It is known that the excitation of many materials by femtosecond laser pulses leads to the generation of subpicosecond coherent electromagnetic pulses with terahertz (THz) frequencies [1]. The idea of the conversion of the energy of ultrashort laser pulses to coherent THz radiation in nonlinear crystals owing to the generation of the difference frequency (or the optical rectification of laser pulses with a broadened frequency spectrum) was proposed for the first time in 1974 [2]. Experimental results confirming the possibility of converting the energy of laser pulses to THz radiation in nonlinear crystals appeared in the mid-1980s [3, 4]. Few-cycle THz pulses have already been generated in semiconductors, metals, dielectric crystals, and even in gases and liquids (see, e.g., [5] and references therein). The nature of such a THz generation is generally due to the excitation of a fast dipole or a short photocurrent burst in a material or a structure [6, 7]. The amplitude of a THz wave \({{E}_{{{\text{THz}}}}}\) is proportional to \(\frac{{{{\partial }^{2}}P}}{{\partial {{t}^{2}}}}\) or \(\frac{{\partial J}}{{\partial t}}\), where \(P(t)\) and \(J(t)\) are the time-dependent dipole moment and current induced by exciting laser radiation, respectively [6, 7]. Terahertz radiation thus generated is widely used in THz time-domain spectroscopy (THz TDS) and THz visualization of various objects [8].

A number of schemes were proposed to efficiently generate coherent THz radiation in bulk semiconductors and semiconductor structures under interband femtosecond laser photoexcitation (see, e.g., review [9] and original works [10–12]). The most popular semiconductor emitters for applications are THz emitters based on large-aperture photoconductive antennas [13] and THz emitters based on the excitation of the surface of a semiconductor, e.g., an InAs crystal where THz radiation is caused primarily by the Dember effect (see, e.g., [14] and references therein). The authors of [15] showed that the generation of the fast photocurrent in a Si p–i–n photodiode photoexcited by ultrashort laser pulses also produces THz radiation.

In this work, THz radiation is generated in \(p{-} n\) heterostructures based on a-Si:H/a-SiC:H/c-Si (solar cells based on a-Si:H/a-SiC:H/c-Si heterojunctions) photoexcited by femtosecond laser pulses. The observed THz radiation has a number of interesting properties reflecting both the dynamics of photoexcited charge carriers in structures and features of the propagation and emission of radiation from structures.

We used \(p{-} n\) heterostructures based on a-Si:H/a-SiC:H/c-Si. The heterostructures are silicon heterojunction (SHJ) solar cells [16, 17], which capture a significant part of the spectrum of solar radiation and have a fairly high efficiency [18]. The schematic of heterostructures used in this study is shown in Fig. 1. The thickness of each ITO (indium tin oxide) layer was 100 nm, the \((n)\) c-Si substrate was 140 μm thick, and the a-Si:H and a-SiC:H layers had a total thickness of 20 nm [18] in both the upper and lower parts of the structure (see Fig. 1). The measurements were performed with 7 × 7-mm solar cells.

Fig. 1.
figure 1

(Color online) Schematic of the studied solar cell based on a-Si:H/a-SiC:H/c-Si and the excitation direction of the terahertz experiment.

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Structures were excited by p-polarized radiation from a femtosecond Ti:sapphire laser generating ~15‑fs pulses with a central wavelength of 800 nm at a repetition frequency of 80 MHz. Pump radiation with the energy per pulse of 2.2 nJ was incident at an angle of 45° on the top ITO layer and was focused into a ~100 μm spot. Generated THz radiation was collected in the specular reflection direction and was focused on a 1-mm ZnTe crystal serving as a THz detector included in the scheme of electro-optical sampling of THz waveforms, which made it possible to detect both the amplitude and the phase of pulsed THz radiation. The used THz TDS setup was described in detail in [19].

The generation of THz radiation was observed from the solar cell under the application of a reverse bias voltage. The THz radiation signal from the structure at zero and low direct bias voltage is very weak and can hardly be distinguished from noise. Figure 2 presents characteristic waveforms of the observed THz signal and amplitude spectra of THz radiation at several reverse bias voltages.

Fig. 2.
figure 2

(Color online) (a) Waveform of THz radiation generated in the solar cell at a reverse bias voltage of 9 V. Arrows mark the positions of the maxima of (dashed arrow) the first and (solid arrows) subsequent echo pulses of THz radiation. (b) Waveform of THz radiation generated at a reverse bias voltage of 20 V. The insets show the amplitude spectra of THz radiation at a reverse bias voltage of (a) 9 and (b) 20 V.

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As seen in Figs. 2a and 2b, the main THz pulse is accompanied by a series of three or four echo pulses, which have the same polarity and follow in time intervals of about 3.1 ps. The appearance of such repeated THz pulses can be attributed to the multiple reflection of THz radiation, generated in the region of entry of pump radiation into the structure, from the top and bottom ITO layers, i.e., to the Fabry–Perot effect. The thickness of ITO layers (100 nm, see above) is much smaller than the wavelength of radiation and the thickness of the skin layer (using the data from [20, 21], the thickness of the skin layer for ITO at a frequency of 1 THz is estimated at 0.5–1 μm). Consequently, the ITO layer in the solar cell under study behaves in the THz range as an optically thin metal film whose optical properties are determined by its resistivity and thickness [22]. Terahertz radiation is partially transmitted through such a layer and is partially reflected from it. Internal reflections of THz radiation from ITO layers as from optically denser media compared to surrounding materials ensure the observed conservation of the polarity of THz echo pulses (Fig. 2). The time interval between echo pulses about 3.1 ps agrees with the double pass of radiation through the ~140 μm structure and a refractive index of about 3.4 (the refractive index of c-Si in the THz range [23]). Amplitude spectra of observed THz radiation (insets of Figs. 2a and 2b) demonstrate a frequency comb corresponding to Fabry–Perot resonances.

Figure 3 shows the amplitude THz transmission spectrum of the structure under study in the frequency range of 0.2–2.9 THz. These measurements were also performed at the THz TDS setup [19] with a n-InAs crystal as a THz emitter excited by radiation from the femtosecond Ti:sapphire laser that is incident at an angle of 45°. Figure 3 also presents spectra of THz radiation normalized to the maximum, which is generated in the structure at reverse bias voltages of 9 and 20 V. The transmission spectrum demonstrates the manifestation of the interference of THz radiation in the structure. It is seen that low-frequency maxima in transmission corresponding to constructive interference are close in spectral positions to the maxima of the frequency comb in spectra of THz generation.

Fig. 3.
figure 3

(Color online) (1) Spectrum of the amplitude THz transmission of the solar cell based on a-Si:H/a-SiC:H/c-Si and (2, 3) spectra of THz radiation normalized to the maximum, which is generated in the solar cell at a reverse bias voltage of (2) 9 and (3) 20 V. The spectral resolution is 50 GHz.

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The spectrum-average amplitude THz transmission coefficient is about 17% (see Fig. 3). Taking into account this THz transmission coefficient of the structure and absorption on free carriers in the \((n)\) c‑Si layer (material with a resistivity of 1.5 Ω cm) and neglecting absorption in thin a-Si:H and a-SiC:H layers, one can estimate the spectrum-average amplitude THz transmission coefficient of one ITO layer at about 43%. The spectrum-average amplitude THz reflection coefficient of the ITO layer using the above transmission coefficient and the calculation method described in [22] is estimated at no less than 50%. For this reason, THz radiation generated in the region of entry of pump radiation into the structure under study is quite well emitted from the structure through the top ITO layer and is also reflected from it back (see Fig. 2).

According to Fig. 2, THz radiation pulses at reverse bias voltages of 9 and 20 V have opposite polarities. Figure 4 presents the dependence of the amplitude of the main THz pulse (first in time) on the reverse bias voltage. It is seen that the THz signal first increases with the bias voltage, reaches a maximum at a bias voltage of about 9.4 V, then decreases, passes through 0 (at \(U \sim 12.7{\kern 1pt} \) V), and further change sign and increases significantly. Measurements shown in Fig. 4 were limited by the maximum bias voltage of 24 V in order to minimize the effect of the parasitic heating of the sample by the steady-state leakage current on the measurements.

Fig. 4.
figure 4

Amplitude of the main THz pulse versus the reverse bias voltage across the solar cell based on a-Si:H/a-SiC:H/c-Si.

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A change in the polarity of the THz pulse indicates a change in the direction of the fast photocurrent responsible for the generation of THz radiation in the solar cell under study with an increase in the reverse bias voltage.

Pump radiation with a wavelength of 800 nm incident on the solar cell from the side of \((p)\) a-Si:H (Fig. 1) passes almost without absorption through the broad-band-gap a-Si:H and a-SiC:H layers and is completely absorbed in the crystalline n-silicon layer, penetrating into it to a depth of about 12.5 μm [24]. The built-in field near the a-SiC:H/c-Si heterojunction and, correspondingly, nonequilibrium charge carriers produced by pump near this heterojunction apparently play an important role in the formation of the initial fast photocurrent \({{J}_{1}}(t)\) at low bias voltages. The photocurrent \({{J}_{1}}(t)\) possibly flows from the interface of the heterojunction to the bulk of c-Si. An increase in the bias voltage on the solar cell can likely increase the spatial region of localization of the built-in field near the heterointerface of a-SiC:H/c-Si and, therefore, increase the number of nonequilibrium charge carriers involved in the formation of the fast photocurrent \({{J}_{1}}(t)\). This in turn leads to the initial increase in the THz generation signal with increasing bias voltage (Fig. 4).

The voltage drop across the c-Si layer increases significantly with the reverse bias voltage. Correspondingly, the contribution to the fast photocurrent \({{J}_{2}}(t)\) from nonequilibrium charge carriers produced in the c-Si layer increases. The total photocurrent \({{J}_{\Sigma }}(t)\) responsible for THz generation is the sum of the photocurrents, i.e., \({{J}_{\Sigma }}(t) = {{J}_{1}}(t) + {{J}_{2}}(t)\). Since the direction of the fast photocurrent \({{J}_{2}}(t)\) is determined by the direction of the electric field in the c-Si layer, it flows toward the heterointerface of a-SiC:H/c-Si and is opposite to the photocurrent \({{J}_{1}}(t)\). The photocurrent \({{J}_{2}}(t)\) will increase with the bias voltage also because of an increase in the velocity of nonequilibrium charge carriers in the c-Si layer. This can explain the change in the polarity of a generated THz pulse and an increase in its amplitude at high bias voltages (Fig. 2).

In addition to the above current mechanism, the contribution to observed THz generation from the optical rectification induced by the electric field cannot be completely excluded [25, 26].

To summarize, coherent THz radiation has been generated in the solar cell based on a-Si:H/a-SiC:H/c-Si photoexcited by 800-nm femtosecond laser radiation at a reverse bias voltage. It has been found that an increase in the bias voltage is accompanied by a change in the polarity of THz radiation and by a significant increase in its amplitude. The properties of observed THz radiation can be explained by the fact that the contributions to the formation of THz radiation come from two fast photocurrents generated in the structure by femtosecond laser pump that have opposite directions and vary with an increase in the bias voltage. Studies of processes of THz generation can be used to analyze in detail the behavior of nonequilibrium charge carriers in complex HJT solar cells at subpicosecond times. After a certain optimization of the structure of solar cells based on a-Si:H/a-SiC:H/c-Si, e.g., after an increase in the illuminated area of these solar cells and an increase in the energy of femtosecond pulses, these cells could possibly be used as emitters of coherent THz radiation.