1. Introduction

V-VI compounds, such as Bi₂Te₃, Bi₂Se₃ and Sb₂Te₃ have attracted intense interests due to their unique properties. Their high surface conductivity and low thermal conductivity provide prerequisite in the application of making thermoelectric devices [1]. Besides, they have been experimentally proved as a new quantum phase of matter called topological insulator (TI), who has a bulk gap and robust surface Dirac cones protected by time-reversal symmetry [2, 3]. Their unusual electron structure leads to extraordinary physical properties, such as high surface mobility and strong spin-orbital coupling, making them potential candidates for electronic and spintronic devices [4, 5]. To investigate the carrier and phonon dynamics of TI materials, various methods have been applied, such as optical pump-optical probe (OPOP) [6–13], optical pump-terahertz probe (OPTP) [14], Raman spectroscopy [15], angle-resolved photoemission spectroscopy (ARPES) [16], second harmonic generation (SHG) [17] and time-resolved photoluminescence spectroscopy (TrPLS) [18]. All of these methods have been proven to be effective ways of studying carrier dynamics.

With ultrafast optical pump-probe technology, the carrier and phonon dynamics of V-VIcompounds have been intensively investigated [8,19–26]. Commonly, the transient absorbance change signal comprises both the damped oscillatory part and the non-oscillatory part, induced by coherent phonons and hot-carrier relaxation respectively. Chirped damping harmonic oscillators are used to characterize both the high-frequency and low-frequency oscillatory parts, while multiple exponential decay functions are used to fit the non-oscillatory signal. J. L. Wang et al. reported the non-oscillatory part of the transient absorbance change signal of Bi₂Te₃ thin films thoroughly by attributing the non-oscillatory signal to 3 processes including the free carrier absorption, band filling effect, and electron-hole recombination [26].

The materials used in the studies mentioned above are usually grown in the following ways, pulsed laser deposition (PLD) [14], molecule beam epitaxy (MBE) [15] and chemical vapor deposition (CVD) [25]. Among the three methods of growing materials, MBE is the best way to get high-quality single-crystal materials with least impurity induced, and the thickness of the sample can be strictly controlled to the order of quintuple layers (QL) [27]. The samples used in this study were grown by MBE. Thus, the possible influence caused by impurity or the imperfection of the sample can be deduced to the minimum within our capability.

In former studies, thickness dependent research on TIs have been carried out by different groups. A thickness-dependent Raman study on nanoscale Bi₂Te₃ thin films showed the Raman peaks shifted with changing the sample thickness [15]. Another research wok showed the surface state of Bi₂Se₃ changed a lot when the thickness changed from 1 nm to 6 nm [28]. So it is natural to think about the thickness dependent carrier dynamics of Bi₂Te₃ thin films. Y. Wang et al. reported a thickness-dependent study on Bi₂Te₃ thin films with a two-color pump-probe setup, the thickness of the samples varies from 5 nm to 100 nm [25]. The results indicated that the high-frequency oscillation signals induced by coherent optical phonons vanished when the thickness decreased to less than 10 nm. While in our study, the high-frequency oscillation signals of Bi₂Te₃ thin films were still visible at the thickness of 3 nm. Thus, it is important to investigate the thickness-dependent carrier and phonon dynamics of Bi₂Te₃ materials at the atomically-thin order if we are going to put it into application.

In this study, Raman spectroscopy of Bi₂Te₃ films were acquired to characterize the samples. Ultrafast time-resolved optical pump-probe experiments were carried out to get the transient absorption profiles of the Bi₂Te₃ films. Hence, the carrier thermalization and relaxation process in the samples radiated by the pump light are presented.

2. Experimental Implementation

The Bi₂Te₃ films used in this study were synthesized by MBE at Tsinghua University. During the MBE growth of Bi₂Te₃ film on STO (111), the growth rate is checked by ex situ atomic force microscopy (AFM) measurement. Figure 1(a) shows a typical $1\times 1$ reflection high-energy-electron diffraction (RHEED) patterns of an 8 QL Bi₂Te₃ film. The sharpness of the RHEED patterns provide an evidence for the high quality of our sample. Figure 1(b) displays the AFM image of an 8 QL Bi₂Te₃, and we can see a flat platform with some steps with the height of ~1 nm (Fig. 1(c)), corresponding to 1 QL Bi₂Te₃ film. The AFM and RHEED results of other samples with different thickness are similar to 8 QL and are omitted here.

 

Fig. 1 (a) RHEED patterns of a Bi₂Te₃ film. (b) AFM image of a Bi₂Te₃ film (500 nm × 500 nm). (c) The line profile along the red line in (b).

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Raman experiments were carried out with 532.8 nm laser light, the Raman scattering light was detected using a spectrograph with the lowest Raman shift of 60 cm⁻¹. The Raman spectra of samples with different thickness are shown in Fig. 2. Three Raman peaks are observed representing the $A_{1g}^1$, $E_g$ and $A_{1g}^2$ optical phonon modes respectively. And the corresponding center frequencies are 1.88 THz, 3.09 THz and 4.02 THz which are consistent with former Raman studies on Bi₂Te₃ [7].

 

Fig. 2 The Raman spectra of samples with different thickness. Three peaks characterizing $A_{1g}^1$,${\text{E}}_g$ and $A_{1g}^2$ coherent optical phonon modes respectively.

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In order to investigate the ultrafast excited carrier dynamics of Bi₂Te₃ samples, femtosecond pump-probe technique is used in this paper. The experimental setup of pump-probe spectra system has been well described in our previous work [29,30].

3. Results and discussion

3.1 Carrier dynamics of Bi₂Te₃

The transient absorption profiles were acquired using 400 nm pump light with a fluence of 100$\mu J/c{m}^2$. Figure 3 shows the transient absorption profile of 20 QL Bi₂Te₃ film with 584 nm probe light in both long time range (0-150 ps) and short time range (0-15 ps). According to a former research, the longtime range profile exhibits the carrier thermalization and relaxation process, while in the short time range of about 10 ps, the high frequency oscillation signal presents the absorbance change induced by optical phonons [8].

 

Fig. 3 (a)The transient absorbance change of the 20 QL Bi₂Te₃ film in the long-time range of 0-60 ps showing the carrier behavior of the sample. The red dots represent the experiment data, while the blue line is the fitting curve. (b) Transient absorbance change of 20 QL Bi₂Te₃ film in the short time scale of 0-15 ps.

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Regardless of the high frequency oscillation in the first 10 ps, the profile can be fitted with three exponential decaying functions and a damped sinusoidal oscillation referring to previous studies [8,25,26], as shown in Eq. (1).

In the function, the three exponential decaying functions stand for the electron-electron interaction, electron-lattice interaction and electron-hole recombination process respectively. While the damped sinusoidal function represents the transient absorbance change induced by electron-acoustic phonon interaction process. By fitting the 20 QL signal, the characteristic figures are thus acquired and shown in Table 1.

Table 1. Characteristic figures of the fitting signal of 20 QL films

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With the characteristic figures in the table, it is revealed that in the very short time range of about 0.3 ps after the pump, the electron-electron interaction process dominates the absorbance change. While in the time range of about 0.3-20 ps, the electron-lattice interaction and the electron-acoustic phonon interaction process influence the absorbance change together. After the electron has reached equilibrium with lattice, the influence of the electron-hole recombination process become dominant. Moreover, we can see the amplitude of f_e is negative, this represents the rising part of the signal.

Applying this fitting method to all the Bi₂Te₃ films with different thickness, there are only 3 characteristic figures obviously vary with the thickness including the electron- hole recombination time, the initial amplitude of the electron-hole recombination process and the initial amplitude of electron-lattice interaction process, as shown in Fig. 4. While the other figures stay almost the same as in Table 1.

 

Fig. 4 The black line presents the thickness dependence of electron-hole recombination time. The blue line and red line exhibit the thickness dependence of initial amplitude of electron-hole recombination and electron-lattice interaction process respectively.

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In Fig. 4, the increasing initial amplitude of the recombination process may be the result of the increasing number of carriers in thicker samples. While the initial amplitude of electron-lattice interaction process decreases with the increasing thickness, indicating the electron-lattice interaction gets weaker and becomes less important in thicker samples. All these phenomena show that the electron-hole recombination gradually dominants the hot carrier relaxation process when the sample get thicker, meanwhile the electron-lattice interaction is weakened.

It is obvious that the carrier lifetime increases with the sample thickness in Fig. 4. The possible reason is the influence of surface recombination. The contribution of surface recombination is less important for thicker films and results in longer carrier life. The recombination process can be described by Eq. (2), where V and S are the volume and area of films, respectively. U_bulk is the bulk recombination rate, and U_surf is the surface recombination rate.

From Eq. (2), we get

From Eq. (4), it is found that the carrier lifetime increases with the thickness of films, which is in agreement with the experimental results. We can also find that U_bulkd is much smaller than U_surf because the carrier lifetime increases nearly linearly with the film thickness.

3.2 Optical phonon dynamics of Bi₂Te₃

Analysis has also been done to the high frequency oscillation signal in the first 15 ps. Figure 5 shows the transient absorbance change signals (ΔR/R) of Bi₂Te₃ samples on a short timescale (0-15 ps) with 400 nm pump and 584 nm probe light. Different from a previous work where high frequency oscillations couldn’t be found when the sample is thinner than 10QL [25], obvious oscillations of sub-picosecond time scale are found in the ΔR/R signals of Bi₂Te₃ films from 3 to 10 QL. The difference might be caused by the different way of growing samples. However, the magnitude of oscillations does not monotonously depend on the thickness of films. It is found from Fig. 5 that the oscillations are the most significant in the 4 QL-8 QL samples and the signal gets weaker when increase or decrease the thickness. Apart from the change of magnitude, the time evolution of oscillations in films with different thicknesses are similar, which indicates that the oscillations do not originate in the film geometry, but the intrinsic properties of the material, i.e. coherent optical phonons (COP). However, it is readily found that the periods of oscillations vary with time.

 

Fig. 5 The transient absorbance change of Bi₂Te₃ films with different thickness shown in short-time range of 0-15 ps.

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In order to get a better insight to this phenomenon, the non-oscillating components in Fig. 5 are filtered with a high pass filter and the remaining components are shown in Fig. 6.

 

Fig. 6 The extracted high-frequency signals induced by coherent optical phonons. The red dashed box shows the obvious period change of the oscillation signals.

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Observing that the changing patterns of different samples are similar, the following analysis will take the signal of 6 QL sample as an example. The fast Fourier transformation (FFT) spectrum of the oscillations in 6 QL film is shown in Fig. 7(a). It is found that there are multiple peaks near the frequency of 2 THz, covering the wide range between 1 to 2.2 THz.

 

Fig. 7 (a) The FFT spectrum of the COP induced oscillations in 6 QL film. The red dash line indicates the 1.88 THz phonon mode observed in Raman spectra. (b)The short-time Fourier transformation results of the signals of 6 QL Bi₂Te₃.

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According to our continuous-wave (CW) Raman spectra results (Fig. 2) and previous works [15], the most significant COP mode within the range of 1.6 to 2.0 THz is the $A_{1g}^1$ mode, which has a central frequency at 1.88 THz. The Raman results and the varying periods of oscillations indicate that the sub-picosecond oscillations are not only caused by the $A_{1g}^1$ COP mode.

It is found that the varying of oscillation periods also has its periods (between vertical dash lines approximately). The short-time Fourier transformation results (Fig. 7(b)) of the signals of 6 QL Bi₂Te₃ show that the oscillating frequency varies nearly periodically, which indicates a frequency modulation (FM) on the $A_{1g}^1$ COP mode. The period of the FM is about 5 ps, and the corresponding frequency and wavenumber are 0.2 THz and 7 cm⁻¹, respectively.

Now we discuss the origin of the FM phenomena. The thicknesses of the Bi₂Te₃ layer are under 20 nm. Therefore, the time scale of the reflected light interference between film surfaces is sub-femtosecond. Thus, we can exclude the influence of the light interference, and attribute the FM phenomena to other vibration mode of the sample. The intrinsic vibration frequencies of optical phonon of Bi₂Te₃ are above the FM frequency of 0.2 THz, so the intrinsic vibration mode of Bi₂Te₃ cannot contribute to the FM phenomena. Here we propose a possible driving force according to the results of a previous study [31], where the Raman wave numbers of longitudinal interface vibration modes are measured. The Raman wave numbers of the interface vibration mode between Bi₂Te₃ and SiO₂/Si are around 10 cm⁻¹, which are within the same order of our FM results.

4. Summary

In conclusion, optical pump-probe experiments were carried out on the Bi₂Te₃ thin films with different thicknesses. In the experiment, we found that the electron-hole recombination become more important to the hot-carrier relaxation process with increasing the thickness of the film. However, the electron-lattice interaction gets weaker and the electron-acoustic phonon interaction stays the same. More interesting, a frequency modulation phenomenon is observed on the COP characterized signal, we currently suspect that it has something to do with the interface vibration, while the exact driving force still needs further study.