Resonant Excitation of the Ferroelectric Soft Mode by a Narrow-Band THz Pulse

1. Introduction

Today, an important task is to develop methods for ultrafast control of the ferroelectric order parameter. Solving this problem will allow to create the new energy efficient optoelectronic devices such as memory cells and modulators [1,2,3,4]. In magnetic materials, this problem has already been solved using optical [5,6] or terahertz [7,8,9] pulses. However, in the case of ferroelectrics, this problem remains unsolved, since the mechanisms that allow to achieve ultrafast switching remain anclear [10,11,12,13].

At present, there are some theoretical [14,15,16,17,18] and experimental works that show the possibility of influencing the ferroelectric order parameter by optical [19,20,21] or THz [22,23,24,25] pulses. However, full and stable ultrafast polarization switching has not been demonstrated. The state of polarization in a ferroelectric is directly related to the soft phonon mode. In previous studies, broadband THz pulses have been used for ultrafast switching of ferroelectric materials. However, the result was not achieved. Therefore, we decided to try narrow-band THz pulses for direct resonant excitation of the soft phonon mode and thus influence the ferroelectric order parameter.

One of the promising materials for this is B_0.8Sr_0.2TiO₃ (BST). It is radiation resistant, energy efficient, as well as has fast switching time and stable parameters in a wide temperature range, and low dielectric loss [26]. BST is uniaxial ferroelectric with perovskite structure. At room temperature BST is in ferroelectric phase with tetragonal unit cell (space group P4mm) and goes to paraelectric phase with a cubic unit cell (space group Pm3m) above the Curie temperature. For the study, we chose BST films on two types of substrates with different orientations: MgO(001), MgO(111) and Si(001).

Мagnesium oxide was chosen because is a typical substrate material for BST films and other perovskite-like ferroelectrics, since they have fairly close cell parameters, and there is a well-established deposition technology, which makes it possible to obtain high-quality films. Silicon was chosen because the integration of ferroelectric films into silicon technology is currently a topical issue [27]. The use of ferroelectrics as a gate in a field-effect transistor makes it possible to create a non-volatile and electrically reprogrammable memory sells [28]. It should be noted that ferroelectric materials are deposited on silicon substrates at high temperatures. This leads to the mutual diffusion of the components at the ferroelectric-semiconductor interface, the formation of a transition layer, and deterioration of the crystal structure [29]. As a result, instability of the polarized state occurs and the number of rewriting cycles is reduced. To solve these problems, transition layers based on simple oxides such as (Ba,Sr)TiO₃ [30,31] with a thickness of several nanometers are formed at the interface between the semiconductor and the ferroelectric [32].In addition, depositing BST on silicon when creating solar cells enables more efficient absorption of visible and ultraviolet radiation [33,34], which significantly increases their efficiency.

Here we present the investigations results of the strong narrow-band THz pulses effect on ferroelectric soft mode at B_0.8Sr_0.2TiO₃ films deposited on MgO(001), MgO(111) and Si(001) substrates.

2. Materials and Methods

We investigated the nonlinear optical response dynamics in three barium-strontium titanate (B_0.8Sr_0.2TiO₃, BST) films under excitation by narrow-band THz pulses of few picoseconds duration. These samples were fabricated by radio-frequency (RF) sputtering of a B_0.8Sr_0.2TiO₃ ceramic target. The first sample was a 375 nm thick BST film deposited on a (001)-oriented MgO substrate. The second sample had the same thickness and composition, but with a sublayer of the same film with a thickness of 2.5 nm and deposited on a silicon substrate. The substrate was the monocrystalline p-type silicon with a resistivity of 12 Ohm/cm and crystallographic orientation (001) [34]. The third sample was an 800 nm thick BST film on a (111)-oriented MgO substrate The sample fabrication processes are described in more detail in [27,32,34].

The XRD patterns of BST/MgO(001) ,BST/Si(001) and BST/MgO (111) samples are shown in Figure 1a), 1b) and 1c), respectively.

Figure 1a) shows that the 375 nm thick BST film on the MgO (001) substrate is monocrystalline, with the spontaneous polarization vector directed perpendicularly to the substrate surface. The lattice parameter c for this sample is 0.04041 nm. In contrast, Figure 1b) demonstrates that the 375 nm thick BST film on the (001)-oriented silicon substrate is polycrystalline, containing crystallites with (001) and (011) plane orientations parallel to the substrate plane. The spontaneous polarization vector for (001) crystallites is perpendicular to the substrate surface, while for (011) crystallites, it is at an angle of about 45 degrees. The lattice parameter for this film is c = 0.4035 nm.

Figure 1c) shows that the BST film on the MgO(111) substrate is epitaxial and contains only a rhombohedral phase, with polarization directed perpendicularly to the substrate. The unit cell parameters are a = 0.39616 nm and α = 89.519°. The XRD pattern demonstrates that the film is oriented along the [111] direction, so [111]_film || [111]_MgO. The unit cell volume of the rhombohedral BST film is 1.5% less than that of the tetragonal ceramic target.

It should be noted that the BST/MgO(001) film has strong stress at the film/substrate interface, significantly higher than in the BST film on the (111)MgO substrate. In the silicon film, this stress are also considerably lower due to the 2.5 nm thick BST sublayer, which inhibits mutual diffusion of the components and encourages BST crystallization in the ferroelectric phase [27].

The dynamics of nonlinear optical response in BST films when they are excited by narrow-band THz pulses was investigated using a modified experimental setup described in [35].

A Cr:forsterite laser system with a wavelength of 1240 nm, a pulse repetition rate of 10 Hz, and a duration of 100 fs was used to generate narrow-band THz pulses. THz pulse generation occurred in the organic crystal OH1. To generate narrow-band THz pulses, the amplified laser pulse was split into two parts, with each passing through one arm of a Mach-Zehnder type interferometer. By adjusting the delay between these pulses before compression, it was possible to achieve beating of the optical pulses at a necessary frequency. The resulting frequency-modulated optical chirp irradiated the OH1 crystal, generating narrow-band terahertz radiation. The spectral line width was 0.1-0.2 THz, depending on the central frequency. Measurements of the temporal waveform of narrow-band THz radiation pulses were performed in the electro-optical detection scheme on a 1 mm thick ZnTe crystal [36]. Figure 2 shows (a) the temporal waveform and (b) the corresponding spectrum of narrow-band THz pulses at a frequency of 1.2 THz.

Similar measurements of temporal waveforms were made in a frequency range of 1.2 to 2.0 THz. To estimate the electric field strength of THz pulses at various frequencies, we measured the energy of THz pulses and the spatial distribution of the THz beam in the focal plane of the focusing off-axis parabolic mirror THz pulse energy measurements were made using a Golay cell, while the spatial distribution was measured with a terahertz camera. Thus, we obtained a comprehensive set of experimental data on the terahertz source parameters enabling us to estimate the electric field strength at different frequencies. The electric field ranged was estimated according to [37] as 320 kV/cm - 1.45 MV/cm, depending on the central generation frequency.

Detection occurred at the frequency of the second optical harmonic. This technique is one of the most sensitive methods to study the order parameter of ferroelectrics [38,39,40]. The BST films deposited on the MgO substrate were measured in transmission geometry while the film on the Si substrate was measured in reflection geometry.

Table 1 displays a comparison of the samples.

3. Results

Figure 3 (a-c) demonstrates the dependence of the normalized THz-induced second harmonic signal dynamics on the time delay between pump and probe pulses in BST/MgO (001), BST/Si (001), and BST/MgO (111) films, respectively, when the narrow-band pump pulses were in the range of 1.2 THz - 2.0 THz.

As can be seen from Figure 3 (a)-(c), the intensity of the THz-induced SHG signal for all three samples correlates with the temporal waveform of the excitation THz pulse, shown in Figure 1 (a). In addition, the figure shows that for the BST/MgO (001) film, the highest SHG intensity is observed at the excitation THz pulse frequency of 1.6 THz. In Figure 3b,c it is not possible to unambiguously identify the pumping frequency that provides the highest SHG signal.

Figure 4(a)-c) demonstrates the frequency spectrums of the dependencies shown in Figure 3, obtained by the Fourier transform in the region up to 2.5 THz. For comparison, the green dashed lines represent the spectrum of the SHG signal measured when the samples are excited by broadband THz pulses with electric field up to several MV/cm [41].

It should be noted that, for a correct comparison, the obtained frequency dependences were successively normalized to the probe power, film thickness with regard to the coherence length, and the electric field of THz radiation. The effect of pulse propagation in the MgO substrate was also taken into account [35]. The coherence length was estimated using the expression l_coh=λ_ω/4(n_ω± n_2ω),, where n_ω and n_2ω being the refractive indices for the fundamental and SHG waves, and + (-) refers to the reflection (transmission) geometry, respectively. Thus, for BST films on MgO substrates, the coherence length was found as1150 nm. This value exceeds the film thickness, allowing us to use the exact sample thickness for normalization. For the BST film on Si substrate the coherence length was estimated as 70 nm. This value was used in the normalization.

Normalization on the THz field was performed relative to the first degree of its strength. This is due to the fact that in the presented frequency spectrums only the peaks corresponding to the frequency of excitation THz pulses are observed.

Figure 4(a) demonstrates that the spectral amplitude of the signal measured at the excitation pulse frequency of 1.6 THz significantly exceeds the spectral amplitudes of the signals obtained at other excitation pulse frequency. This can be explained as follows. The soft ferroelectric mode in the BST film on the MgO (001) substrate has a frequency of about 1.67 THz [22,35,42]. By exciting this material with narrow-band THz pulse of a suitable central frequency, we acting on the polar ion more effectively, displacing it from the equilibrium state, thereby increasing the polarization of the medium. Since the SHG signal intensity is proportional to the second degree of the polarization, the amplification of the SHG signal at 1.6 THz shown in Figure 4(a) may be explained by the resonance effect on the polar ion.

Figure 4(b) shows that, for the BST/Si (001) film the spectral amplitudes are not significantly different, while the amplitude for the 2.0 THz pump frequency it is considerably smaller. It is important to note that in this case there is no pronounced resonance amplification of the signal. This can be explained by the fact that the sample BST/Si (001) is polycrystalline with regions with different polarization directions relative to the sample surface, which are not affected equally by excitation THz pulses.

Figure 4(c) demonstrates the frequency spectrum for the BST/MgO (111) film in the range up to 2.5 THz. It can be seen that the peak corresponding to the excitation pulse frequency of 1.8 THz has the highest intensity. This can be explained by the fact that according to work [43] the soft ferroelectric mode in Ba_0.8Sr_0.2TiO₃ film on MgO substrate with crystallographic orientation (111) has a frequency of about 1.9 THz. The maximum amplitude of the peak with a frequency of 1.8 THz, rather than 1.9 THz, can be explained by the width of the spectral line in this range of about 0.2 THz.

Thus, Figure 4 a) and c) demonstrate that the use of narrow-band THz pulses to excite phonon modes is much more efficient than broadband THz pulses. In particular, they make possible the resonant excitation of the soft phonon mode in ferroelectrics.

Figure 5 presents the frequency spectrums for the BST/MgO (111) film in the range from 2.2 THz to 4.5 THz. For this sample, the frequency spectrums show a second peak at double frequency of the excitation THz pulse. No second peak is observed in the frequency spectrums of the other two samples. These dependences were normalized to the second degree of the THz field strength.

The presence of two peaks in the spectrum at the fundamental and at the doubled frequency can be explained by the fact that the dependence of the SHG intensity on the external electric field is quadratic. Indeed, the SHG intensity in the THz field can be represented as a decomposition either by the THz field E_Ω in the case of a non-ferroelectric crystal:

$$I^{2\mathsf{\omega }}(E_{\Omega })\propto {({\mathsf{\chi }}^{(2)}+{\mathsf{\chi }}_{\mathrm{E}}^{(3)}{E}_{\Omega })}^2{(I^{\mathsf{\omega }})}^2,$$

(1)

or by polarization P(E_Ω) in the case of a ferroelectric crystal

$$I^{2\mathsf{\omega }}(P(E_{\Omega }))\propto {(P_0+{\mathsf{\chi }}_{\mathrm{P}}^{(3)}P(E_{\Omega }))}^2{(I^{\mathsf{\omega }})}^2,$$

(2)

where χ⁽²⁾(2ω; ω, ω) - crystallographic quadratic susceptibility, ${\mathsf{\chi }}_{\mathrm{E}}^{(3)}(2\omega ;\Omega ,\omega ,\omega )$ - cubic susceptibility. The cubic susceptibility can be considered as a measure of polarization switchability: the higher the value of χ⁽³⁾_, the lower THz field is required to control (switch) polarization.

Obviously, in the case of linear dependence of P(E_Ω), for example, in weak fields, relations (1) and (2) are identical. In the general case, in order to distinguish (1) and (2), it is necessary to investigate the dependences of the SHG intensity on the THz field.

When decomposing the second degree of the sum, two field-dependent terms appear: linear I₂ and quadratic I₃:

$$I_2\propto {\mathsf{\chi }}^{(2)}{\mathsf{\chi }}_{\mathrm{E}}^{(3)}{E}_{\Omega },$$

(3a)

$$I_3\propto {({\mathsf{\chi }}_{\mathrm{E}}^{(3)})}^2{(E_{\Omega })}^2.$$

(3b)

These terms in the Fourier decomposition give, respectively, signals at the fundamental Ω and doubled 2Ω frequencies of the incident wave.

4. Conclusions

In conclusion, we demonstrated two important issues of the developed technique. Firstly, the narrow-band THz pulse may excite the specific modes in ferroelectric, including the soft mode. This should result in a dynamical polarization switching, analogously to the case of a broadband excitation. Secondly, excitation is much stronger for frequencies close to a specific mode, which means a resonant excitation. This is in contrast to a broadband excitation, where the resonances cannot be isolated.

The developed narrow-band THz spectroscopy allows us to compare the impact of the input THz field on ferroelectric polarization measured by SHG in different samples. The highest impact or the highest switchability was achieved in 800 nm thick BST film on an MgO (111) substrate. This can be explained by the presence in this sample of polarization component parallel to the THz field. The lowest impact or the lowest switchability was obtained in 375 nm thick BST film on a Si (001) substrate. This is due to it`s polycrystalline structure. The single crystalline BST film on an MgO (001) substrate demonstrates intermediate impact.