Black silicon (BS) is a term used to describe silicon with micro (and/or nano)-scale conical surface structures that are induced by short and ultrafast laser pulse irradiation or plasma etching.^[1–3] Because of its strong absorption in the visible light and infrared regime, BS has drawn a great deal of attention for its optoelectronic applications like light harvesting in solar cells and light-emitting devices.^[4,5] The BS formed in SF₆, featuring a narrowed band gap due to the sulfur doping, has a broad spectral band of absorption, extending to the THz.^[6] For BS structured in air, without band gap modification the strong spectral absorption band ends at 1200 nm, making it potentially useful for enhancing the emission of THz radiation from natural surface emitter.^[7] However, the absorption of the enhanced THz emission, changed by BS micro (nano)-structured surface, to the best of our knowledge, has not been comprehensively studied, which is probably because the identifying of localization effects and ultrafast carrier dynamics of micro- (or nano-) structured surface is not trivial, and they exhibit process-dependent and surface-sensitive properties.

Terahertz time-domain spectroscopy (THz-TDS) is an excellent technique for studying optical properties of various materials including semi-conductors and conducting polymers in forms of nanoparticles, nanowires, nanodisks, hollow spheres, etc.^[8–13] It probes the far-infrared (30 μm–3 mm, 0.1 THz–10 THz) region of the spectrum, which closely matches typical carrier scattering rates of 10¹² s⁻¹ to 10¹⁴ s⁻¹.^[14–16] Furthermore, THz transmission or absorption is sensitive to the density and transportation of carriers. Thus, THz-TDS can directly infer the influence of micro (nano)-scale disorder and size effect on carrier motion from the response of surface conical structure to electromagnetic field in the terahertz frequency range. In this study, we report the absorption responses of blank silicon and BS wafers to an 808-nm continuous-wave (CW) laser at room temperature by terahertz time-domain spectroscopy system (THz-TDS).

The micro (or nano)-structured surface geometry used in the experiment was fabricated by direct-laser-writing (DLW) technique on a double-side polished 〈100〉 Si wafer with a resistivity of 1000 Ω⋅cm. Compared with the conventional fabrication methods such as plasma or chemical etching, DLW is simple and cost effective.^[17–19] In addition, the DLW technique allows for precise control over the dimensions of the surface micro-structures and enables systematic and highly reproducible studies of its geometry-dependent optical properties. In air, the BS was micro-structured by a solid-state nano-second laser (Enpon-Nano-H532) with a 355-nm wavelength and 6-ns pulse duration. The wafers were ultrasonically cleaned in an acetone bath, and then dried in a nitrogen gas flow. The laser fluence was fixed at 11.8 J/cm². By controlling the laser scanning speed, overlap ratio and intervals between successive laser scan tracks, we obtained four micro-structured BS surfaces (numbered 01, 02, 03 and 04, accordingly), with increasing unity size as shown in Fig. 1.

Fig. 1.

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	Fig. 1. (color online) Four BS samples and their scanning electron micrographs. The sizes of surface conical structure are approximately 5 μm–8 μm (BS01), 8 μm–15 μm (BS02), 18 μm–25 μm (BS03), 30 μm–40 μm (BS04), respectively.

We measured the total (specular and diffuse) reflectance (R) and transmittance (T) to determine the absorptance (A = 1 − R − T) of the structured surfaces in spectrum range from 620 nm to 1050 nm. The measurements were performed by using a spectrophotometer equipped with an integrating sphere detector. Figure 2 shows the wavelength-dependent absorptions of the structured BS surfaces and blank silicon. The absorption of the BS is evidently twice superior to that of the blank silicon over the spectrum range investigated. Thus, any wavelength in the range is suitable for the following THz experiment.

Fig. 2.

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	Fig. 2. (color online) Absorptions of four BS and Si wafers in the spectrum range from 620 nm to 1050 nm.

We characterized absorption tunabilities of blank silicon and BS by using a terahertz time-domain spectroscopy system with a couple of photoconductive antennas for both terahertz generation and detection as shown in Fig. 3. A mode-locked Ti: sapphire laser with a central wavelength of 800 nm, pulse duration of 100 fs, and repetition rate of 82 MHz was used as an optical source. An all-solid-state CW laser (808 nm, 4.8 W/cm²) was used as an external pumping source to excite photo-generated carriers in the silicon wafers. The spot diameters of THz beam and the CW laser were about 8 mm and 15 mm, respectively. The detailed description of the system setup and data handling can be found in previous work.^[20]

Fig. 3.

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	Fig. 3. (color online) THz-TDS system with optical modulation used for absorption tenability experiment.

The transmitted THz spectra of two different structure types, i.e., blank silicon and BS, without and with optical pumping, are shown in Figs. 4(a) and 4(b). As can be seen in Fig. 4(a), without optical pumping, the spectra of the two structure types differ very little throughout 0.5 THz–2.5 THz spectrum range. It implies that without pumping, the THz transmission is independent of surface micro-structure. However, under a 4.8-W/cm² optical pumping, the transmitted spectra (see in Fig. 4(b)) exhibit a pronounced difference between structured and unstructured silicon. The transmission of blank silicon with smooth surface strongly decreases and the residual transmission is less than 50%, whereas the transmission of the BS is much less influenced by optical pumping. In addition, four BS samples with different geometric structures show transmissions different from each other: the greater the surface micro-structure unity size, the lower the THz transmission is.

Fig. 4.

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	Fig. 4. (color online) Transmitted THz spectra of Si wafers with smooth and micro-structured (a) without pumping and (b) with 4.8-W/cm2 optical pumping.

The BS absorption at 808-nm pump beam is twice more than the blank silicon absorption. Furthermore, the THz-TDS experimental results show that, without pump, the THz transmission is independent of surface micro-structure. Thus, we attribute the abnormal THz absorption by BS under optical pumping to special carrier dynamics in surface micro-structure.

In order to explain the proposed mechanism of photo-generated carrier dynamics and validate our hypothesis, the real part of conductivity of the refractive index n of the sample through the relationship:

Fig. 5.

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	Fig. 5. (color online) Plots of non-photo-excited conductivities of Si, BS01, BS02, BS03, and BS04 without optical pump versus frequency, where solid lines refer to Lorentz fitting curves.

What is more, we have calculated the transient frequency-dependent complex photoconductivity parameters and from the transmitted terahertz waveform under the conditions with and without the optical pumping, respectively. The complex Fourier transform of the time-dependent field is related to the complex conductivity , and given as follows:^[24–27]

Fig. 6.

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	Fig. 6. (color online) Photo-excited conductivities of Si, BS01, BS02, BS03, and BS04 with optical pump, where solid lines represent Drude–Smith fitting curves.

The Drude model is ordinarily suitable for two-dimensional free electron gas with complete momentum randomization following elastic scattering events. However, in the 10-μm photo-excited layer and micro/nano-conical surface structures in BS samples, more photo-excited electrons reflect from interfaces and surfaces. Such a backward scattering event can be modeled by modifying the Drude model according to Smith by including the persistence of velocity parameter to describe the scattering event.^[32,33] The Drude Smith model is given by

Based on the curve fitting of photoconductivity σ_r(ω) to the Drude–Smith model, fitting parameters of electron density N, characteristic scattering time τ, and back-scattering rate c₁ are derived and summarized in Table 1. The parameters N, τ, c₁, vary monotonically with conductivity. In order to illustrate the relationship between the carrier dynamics and the surface micro-structure geometry, we plot these fitting parameters against surface structure of sample in Fig. 7.

Fig. 7.

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	Fig. 7. Trends of electron density (N), scattering time (τ), backscattering rate (−c1) of samples according to Table 1.

Table 1.

Table 1.

Table 1. Parameters for Drude–Smith fits of conductivity. . Sample N/(1016/cm3 τ/fs c1 BS01 0.60 92.9 –0.17805 BS02 2.70 99.4 –0.16403 BS03 5.26 100.2 –0.12202 BS04 6.45 107.3 –0.11398 Si 9.18 141.8 –0.05404 Note: N is electron density; τ is scattering time; c1 is backscattering rate.

Table 1. Parameters for Drude–Smith fits of conductivity. .

According to Fig. 2, the absorption of BS at 808-nm wavelength is more than blank silicon’s, but in a longer time window, the electron density is smaller in BS. Besides, with increasing the size of surface structure, the electron density N rises. As a result, one would assume that the recombination rates between electrons and holes in BS with different surface micro-structure sizes should be different from each other. The characteristic scattering time τ obtained from Drude–Smith fits turns longer with increasing the size of the surface structure. Nonetheless the variation of τ between BS remains small and the characteristic scattering time of the BS is much shorter than that of the blank silicon. It implies that the size of surface structure may be a key factor for an average time interval between collision events. At a flat surface without complex geometry or space confinement, for instance, the surface of blank silicon, the photo-generated carriers more easily move around hence scattering time becomes longer. As an additional contribution to the standard Drude term, c₁ describes the persistence of the initial velocity of carrier after of the first scattering event. The persistence of velocity is all negative (see the 4th column in Table 1). We attribute the negative values to preferential backscattering of the electrons after the collisions. A fraction, but not all, of the backward scattering is a result of the electron reflecting from the surfaces, grain boundaries or defects. It could also result from a Coulombic restoring force originating from positively charged holes or defects. This restoring force or backward scattering can be modeled by modifying the Drude model, according to Smith, by including a persistence of velocity parameter to describe the scattering event.^[32] Here negative values of c₁ are plotted in Fig. 7(c), and the curve drops with increasing the size of surface structure, suggesting that the number of backscattering electrons diminish. In other words, less collisions occur at a surface with bigger surface microstructure than at a smaller sized counterpart. In contrast, the more the collisions, the lower the kinetic energy of optical-generated carriers is and the higher the recombination rate between electrons and holes. This correlates with longer scattering time interval, and consequently, there may be less carriers in BS surface with smaller micro-structures. The interpretation is fully consistent with the evolutions of N and τ, and −c₁.

The optically induced changes in THz transmission and absorption of silicon wafers with two types of surfaces, i.e., unstructured blank silicon and micro-structured BS, are investigated at room temperature by using an NIR pump-terahertz probe system with an 808-nm CW laser pump. It is shown that BS structure causes not only a strong anti-reflection effect but also significant absorption enhancement at 808-nm wavelength due to localization effect and light trapping. The increases of the surface area and the photo-generated carrier concentration contribute to the absorption enhancement. Remarkably, with the optical pumping, the THz transmission spectra of blank silicon and BS are very different in the whole range of 0.5 THz–2.5 THz. It is proposed based on our measurements along with the model fitting that the carriers excited in BS surface with conical structure should have a stronger localization effect according to the backscattering behaviors in small-size micro-structures and the higher recombination rate due to increased electron interactions with other electrons, the interfaces and grain boundaries. Therefore, in the bigger conical geometry structure the excited carriers may move around more easily and as a consequence less collision would occur, which is related to higher THz absorption. Our work paves the way for a better understanding of the influence of the different geometrical- and optical-induced absorption of THz wave and the future applications of the black silicon.