (<1 W/m·K), and 60 nm of SiNx is thick enough to insulate as well as a much thicker SiO2 layer. Therefore, the SiNx layer induces minimal temperature rise in the 3ω measurement for improved accuracy. The filament widths were chosen such that the wide filaments were much wider than film thickness to ensure 1D heat transport, while the widths of the narrow filaments were about the same as the film thickness to increase the accuracy of the in-plane thermal conductivity measurement.

Fig. 1 Measured frequency-dependent temperature rise ΔT of the narrow filaments on the thin film (solid circles) and on the substrate (open circles) of Samples A (thin cladding) and B (thick cladding). The fitted ΔT of the filaments on the thin film and substrate are shown in solid lines and dashed lines, respectively. The insets show the cross-sectional layer structures of the samples. (a) For Sample A, the wide filaments on the buffer layer and the substrate were used to measure the cross-plane thermal conductivity of the buffer layer, while the narrow filaments on the buffer layer and the SL were used to measure the in-plane and cross-plane thermal conductivity of the InAs/AlSb superlattice. (b) For Sample B, the narrow filaments on the substrate and the SL were used to measure the in-plane and cross-plane thermal conductivities of the InAs/AlSb superlattice. Samples C and D were measured in a similar manner, using multiple etch steps with Au filaments at each step for each individual layer.

We first measured the 30-μm-wide filament to determine the substrate thermal conductivity κGaSb,sub and the cross-plane thermal conductivity of the films κyyf:
κGaSb,sub=P2πld(lnω)d(ΔT),
(1)
κyyf=Pdf2blΔTf
(2)
where P is the power applied to the heater, and l is the length of the Au filament. ΔTf = ΔTf+s − ΔTs, where ΔTf+s and ΔTs are the temperature oscillation amplitude of the Au filament on the film-plus-substrate and on the substrate alone, respectively.

To quantify the measurement error, we calculated the error for various fit parameters by varying the parameter values by 20% from their best fit and summing the squared error: [10

10. C. Zhou, G. Koblmuller, M. Bichler, G. Abstreiter, and M. Grayson, “Thermal conductivity tensor of semiconductor layers using two-wire 3ω method,” Proc. of SPIE , 8631, 863129 (2013). [CrossRef]

]
ε=jΔ(lnωj)[ΔTfit(ωj)ΔT(ωj)]2,Δ(lnωj)=ln(ωj/ωj1)
(6)
where ΔTfit(ωj) and ΔT(ωj) are the fitted and measured ΔT at the angular frequency ωj, respectively. The best fit value for each parameter gives the smallest total error ε in units of K2.

3. Results and Discussion

The error analyses are shown in Fig. 2, in which the errors for the in-plane and cross-plane thermal conductivities of the layer of interest are plotted as solid curves and for other fit parameters are plotted as dashed curves. The widths of the narrow filaments are the most important fit parameters for all the samples, the uncertainty of which depends on the lithography and lift-off quality. For each multilayer sample, the fitted thermal conductivity also depends on the actual thicknesses of the thin film of interest and the buffer layer underneath it.

Fig. 2 Following the error analysis method of Ref. [10], plot of the mean-squared fitting error ε for the narrow filament data calculated from Eq. (6) when the value of each fit parameter is varied by 20% around the global minimum error. Only the parameters with errors greater than 0.01 K2 mean-squared error are plotted for the error analysis. Thermal conductivities for the layers of interest are plotted in solid lines and other fit parameters are plotted in dashed lines. The parameters’ names are listed on the right of each plot in the same sequence as the curves. (a) 2 μm Au filament on Sample A (thin cladding). (b) 4 μm Ni filament on the superlattice of Sample B (thick cladding). (c) 2 μm Au filament on the superlattice of Sample C (W-active). (d) 2 μm Au filament on the superlattice of Sample D (T2SL).

For the ICL samples, the uncertainties of the in-plane thermal conductivity determined for the InAs/AlSb SL in Sample A (thin cladding) and the InAs/GaInSb/InAs/AlSb W-active QWs for Sample C are about 20%, while it is about 10% for the InAs/AlSb SL in Sample D (thick cladding). The uncertainties for the in-plane thermal conductivities are larger for the former two samples because their narrow filament widths are larger than the superlattice thickness, whereas the narrow filament width is smaller than the SL thickness for the thick cladding sample. The uncertainty of about 20% for the AlAsSb digital alloy depends on the uncertainties of the width of the narrow filament 2b, the thickness of the alloy buffer layer dbuf, and the cross-plane thermal conductivity of the superlattice layer κyyInAs/AlSbSL,f. For Sample D, the uncertainty for the InAs/GaSb T2SL in-plane thermal conductivity is about 20%, depending on the accuracies of the thickness and cross-plane thermal conductivity of the InAsSb buffer layer.

Fig. 3 In-plane (solid circles) and cross-plane (crosses X) thermal conductivities for the T2SL, M-structure, 1-μm InAs/AlSb SL, 7-μm InAs/AlSb SL, AlAsSb digital alloy, and InAs/GaInSb/InAs/AlSb W QWs, compared to previously published values in grey (reference numbers indicated next to the data points).

4. Conclusion

While a full comparison of the experimental thermal-impedance values for interband cascade laser structures with finite-element simulations of the heat conduction will be reported elsewhere, that modeling is broadly consistent with InAs/AlSb SL cross-plane thermal conductivities in the 2–3 W/m·K range when the insulator thermal conductivity of 1.7 W/m·K derived in the present work is employed. The thermal conductivity tensors obtained from the present study imply a net thermal impedance only <10% lower than the experimental value derived from characterization of an 8-μm-wide epi-down-mounted ICL ridge. It should be emphasized that a precise fit would require full incorporation of all the minor structural details of the processed ICL structure, and assuming the absence of any thermal bottleneck at the bonded device/heat-sink interface. In view of these uncertainties, the agreement with the results of the present work is quite good. The fits are much less sensitive to the SL in-plane thermal conductivity than the cross-plane value, owing to the poor conductance of the insulator layer and the presence of highly-conductive GaSb layers in the structure.

Acknowledgments

The work at Northwestern was supported by AFOSR grants FA-9550-09-1-0237 and FA-9550-12-1-0169, Initiative for Sustainability and Energy at Northwestern (ISEN) and NSF MRSEC grants No. DMR-0520513 and No. DMR-0748856 through both instrumentation grants and an NSF MRSEC Fellowship. Work at NRL was supported by ONR.

References and links

1.

S. Abdollahi Pour, E.K. Huang, G. Chen, A. Haddadi, B.M. Nguyen, and M. Razeghi, “High operating temperature midwave infrared photodiodes and focal plane arrays based on Type-II InAs/GaSb superlattices,” Appl. Phys. Lett., 98, 143501 (2011). [CrossRef]

2.

E.K. Huang, M.A. Hoang, G. Chen, S.R. Darvish, A. Haddadi, and M. Razeghi, “Highly selective two-color mid-wave and long-wave infrared detector hybrid based on Type-II superlattices,” Optics Letters , 37, 4744 (2012). [CrossRef] [PubMed]

3.

D. Caffey, T. Day, C. S. Kim, M. Kim, I. Vurgaftman, W. W. Bewley, J. R. Lindle, C. L. Canedy, J. Abell, and J. R. Meyer, “Performance characteristics of a continuous-wave compact widely tunable external cavity interband cascade lasers,” Optics Letters , 18, 15691 (2010).

4.

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. Topics Quantum Electron. , 17, 1435 (2011). [CrossRef]

5.

C. Zhou, S. Birner, Tang Yang, K. Heinselman, and M. Grayson, “Driving perpendicular heat flow: p× n type transverse thermoelectrics for microscale and cryogenic peltier cooling,” Phys. Rev. Lett. 110, 227701 (2013). [CrossRef]

6.

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 Thermophysical Engineering 5225 (2001). [CrossRef]

7.

T. Borca-Tasciuc, A.R. Kumar, and G. Chen, “Data reduction in 3ω method for thin-film thermal conductivity determination,” Rev. Sci. Instrum. , 72, 2139 (2001). [CrossRef]

8.

T. Borca-Tasciuc, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Nosho, L. J. Whitman, H. Lee, R. U. Martinelli, G. W. Turner, M. J. Manfra, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93and Al0.9Ga0.1As0.07Sb0.93alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys. , 92, 4994 (2002). [CrossRef]

9.

C. Zhou, B.-M. Nguyen, M. Razeghi, and M. Grayson, “Thermal conductivity of InAs/GaSb Superlattice,” J. Elect. Mat. , 41, 2322 (2012). [CrossRef]

10.

C. Zhou, G. Koblmuller, M. Bichler, G. Abstreiter, and M. Grayson, “Thermal conductivity tensor of semiconductor layers using two-wire 3ω method,” Proc. of SPIE , 8631, 863129 (2013). [CrossRef]

11.

J. Garg, N. Bonini, and N. Marzari, “High thermal conductivity in short-period superlattices,” Nano Lett. , 11, 5135 (2011). [CrossRef] [PubMed]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(140.6810) Lasers and laser optics : Thermal effects
(260.3060) Physical optics : Infrared
(310.6870) Thin films : Thin films, other properties

ToC Category:
IR Materials

History
Original Manuscript: July 1, 2013
Revised Manuscript: August 5, 2013
Manuscript Accepted: August 5, 2013
Published: September 6, 2013

Virtual Issues
Mid-IR Photonic Materials (2013) Optical Materials Express

Citation
Chuanle Zhou, I. Vurgaftman, C. L. Canedy, C. S. Kim, M. Kim, W. W. Bewley, C. D. Merritt, J. Abell, J. R. Meyer, A. Hoang, A. Haddadi, M. Razeghi, and M. Grayson, "Thermal conductivity tensors of the cladding and active layers of antimonide infrared lasers and detectors," Opt. Mater. Express 3, 1632-1640 (2013)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-3-10-1632


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References

  1. S. Abdollahi Pour, E.K. Huang, G. Chen, A. Haddadi, B.M. Nguyen, and M. Razeghi, “High operating temperature midwave infrared photodiodes and focal plane arrays based on Type-II InAs/GaSb superlattices,” Appl. Phys. Lett.,98, 143501 (2011). [CrossRef]
  2. E.K. Huang, M.A. Hoang, G. Chen, S.R. Darvish, A. Haddadi, and M. Razeghi, “Highly selective two-color mid-wave and long-wave infrared detector hybrid based on Type-II superlattices,” Optics Letters, 37, 4744 (2012). [CrossRef] [PubMed]
  3. D. Caffey, T. Day, C. S. Kim, M. Kim, I. Vurgaftman, W. W. Bewley, J. R. Lindle, C. L. Canedy, J. Abell, and J. R. Meyer, “Performance characteristics of a continuous-wave compact widely tunable external cavity interband cascade lasers,” Optics Letters, 18, 15691 (2010).
  4. 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. Topics Quantum Electron., 17, 1435 (2011). [CrossRef]
  5. C. Zhou, S. Birner, Tang Yang, K. Heinselman, and M. Grayson, “Driving perpendicular heat flow: p× n type transverse thermoelectrics for microscale and cryogenic peltier cooling,” Phys. Rev. Lett.110, 227701 (2013). [CrossRef]
  6. 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 Thermophysical Engineering5225 (2001). [CrossRef]
  7. T. Borca-Tasciuc, A.R. Kumar, and G. Chen, “Data reduction in 3ω method for thin-film thermal conductivity determination,” Rev. Sci. Instrum., 72, 2139 (2001). [CrossRef]
  8. T. Borca-Tasciuc, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Nosho, L. J. Whitman, H. Lee, R. U. Martinelli, G. W. Turner, M. J. Manfra, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93and Al0.9Ga0.1As0.07Sb0.93alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys., 92, 4994 (2002). [CrossRef]
  9. C. Zhou, B.-M. Nguyen, M. Razeghi, and M. Grayson, “Thermal conductivity of InAs/GaSb Superlattice,” J. Elect. Mat., 41, 2322 (2012). [CrossRef]
  10. C. Zhou, G. Koblmuller, M. Bichler, G. Abstreiter, and M. Grayson, “Thermal conductivity tensor of semiconductor layers using two-wire 3ω method,” Proc. of SPIE, 8631, 863129 (2013). [CrossRef]
  11. J. Garg, N. Bonini, and N. Marzari, “High thermal conductivity in short-period superlattices,” Nano Lett., 11, 5135 (2011). [CrossRef] [PubMed]

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