Phonon anharmonicities and ultrafast dynamics in epitaxial Sb2Te3

In this study we report on the investigation of epitaxially grown Sb2Te3 by employing Fourier-Transform transmission Spectroscopy (FTS) with laser-induced Coherent Synchrotron Radiation (CSR) in the Terahertz (THz) spectral range. Static spectra in the range between 20 and 120 cm−1 highlight a peculiar softening of an in-plane IR-active phonon mode upon temperature decrease, as opposed to all Raman active modes which instead show a hardening upon temperature decrease in the same energy range. The phonon mode softening is found to be accompanied by an increase of free carrier concentration. A strong coupling of the two systems (free carriers and phonons) is observed and further evidenced by exciting the same phonon mode at 62 cm−1 within an ultrafast pump-probe scheme employing a femtosecond laser as pump and a CSR single cycle THz pulse as probe. Separation of the free carrier contribution and the phonon resonance in the investigated THz range reveals that, both damping of the phonon mode and relaxation of hot carriers in the time domain happen on the same time scale of 5 ps. This relaxation is about a factor of 10 slower than expected from the Lorentz time-bandwidth limit. The results are discussed in the framework of phonon scattering at thermal and laser induced transient free carriers.

Scientific RepoRtS | (2020) 10:12962 | https://doi.org/10.1038/s41598-020-69663-y www.nature.com/scientificreports/ rather large concentration of p-type carriers around 10 20 cm −3 1 due to the presence of native antisite defects-Sb atoms occupying Te lattice sites-and is diamagnetic. In literature, lattice dynamics and infrared-active lattice vibrations of in the rhombohedral V 2 -VI 3 compounds Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 can be found 12,13 . Those, together with their thermal conductivity investigation of Bi 2 Te 3 and Bi 2 Se 3 as a function of various doping materials, revealed the influence of considerable anharmonic effects for this class of materials.
However, the fundamental understanding of carrier behavior in Sb 2 Te 3 remains controversial, being affected by the contribution of topological and bulk states to the carrier behavior and by the structural properties of the material. Both can vary depending on the fabrication technique [14][15][16] . The work is organized into a first part in which static THz spectroscopy is used to probe an in-plane phonon mode at equilibrium upon changing temperature. In a second part instead, the same phonon mode is probed dynamically on an ultrafast timescale within a pump-probe scheme employing a femtosecond laser as pump and the THz light as probe. Results are discussed in the framework of strong electron-phonon interaction and phonon mode damping by hot free carriers.

Results and discussion
Part 1: Temperature dependent measurements. We report here on temperature dependent measurements of Sb 2 Te 3 far-infrared spectra acquired in transmittance configuration over a broad range of frequencies (20 to 90 cm −1 ) and temperatures (300 K down to 5 K). The spectra are normalized to the spectra taken without sample at the same temperature (T) ("empty case"). The semi-insulating Silicon substrate's (R > 5 kΩ cm) transmission change can be neglected in this range of T, as found by reference measurements (not shown). Transmission spectra, in general, reflect the two contributions of free-carrier and phonon absorption. In this study the spectra were collected with the THz electric field vector oriented parallel to the [111] oriented c-axis (see Fig. 2b) to probe predominantly the in-plane charge dynamics. The results are shown in Fig. 1a. The absorption feature centered at 62 cm −1 (300 K) is attributed to the transverse optical (TO) IR-active E u mode of Sb 2 Te 3 , vibrating perpendicularly to the c-axes, according to Richter et al. 11 Note that in our previous study 9 it has been erroneously attributed to an IR active A u mode. As temperature is decreased, a total decrease of THz transmittance is Curves are normalized to the empty case with a baseline becoming more noisy at around 300 K. (b) E u phonon mode softening upon temperature decrease. (c) Experimental change (squares) of the peak width (FWHM) and fit (red line) as described in the text. (d) Raman spectra of the same Sb 2 Te 3 sample measured at 300 K and 10 K with labeled modes 1,6 . Hardening of all modes is observed as T is decreased, as opposed to the IR active mode in (b). (e) Electrical measurement of free carrier increase upon temperature change. The error on the carrier measurement is < 4%. Color code corresponding to the different temperatures is reported in the legend in (a). Colored graded arrows indicate mode softening for the IR-active mode and mode hardening for all Raman modes upon temperature decrease, respectively. Scientific RepoRtS | (2020) 10:12962 | https://doi.org/10.1038/s41598-020-69663-y www.nature.com/scientificreports/ observed (~ 33%), phenomenologically attributed to an increase of conductivity due to a raise of free carrier concentration and/or increase of carrier mobility. The temperature-dependent carrier concentration in the same sample, obtained by Hall measurement, is shown in Fig. 1e. Indeed, an increase of the free carrier concentration upon decreasing T is observed which is typical for Sb 2 Te 3 , as reported in previous studies 17 . Moreover, recent density functional theory (DFT) calculations show that the band gap of Sb 2 Te 3 increases with increasing temperature due to the thermal expansion of Sb 2 Te 3 18 and such raise of the bandgap would result in a reduction of the free carrier concentration. Experimental verification of the theory can be found in Boschker et al. 19 .
Interestingly, as temperature is decreased the frequency position (ν 0 ) of the peak progressively shifts toward lower wavenumbers from ν 0 = 62 cm −1 (300 K) to ν 0 = 52 cm −1 (5 K), as shown in Fig. 1b. However, the peak position change tends to saturate below 20 K and becomes less pronounced close to 300 K. The slight asymmetric line shape of the dip at 62 cm −1 evolving upon temperature ( Fig. 1a) was fully reproduced by the Drude-Lorentz simulation of the film transmission (see also Fig. S1).
The interpretation of the transmittance in the THz range is not trivial for Sb 2 Te 3 and similar materials as also reported in literature 11 , since the contribution to both reflectivity and transmittance measurements stem from both free carriers and phonons, and the decoupling of the two contributions is not straightforward. However, for Sb 2 Te 3 a strong phonon resonance can be well separated from the relatively broad spectral feature induced by the free carrier contribution to the complex refractive index 20 .
Indeed, also in our case, the transmittance curves in Fig. 1a can be modeled by a frequency dependent Drude like background and by a Lorentzian phonon resonance at ν 0 = ω 0,L /2π = 62 cm −1 using the dielectric function: The first term ε ∞ is the dielectric function at high frequency, the second and third are the Drude and phonon contributions, respectively (see SI for details). Employing a model for the transmittance 21 in which multiple reflections in the sample can be taken into account, the plasma frequency ω p,D and the Drude damping constant Γ D can be obtained by a fitting procedure (see supplementary information) . In the transmittance curves in Fig. 1a, the plasma frequency ω p,D controls the total transmittance value and Γ D the transmittance slope increase over the considered bandwidth. At room temperature, the value of ω p,D / 2π = 7,305 cm −1 is remarkably close to the value determined from Hall effect data 19 in bulk material. Moreover, ω p,D is related to the free carrier concentration and their effective mass m * via ω 2 p,D = Ne 2 ε 0 m * . Inserting the value for ω p,D obtained from our fit (SI, Fig. S1), and using the measured N obtained within the Hall measurements (N = 1.3 . 10 20 cm −3 of holes at 300 K, see Fig. 1e), an effective mass of m * = 0.19⋅m e is obtained and it compares well with values determined for bulk material 22 (0.18⋅m e ). Concerning the value of Γ D = 205 cm −1 (300 K), it is only 8% smaller than the value for the bulk case and this might be related to a slightly different stoichiometry or to some structural difference between bulk and thin film structure. The temperature dependent fits of the transmittance data in Fig. 1a indicate an increase in ω p,D by 20% at 5 K compared to the 300 K case www.nature.com/scientificreports/ (see SI for details). Considered that ω 2 p,D ∼ N , the finding is consistent with the measured increase of carrier density upon decreasing temperature (Fig. 1e).
In contrast to the commonly expected behavior, the frequency of the IR-active E u phonon mode decreases when the temperature is lowered. Commonly, phonon frequencies decrease (soften) with raising temperature due to the increase in interatomic separations resulting from the thermal lattice expansion 23 . In fact, this conventional behavior is observed for the Raman-active phonon modes, as demonstrated in Fig. 1d by Raman spectra measured in the same temperature range. All Raman-active phonon modes exhibit a shift towards lower frequencies (softening), as expected in case of thermal lattice expansion 23 . From this result we can also exclude that the softening of the IR-active phonon mode is dominated by temperature-dependent strain induced by the mismatch between the thermal expansion of the silicon substrate and that of the Sb 2 Te 3 film. Hence, only the E u -type IR-active mode shows the peculiar behavior upon T change-softening upon temperature decrease/ hardening upon temperature increase-. This, and the fact that an energy shift reported in literature for similar materials (see below) is way smaller than 10 cm −1 as found in our case, suggests that the specific mode (E u ) under investigation is strongly affected by anharmonicities 32,34 .
Shifts of soft phonon modes which usually cover a comparably large range of frequencies have been reported in literature and are usually attributed to low-temperature phase transitions. The most common ones are martensitic transitions or ferroelectric transitions 24,25 . Nevertheless both can be excluded since Sb 2 Te 3 is known to be not ferroelectric 26 . Furthermore, Raman measurements performed in the same temperature range (see Fig. 1d) do not exhibit a qualitative change indicating a low-temperature phase transition. A further possible explanation could be the coupling of the phonon mode with the electronic system, which is treated as anharmonic contribution to the phonon self-energy. In semiconductors, the most general form of interaction between electronic excitations and phonons is the so-called deformation-potential mechanism 27 treated as anharmonic contribution of the harmonic lattice dynamics phonon together with other sources of anharmonicities such as thermal expansion effects and phonon decay into multiple phonons. The thermal expansion is referred as the quasi-harmonic approximation and its contribution to frequency shifts is very small at low T. In literature there are many examples of doping induced renormalizations of the frequency as well as the lifetime of the phonons at low T 27 . Shifts to lower frequencies of phonon lines in Raman spectra and a broadening of these lines were reported in n-and p-type Si and p-type Ge 28,29 . Similar results have also been found for heavily doped GaAs 30 . Furthermore, several examples for transition-metal chalcogenides 31,32 and other narrow band gap semiconductors 33 have been given. In our case, the measured hole concentration changes in the unintentionally p-doped Sb 2 Te 3 in Fig. 1e) and its corresponding peculiar E u peak behavior upon decreasing T. Such behavior points toward strong anharmonicities contribution on the phonon self-energy. Those results compare well with similar topological insulators systems such as Bi 2 Te 3 and Bi 2 Se 3 32,34 , in which the anharmonic contributions are attributed to coupling between surface phonons and surface plasmon originated by the bulk free carriers 32 .
Besides the temperature-dependent frequency shift, the E u phonon mode exhibits also a pronounced broadening with increasing temperature, as shown in Fig. 1c. The phonon line width Γ L , extracted by fitting the transmittance data in Fig. 1a utilizing the model for the dielectric function (third term in the formula, see SI), decreases with decreasing temperature T, changing from Γ L = 12.6 cm −1 (300 K) to Γ L0 = 6.7 cm −1 (5 K), where Γ L0 is the line width for T → 0 K. The trends for Γ L and τ are qualitatively in line with what observed for optical phonons in most semiconductors 35 but, the lifetime of a phonon τ is limited by interactions with boundaries, defects, free carriers, and other phonons. Decoupling of the multiple anharmonic contributions to the phonon self-energy is not trivial, especially for highly doped materials such as in our case, where strong influence of the band gap and carrier densities starts to play a role.
To understand the observed temperature dependence of the peak width Γ L , the experimental data from Fig. 1c were fitted by the relation Ŵ L (T) = Ŵ 1 +Ŵ 0 1 + 2/(e ℏω 0 2kT − 1) within the model of Klemens 36 , who assumed a phonon decay via the so-called three phonon decay channel, where the phonon at ω 0 decays into two phonons of ± ω 0 /2. Following such a symmetrical decay like in Beechem et al. 37 , one finds Ŵ 1 = 6.02 cm −1 , Ŵ o = 0.54 cm −1 as free fit parameters with Ŵ 1 + Ŵ 0 =Ŵ L (0) and ω 0 = 2πν 0 (ν 0 = 61.7 cm −1 ) the resonant frequency of the E u phonon mode for T → 0, as derived from Fig. 1b. As compared in Fig. 1c, the simple model and the measured values of Ŵ L show excellent agreement at low temperatures but become gradually different as temperature approaches room temperature values. At higher temperatures > 125 K, the Fermi-Dirac occupation of charge carriers and Boltzmann occupation of phonon states as well as thermal expansion effects along with a gap change 18 dominate the slope rather than the pure microscopic decay mechanism. Part 2: Time resolved measurement. The phonon-carrier interaction has been also investigated within a time-resolved experiment employing the THz probe-fs-laser pump setup depicted in Fig. 2a (see "Methods" and SI Fig. S3). Figure 2c shows the temporal evolution of THz transmittance for Sb 2 Te 3 on Si (111) in the spectral range between 10 and 100 cm −1 at low (0.6 mJ/cm 2 ) and high (3 mJ/cm 2 ) laser fluences. Let's recall that a pump-induced decrease of the THz transmission can be phenomenologically attributed to an increase of the conductivity in the material due to generation of free carriers. Indeed, both signal evolutions show a resolution limited drop (~ 0.7 ps) attributed to the photo-injection of carriers. The drop is deeper for higher pump fluences, indication of higher carrier density production in respect to the low fluence case, as expected. For the high fluence case, the signal recovery displays an exponential increase with a fast time constant of τ f2 = 4.2 ± 0.4 ps followed by a second recovery with slower time constant of τ s = 169 ± 17 ps (see Fig. 2b). At low fluence instead, the signal recovery can be fitted with only one fast time constant of τ f1 = 5.1 ± 0.5 ps (~ 18% slower decay compared to τ f2 of high fluence case). This suggests that the higher the density of photoexcited carriers and their energy (larger width in the frequency domain), the faster the phonon damping (τ f1 > τ f2 in the time domain), as also found for silicon 38 .
Scientific RepoRtS | (2020) 10:12962 | https://doi.org/10.1038/s41598-020-69663-y www.nature.com/scientificreports/ Within the fast decay time (τ f1 and τ f2 ), it is reasonable to assume an interplay between different fast carrier thermalization and recombination pathways such as phonon emission and recombination via traps and defects. The slower recovery might be linked to the presence of ordered vacancy layers. The latter could represent another recombination channel for photo-excited carriers that cannot recombine through alternative faster pathways 5 . Therefore, here we focus on spectrally resolved ultrafast response in the low fluence case only. Spectrally resolved snapshots (resolution of 1 cm −1 ) at given delay time can also be measured in the spectral range between 25 and 120 cm −1 under specific operation of the setup depicted in Fig. 2 (see "Methods").
A full color-coded plot of the transmittance spectra T(t) = I/I 0 , where I is the detected signal and I 0 is the incident THz signal is shown in Fig. 3a. In Fig. 3b instead, we show selected spectra of the absorbance A = log [1/T(t)] (normalized to the spectra taken at −14 ps delay before time zero) and corresponding Lorentz fits from before (−14 ps) and after (+2 ps) time-zero, in other words, the THz probe before and after the pump excitation ("unpumped" and "pumped" labels, respectively). The color-coded plot of the transmittance in Fig. 3a reveals some interesting features: (1) the total broad band transmittance significantly drops in a transient state immediately after laser excitation (−43% transmittance due to an increase of absorbance) and the THz signal recovers within ~ 20 ps; (2) the observed main transmittance dip at ~ 62 cm −1 corresponds to the E u phonon resonance discussed within the static temperature dependent experiment. The satellite dip at ~ 40 cm −1 was previously reported and attributed to the E g (1) phonon mode 39 . In the following we focus only on the main resonance at ~ 62 cm −1 because no dynamic change at our available resolution could be observed for the satellite feature; (3) a width change within a time interval < 20 ps is measured, but no frequency shift is observed. A more quantitative analysis has been done by fitting the absorption peaks in Fig. 3b within the framework of a Drude-Lorentz model (see "Methods" and SI for fitting details). www.nature.com/scientificreports/ To extract the E u phonon parameters from our dynamic data for the pumped (A p and Γ p ) and unpumped (A u and Γ u ) cases, we disentangled the time dependent Drude-background intensity and we compared its temporal intensity evolution in Fig. 4 to the total and the phonon related absorption contributions, as well as to the peak width change Γ p /Γ u determined from the fits plotted there. The main result of that comparison is that both, the phonon recovery as well as the dynamics of the Drude-like free carriers, are damped within the same time constant of τ ~ 5 ps.
The phonon lifetime corresponding to the phonon damping constant Γ L shown in Fig. 1c varies between 0.8 ps > τ =ℏ / Γ L > 0.45 ps according to Heisenberg's uncertainty relation (see SI, Fig. S2). The room-temperature value τ ~ 0.45 ps is, thus, one order of magnitude smaller than what is observed by our time-resolved experiments. This finding and the same decay time for both carrier and lattice dynamics might be explained by a high correlation of the two systems, as also emerged for the time dependence experiment. Moreover, the time resolved experiment suggests that energy thermalization of laser-excited carriers via the emission of phonons is the main mechanisms on the fast time scale of ~ 5 ps. Within this simulation we also cross-checked (see SI, Figs. S4-6) that after excitation at low fluence, laser induced lattice strain in the first 20 ps has negligible influence on the observed fast dynamics (< < 1%) 40 .
If we recall the static experiment in the previous section, we learned that both, peak width and frequency strongly decreased upon temperature decrease between 300 and 5 K. In the time resolved experiment instead, the phonon peak width shows a transient rise (15% between pumped and unpumped shown in Fig. 3b) but no frequency shift is detected. A reason could be that we are performing the experiment at T > 300 K, a temperature at which the phonon frequency shift might be less significant and saturate, as also observed in the static case at ~ 300 K (see Fig. 1b, c). Note that within the framework of lattice temperature simulations (see SI, Figs. S4-S6) it is calculated that the temperature increases of the total system at 300 K, induced by the pump laser, is of only 10 K. Moreover, the total absence of any frequency shift might also be attributed to the fact that the optical excitation of Sb 2 Te 3 at 800 nm (1.55 eV) generates free electron-hole pairs by interband transitions. The effect of hole or electron doping on the phonon shift would be in opposite directions 41 , giving an average cancelation of the peak shift.

conclusions
In summary, the combination of static and time resolved FIR, Raman and THz spectroscopy techniques have been employed to investigate electron-phonon coupling in epitaxial Sb 2 T 3 at thermal equilibrium as well as in transient states after femtosecond laser excitation.
First, static THz spectroscopy is used to probe an in-plane phonon mode at thermal equilibrium upon changing temperature. The absorption feature at ~ 62 cm −1 is assigned to the IR-active E u phonon mode, which shows a peculiar softening of 10 cm −1 wavenumbers upon temperature decrease. Comparison with Raman measurements shows that such behavior is only observed for this phonon mode suggesting how strongly it is affected by anharmonicities as found in similar material systems 41 . At low temperatures the phonon linewidth Γ L follows the microscopic two phonon decay model 36,37 but deviates from that at temperatures > 125 K, where Fermi-Dirac occupation of charge carriers and Boltzmann occupation of phonon states as well as thermal expansion effects along with a gap change 18 come gradually into play.
Then, by ultrafast time resolved measurements we have demonstrated that laser excitation of the films at very low fluences leads to strong changes of both, the same phonon mode and free carriers. The recoveries after the laser excitation of the two systems are decoupled in the analysis and it was found that both systems relax on . Normalized transient THz transmittance delay traces from the total signal ( +) and the peak transmittance dip (black dots) of the phonon resonance compared to single exponential fits (red line) with a recovery constant of τ = 5.1 ps. Green dots are width measurements and orange diamonds the free carrier offset change as derived from Lorentz fits to the phonon peak and its spectral background. The green line is a single exponential fit to width data using the same τ as for the red line. The derivative of the total trace (black stars) is compared to a Gaussian as derived from the fits (blue line) indicating the time resolution limit.
Scientific RepoRtS | (2020) 10:12962 | https://doi.org/10.1038/s41598-020-69663-y www.nature.com/scientificreports/ the same time scale of ~ 5 ps, a factor of 10 slower than expected from the time-bandwidth limit of the phonon resonance. This again points toward a strong coupling of carrier and lattice through scattering of photoexcited carriers with the IR active phonon mode. The results also show that THz spectroscopy techniques are powerful tools to investigate Sb 2 Te 3 properties that can be exploited for applications such as in photonic and electronic memories and processors, in THz detection and thermoelectric devices. These findings combined to material engineering could illuminate future avenues for device improvements.

MBE growth.
A series of Sb 2 Te 3 films, unintentionally doped, were deposited by MBE on a highly resistive (5 kΩcm −1 ) crystalline Si (111) − (√3 × √3)R30-Sb surface with a thickness ranging between 30 and 80 nm 42 . The samples were capped with 35 nm of ZnS-SiO 2 by sputtering to prevent oxidation of the films.
Raman measurement. Raman spectra were acquired exciting samples with the 632.8 nm line of a He-Ne laser and the scattered light was analyzed using a single spectrograph (Horiba/Jobin-Yvon LabRam HR Evolution) equipped with an LN 2 -cooled charge-coupled device detector. The spectra were recorded in backscattering geometry from the sample surface. For the low temperature measurements, a continuous-flow microscope cryostat (Cryovac KONTI) was employed during Raman spectra acquisition.
Static far infrared measurements. Measurements in the far-infrared regime were carried out under vacuum conditions in transmission geometry using a high-resolution Fourier transform infrared spectrometer (BRUKER IFS 125HR) of the THz beamline at Helmholtz-Zentrum Berlin (HZB, BESSY II) 43 . The spectral range in the presented experiments covered wavenumbers between 20 and 120 cm −1 (i.e., frequencies from 0.6 to ~ 3.6 THz) and was limited by the selected source(s), the 6 µm multilayer-Mylar beamsplitter and the detector, a 4.2 K Si-Bolometer from Infrared Labs. Static measurements were also repeated using Coherent Synchrotron radiation (CSR) from the slicing source (see "Methods" below) to prepare time-resolved studies. Low temperature measurements were performed by employing an optical LHe-cryostat Oxford Optistat CF2 equipped with Quartz windows and installed in-vacuum inside the sample compartment of the IFS125 HR in transmission geometry.

Ultrafast THz-Fourier transform spectroscopy (THz-FTS).
Optical pump-THz spectral probe measurements were carried out using the laser-slicing method at the BESSY II storage ring 44,45 . Here single cycle THz pulses are generated by laser-energy modulation of relativistic electrons at 6 kHz repetition rate, extracted from a dipole source in the ring and merged again with the naturally synchronized laser pulse about 17 m after the interaction in the sample compartment of the Fourier transform spectrometer IFS125 HR 43 . As depicted in Fig. 1a, a part of the slicing laser (few 100 µJ pulse energy, 100 fs length, λ = 800 nm) is used to excite the sample (absorption in film see SI Fig. S3) while the naturally synchronized THz pulse probes the relative transmittance change in the Sb 2 Te 3 film. The diameter of the THz pulse was set by apertures to ~ 1.5 mm diameter adopting the laser spot to somewhat larger in size than the THz probe allowing for fluence values up to few mJ/cm -2 on the sample. The angle of incidence between laser and THz pulse was about 20° limiting the time-resolution to ~ 0.7 ps FWHM by geometrical pulse elongation. Time resolved spectra were acquired performing FTS with a 4.2 K Si-bolometer as detector and gated detection at 6 kHz using the UHFLI 46 lock-in device and its digital boxcar function. The laser is modulated with a 3 kHz mechanical chopper as in Fig. 2a to probe the pumped and un-pumped cases separately. Time resolution is achieved by measuring spectra at different arrival time delays between fs-laser and THz probe pulse as controlled by a mechanical delay stage equipped with optical encoders. The spectral bandwidth of the THz pulse was thoroughly obtained in Ref. 10 , it peaks at about 2 THz ranging from 0.3 to 3 THz (~ 10 to 100 cm −1 ). All THz transmittance spectra were determined using the same optical geometry, but without Sb 2 Te 3 , film as a reference. The laser fluences are determined as described in SI.