THERMAL CONDUCTIVITY OF III-V SEMICONDUCTOR SUPERLATTICES

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1 THERMAL CONDUCTIVITY OF III-V SEMICONDUCTOR SUPERLATTICES Song Mei, Zlatan Aksamija, and Irena Knezevic Electrical and Computer Engineering Department University of Wisconsin-Madison This work was supported by the NSF under Award No

2 Why III-V SLs? Solder Contact: Au Phononics Thermoelectrics Optoelectronics QCL Self-heating Thermal modeling Insulation: Si 3N 4 GaAs cladding 4.5 μm Active core 1.6 μm GaAs cladding 4.5 μm GaAs substrate Key feature: multiple interfaces Interfacial transmission/reflection Anisotropic thermal transport

3 Thermal Conductivity Model (Bulk) Bulk thermal conductivity tensor κ ( T) = C( qt, ) τ ( qtv, ) ( qv ) ( q) αβ α β b b b b bq, Phonon scattering mechanisms Phonon-phonon scattering Umklapp process Normal process Isotope scattering Impurity scattering (doped) Mass-difference scattering (ternary)

4 Phonon Dispersion Calculation Adiabatic Bond Charge model 1 (ABC) + Virtual Crystal Approximation 2 (VCA) for ternaries Phonon Dispersion and Density of States of In 0.53 Ga 0.47 As 1. K. Rustagi, W. Weber, Adiabatic bond charge model for the phonons in A3B5 semiconductors, Solid State Commun. 18, 673 (1976) 2. B. Abeles, Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures, Phys. Rev. 131, 1906 (1963)

5 Bulk Thermal Conductivities GaAs Umklapp process γω( q) τ Θ b b bu, ( q, T ) = 2 Mvb( q) bd, Te Θ bd, /3 T Normal process τ 1, ( qt bn, ) = T 4 BNω b( q) T, b = TA L 2 3 B ω ( q) T, b = LA N b B, B γ T L 2 N N b L. Lindsay et al., Ab initio thermal transport in compound semiconductors, Phys. Rev. B 87, (2013) A.V. Inyushkin et al., Thermal conductivity of isotropically enriched GaAs crystal, Semicond. Sci. Technol. 18, 685 (2003) R. O. Carlson et al., Thermal conductivity of GaAs and GaAsP Laser semiconductors, J. Appl. Phys. 36(2) (1965) A. Amith et al., Electron and phonon scattering in GaAs at high temperatures, Phys. Rev. 138(4A) (1965)

6 Bulk Thermal Conductivities InAs AlAs L. Lindsay et al., Ab initio thermal transport in compound semiconductors, Phys. Rev. B 87, (2013) E. M. Heckman et al, Measurement of optical and thermal properties of Hg 1-x Cd x Te, Appl. Optics, 47 (2008) P. V. Tamarin et al., Thermal conductivity and thermoelectric power of indium arsenide at low temperatures, Sov. Phys. Semicond. 5(5), 1097 (1971) G. Guillou et al., Phonon conductivity of InAs, Phys. Rev. B 5(6), 2301 (1972) R. Bowers et al., InAs and InSb as thermoelectric materials, J. Appl. Phys. 30(6), 930 (1959) C. A. Evans et al., Thermal modeling of terahertz Quantum-Cascade Lasers: Comparison of optical waveguides, IEEE J. Quantum Electron. 44(7) (2008) M. A. Afromowitz, Thermal conductivity of Ga 1-x Al x As alloys, J. Appl. Phys. 44, 1292 (1973)

7 Bulk Thermal Conductivities AlGaAs InGaAs M. A. Afromowitz, Thermal conductivity of Ga 1-x Al x As alloys, J. Appl. Phys. 44, 1292 (1973) B. Abeles, Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures, Phys. Rev. 131, 1906 (1963) S. Adachi, Lattice thermal resistivity of III-V compound alloys, J. Appl. Phys. 54(4) (1983) M. Abrahams et al., Thermal, electrical and optical properties of (In,Ga)As alloys, J. Phys. Chem. Solids 10, 204 (1959).

8 What Are the Interfaces Like? Very good quality Smooth on large scale Similar interfaces Not perfect Interfacial mixing Atomic roughness Effective rms roughness Δ

9 Twofold Influence of the Interface (1) Partially diffuse interfacial reflection Affect all phonons Change phonon distribution inside a layer Effective boundary scattering rate Specularity parameter p ( q) = exp( 4 q cos θ ) spec Layer thermal conductivity Z. Aksamija and I. Knezevic, Thermal conductivity of Si 1-x Ge x /Si 1-y Ge y superlattices: Competition between interfacial and internal scattering, Phys. Rev. B 88, (2013)

10 Twofold Influence of the Interface (2) Transmission Models Acoustic Mismatch Model (AMM) Diffuse Mismatch Model (DMM) Partially diffuse interfacial transmission Affect phonons trying to cross an interface Thermal boundary resistance R = 2 vb,1, qcbt, qt1 2 ω1 q 1 bq, 1 2 ω ω1 ( ) ( ) ( ( )) 1 t ( ( q)) t ( ( q)) 2 AMM DMM tb( q) = pspec ( q) tb ( q) + 1 pspec ( q) tb ( q)

11 Thermal Conductivity Model (SL) In-plane and cross-plane thermal conductivity can be calculated from the layer thermal conductivity κ i and thermal boundary resistance between adjacent layers R 1 i= 1 κ in plane = n i = 1 n Lκ i L i i R 2... κ = cross plane n i= 1 L n i= 1 L i κ + R i i i + i 1 R i R 1 R 1 2 R 2... R i

12 Results (GaAs/AlAs SL) In-plane Cross-plane L=70 nm Δ=3.7Å X. Y. Yu et al., Temperature dependence thermophysical properties of GaAs/AlAs periodic structure, Appl. Phys. Lett. 67(24), 3554 (1995) W. S. Capinski et al., Thermal-conductivity measurements of GaAs/AlAs superlattices using a picosecond optical pump-and-probe technique, Phys. Rev. B. 59(12), 8105 (1999)

13 Conclusion Accurately describe the bulk thermal conductivities of binary (GaAs, InAs, AlAs) and ternary (In x Ga 1-x As, Al x Ga 1-x As) III-V with arbitrary compositions using full dispersion. Single free parameter captures twofold influence of interface on thermal transport in SL. Calculated in- and cross-plane thermal conductivities agree well with experimental data over a large temperature range.