Terahertz surface and interface emission spectroscopy for advanced materials

Figure 1(a) demonstrates a schematic of THz emission spectroscopy system. An ultrafast laser with fs pulse duration is usually used as a laser source. The pulses are divided into two parts via a beam splitter. The transmitted beam with the majority of the pulse energy is used to pump samples, from which the emitted THz pulses are collected, collimated, and focused onto a detection crystal such as ZnTe (1 1 0) by a pair of parabolic mirrors. At the same time, the probe beam with the minority of the pulse energy is focused onto the detection crystal and overlaps with the pump beam. Then the generated THz radiation can be detected and recorded by an electro-optical sampling technique [47], and the parallel and perpendicular components of the THz radiation can be extracted with the help by a pair of wire-grid polarizers [48].

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Figure 1(b) depicts a THz radiation signal oscillating in ps time scale, of which both amplitude and phase spectra in frequency domain are derived after Fourier transformation of the time-domain signal (figures 1(c) and (d)). The full width at half maximum in amplitude spectrum represents bandwidth of the THz emitter, which is related to the dynamics of the photoexcited species in the samples and the detection bandwidth of the THz system. The detection bandwidth of the THz system can be improved via different electro-optical crystals with wide bandwidth such as GaP and GaSe [49]. Laser-induced plasma [50] and photoconductive antenna [51] are also alternative detection methods with broad detection bandwidth.

In general, THz radiation is related to the time derivative of the photogenerated carriers or the polarization/magnetization by the ultrafast intensive laser pulses, which can be described as follows:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\vec {E}}_{{\rm THz}}}\propto \frac{\partial {}^{2}\vec {P}}{\partial {{t}^{2}}}+\frac{\partial \vec {J}}{\partial t}+\frac{\partial }{\partial t}(\nabla \times \vec {M})\nonumber \end{align} \tag{ 1 }$$

where $\vec {P}$ is the nonlinear polarization, $\vec {J}$ is the photocurrent density, and $\vec {M}$ is the magnetization. Here, we mainly discuss the nonmagnetic materials with $\vec {P}$ or $\vec {J}$, while the THz radiation from magnetic materials are discussed in the previous review [52]. The nonlinear polarization refers to the optical rectification process (figure 2(a)) when the incident photon energy is below the bandgap of materials [53]. The incident photons can induce a low frequency electric field via difference-frequency generation. Such process is described by the nonlinear dielectric polarization P (Ω) as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle P_{i}^{(2)}(\Omega)=\sum\limits_{j,k}{{{\varepsilon }_{0}}\chi _{ijk}^{(2){\rm ef\,\!f}}}(\Omega ,\omega +\Omega ,-\omega){{E}_{j}}(\omega +\Omega)E_{k}^{\ast }(\omega)\nonumber \end{align} \tag{ 2 }$$

where $\chi _{ijk}^{(2){\rm ef\,\!f}}$ is an effective second-order nonlinear susceptibility and ω is fundamental angular frequency. Due to the symmetry, this second-order nonlinear optical effect can only exist in non-centrosymmetric materials. However, as the surface or interface will break the bulk symmetry materials, this optical rectification process can also happen at the surface or interface. The strength of optical rectification is directly relevant to the nonlinear optical coefficients of materials. Early studies focusing on the THz radiation from LiNbO₃ [54], ZnTe [55], GaSe [56], and organic crystal dimethyl amino 4-N-methylstilbazolium tosylate [57] make great contributions to the development of THz time-domain spectroscopy. Moreover, a surface depletion field will enhance the optical rectification, which can also happen in centrosymmetric materials. Different from the bulk optical rectification, the effective nonlinear susceptibility of surface optical rectification with the help of the surface electric field is expressed as: $\chi _{ijk}^{(2){\rm surf}}=3\chi _{ijkl}^{(3)}E_{z}^{{\rm surf}}$ [58, 59], where $\chi _{ijkl}^{(3)}$ is a third-order susceptibility tensor and $E_{z}^{{\rm surf}}$ is the surface depletion field. The bulk and surface optical rectification contributions can be distinguished according to the THz radiation as a function of azimuthal angle, i.e. rotational symmetry of a crystalline surface as the difference between nonlinear susceptibility tensors will lead to different nonlinear polarization and azimuthal angle dependence.

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When the incident photon energy is above the bandgap of materials, photogenerated carriers will accelerate under intrinsic electric fields and further induce THz radiation. Surface depletion field is one of the intrinsic fields induced by the band bending at the surface as shown in figure 2(b). Both conduction and valence bands bend due to the Fermi level difference between surface and inferior region of semiconductor. This surface field will introduce the photocurrent surge, which is among the earliest THz radiation mechanism of semiconductor materials [11]. Such process often occurs in semiconductors with wide band-gap, such as GaAs (1.43 eV), InP (1.34 eV), and CdTe (1.4 eV). Figure 2(b) demonstrates n-type semiconductors with the upward surface band bending, while p-type semiconductors will bend downwards. This difference of band bending in n-type and p-type semiconductors will reverse the polarity of THz time-domain signal as the photocarriers in n-type and p-type semiconductors accelerate along opposite directions [11, 60]. Moreover, the surface electronic states of materials can be modified by surface engineering with physical or chemical methods such as introducing surface roughness [61], coating metallic film [62], and chemical passivation [63]. This modification will change the surface depletion field and the quantum yield of photocarriers in materials, which will be reflected in THz radiation signal. From the variation of the THz radiation signal combined with THz radiation models, the nature of surface field, band bending, and carrier transport dynamics can be obtained by THz emission spectroscopy.

In narrow band-gap semiconductors such as InAs (0.36 eV) and InSb (0.17 eV), significant difference between electron and hole mobility will introduce the separation of the photoexcited electrons and holes at the surface as shown in figure 2(c). This separation will introduce the diffusion photocurrent due to the concentration gradient of photocarriers from the surface to the bulk, and the drift photocurrent under the Dember electric field [64]. This process is the so-called photo-Dember effect, of which the Dember electric field is perpendicular to the surface and the THz radiation pattern is parallel along the surface as indicated with the orange dumbbells in figure 2(c). This suggests that to detect THz signal, it will be better to set the experiments at oblique incidence and in the reflection geometry (as shown in figure 1(a)) so that the carrier gradient and the resulting THz radiation pattern are tuned with an angle to the surface. If the surfaces are modified by metallic particles or strips as shown in figure 2(d), a strong photocarrier gradient parallel to the surface can be formed [65, 66]. This will introduce a lateral photo-Dember field with the photocurrent along the surface and the THz radiation perpendicular to the surface. With the lateral photo-Dember effect, THz radiation can be observed from GaAs (1 0 0) surface coated with rough gold film at normal incidence [62]. This lateral photo-Dember effect can be used to enhance THz radiation from traditional GaAs photoconductive switches [66].

Based on second-order nonlinear processes, photogalvanic effect (PGE) and PDE can generate transient photocurrent from real carriers under resonant excitation (above bandgap) instead of nonlinear polarization of virtual carriers under nonresonant excitation (below bandgap) [53, 67]. These two effects can also introduce THz radiation. Take linearly polarized excitation as an example, linear PGE originates from the spatial charge transfer during the transition from valence band to conduction band in non-centrosymmetric materials (figure 2(e)), hence the resulting photocurrent flowing along the inherent polar direction in materials. PGE can occur in any materials with a polar axis or without inversion symmetry, and the photocurrent is controlled by the crystalline symmetry of materials [68]. This is different from the photocurrent surge governed by either surface electric field or spatial carrier inhomogeneity.

However, the PDE arises from the momentum transfer from the incident photons to the electrons near the surface in the penetration depth as shown in figure 2(f). The charge carriers in materials will move along the direction of the incident light and generate transient photocurrent, and thus the PDE is related to the incident wave-vector. In contrary to the PGE, the PDE is not restricted by inversion symmetry of materials, and it usually happens in materials with rich free carriers such as doped semiconductors and metal. The photocurrent density from PGE and PDE effects can be expressed as [69, 70]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \begin{array}{@{}lllllllllllllllllllllllllllllllllllllll@{}} & {{J}_{i}}={{\chi }_{ijk}}{{E}_{j}}E_{k}^{*}+\frac{i}{2}{{T}_{ijkl}}\left\{{{E}_{j}}({{\nabla }_{l}}E_{k}^{*})-({{\nabla }_{l}}{{E}_{j}})E_{k}^{*} \right\} \nonumber \\ &\quad ={{\chi }_{ijk}}{{E}_{j}}E_{k}^{*}+{{T}_{ijkl}}{{q}_{l}}{{E}_{j}}E_{k}^{\ast } \end{array}\nonumber \end{align} \tag{ 3 }$$

where E is the complex electric field of pump beam; q is the incident wave vector; ${{\chi }_{ijk}}$ and ${{T}_{ijkl}}$ are third and fourth order susceptibility terms describing the PGE and PDE, respectively. According to equation (3), the photocurrent introduced by the PDE is directly related to the wave vector q while that from the PGE is independent on q, hence the contributions from such two effects on photocurrent generation and THz radiation can be distinguished via changing the propagation direction of pump beam [70].

As one of typical 2D materials, graphene has a linear dispersion relation [71], a high electron mobility (~2.5  ×  10⁵ cm² V⁻¹ s⁻¹ at room temperature) [72], fine structure constant determined optical absorption (πα  ≈  2.3%) [73], and many other remarkable properties. In THz region, negative photoconductivity with the transient response on a time scale of 1–2 ps in highly doped monolayer graphene was observed via optical pump THz probe spectroscopy (OPTP) [74–76]. This phenomenon is ascribed to the increase of scattering rate (Г), of which the contribution is more significant than that from the Drude weight (D) in the real part of the conductivity ($\sigma =D/\pi \Gamma$) [74]. Further experiments with the gate-tuned carrier densities suggest positive photoconductivity near the charge neutrality point and negative photoconductivity at high carrier density, which is due to the interplay between photoinduced changes of both D and Г [76]. Under different optically doping density and different excitation photon energy, hot carrier and multiple hot-carrier generation have been observed with the dynamics dominated by carrier-carrier scattering instead of carrier-optical-phonon scattering [75, 77]. These scattering processes are crucial for the conversion of light into free electron–hole pairs and the consequent photocurrent formation in graphene [75]. As the carrier dynamics of graphene exhibit sensitive, broadband, tunable, and ultrafast response [78], graphene has many applications in THz region, such as THz detector [79], THz modulation [80], THz antireflection coating [81], THz modulators [82, 83], and so on. As proposed by Novoselov et al in the graphene roadmap for future photonic applications [84], graphene based THz generators are also very promising in the 2D photonics for the integration. Early studies suggested ballistic electric currents in graphene could induce the coherent THz radiation using quantum interference of one- and two-photon absorption pathways [85]. In 2012, Prechtel et al [86] demonstrated photocurrent induced THz radiation in a graphene–metal interface by photocurrent measurement, and revealed two dominant mechanisms of the photocurrent generation. One is carrier separation by a built-in electric field due to potential difference between layers, and the other is photothermoelectric effect (PTE) due to thermoelectric power difference [87]. PTE originates from a temperature gradient generated by light across an interface, where hot carriers tend to diffuse to maximize the entropy and thus the carrier flowing results in the transient photocurrent. In recent years, the THz radiation investigations of monolayer graphene [43], multilayer graphene [44, 48, 69], and vertical grown graphene [70] indicate that PDE dominates the transient photocurrent generation of graphene deposited on dielectric substrates. As shown in figure 3(a), when a graphene sample is excited by fs laser, momenta of the incident photons are transferred to those of electrons in the graphene, which drives the electron flowing along the propagation direction of the photons. This current flow further induces transient photocurrent, resulting in THz radiation at graphene surface [43]. Based on equation (3), the photon drag currents are determined by the electric components of the incident lasers, and thus the photocurrent components have dependences on the incident polarization angle α as: ${{j}_{u}}\propto 3/2{{\cos }^{2}}\alpha -{{\sin }^{2}}\alpha$, and ${{j}_{v}}\propto \cos \alpha \sin \alpha$. Since x- and y -components of the generated THz radiation (with the coordinate system shown in figure 3(a)) depend on the photocurrent components as: $E_{{\rm THz}}^{x}\propto \partial {{j}_{u}}/\partial t$, $E_{{\rm THz}}^{y}\propto \partial {{j}_{v}}/\partial t$, the THz radiation components have dependences on the incident polarization angle as: $E_{{\rm THz}}^{x}\propto 3/2{{\cos }^{2}}\alpha -{{\sin }^{2}}\alpha$, and $E_{{\rm THz}}^{y}\propto \cos \alpha \sin \alpha$. These relations are consistent with the experimental results as shown in figures 3(b) and (c), verifying the dominant contribution of PDE for transient photocurrent generation in graphene. In this way, THz emission spectroscopy provides a contactless tool for probing the ultrafast photocurrent without electrodes, which would be superior to the conventional photocurrent measurement as it is based on a digital oscilloscope with external electrodes and limited time resolution and bandwidth [48].

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To gain a deep understanding of transient photocurrents in graphene, Maysonnave et al demonstrated the microscopic physics of dynamic PDE according to the carrier distributions after fs laser excitation [44]. As shown in figure 3(d), the populations of nonthermal electrons and holes are asymmetric along the center of Dirac cone when graphene is under oblique incident illumination. This will drive carrier motions and induce transient net current, which results in the THz radiation. While the populations of electrons and holes are symmetric along opposite wave vectors at normal incidence, hence the momentum contributions cancel with each other and could not emit THz radiation. This microscopic mechanism is based on a tight-binding model, and the density matrix ρ evolution in the standard perturbation formalism as [44]: ${\rm i}\hbar \partial {{\rho }^{(n)}}/\partial t=\left[ {{H}_{0}},{{\rho }^{(n)}} \right]+\left[ {{V}_{{\rm dip}}},{{\rho }^{(n-1)}} \right]-{\rm i}\hbar {{\Gamma }_{n}}{{\rho }^{(n)}}$ where n  =  1, 2 is the order number; ${{\Gamma }_{n}}$ is the phenomenological damping; ${{V}_{{\rm dip}}}$ is the dipolar perturbation. The photocurrent induced THz radiation is proportional to the time-derivative of the second-order current [44]: ${{\vec {E}}_{{\rm THz}}}(t)\propto \partial Tr\left[ \vec {p}{{\rho }^{(2)}} \right]/\partial t$ where Tr is the trace operation; $\vec {p}$ is the momentum. Thus, the calculation of the THz radiation is governed by the diagonal elements of ${{\rho }^{(2)}}$, which reflects the transient electron and hole nonlinear populations induced by the pump laser. Based on this theoretical model, the THz signals are reproduced and consistent with the measured THz signals in both time and frequency domains, as shown in figures 3(e) and (f). Furthermore, the calculated THz spectrum indicates that nearly 60 THz bandwidth signal is generated when graphene is excited by 15 fs pulse laser, making graphene a candidate as a compact and ultrabroadband THz emitter. Regarding the microscopic mechanism of the PDE, THz emission spectroscopy is also a new way to probe the dynamics of nonequilibrium carrier populations.

As another kind of advanced materials, TMDs present complementary yet distinctive properties compared with graphene. TMDs possess sizable bandgaps which can change from indirect to direct when TMDs are tuned from few-layer or bulk structures to monolayer structures [88, 89]. The strong spin–orbit coupling from d orbitals of heavy metal atoms endows TMDs new physics in spintronics and valleytronics [28]. Besides, TMDs have strong excitonic effects due to large exciton binding energy and low dielectric screening of Coulomb interactions between charge carriers [90, 91]. In THz region, TMDs also present extraordinary optoelectronic properties. For instance, both free carriers and bounded excitons are observed in tungsten diselenide (WSe₂) by OPTP [92], and the transient THz photoconductivities of monolayer molybdenum disulfide (MoS₂) and WSe₂ reach ultrafast response time of 350 fs and 1 ps, respectively [93]. Negative THz photoconductivity was observed in doped monolayer MoS₂ due to strong many-body interaction, which converts the 2D electron gas into a charged trion gas [94]. However, the widely used OPTP or THz time-domain spectroscopy is limited to achieve the surface and interface research on TMDs. Yet, surface/interface characterization is essential to device performances in photonic and optoelectronic applications.

Using THz emission spectroscopy, we observed resonant optical rectification process in the surface region of layered MoS₂ crystal [95]. The optical rectification process is confined to an interactive volume above the crystalline surface (at Z  =  0 in figure 4(a)). In this process, the generated THz radiation is proportional to the second order time derivative of the nonlinear polarization as: ${{E}_{{\rm THz}}}\propto {{\partial }^{2}}P/\partial {{t}^{2}}$, which gives rise to an azimuthal angle (φ in figure 4(a)) dependence of THz radiation as the nonlinear susceptibility tensor and the nonlinear polarization are related to φ. As such, the optical rectification induced THz radiation as a function of φ can be expressed as [95]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{{\rm THz}}}\propto 0.97[{{d}_{22}}\sin (3\varphi)-2{{d}_{15}}]+0.24({{d}_{31}}+{{d}_{33}})\nonumber \end{align} \tag{ 4 }$$

where d₂₂, d₁₅, d₃₁, and d₃₃ are effective nonlinear coefficients, and the 3φ rotational symmetry agrees well with the experimental results as shown in figure 4(b). This indicates that although the hexagonal 2H–MoS₂ is centrosymmetric belonging to D_6h space group, the surface breaks the bulk symmetry and thus the nonlinear effect on the surface obeys the three-fold rotational symmetry. Different from the azimuthal angle dependence, the THz amplitude as a function of the incident polarization angle (α in figure 4(a)) exhibits 2α rotational symmetry (as shown in figure 4(c)) as [96]: ${{E}_{{\rm THz}}}\propto A\cos \alpha +B\sin \alpha +C\cos (2\alpha)+D\sin (2\alpha)+E$, where A, B, C, D, and E are fitting constants related with the nonlinear coefficients. This is due to that the nonlinear polarization is given based on the interaction between susceptibility tensor and the incident electric field according to equation (2). The azimuthal angle contributes to the variation of susceptibility tensor, while the polarization angle changes the incident electric field. Hence the nonlinear polarization and the induced THz radiation have different dependences on the azimuthal angle and incident polarization angle.

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In general, several competing physical processes happen simultaneously when the advanced materials are excited by the pump beam. Thus, we have also investigated new emergent physical processes of MoS₂ by THz emission spectroscopy with the transmission configuration as the reflection configuration has a limitation on steering an incident angle [96]. As shown in figures 4(d) and (e), the THz radiation at  −40° incidence increases and significantly shifts toward the positive direction (indicated by the purple arrow in figure 4(e)) compared with the values at normal incidence. Such shift mainly stems from the THz radiation contribution induced by photocurrent surge. Since the photo-Dember effect is negligible in MoS₂ due to the same order of magnitude for mobility and masses between electrons and holes, origin of the photocurrent surge is ascribed to the surface depletion field. This surface depletion field with ~0.13 µm in the penetration depth forms near the air–MoS₂ interface, and the maximum value of the surface depletion field is approximately 1.45  ×  10⁴ V cm⁻¹. Comparing the physical processes at MoS₂ surfaces, the resonant optical rectification is related to the nonlinear susceptibility and can be influenced by the crystalline symmetry i.e. the azimuthal angle, while the surface depletion field is associated with surface potential and carrier concentrations, and it is independent on the azimuthal angle. Thus, the THz radiation contribution from resonant optical rectification and from surface depletion field were estimated according to the azimuthal angle dependence of the generated THz signals. The results indicate that the contribution from resonant optical rectification decreases from 90% to 40% with the incident angle changing from 0° to  −40° [96].

Tungsten disulfide (WS₂) is an analog to MoS₂ due to their similar electronic structure and physical properties. However, we observed that the dominant physical process of WS₂ in THz emission is different from that of MoS₂ [97]. As shown in figure 5(a), the generated THz signals of layered WS₂ crystal are insensitive to the azimuthal angle and demonstrate an isotropic response in the polar coordinate, suggesting different features from the 3φ rotational symmetry of MoS₂. With respect to the incident polarization angle, the THz signals of WS₂ and MoS₂ both exhibit 2α rotational symmetry as shown in figure 5(b). Nonetheless, the amplitude modulation of MoS₂ is much larger than that of WS₂ and the THz amplitude of WS₂ shifts significantly towards positive direction. These azimuthal- and polarization-angle-insensitive properties of THz radiation from WS₂ suggest that the photocurrent surge rather than the nonlinear polarization governs the physical mechanism of THz radiation in WS₂. This is primarily due to the difference of nonlinear coefficients between MoS₂ and WS₂. According to equation (4), sin(3φ) term is related to the coefficient d₂₂, while the azimuthal-angle-independent terms contain coefficients d₁₅, d₃₁, and d₃₃. The calculated nonlinear optical coefficients indicate that d₂₂ is the largest coefficient among nonzero susceptibility terms of MoS₂ and other terms are almost zero [96], while d₂₂ of WS₂ is approximately zero (figure 5(c)) and further results in the isotropic behavior for THz radiation. Thus, the dominant mechanism of THz radiation from WS₂ is photocurrent surge (contribution ratio ~88%), which is induced by the surface depletion field rather than photo-Dember effect since the mobility and masses of electrons and holes are almost identical in WS₂. The maximum value of the depletion field is calculated as 1.2  ×  10⁵ V cm⁻¹ with approximately 94 nm width. Moreover, the THz emission spectroscopy of layered WSe₂ crystal presents similar features with WS₂ including azimuthal angle independent THz radiation, weak modulation of incident polarization angle, and the THz amplitude shift towards positive direction. Thus the surface depletion field also plays an important role for the photocarrier acceleration and THz radiation in WSe₂ [98].

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Topological insulators have become the 'star material' after graphene in optics, electronics, condensed matter physics, and so on [99] due to their unique properties such as narrow bandgap in bulk and nearly linear energy-momentum dispersion relationship at the surface, time-reversal symmetry protected surface, and strong spin–orbit interaction at surface states [40, 100]. What's more, with the existence of Dirac cone-like surface state, surface photocurrents with ps timescale can be induced in topological insulators after optically excited by fs laser. Thus THz emission spectroscopy enables in-depth studies of the surface state, Dirac fermions, and photocurrent distributions of topological insulators. Luo et al pointed that the THz radiation generated inside a bulk Bi₂Se₃ experienced a free carrier absorption, of which Dirac fermion contribution is more efficient than the carrier contribution from the bulk [40]. Zhu et al [101] and Tu et al [102] demonstrated that the energy difference between a second Dirac surface state and bulk bands matches the 1.55 eV photon energy of excitation wave, which are essential for photoexcited carriers at surface resulting in THz radiation. Choi et al observed that the THz polarities of an as-grown Bi₂Se₂Te and annealed samples are opposite. This is due to that Bi₂Se₂Te sample can be transformed from amorphous film with p-type polarity into single crystalline Bi₂Se₂Te₁ with n-type polarity via annealing process, revealing the surface depletion field contribution to the THz radiation [39].

Furthermore, Braun et al quantitatively extracted the ultrafast photocurrent components J_x and J_yz in Ca-doped Bi₂Se₃ by THz emission spectroscopy [103]. Firstly, a THz electric field E(t) is extracted from the measured THz signal S(t) by deconvolution of the system response function h(t), which has the relationship in the frequency domain as: ${{S}_{x}}(\omega)=h(\omega){{E}_{x}}(\omega)$. This relation is also applied in E_yz component. Secondly, THz electric fields due to the photocurrents are given through generalized Ohm's law in the frequency domain as [104]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{x}}(\omega)=-\frac{{{Z}_{0}}}{\cos \theta +\sqrt{{{n}^{2}}-{{\sin }^{2}}\theta }}{{J}_{x}}(\omega)\nonumber \end{align} \tag{ 5 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{yz}}(\omega)=-\frac{{{Z}_{0}}\sqrt{{{n}^{2}}-{{\sin }^{2}}\theta }}{{{n}^{2}}\cos \theta +\sqrt{{{n}^{2}}-{{\sin }^{2}}\theta }}{{J}_{yz}}(\omega)\nonumber \end{align} \tag{ 6 }$$

where Z₀  ≈  377 Ω is vacuum impedance; n is refractive index of Bi₂Se₃; θ  =  45° is incident angle. Finally, the time-resolved photocurrent components are portrayed after inverse Fourier transformation of the current spectra as shown in figure 6(a). The physical origin of the photocurrent components can be understood based on the established THz radiation mechanisms: shift current, injection current, and optical rectification, which are proposed by Sipe et al [105] and Driel et al [53] for the photocurrent generation by an optical transition |i  〉  →  |f   〉. Among them, optical rectification has been demonstrated in figure 2(a), and injection currents arise from the asymmetric band depopulation since the electrons are excited from the Dirac cone to higher-lying states with different group velocity under circularly polarized excitation (figure 6(b)). While shift currents are caused by the spatial shift of electron density distribution along Se-Bi bond when electrons are excited from state |i  〉  to |f   〉  (figure 6(c)). Although both the injection and shift currents follow the waveform of optical pulse, the characteristic shape of the injection current is unipolar while the shape of the shift current is bipolar. Regarding to the portrayed photocurrent components, J_x with relaxation time τ ~ 22 fs has bipolar waveform, which is consistent to the theoretical photocurrent waveform based on the shift current model (dash line in figure 6(a)). Thus, J_x component is caused by the shift current occurring on the first 1 to 2 quintuple layers (1–2 nm) of the Bi₂Se₃ surface. As for the J_yz component, its approximately 40 fs rising time is slower than the pulse duration of excitation wave (~20 fs), and thus J_yz does not rise from the initial optical transition. Since a surface field can be formed by band bending in Bi₂Se₃ according to previous demonstrations [101, 102], J_yz is ascribed to carrier drift induced by the surface depletion field along the surface normal with ~15 nm into the depth of the Bi₂Se₃.

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The electronic band structure of Bi₂Se₃ is shown in figure 6(d), where BB1 (BB2) and SS1 (SS2) represent bulk bands and surface states below (above) the Fermi level, respectively. The dash black and red lines indicate the shift of SS1 and SS2 by the optical excitation. The red arrows denote various interband transitions involving surface states under 1.57 eV pump energy: (1) surface-to-bulk; (2) bulk-to-surface; (3) surface-to-surface. All these optical transitions can drive the ultrafast transfer of electron density and then the charge carriers experience multiple scattering processes and consequently lead to isotropic distributions. This process has ultrafast relaxation time of 22 fs for J_x component, which is much shorter than the dynamics of electrons (~1 ps) studied by time-resolved photoemission spectroscopy [106]. Therefore, THz emission spectroscopy offers a promising way to probe the photocurrent dynamics within 20 fs timescale resolution. The ultrafast shift current could also be used to manipulate the surface via optical methods and further modify the surface properties of topological insulators.

Hybrid perovskites are a class of solution-processed crystalline materials consisting of ABX₃ structure, where A and B are cations with different sizes and X is an anion [107]. Recently, perovskites raise the new prospect of solar cell devices due to high power conversion efficiencies and low processing costs based on their extraordinary photophysical properties [108], such as strong solar absorption, low non-radiative carrier recombination rates, high carrier mobility, and so on [109]. Notably, photovoltaic effect of perovskites is the direct conversion of light into electricity [110], which refers to the photocurrent generation and above bandgap photovoltage. Since the photovoltaic properties are directly related to charge separation [110], hot carrier transport [111], surface fields and diffusion [112] etc, the time-resolved characterization of carrier dynamics and ultrafast photocurrent generation is crucial for the photovoltaic device performance.

Figure 7(a) demonstrates the THz radiation of hybrid perovskites methylammonium lead iodide (CH₃NH₃PbI₃, MAPI) [113], where ultrafast photocurrents are induced along the normal direction of surface, and the resulting THz radiation increases linearly with the pump fluence spanning from 8 nJ cm⁻² to 2 µJ cm⁻² (figure 7(b)). These values correspond to 1 sun equivalent intensity and ~100 sun equivalent intensity, which are in accordance to the photogeneration conditions of normal solar cell operation. With respect to the photocurrent type, optical rectification contribution is firstly eliminated as measurable THz signal is not generated when MAPI is excited under 790 nm (below bandgap) pump beam, as shown in figure 7(c). While the THz signal under 400 nm excitation is more than an order of magnitude larger than that under 770 nm excitation. This is consistent with the photocurrent features induced by either surface depletion field or photo-Dember effects. The surface field can be ruled out as the THz signal is hardly modified by surface passivation of MAPI. Thus, the ultrafast photocurrents are generated through photo-Dember effect as: ${{J}_{{\rm s}}}={{J}_{{\rm n}}}+{{J}_{{\rm p}}}$, where ${{J}_{{\rm n}}}=-e{{D}_{{\rm n}}}\frac{\partial \Delta n}{\partial z}$, and ${{J}_{{\rm p}}}=e{{D}_{{\rm p}}}\frac{\partial \Delta p}{\partial z}$ are photocurrents from the diffusions of electrons and holes, respectively. D_n (D_p) is the diffusivity, and $\partial \Delta n/\partial z$ is the spatial gradient of electrons along the excitation direction. The THz radiation generated from photocurrents can be described by [113]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{{\rm THz}}}=\eta e\Delta D{{N}_{0}}(1-{{e}^{-1}})/{{\varepsilon }_{0}}c\nonumber \end{align} \tag{ 7 }$$

where η is an outcoupling coefficient; N₀ is the peak carrier density; ΔD is the carrier diffusivity difference; term (1  −  e⁻¹) represents the averaging of the carrier density gradient along the penetration depth of the film. Based on the measured THz signals at different excitation wavelengths and equation (7), the mobility of electrons and holes are calculated as: µ_n  =  10.55 cm² V⁻¹ s⁻¹, µ_p  =  14.45 cm² V⁻¹ s⁻¹, and the diffusivities for D_n  =  9.17 cm² s⁻¹, D_p  =  8.28 cm² s⁻¹ under 400 nm excitation. After 1 ps excitation, hot electrons and holes migrate average 30 and 28 nm, respectively. As such, THz emission spectroscopy provides a direct and high time-resolution method for hot-carrier extractions, which are crucial factors to improve the power conversion efficiencies beyond the Shockley–Queisser (S–Q) limit in solar cell devices.

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Moreover, Obraztsov et al proposed that strong spin–orbit coupling exists in heavy Pb atom and inversion symmetry is broken in MAPI, which result in Rashba type spin splitting [114]. This allows the lifted spin degeneracies of the conduction and valence bands and further gives rise to 'inner' and 'outer' bands with opposite spin textures [115]. Due to the angular momentum selection rules and spin-momentum locking, the interband optical transitions respond asymmetrically under left and right circularly polarized excitations, which further induce different THz radiation amplitude when MAPI is excited under opposite helicity [114]. Hence, THz emission spectroscopy is expanded as a sensitive tool to study the spintronic physics and hybrid perovskites could also be put forth as model materials for spintronic applications.

Interface plays a pivotal role in electronic and optoelectronic devices as it is capable of controlling the dynamics of various carriers, lifting an inversion symmetry, and enhancing the interactions between layers. Appropriate interface engineering can effectively modify the band alignment, carrier distribution, charge transport and so on, which are important for the optimization of photonic and optoelectronic devices [116, 117]. With the development of 2D materials, mixed-dimensional vdW heterostructures provide promising platforms for the interface engineering as any passivated, dangling-bond-free surfaces interact with others by vdW forces to form 2D–3D heterostructures [35]. Therefore, it is important to probe the interfacial effects and deepen the understanding of the interface physics of mixed-dimensional heterostructures.

THz radiation from graphene/SiO₂/Si heterostructure has been enhanced effectively compared with that from bare Si substrate in the same experimental condition as shown in figures 8(a) and (b) [118]. This enhancement is ascribed to the photocarriers in the interface layer as the pump fluence is insufficient to induce THz radiation from graphene. Since the inversion symmetry of Si is broken by the interface depletion field with a built-in potential φ_d, the effective second-order nonlinear susceptibility of the interface region is expressed as [58]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \chi _{{\rm ef\,\!f}}^{(2)}(0;\omega ,-\omega)={{\chi }^{(3)}}(0;\omega ,-\omega){{E}_{{\rm DC}}}(z)\nonumber \end{align} \tag{ 8 }$$

where χ⁽³⁾ is the third-order nonlinear susceptibility, and E_DC is the electric depletion field, which varies along the penetration depth of the pump beam. Thus, the nonlinear process induced by interface depletion field is described as [119]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle P_{{\rm ef\,\!f}}^{(2)}(\Omega)={{\varepsilon }_{0}}{{\chi }^{(3)}}E(\omega +\Omega){{E}^{*}}(\omega)\int{{{E}_{{\rm DC}}}(z)}{\rm d}z\propto {{\varphi }_{{\rm d}}}.\nonumber \end{align} \tag{ 9 }$$

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This is the nonlinear polarization from electric field induced optical rectification (EFIOR), hence the emitting THz radiation is proportional to φ_d. Such interface potential can be tuned by a gate voltage (V_g) to induce an active THz emission, as shown in figure 8(c). As V_g tuning from 6 V to  −6 V, the THz radiation as well as φ_d present saturation under  −3 V, and the saturation interface potential is calculated as  −0.22 V based on [120]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\varphi }_{{\rm dm}}}=-\frac{2{{k}_{0}}T}{e}\ln (\frac{{{N}_{{\rm D}}}}{{{N}_{0}}})\nonumber \end{align} \tag{ 10 }$$

where temperature is T  =  300 K, N₀ and N_D are the intrinsic carrier concentration and doping concentration, respectively. On the basis of the relation between the saturation φ_dm and the THz amplitude, φ_d as a function of V_g can be extracted (figure 8(d)) according to the THz radiation contribution from pure EFIOR effect. Therefore, this active THz emission enables evaluation of interface built-in potential, which is directly related to carrier distributions, dynamics and band bending, and further determines the performance of mixed-dimensional vdW heterostructure-based devices.

The Fermi level of graphene is sensitive to the external environmental influence such as gas molecule adsorption/desorption and surface/interface processing, and thus the electric and optical properties of graphene-based heterostructures could be influenced by the surface perturbations. Tonouchi et al utilized THz emission spectroscopy as a quantitative and nondestructive measurement tool to probe the gas molecule adsorption/desorption dynamics in graphene-based mixed-dimensional heterostructures. They observed that the THz radiation from graphene-coated InP is related to the adsorbed oxygen (O₂) induced localized electric dipoles, which further cause band structure modification in the surface depletion layer of InP [121]. While at graphene/InAs interface, O₂ adsorption/desorption showed negligible impact on the THz emission, which was mainly generated by transient diffusion photocurrent [122]. Moreover, they also realized the evaluation of adsorption energy of O₂ molecules on graphene- and WS₂-based heterostructures due to thermal desorption [123]. As adsorption energy embodies the interaction strength between adsorbates and 2D materials, it is important yet conflicting due to the lack of proper approximation functions to describe dispersion forces [124, 125]. As shown in figure 8(e), take graphene/InP as an example, the generated THz radiation exhibit bipolar waveform at the onset of fs excitation. O₂ molecules are adsorbed on the graphene surface and the transient photocurrent flows towards the InP surface. After vacuum pumping, the significant desorption of O₂ results in the decreasing of adsorbate concentration and thus influences the photocurrent in InP, which makes the THz signal evolve into a unipolar waveform with a peak at ~2 ps. After further adsorbate removal by annealing, the photocurrent flows towards InP bulk and the resulting THz radiation of graphene/InP is similar to that of bare InP. During this process, the THz radiation contribution of localized electric dipoles induced by O₂ adsorbates can be obtained by the variation of THz radiation [123]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{{\rm THz},2}}-{{E}_{{\rm THz},1}}\propto \frac{\partial {{J}_{2}}}{\partial t}-\frac{\partial {{J}_{1}}}{\partial t}\propto {{E}_{{\rm d},2}}-{{E}_{{\rm d},1}}={{E}_{{\rm dipole}}}\nonumber \end{align} \tag{ 11 }$$

where the subscripts 1 and 2 denote the states without and with O₂ adsorbates, respectively. The electric field E_dipole is directly related to the adsorbate concentration N_ad. Based on this concentration and its dependence on annealing temperature, the adsorption energy of O₂ molecules on graphene is estimated as ~0.15 eV. Regarding the adsorption/desorption dynamics, THz emission spectroscopy is not only a direct and contactless tool for molecular surface/interface science, but also facilitates the development of gas sensor devices.