Direct measurement of coherent thermal phonons in Bi 2 Te 3 /Sb 2 Te 3 superlattice

Transcription

1 Appl. Phys. A (2016) 122:777 DOI /s z Direct measurement of coherent thermal phonons in Bi 2 Te 3 /Sb 2 Te 3 superlattice Feng He 1,2 Wenzhi Wu 1,3 Yaguo Wang 1,2 Received: 11 May 2016 / Accepted: 24 July 2016 / Published online: 1 August 2016 Springer-Verlag Berlin Heidelberg 2016 Abstract Coherent thermal phonons (CTPs) play an important role in thermal transport in superlattice (SL) structures. To have a profound understanding of CTP transport in SL, direct measurement of CTP properties is necessary. In this study, coherent phonon spectroscopy has been utilized to generate and detect CTP in Bi 2 Te 3 /Sb 2 Te 3 SL. Phonon lifetimes have been extracted from experimental data, with which mode-wise thermal conductivities have been calculated. Comparing with bulk Bi 2 Te 3, the estimated mode-wise thermal conductivity of longitudinal acoustic phonons shifts to higher frequencies, due to constructive coherent phonon interference. Our results suggest that it is possible to use SL structure to manipulate coherent phonon propagation and to tailor thermal conductivity. 1 Introduction Phonons are quantized lattice vibrations, characterized with frequency x, wave vector k, phonon velocity v and lifetime s. Phonons are major heat carriers in most crystalline solids. Lattice thermal conductivity is a macroscopic parameter summing over all phonon modes in the material j Lattice = P j a = P ac a v a 2 s a where C is specific heat and a represents individual phonon mode [1]. Not all phonons & Yaguo Wang yaguo.wang@austin.utexas.edu Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712, USA The Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA School of Electronic Engineering, Heilongjiang University, Harbin , China contribute to heat transport process equally. For example, in bulk Bi 2 Te 3, phonons with wavelength (k = 2pv/x) from 2 to 6 nm contribute to 60 % of total lattice thermal conductivity [2]. Phonons that are thermally important are called thermal phonons. Thermal phonons usually mean acoustic phonons. Optical phonons, even though are thought not significant in most materials to thermal transport because of small group velocity, can still play a role by scattering acoustic phonons [3, 4]. Similar to other fundamental particles (photons, electrons), phonons possess both wave-like and particle-like characters. When consider phonons as lattice waves, they can be called coherent phonons if atomic movements induced by the lattice wave are correlated. The distance that coherent phonons can travel before losing their coherence is called phonon coherence length l c [5]. When consider phonons as particles, phonons can be scattered by other particles (electrons, phonons and defects) or boundaries/interfaces. The average distance phonons can travel before being scattered is phonon mean free path K = v s. Since lattice wave could not extend further after the phonon get scattered, usually l c is shorter than K. In bulk materials, where the sample thickness L bulk is much longer than phonon coherence length l c and phonon mean free path K, phonons are treated as incoherent and travel diffusively, which means atomic movements are random and phonons lose track of their original directions because of numerous scattering events. In nanostructures, if the characteristic length L nano is comparable to or less than phonon mean free path K. Phonons can travel through the material without any scattering, which is called ballistic heat transfer. If the characteristic length further reduces to be less than phonon coherence length l c, the wave features of phonons should be considered. Ballistic phonon transport has been studied extensively over decades [6 8]. However, the importance of coherent

2 777 Page 2 of 5 F. He et al. phonons to the overall thermal transport has only recently been addressed by recent two recent experimental studies: (a) Luckyanova et al. [9] reported that thermal conductivity of GaAs/AlAs SLs increases almost linearly with the total sample length L SL over a wide temperature range K, which was explained with coherent thermal phonon (CTP) transport. The phonons are called coherent in their study because sample length is shorter than phonon mean free path (L SL \ K). Even though similar phenomena have been observed in molecular dynamic simulations [10 14], the role of CTP was not mentioned in these studies. (b) Ravichandran et al. [15] demonstrated a transition region from incoherent heat conduction to coherent phonon conduction by measuring a minimum thermal conductivity around certain period thickness d SL in SiTiO 3 /BaTiO 3 superlattice (SL), which was attributed to competition between interface scattering and phonon folding in the transition region. In fact, the minimum thermal conductivity has been observed in many other experiments [10, 15 20]. Later, several groups conducted molecular dynamics studies to further understand the CTP transport observed in experiments, respectively [2, 21]. Very recently, Latour et al. [22] introduced a criterion to distinguish coherent versus incoherent heat conductions, trying to reconcile the disagreements observed in experiments. Even though this picture provides some guidance for understanding coherent phonon conduction, it fails to interpret some experimental results. For example, in GaAs/ AlAs SL, l c is estimated to be 1 2 nm [15], and K bulk is about 1 lm. Based on Latour s picture, with d SL = 12 - nm [ l c, thermal conductivity k should be independent of sample length L. But Luckyanova s experimental results showed that k has a strong dependence on sample length L. Second problem is that Latour defines phonons as coherent only when phonon coherence length l c is greater than SL period thickness d SL. In Luckynova s experiment, phonons are called coherent because phonon mean path K is greater than sample length L. To provide an unambiguous picture of coherent phonon transport in superlattices, direct measurement of coherent phonons is necessary. In this study, coherent phonon spectroscopy (CPS) using femtosecond laser pump probe technique is utilized to generate and detect CTP in Bi 2 Te 3 /Sb 2 Te 3 superlattice. Bi 2 Te 3 /Sb 2 Te 3 superlattices can be grown with metal-organic chemical vapor deposition (MOCVD) technique with high-quality interfaces [23]. Studies have shown that crossplane thermal conductivity for Bi 2 Te 3 /Sb 2 Te 3 superlattice is significantly lower than its bulk counterparts, even lower than its corresponding alloy, making it promising for achieving high ZT thermoelectric materials [24, 25]. Thermal conductivity measurements of Bi 2 Te 3 /Sb 2 Te 3 superlattices have also shown a minimum thermal conductivity around period thickness of 4 6 nm [24], similar to that observed in SiTiO 3 /BaTiO 3 superlattices [15]. Therefore, coherent phonon conduction could also play an important role in Bi 2 Te 3 /Sb 2 Te 3 superlattices. Phonon lifetimes have been extracted from experimental data, with which mode-wise thermal conductivities have been calculated. Comparing with bulk Bi 2 Te 3, the estimated mode-wise thermal conductivity of longitudinal acoustic phonons shifts to higher frequencies, due to constructive coherent phonon interference. 2 Experimental technique Using a mode-locked Ti: Sapphire femtosecond laser (Tsunami, Spectra Physics), single-color pump probe experiment is performed in non-collinear reflection geometry at room temperature. Both pump and probe pulses have 800 nm central wavelength, 35 fs pulse width and 76 MHz repetition rate. Pump and probe beams are focused onto the sample surface by a 72.5 mm lens, with spot sizes of 30 lm and 24 lm, respectively. An optical delay line placed in the pump beam optical path is used to control the delay time between pump and probe beams. The difference between reflected and reference probe beams is measured by subtracting signals from two single detectors (DET110, Thorlabs). A lock-in amplifier (model 7265, Signal recovery) with a chopper working at 2.2 khz is used to acquire the data. A mechanical shaker was incorporated into the spectrometer for fast averaging. The sample studied is a Bi 2 Te 3 /Sb 2 Te 3 SL grown with the metal-organic chemical vapor deposition (MOCVD) technique on GaAs (100) substrates along the c axis of the films [23, 26]. The SL has about 200 periods with a 1 nm Bi 2 Te 3 layer and a 1 nm Sb 2 Te 3 layer for each period. A Bi 2 Te 3 buffer layer is placed between the SL and the substrate. 3 Results and discussion Generation and detection of high-frequency coherent acoustic phonons have been persistently pursued for decades by researchers in ultrasonics field. Recently, several groups have detected THz coherent acoustic phonons with coherent phonon spectroscopy [27, 28]. Coherent acoustic phonons can be generated with femtosecond laser pulses via launching a strain wave near sample surface, which is a group of coherent phonons traveling with the same velocity. As shown in Fig. 1a, the strain wave propagates into the sample and be partially transmitted/reflected at interface. When a probe photon is scattered by a phonon, maximum phonon vector that can be detected is k phonon = 2k probe (backscattering of probe photon), to

3 Direct measurement of coherent thermal phonons in Bi 2 Te 3 /Sb 2 Te 3 superlattice Page 3 of satisfy momentum conservation. This process is called stimulated Brillouin light scattering (SBLS). If the probe laser has shorter penetration depth, it will only detect the acoustic wave packet after it is reflected at interface and travels back to sample surface. Acoustic wave packet detected in Bi 2 Te 3 /Sb 2 Te 3 superlattice is shown in Fig. 1b [29]. The temporal expansion of the acoustic echo (Dt) corresponds to coherence time, which is related to phonon coherence length, l c = v Dt. The difference of time delays when the acoustic wave packet is detected first time (s 1 ) and second time (s 2 ) is the round-trip time that coherent phonon travels in the sample. Phonon group velocity can be derived as: v ¼ 2 L s 2 s 1. It can also be seen in Fig. 1b that the amplitude of coherent phonon decreases after propagating a longer distance. Eventually, the acoustic wave packet will disappear when all phonons are scattered. This time constant of phonon amplitude decay is called coherent phonon Fig. 1 a Schematic picture of coherent phonon generation/propagation in bulk; b Acoustic echo measured in Bi 2 Te 3 /Sb 2 Te 3 SL [Adapted from Ref. 29]; and c Acoustic phonon dispersion in two SL structures with different periods calculated with an elastic continuum model; SL with larger period introduces more phonon folding lifetime, which is related to phonon mean free path, K = v s. In bulk materials, phonons with k phonon = 2k probe usually have very low frequency and hence are not thermally important. Figure 1c shows acoustic phonon dispersion in two SL structures with different periods calculated with an elastic continuum model [30, 31]. In SL, due to phonon folding, many high-frequency phonons also fall into 0 2k probe region, and hence, more coherent phonons can be generated and detected. Broadband coherent optical phonons up to 2.5 THz have been detected in InGaN/GaN SL with coherent phonon spectroscopy [28]. Figure 2a shows transient reflectivity signal measured in Bi 2 Te 3 /Sb 2 Te 3 superlattice with degenerate CPS, with 800 nm wavelength, 35 fs pulse width for both pump and probe beams. The sharp decrease around zero-time delay is due to electron excitation by pump pulse. The decaying background represents electron relaxation, mainly a result of electron phonon scattering. The oscillatory component is related to coherent phonons generated in SL structure. Inset of Fig. 2a shows pure coherent phonon signals after removing electronic signals with a digital high-pass filter. The complex feature shown in coherent phonon signals comes from superposition of multiple phonon waves, which makes direct fitting to extract phonon information impractical. Instead, short-time Fourier transform (STFT) has been applied to the pure coherent phonon signals to extract phonon frequencies and to reveal the evolution of coherent phonons with time. A proper window size has been chosen to achieve reasonable resolutions in both time and frequency domains. From the frequency axis, two groups of phonons are clearly shown: acoustic phonons with frequency below 1 THz and optical phonons with frequency between 1 and 2 THz, with a gap present between these two groups of phonons. A similar trend has been observed for phonons in bulk Bi 2 Te 3 [2]. STFT amplitudes of a phonon mode at 0.57 THz are plotted in Fig. 3a. A decaying exponential function is used to fit STFT amplitudes to extract phonon lifetime, which is Fig. 2 a High-frequency coherent phonons measured in Bi 2 Te 3 /Sb 2 Te 3 SL. Inset shows coherent phonon signals after removing electronic background; b Short-time Fourier transform (STFT) of phonon oscillations showing both optical and acoustic phonons

4 777 Page 4 of 5 F. He et al. Fig. 3 a STFT amplitudes of coherent phonon at 0.57 THz and its exponential fitting; the extracted phonon lifetime is about 2.2 ps; b Phonon lifetimes of longitudinal acoustic and optical phonons extracted from STFT Fig. 4 Normalized mode-wise thermal conductivities of longitudinal acoustic phonons along C Z direction. Comparing with bulk Bi 2 Te 3, spectrum of mode-wise thermal conductivities in Bi 2 Te 3 /Sb 2 Te 3 SL shifts to higher frequencies. The line and the shaded area are just for eye guidance about 2.2 ps for phonon at 0.57 THz. Figure 3b plots extracted phonon lifetimes of both acoustic and optical phonons in Bi 2 Te 3 /Sb 2 Te 3 SL. Lifetimes of acoustic phonon range from 1 to 9 ps; those of optical phonons range from 2.5 to 7.5 ps. Acoustic phonons below 300 GHz are not plotted due to large uncertainties. In bulk Bi 2 Te 3, the previously measured lifetime of A 1g optical coherent phonon (1.88 THz) is about 5 ps [32], which falls into the same range with optical phonon lifetimes measured in this work. Lifetimes of acoustic phonons are generally shorter than that calculated in bulk Bi 2 Te 3 [2], due to scattering at SL interfaces. Plotted in Fig. 4 are the normalized mode-wise thermal conductivities of longitudinal acoustic phonons along C Z direction, j L;z ¼ C av 2 a s a ðc a v 2 a s, for both bulk Bi aþ 2 Te 3 and Bi 2 Te 3 / max Sb 2 Te 3 SL. Phonon velocities of bulk Bi 2 Te 3 are derived from dispersion curves calculated with lattice dynamics (GULP [33]), and phonon lifetimes of bulk Bi 2 Te 3 are adapted from Ref. [2], calculated with normal mode analysis (NMA) [2]. Specific heat per phonon mode is approximated as 1/2k B (Boltzmann constant) because Debye temperature of both Bi 2 Te 3 (155 K) [2] and Sb 2 Te 3 (165 K) [34] is much lower than room temperature. Phonon velocities of Bi 2 Te 3 / Sb 2 Te 3 SL are approximated as the same as those of bulk Bi 2 Te 3 at the same frequency, because Bi 2 Te 3 and Sb 2 Te 3 have very similar elastic properties [35, 36]. Since the phonon velocity reduction caused by folding does not depend on phonon frequency, its effect is not reflected in normalized mode-wise thermal conductivity. In bulk Bi 2 Te 3, j L;z decreases with phonon frequency, while in SL, j L;z spectrum shows a broad peak at intermediate frequencies, with much smaller values at lowest and highest frequencies. This spectrum shift of j L;z in SL has several important implications: (a) with coherent phonon spectroscopy, only coherent phonons near the zone center region can be detected (k ph \ 2k probe ), while results of bulk Bi 2 Te 3 calculated with NMA include all the k points along C Z direction. Successful detection of high-frequency coherent acoustic phonons in SL is a direct evidence of phonon zone folding in SL, which generates new phonon modes near the zone center region. (b) Phonon scattering in SL structure is selective, weaker on some modes, while stronger on others. (c) SL structure can preferably allow propagation of certain coherent phonon modes, which is a result of constructive interference. So it is possible to manipulate CTP in SL structures in a similar way to photons. In summary, coherent phonon spectroscopy has been applied to excite and detect CTP in Bi 2 Te 3 /Sb 2 Te 3 superlattice. Phonon lifetimes have been extracted by exponential fitting of the decaying STFT amplitudes. Comparing with bulk Bi 2 Te 3, spectrum of mode-wise thermal conductivities of longitudinal acoustic phonons along C Z direction in SL shows a shift to higher frequencies. Our results suggest that it is possible to use SL structure to manipulate coherent phonon propagation and to tailor thermal conductivity.

5 Direct measurement of coherent thermal phonons in Bi 2 Te 3 /Sb 2 Te 3 superlattice Page 5 of Acknowledgments The authors are grateful for the support from National Science Foundation (Grant No. CBET ). Wu also acknowledges the support from National Science Foundation of China (Grant No ), New-Century Training Program Foundation for the Talents by Heilongjiang. Province (Grant No NCET- 018), Foundation for University Key Teacher by Heilongjiang Province (Grant No. 1252G047), Heilongjiang Province Postdoctoral Science Foundation (LBH-Q14139) and Science Foundation of Heilongjiang University for Young Scholars (Grant No. JCL201205). References 1. M. Kaviany, Heat transfer physics, 2nd edn. (Cambridge University Press, Cambridge, 2014) 2. Y. Wang, B. Qiu, A.J. McGaughey, X. Ruan, X. Xu, J. Heat Transf. 9, (2013) 3. Y. Zhang, Y. Wang, Appl. Phys. A 4, (2014) 4. Y. Wang, X. Xu, Appl. Phys. A 3, (2013) 5. G. Chen, J. Heat Transf. 2, (1997) 6. G. Chen, Phys. Rev. B 23, (1998) 7. A. Joshi, A. Majumdar, J. Appl. Phys. 1, (1993) 8. H. Chiu, V. Deshpande, H.C. Postma, C. Lau, C. Miko, L. Forro, M. Bockrath, Phys. Rev. Lett. 22, (2005) 9. M.N. Luckyanova, J. Garg, K. Esfarjani, A. Jandl, M.T. Bulsara, A.J. Schmidt, A.J. Minnich, S. Chen, M.S. Dresselhaus, Z. Ren, E.A. Fitzgerald, G. Chen, Science 6109, (2012) 10. R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O quinn, Nature 6856, (2001) 11. K. Imamura, Y. Tanaka, N. Nishiguchi, S. Tamura, H. Maris, J. Phys. Condens. Matter 50, 8679 (2003) 12. E. Landry, A. McGaughey, Phys. Rev. B 7, (2009) 13. V. Samvedi, V. Tomar, Nanotechnology 36, (2009) 14. K. Lin, A. Strachan, Phys. Rev. B 11, (2013) 15. J. Ravichandran, A.K. Yadav, R. Cheaito, P.B. Rossen, A. Soukiassian, S. Suresha, J.C. Duda, B.M. Foley, C. Lee, Y. Zhu, Nat. Mater. 2, (2014) 16. M. Simkin, G. Mahan, Phys. Rev. Lett. 5, 927 (2000) 17. B.C. Daly, H.J. Maris, K. Imamura, S. Tamura, Phys. Rev. B 2, (2002) 18. B. Yang, G. Chen, Phys. Rev. B 19, (2003) 19. Y. Chen, D. Li, J.R. Lukes, Z. Ni, M. Chen, Phys. Rev. B 17, (2005) 20. J. Garg, G. Chen, Physical Review B 14, (2013) 21. X. Mu, T. Zhang, D.B. Go, T. Luo, Carbon 83, (2015) 22. B. Latour, S. Volz, Y. Chalopin, Phys. Rev. B 1, (2014) 23. R. Venkatasubramanian, T. Colpitts, E. Watko, M. Lamvik, N. El-Masry, J. Cryst. Growth 1, (1997) 24. R. Venkatasubramanian, Phys. Rev. B 61, 3091 (2000) 25. M. Touzelbaev, P. Zhou, R. Venkatasubramanian, K. Goodson, J. Appl. Phys. 2, (2001) 26. R. Venkatasubramanian, T. Colpitts, B. O Quinn, S. Liu, N. El- Masry, M. Lamvik, Appl. Phys. Lett. 75, 1104 (1999) 27. V.V. Temnov, Nat. Photonics 11, (2012) 28. A. Maznev, K.J. Manke, K. Lin, K.A. Nelson, C. Sun, J. Chyi, Ultrasonics 1, 1 4 (2012) 29. Y. Wang, C. Liebig, X. Xu, R. Venkatasubramanian, Appl. Phys. Lett. 8, (2010) 30. C. Colvard, T. Gant, M. Klein, R. Merlin, R. Fischer, H. Morkoc, A. Gossard, Phys. Rev. B 4, 2080 (1985) 31. S. Tamura, D. Hurley, J. Wolfe, Phys. Rev. B 2, 1427 (1988) 32. Y. Wang, X. Xu, R. Venkatasubramanian, Appl. Phys. Lett. 93, (2008) 33. J.D. Gale, A.L. Rohl, Mol. Simul. 5, (2003) 34. X. Yang, Z. Zhou, Y. Wang, R. Jiang, W. Zheng, C.Q. Sun, J. Appl. Phys. 8, (2012) 35. S. Giraud, R. Egger, Phys. Rev. B 24, (2011) 36. S. Giraud, A. Kundu, R. Egger, Phys. Rev. B 3, (2012)