ANALYTICAL SCIENCES APRIL 2001, VOL.17 Special Issue s245 2001 © The Japan Society for Analytical Chemistry

Picosecond Ultrasonics Study of Periodic Multilayers

Clément Rossignol††† and Bernard Perrin

Laboratoire des Milieux Désordonnés et Hétérogènes, UMR 7603 - Université Pierre & Marie Curie - CNRS T22-E4, casier 86, 4 pl. Jussieu, 75252 Paris cedex 05, France

We present theoretical and experimental studies of vibrational properties of periodic multilayered structures. Experiments were performed in a series of opaque and semi-transparent superlattices, with a large range of periods, by the picosecond ultrasonics technique coupled with an interferometric setup. Acoustic pulses propagating in the whole structure and folded modes with frequencies up to 2.25 THz have been observed. The period dependence of the ratio between the respective amplitudes of low frequency and high frequency phonons is in good agreement with our theoretical model.

(Received June 29, 2000; Accepted August 22, 2000)

We present in this work theoretical and experimental studies perturbations induce a change ∆r(t) in the optical reflectivity of periodic multilayers by picosecond ultrasonics. An r0 of the structure. The reflection of the light probe pulse on interferometric set-up combined with a pump-probe technique, the multilayered sample gives the relative change of the based on a femtosecond laser, allows the simultaneous optical reflectivity coefficient of the perturbed structure [5] : measurement of the relative change in the amplitude and phase ∆r(t)/r0. These acoustic perturbations are probed by transient of a reflected probe pulse, induced by the acoustic field interferometric detection [2]. excited by the pump pulse [1,2]. An analytical model, allowing calculations in multilayered Theory samples has been developed. This model allows to understand, to analyze and to predict experimental results obtained by this We calculate the relative change of reflectivity of technique. The comparison of the experimental results with multilayered samples. This calculation uses rigorous physical the theoretical model gives accurate information on the elastic models for the description of the optical and acoustical properties of the different layers. properties of the samples. We calculate first the heat deposited The particular case of the relative change in reflectivity of in each layer of the structure using a set of optical constants. semi-infinite periodic multilayered samples has been We deduce the initial photothermal stress in the whole extensively studied. On the one hand, high frequency modes, multilayer from the heat distribution. Then we determine the located at the surface of the sample, can be observed in such acoustic field in each layer of the sample. Finally, we calculate structures (localized modes, edge band gap modes and time-dependent perturbation induced, on the reflected probe propagating modes). On the other hand, picosecond acoustic pulse, by the elastic field. Acoustic attenuation, mechanic pulses bouncing back and forth in the whole multilayered adhesion and roughness of the interfaces have also been structure give rise to echoes at the surface ; an effective considered in the model. medium theory has been developed to describe their excitation, The dispersion curves for longitudinal vibrations propagating propagation and detection. along the stacking axis of a superlattice are displayed on Fig. 1 Experiments have been performed to test the validity of our in the reduced Brillouin zone scheme. Bulk modes belonging model : vibrations at very high frequencies (above 2 THz) to the low frequency branch can propagate along the stacking have been detected in metallic and semi-conducting axis in the multilayer with an effective sound velocity given by superlattices. a long wavelength expansion of the dispersion relation. In opaque systems these modes give rise to echoes bouncing Experimental set-up back and forth in the whole structure. In semi-transparent multilayers, the reflected probe beam is scattered by these The picosecond ultrasonics technique [3] is based on a acoustical modes as they propagate and only modes satisfying time-resolved pump-probe setup using femtosecond laser the selection rule q±2k=0 are detected and give rise to a pulses (wavelength 750 nm, duration 100 fs and energy 15 nJ) so-called Brillouin oscillation ; q and k are the acoustical and generated by a Ti : sapphire laser with a 82 MHz repetition optical wave numbers respectively. rate. A lock-in detection scheme working at 2 MHz was used. Band gaps, in which no propagating modes are allowed, open The probe pulse is delayed with respect to the pump pulse up both at the center (q=0) and the boundary (q=π/d) of the to a few ns with a temporal accuracy of a few tens of fs by Brillouin zone (d is the period). The group velocity for bulk means of a variable optical path. modes at gap edges is equal to zero. When the top layer has the The absorption of the light pump pulse sets up a local thermal lowest acoustic impedance, localized modes, with frequency stress. The relaxation of this stress generates elastic strain located within the gaps and vibrating within the very first pulses propagating along the stacking axis of the sample and layers of the superlattice, can be excited [6,7]. resonant acoustic modes at the surface [4]. Acoustic

† To whom correspondence should be addressed : [email protected] s246 ANALYTICAL SCIENCES APRIL 2001, VOL.17 Special Issue

1.0 (a) (b) 1st zone center band gap 0.8

0.6 0.48 | (u.a.)

THz 0

0.4 r/r 0.44 |∆ Frequency (THz) Frequency 0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.42 0.44 0.46 0.48 0.50 Vecteur q (π/d) Frequency (THz)

Fig. 1 (a) : Acoustic dispersion curve of a periodic multilayer. 3 kinds of high frequencies modes can be excited and detected by picosecond ultrasonics : localized (square), edge gap (circle) and propagating (triangle) modes. The vertical dotted line corresponds to the selection rule q=2k. The first zone center gap is displayed in the inset. (b) : Calculated spectrum of the relative change of reflectivity centered in first zone center gap of a semi-transparent superlattice ; each peak corresponds to a different mode.

In opaque systems localized mode in the zone center gaps the first one or two periods of the oscillation ignored. gives the main contribution to high frequency oscillations Our Oscillations are observable both on the real and the imaginary model shows that edge zone center gaps (q=0) could also parts of the relative reflectivity change, except for the thinnest contribute but to a much less extent. period sample. The measured frequencies are 0.71, 0.97, 1.42, In semi-transparent superlattices 3 kinds of modes could give 1.80 and 2.25 THz. The real and imaginary parts are either in rise to more or less pronounced peaks in the spectrum ∆r(ω)/r0 phase or out of phase as predicted by our model. Theoretical of the relative change of reflectivity : frequencies of localized modes are calculated for these • Excitation processes favor edge zone center gaps (q=0) structures. The measured frequencies are very close to the modes (as far as only photothermal processes are calculated values of the localized modes lying in the first zone considered). center gap (Fig. 3) ; this is in agreement with the fact that the • Propagation gives rise to singularities in the spectrum cap layer (Cu) has the lowest acoustic impedance. located at the frequencies of the localized modes ; The best fit to the experimental data for both the round trip contribution of the mode in the first zone center gap is time of the echoes and the localized mode frequencies is much larger than the one in the first boundary zone gap obtained with the following values of the densities and the 3 when the period of the superlattice is short compared to longitudinal sound velocities : ρCu = 8.9 g/cm , vCu = 4.6±0.2 the optical absorption length. nm/ps (corresponding to elastic constants CCu=188±5 GPa) 3 • Detection processes leads to the selection rule q±2k=0 and ρCo = 8.8 g/cm , vCo = 5.9±0.2 nm/ps (CCo=306±5 GPa). [8,9]. Peaks in ∆r(ω)/r0 due to this rule are sharper when These values are close to estimations made within Reuss the period is again much shorter that the effective optical approximation [11] for the bulk materials : CCu=170 GPa and absorption length of the system. CCo=305 Gpa respectively. The localized modes frequencies It should be mentioned that the frequencies of the modes predicted by our model are larger than experimental values for described above can be very close when the acoustic mismatch the thinner bilayers (2.1 and 2.6 nm). This small discrepancy is small. may be due to interface effects or atomic lattice dispersion. The photoelastic model predicts the magnitude of localized Experimental results modes in each band gap. It can be compared to the amplitude of the first echo after propagation through the whole structure. We studied 2 series of opaque and semi-transparent Fig. 4 shows that we have a quantitative agreement between multilayers. These studies allow to test our photoelastic model experimental and theoretical values for this ratio. We also which predicts the contribution of the various high frequency theoretically predict that the amplitude of the first zone center modes and gives the ratio between the respective amplitudes gap mode is ten times as large as the one of the first zone of the low frequency components of the spectrum (echoes or boundary gap mode ; this is coherent with the fact that only the Brillouin scattering oscillations) and high frequency first zone center localized mode was indeed experimentally oscillations. Elastic (and to a less extent optic and observed. photoelastic) coefficients of the layers are determined by the comparison between experimental and theoretical values. Semi-transparent multilayers It should be noted that the conditions for the validity of the We studied a series of 5 semi-conducting semi-transparent effective medium theory are very well satisfied in multilayers made of 3.9 nm thick CdTe layers and MnTe semi-transparent superlattices because of the very large layers with respective thickness 0.3, 0.6, 1.0, 1.1 and 2.5 nm. absorption length of the light compared to the period d. These samples were grown by MBE on a GaAs substrate. These epitaxial layers have a zinc blend structure and the Opaque multilayers stacking axis is along the (100) direction [12]. A MnTe layer is We studied a series of 5 metallic opaque multilayers made of on the top of each multilayer. 1.3 nm thick Co layers and Cu layers with respective thickness The real part of the relative change in reflectivity of a periodic 0.8, 1.3, 2.2, 3.7 and 5.5 nm. These samples were grown by RF multilayer CdTe3.9nm/MnTe2.5nm, deposited onto a 3 µm CdTe sputtering on a silicon cubic substrate (100). In situ RHEED buffer, is shown on Fig. 5. Low frequency (23.9 GHz) and experiments [10] have shown that Co and Cu layers are large amplitude oscillations can be clearly seen in the inset textured with a (100) preferred orientation. Cu layer is on the with the superimposed beating of several modes with top of each structure. frequencies close to 450 GHz. High frequency oscillations are displayed on Fig. 2 where the slowly varying thermal background has been subtracted and ANALYTICAL SCIENCES APRIL 2001, VOL.17 Special Issue s247

Copper thickness - frequency 5.5 nm - 0.71 THz

3.7 nm - 0.97 THz (u.a.) 0

r/r 2.2 nm - 1.42 THz ∆ 1.3 nm - 1.80 THz

0.8 nm - 2.25 THz

0 4 8 12 16

Time (ps) Fig. 2 Amplitude (full line) and phase (dotted line) of the relative change of reflectivity of high frequency oscillations corresponding to the localized modes for copper (5.5 → 0.8 nm) - cobalt (1.3 nm) superlattices. These localized modes are located within the first zone center gap.

3 0.4

2 0.2

Frequency (THz) Frequency 1

Ratio localized mode / echo 0.0

0246 01234567 Copper layer thickness (nm) Copper layer thickness (nm) Fig. 3 Experimental (circle) and theoretical (full line) Fig. 4 Ratio between the respective amplitudes of the first frequencies of the localized modes. These frequencies acoustic echo and the localized mode in terms of the copper belong to the first zone center gap. We use for the layer thickness. The full line is the theoretical prediction and 3 calculations ρCu = 8.96 g/cm , vCu = 4.6 nm/ps and ρCo = 8.8 the circles are the experimental results. 3 g/cm , vCo = 5.9 nm/ps.

The low frequency oscillations correspond to Brillouin We observe oscillations with frequency at 580, 600 and 670 scattering of the probe pulse by the low frequency modes GHz in the other samples with respective MnTe layers propagating within the structure ; we checked that the real and thickness 1.1, 1.0 and 0.6 nm. imaginary parts are in quadrature according to theoretical The calculated frequencies of high frequency modes predictions [2]. (localized and edge band modes for the first zone center gap) The real and imaginary parts of the relative change of are displayed on Fig. 6a. The measured frequencies are close reflectivity exhibit oscillations for all the samples but for the to the calculated frequencies. We use for the calculations ρMnTe 3 3 thinnest period multilayer. High frequency oscillations = 4.46 g/cm , vMnTe = 2.8±0.2 nm/ps and ρCdTe = 5.86 g/cm , observed in the different samples can be fitted by a single vCdTe = 3.0±0.2 nm/ps. frequency except for the largest period superlattice shown on Fig. 5. Acknowledgments For this sample, the spectrum ∆r(ω)/r0 displayed on Fig. 6b1 exhibits three peaks located at 450, 470, 500 GHz. The authors want to acknowledge F. Giron and P. Houdy • The frequency 470 GHz can be clearly attributed to a (Laboratoire d'Electronique Philips) and P. Djemia localized mode within the first zone center gap. (Laboratoire des Propriétés Mécaniques et Experiments done on the same system Thermo-dynamiques des Matériaux) for providing the MnTe2.5nm/CdTe3.9nm, but with CdTe as a cap layer, are cobalt-copper samples and G. Karczewski (Physical Institute shown on Fig. 5b2 ; the peaks at 450 and 500 GHz are of the Science Academia of Poland) for the CdTe-MnTe still present but the mode at 470 GHz is missing as superlattices. expected from the fact that ZMnTe =12.5 is lower than ZCdTe =17.6 where Z is the acoustic impedance. References • Frequencies at 450 and 500 GHz are close to the edge of the first zone center gap. They could correspond to modes 1. B. Perrin, B. Bonello, J.-C. Jeannet and E. Romatet, either at q=0 or q=2k. The difference between these Physica B, 1996, 219 & 220, 681. modes is only 15 GHz which is smaller than our frequency resolution. s248 ANALYTICAL SCIENCES APRIL 2001, VOL.17 Special Issue

0.8 (a)

~ 450 GHz 0.7

0.6 ) (u.a.) 0 0.5 Frequency (THz) Frequency r/r (∆

Re 0.4 23.9 GHz 0123 MnTe layer thickness (nm) 0 100 200 300 400 Time (ps) Localised mode

Fig. 5 Real part of the relative change of reflectivity of a (b1) periodic multilayer CdTe (3.9 nm) – MnTe (2.5 nm) deposited on a CdTe buffer (3mm) shows 2 oscillations : low frequenc y (u.a.) | oscillation (23.9 GHz) and several high frequency modes 0 Edges band gap modes which are beating near 450 GHz (arrow). r/r |∆

2. B. Perrin, C. Rossignol, B. Bonello and J.-C. Jeannet, (b2) Physica B, 1999, 262 & 263, 571. 3. C. Thomsen, H.T. Grahn, H.J. Maris and J. Tauc, Phys. Rev. B, 1986, 34, 4129. Fig. 6 (a) : Experimental0.4 (circle) 0.5 and theoretical 0.6 frequencies 4. H.T. Grahn, H.J. Maris and J. Tauc, IEEE J. Quantum Frequency (THz) Elec., 1989, QE-25, 2562. of localized and edge gap modes. These frequencies belong to ρ 5. B. Perrin, B. Bonello, J.C. Jeannet and E. Romatet, Prog. the first zone center gap. We use for the calculations MnTe = 3 ± ρ 3 Natural Sci., 1996, S6, 444. 4.46 g/cm , vMnTe = 2.8 0.2 nm/ps and CdTe = 5.86 g/cm , ± 6. H.T. Grahn, H.J. Maris, J. Tauc and B. Abeles, Phys. Rev . vCdTe = 3.0 0.2 nm/ps. (b) : Fourier spectrum of the high B, 1988, 38, 6066. frequencies modes for the superlattice with the largest MnTe 7. W. Chen, Y. Lu, H.J. Maris and G. Xiao, Phys. Rev . B, layer (2.5 nm). When a MnTe layer is on the top of the 1994, 50, 14506. superlattice the localized mode appears in the spectrum (b1) 8. A. Yamamoto, T. Mishina and Y. Masumoto, Phys. Rev. and is missing when a CdTe is the cap layer (b2). Let., 1994, 73, 740. 9. A. Bartels, T. Dekorsy, H. Kurz and K. Köhler, Phys. Rev. Let., 1999, 82, 1044. 10. F. Giron, PhD Thesis, University Paris VII, 1993. 11. O.L. Anderson, “Physical Acoustics”, 1965, Warren P. Masson, New York and London, 43. 12. W. Szuszkiewicz, E. Dynowska, E. Janik, G. Karczewski, T. Wojtowicz, J. Kossut and M. Jouanne, Acta Phys. Pol. A, 1996, 88, 357.