Probing photocarrier dynamics in a Bi₂Te₃–Te eutectic p–n junction with a laser terahertz emission microscope

Harvesting and saving energy are essential for a sustainable society. Among these, thermoelectric materials are attracting attention as materials capable of collecting waste heat and converting it directly into electricity.¹ Bismuth telluride (Bi₂Te₃)-based materials are well-known thermoelectric materials that show the highest performance near the room-temperature region.^2–4 To further improve performance, numerous studies have been performed to optimize thermoelectric transport properties through microstructure engineering. By creating hetero-interfaces and p–n junctions with Bi₂Te₃ and other materials, significant performance enhancements of several tens of percent to more than double those of the materials themselves have been reported.^5–7 It has been argued that the main factors responsible for these improvements are phonon scattering at microstructure interfaces, selective carrier transport due to p–n junctions and hetero-interface barrier energy, and anisotropic transport properties due to structural anisotropy.^7–10 Despite great efforts, because it is difficult to directly capture the phonon and carrier dynamics in the micro-region, the main focus is on macroscopic experimental results or discussions based on theories and models. Furthermore, the creation of new functions such as topological insulators/superconductors by Bi₂Te₃-based heterostructures has been reported in recent years.^11–13 Therefore, the evaluation of ultrafast carrier dynamics within structures is one of the most attractive topics not only for understanding thermoelectric properties but also for discovering new functions and their characterization.^14,15

Terahertz (THz) emission spectroscopy and imaging [laser THz emission microscopy (LTEM)] are currently developing methodologies for studying the spatiotemporal photocarrier dynamics excited locally in various materials and their heterostructures.^16–22 THz waves are generated by the transient displacement of photocarriers, and LTEM can discuss the dynamics on a time scale of a few picoseconds and visualize the dynamic photocarrier displacement with a spatial resolution of the laser beam diameter and the transport direction.^23–26 Recently, THz emission spectroscopy has also been recognized as a potential technique for evaluating carrier dynamics in antimony telluride alloys and thermoelectric materials that exhibit characteristics similar to those of the Bi₂Te₃–system.^27–29 Herein, we employ LTEM to study the ultrafast carrier dynamics in a multilayered crystalline Bi₂Te₃–Tellurium (Te) eutectic composite.

Eutectic composites, which are self-organized materials during the eutectic transition of one liquid phase into two solid phases during cooperative growth, provide a potential platform for exploring new properties and functionalities.^30–37 The Bi₂Te₃–Te eutectic composite is successfully grown by the vertical Bridgman method and consists of a pair of single-crystalline Bi₂Te₃ and Te layers with a thickness of a few tens of micrometers.³⁸ Although both are known as narrow bandgap semiconductors with bandgap energies of ∼170 and 330 meV, respectively,^39,40 material parameters such as carrier type, mobility, and relative potential strongly depend on the growth conditions,^41–44 which makes the picture of the heterostructure interface unclear. Furthermore, because the crystalline structures of Bi₂Te₃ and Te are highly anisotropic, determining the anisotropic photocarrier behavior may help improve the thermoelectric properties and bring new functionalities.

In the present work, we first studied the photocarrier dynamics near the interface of Bi₂Te₃–Te junctions. We clarified the carrier types of Bi₂Te₃ and Te and their potential distributions in the structure. Subsequently, we investigated the anisotropic transport properties of the Te layer. The hot carrier dynamics in the Te region showed unique properties, which we explained qualitatively by considering the effective mass of electrons and holes.

Figure 1 shows the schematic of the LTEM system. A Ti:sapphire laser with a center wavelength of 800 nm, a repetition rate of 80 MHz, and a pulse width of ∼100 fs was employed as the optical source. The excitation beam was modulated to 2 kHz using an optical chopper for lock-in detection and focused onto the sample surface vertically with a spot diameter of ∼5 μm. To avoid damaging the sample, we used an excitation power of 6 mW. A spiral-type photoconductive antenna (PCA) fabricated on low-temperature-grown gallium arsenide (GaAs) was used to detect THz waves in the time domain. THz waves generated vertically from the sample surface were reflected on an indium tin oxide (ITO) sheet and focused onto the PCA through two THz lenses. The polarization of the THz waves was detected using a wire-grid polarizer (WGP) placed between the two THz lenses. The sample was mounted on an x-y stage, and the LTEM images were monitored at a fixed time delay. The details of the LTEM have been reported elsewhere.^23,45

The samples used in this study were prepared using the vertical Bridgman method and composed of layered Bi₂Te₃–Te eutectic heterostructures.³⁸ The Bi₂Te₃ is in the minority phase relative to the Te phase in the layered structure, as shown in Figs. 2(a) and 2(b). The surfaces of the prepared samples had $(112̄0)$ and $(101̄2)$ planes. Crystallographic orientation was determined by x-ray diffraction and high-resolution transmission electron microscopy (see Fig. S1 and Ref. 38). Micro angle-resolved photoemission spectroscopy and scanning probe microscopy experiments suggested that the electrical conductivities of Bi₂Te₃ and Te are n- and p-type, respectively.³⁸ The built-in potential of the Bi₂Te₃–Te p–n junction is ∼120 meV with a depletion width of 1.5–2 μm. The possible band diagram derived from this information is shown in Fig. 2(c). E_C, E_V, and E_F are the conduction band, valence band, and Fermi energy levels, respectively, and E_g is the bandgap energy. The details of the materials investigated here and their characterization are described elsewhere.³⁸ 

The LTEM images and THz emission waveforms were monitored for the Bi₂Te₃–Te heterostructure in the region shown in Fig. 3(a). The orientation of the optical field direction was parallel to the Bi₂Te₃–Te interface, as indicated by E_pump in the figure. The white area at the center corresponds to the Bi₂Te₃ crystalline layer, and the blue regions on both sides correspond to the Te phases. The width of the Bi₂Te₃ layer in the measurement area is ∼15 μm. The yellow square corresponds to the exact location where the LTEM images were obtained.

Figure 3(b) (A, B) shows the THz time-domain waveforms emitted from the edge of the Bi₂Te₃ layer at points A and B, as indicated in Fig. 3(a). At these points, the emitted THz waveforms depended on the orientation of the THz electric field. The directions of the perpendicular (E_⊥) and parallel (E_‖) THz electric fields to the long axis of the Bi₂Te₃ layers are shown in Fig. 3(a). The THz emissions are linearly polarized and have strong components of the E_⊥ (red curve), whereas the components of the E_‖ are extremely weak. The waveforms at points A and B were flipped against each other. Figure 3(c) shows the LTEM image of the E_⊥ field superimposed on the optical microscope image shown in Fig. 3(a) and the respective cross-sectional profile. The red and blue colors represent the positive and negative amplitudes, respectively, with the delay stage fixed at ∼7.1 ps in the time domain shown in Fig. 3(b). The THz emission with E_⊥ fields is strong near the Bi₂Te₃–Te interfaces and has an opposite sign at the opposite interfaces. In addition, the strong emission region in Te is wider than that in Bi₂Te₃ because Te is a matrix phase, and Bi₂Te₃ forms layers within the matrix.

In general, THz emission mechanisms can be explained by two different models. One is transient drift photocurrent generation due to the built-in electric field near the surface or interface, and the other is transient diffusion photocurrent generation due to the photo-Dember effects or ballistic transport of excited hot carriers from the surface to the semiconductor inward.^26,46–48

The time derivative of photocurrents is the source of the THz emission. The emission due to the drift current can be described by the following formula:⁴⁹ 

where J is the photocurrent, μ is the carrier mobility, E_B is the built-in electric field, and I_P is laser intensity. The sign of E_THz differs depending on the sign of E_B. Conversely, the THz emission that contributes to ballistic transport can be described as

where E_p is the photon energy, E_g is the bandgap energy, and m* is the effective mass of the carriers. This formula indicates that the THz amplitude is a function of the laser intensity and the square root of the excess energies divided by the effective mass m* in this emission mechanism.⁴⁹ 

At the place near the interface between the Te and Bi₂Te₃ phases, the photocarriers are expected to be driven by the built-in field of the depletion layer, which corresponds to E_B in Eq. (1). Waveforms with similar shapes but flipped signs at points A and B suggest that the carriers excited at these points drift in the opposite direction, revealing that the built-in fields also have opposite signs. A comparison between these waveforms and waveforms from a dipole-type PCA shows that the photocurrents flow from the Bi₂Te₃ layers to the Te phase (see Fig. S2), and the current direction is indicated by red or blue arrows in Fig. 3(c). The positive or negative peaks of the THz amplitude along the interfaces in Fig. 3(c) reflect the photocurrents at the interface, which indicates that the Bi₂Te₃–Te interface forms a p–n junction, as shown in Fig. 4. The photocarriers accelerated by the built-in field of the p–n junctions generated THz emission near the interfaces. In the E_⊥ component, the electric field radiated by the other mechanisms was less than that radiated by the drift current and buried in the detected signal. The smaller E_‖ components (black curves) may be attributed to photocarrier excitation and THz generation in the Te regions. This is discussed later in this study.

The built-in field in the depletion region of the p–n junction is formed by the exchange of charges at the interface to create an equilibrium. The width of the depletion layers in the Bi₂Te₃–Te heterostructure was estimated from the cross-sectional profile in Fig. 3(c) to be ∼3.3 μm based on the full width at half maximum (FWHM) of the E_⊥ peak. A contact potential difference (CPD) profile observed by Kelvin probe force microscopy in Ref. 38 indicated that the transition width of the junction is ∼1.5–2 μm. Because the laser beams have a Gaussian profile with an FWHM of a few micrometers,⁴⁵ the observed transition width roughly agrees with the CPD value. Note that near the edges of the depletion layer, the contribution of the photocarriers to the THz radiation decreases because the built-in fields become weaker. Therefore, the FWHM does not provide an accurate depletion-layer thickness.

In contrast to the THz emission from the interfaces, only E_‖ components of the THz fields were emitted from the Te regions, as shown in Fig. 3(b) (C, D), indicated as points C and D in Fig. 3(a). In our system, the Te surfaces were perpendicularly illuminated by the laser, and we detected only THz emission in the direction normal to the surface. The THz emission from the no-built-in potential region is generally explained by transient photocurrents or nonlinear optical effects. In the case of nonlinear optical effects, such as optical rectification or the photon drag effect, the THz emission shows a strong azimuthal angle dependence of the incident laser. Although the emission from the Te region depended weakly on the polarization angle of the excitation pulse, it was quite different from that reported by Huang and Plank^50,51 (see Fig. S3). Therefore, we ruled out these effects as emission mechanisms. In the photocurrent case, when excited with a large beam spot diameter on the scale of several 100 μm, the phased array effect is induced, which generates THz waves in a direction tilted with respect to the sample surface.⁵² We can detect a small part of this emission. On the other hand, when excited with a small beam spot on a few μm scale, the THz emission is mainly attributed to the formation of a dipole normal to the surface, which emits THz waves in the direction parallel to the surface (see Figs. S4 and S5). Therefore, no THz emission was expected with our system setup; however, the THz emission was clearly observed. We should consider the unique photocarrier dynamics.

To understand the radiation mechanism, the THz emission properties in the Te region were studied further by characterizing the polarization of the emitted waves. Figure 5(a) shows the THz waveforms in the Te region taken with rotating wire-grid polarizer (WGP) angles from 0° to 150°. Rotation angles of 0° and 90° correspond to E_⊥ and E_‖, respectively, as shown in the inset. The waveforms strongly depend on the angles, and both the amplitudes and peak positions vary. The dependence of the peak amplitude on the angles at a delay time of 2.5 ps is summarized in Fig. 5(b). At first glance, one recognizes that a strong THz emission is observed along E_‖ and almost no emissions along E_⊥. The emission was linearly polarized. These results prove that the photocarriers excited in the Te regions travel strongly in either the $[101̄1̄]$ or $[1̄011]$ direction and generate a photocurrent along the E_|| direction. On the other hand, the photocarriers travel in the $[12̄10]$ and $[1̄21̄0]$ directions with the same transport properties, and no THz emission exists along the E_⊥ direction. The traveling directions of the photocarriers in the Te region and at the Bi₂Te₃–Te interface were 90° off. Therefore, the THz emission in the Te region is not due to the contribution of p–n junctions but to a different mechanism. The shift in the peak positions in Fig. 5(a) might be due to the nature of the spiral-type PCA used in the detector (see Fig. S6).

Figure 3(d) shows an LTEM image of the E_‖ fields and their respective cross-sectional profiles. The delay stage is fixed at around 4.3 ps in the time domain of Fig. 3(b). In this case, the THz emission is strong in the Te regions, and there is no sign of inversion. The width of the transition region for E_‖ was estimated from the amplitude of 20–80% to be ∼5.2 μm. Because the THz emission mechanisms for the E_‖ component are different from those for E_⊥ component, the transition region values for these components are different from each other.

These THz emissions from the Te regions show interesting radiation properties with only the E_‖ component explained by a mechanism different from that of the p–n junction model. However, the photocarriers excited at the no-built-in potential regions are expected to emit no detectable THz radiation field with our system, as mentioned above. Here, Bičiūnas reported the THz emission from $(101̄2)$ surface with the electric field having an in-plane component as we observed in this study.⁵⁴ According to the report, the anisotropic effective mass of electrons has an important role in this anomalous THz radiation; however, this role was not discussed in detail. Here, we calculate the effective masses of electrons and holes, incorporate them into Eq. (2), and discuss the anisotropic carrier transport due to the anisotropic effective masses. Although there have been many studies on THz radiation from narrow bandgap semiconductors such as InAs and InSb,^26,46,47,55 the contribution of the anisotropic effective mass has not been taken into account in detail.

Te has helical chains arranged in a hexagonal array, as shown in Fig. 5(c). Atoms in a helical chain form strong covalent-like interactions between the two nearest atoms, and helical chains form van der Waals-like interactions between the nearest chains.⁵⁶ Owing to this anisotropic bonding nature, Te has anisotropic effective electron and hole masses along the directions parallel and perpendicular to the chains (c-axis).^57,58 Figure 5(d) shows a schematic of the energy band diagram of Te in the H–K (parallel to the c-axis) and H–A (perpendicular to the c-axis) lines in the Brillouin zone.⁵³ It should be noted here that the hot electrons and holes are injected into the Te regions at a laser wavelength of ∼800 nm (photon energy of 1.55 eV). The transition points denoted as A_e–D_e (for electrons) and A_h–D_h (for holes) are indicated by red dashed lines. The valence band maximum (VBM) and conduction band minimum (CBM) were located near the H point (1/3, 1/3, and 1/2) in the Brillouin zone, and there was another valence band near the VBM. The hot carriers are excited at k_‖ = 0.36, 0.39 in the H–K line, and at k_⊥ = 0.22, 0.27 in the H–A line.

The effective masses of electrons and holes at the k points are defined by the formula,

Table I gives the estimated effective masses, excess energies, and E_THz, which suggest that the hot electrons contribute to the THz radiation along the direction perpendicular to the c-axis, whereas the hot holes contribute along the direction parallel to the c-axis. Therefore, the net photocurrent having an in-plane component flows, which explains the observed THz emission. This calculation shows that a smaller effective mass of the hole than that of the electron along the c-axis agrees with the experimental result reported by Bičiūnas.⁵⁴ In addition to point H, there are other extrema in both the valence and conduction bands that can also affect the excitation with a Ti:sapphire laser. However, we observed THz emission with an excitation photon energy of 0.79 eV (wavelength of 1560 nm), which is smaller than the next smallest bandgap energy (∼1.09 eV) at point L in the Brillouin zone⁵³ (see Fig. S7). Therefore, we excluded other extrema from the discussion. To understand the relationship between THz emission and carriers excited at the extrema, we need to measure at various excitation wavelengths.

Although the above discussions are entirely speculative, we propose a quantitative picture of the THz emission mechanism for the photoexcited Te regions in Fig. 5(e). The Te phase in the investigated sample had a $(101̄2)$ plane at the surface and the helical chains were diagonally aligned. The main transient photocurrents perpendicular (J_⊥) and parallel (J_‖) to the c-axis were induced owing to the smaller electron and hole effective masses, respectively. Consequently, the entire transient photocurrent J_total, which is the sum of J_⊥ and J_‖ has an in-plane component and generates an unusual THz emission, as shown in Fig. 5(e).

The emission from the inside of the Bi₂Te₃ layer does not have an E_‖ component, which suggests that the diffusion along the $[11̄00]$ and $[1̄100]$ directions in the Bi₂Te₃ layer have the same properties, whereas the E_⊥ component strongly depends on the illumination position (see Fig. S8). This is presumably attributed to the photocarrier excitation with beam tales inside the depletion layer. We attributed the emission from the inside of the Bi₂Te₃ layer to the formation of dipoles perpendicular to the surface, which were not detectable with a small beam diameter (see Fig. S5). To investigate the properties of Bi₂Te₃ layers in detail, it is necessary to improve the imaging resolution. It is also important to apply this method to other smaller self-organized composite structures, as different sizes will give rise to different properties and phenomena. This improvement is currently under way in our laboratory.

To understand the THz radiation mechanism and hot-carrier dynamics in these new materials, we need to consider the effects of impurities, optical or acoustic phonon scattering, anisotropic absorption coefficients, and density of states, which are unexplored areas of research. These discussions are beyond the scope of the present study, and we leave them for future work.

The photocarrier dynamics in multilayered crystalline Bi₂Te₃–Te eutectic composites were investigated and visualized using the LTEM technique. The THz emission at the Bi₂Te₃–Te interface was polarized perpendicular to the interface, revealing that the carrier motion was accelerated by the built-in electric field at the interface. From the polarity of these photocurrents, it is proven that Bi₂Te₃ and Te phases have n- and p-type characteristics in this structure, and p–n junctions are formed at the interfaces. In contrast, strong THz emission with an electric field polarized parallel to the interface was observed in the Te regions. An in-plane THz emission similar to that observed in this study cannot be observed in general semiconductors. This unique THz emission is qualitatively explained through hot photocarrier anisotropic transport by considering the effective mass of electrons and holes for the first time. The difference between the traveling directions of the electrons and holes induces a photocurrent with an in-plane component and generates THz emissions, as shown in Fig. 5(e). In thermoelectric devices, one of the key aspects of device performance is the separation of electrons and holes to improve the thermoelectric power.^59,60 The anisotropic behaviors of electrons and holes discussed here will provide significant insight into thermoelectric materials. LTEM clarified the local carrier dynamics in the microstructures and revealed the potential distribution and anisotropic transport properties. These findings contribute to the exploration of eutectic heterostructures as new functional materials and provide new avenues for cutting-edge thermoelectric and photovoltaic devices.

See the supplementary material to discuss the surface plane of the sample, the photocurrent direction in Fig. 3, the excitation polarization dependence of the THz emission properties emitted from the Te region in the sample, the excitation beam diameter dependence of the THz emission radiated by the photo-Dember effect, detected THz waveforms vs rotation angle of a wire-grid polarizer, the excitation point in the Brillouin zone, and the excitation position dependence of the THz emission waveforms in the Bi₂Te₃–Te structure.

We are grateful to Mr. Yang for exploring the property of THz emissions from InAs shown in Fig. S5. It helped us improve the discussion. This work was supported in part by JSPS KAKENHI under Grant No. JP18KK0140, JSPS core-to-core program, Program for Leading Graduate Schools: “Interactive Materials Science Cadet Program,” JST, CREST under Grant No. JPMJCR22O2, and JST, the establishment of university fellowships toward the creation of science and technology innovation under Grant No. JPMJFS2125. K.B., A.M., and D.A.P. thank the MAB/2020/14 Grant within the IRAP program of the Foundation for Polish Science, co-financed by the European Union under the European Regional Development Fund and Teaming Horizon 2020 program of the European Commission; and the HARMONIA Project (No. 2013/10/M/ST5/00650) from the National Science Center for their support of this work.

The authors have no conflicts to disclose.

All authors contributed equally to this work.

Fumikazu Murakami: Data curation (equal); Formal analysis (equal); Investigation (lead); Methodology (lead); Software (equal); Visualization (equal); Writing – original draft (lead). Kazunori Serita: Data curation (equal); Investigation (supporting); Methodology (equal); Validation (equal); Writing – review & editing (supporting). Iwao Kawayama: Conceptualization (equal); Methodology (equal); Validation (equal); Writing – review & editing (supporting). Hironaru Murakami: Methodology (equal); Validation (equal); Writing – review & editing (supporting). Kingshuk Bandopadhyay: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Andrzej Materna: Investigation (equal); Validation (equal); Writing – review & editing (supporting). Augustin M. Urbas: Conceptualization (equal); Data curation (equal); Writing – review & editing (equal). Dorota A. Pawlak: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Validation (equal); Writing – review & editing (equal). Masayoshi Tonouchi: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.