1. Introduction

Semiconductor nanostructures have become of great importance for optoelectronic applications like light harvesting in solar cells [1, 2], light emitting devices [3, 4] and sensing applications [5]. A rather new field is the application of semiconductor nanostructures to enhance the emission of THz radiation from natural surface emitters [6–11]. The resulting emission enhancement has been mainly attributed to a local field enhancement and the strong increase of the total absorption [6–8, 10], resulting in a strong geometry dependence of the THz emission [9, 10].

However, the complete understanding on the impact of the different geometrical and electronic properties on THz emission is still a very complex problem since the different fabrication methods usually affect all of these characteristics. Furthermore, the impact of the altered absorption properties on the enhanced THz emission from nanostructured surfaces has been given less consideration. Nevertheless, new studies tend to draw more attention to this problem [11].

Especially for the fabrication of deterministic and self-organized silicon nanostructures a great variety of production methods has been developed including electro-chemical [12, 13], wet-chemical [14] or dry etching [15] techniques, pulsed laser irradiation [16] or the vapor-liquid-solid (VLS) synthesis for the preparation of nanowires [17]. The most distinct feature of these nanostructures is the strongly reduced interface reflection in the optical spectral range causing a visually black appearance. For this reason such nanostructures are often referred to as Black Silicon (BS). Nevertheless, the specific structure geometries and electrical properties differ depending on the particular fabrication process. Recently it has been demonstrated that those nanostructured silicon surfaces also emit THz radiation [8, 9]. Consequently a comparison of the THz emission performance of differently processed silicon nanostructures with respect to their specific structural and electrical properties can help to understand the underlying generation mechanisms and THz enhancement of semiconductor nanostructures in general. For example Jung et al. provided a detailed study on the influence of structure height of silicon nanowires on their specific THz emission characteristics [9].

Furthermore silicon nanostructures are of great interest for photovoltaic and sensing applications so a better understanding of their electrical properties is of special importance. Therefore the ongoing discussion on the influence of localization effects and ultrafast carrier dynamics led to an increase of ultrafast pump-probe and THz studies over the last years [18–20].

In this work we present a study on Black Silicon (BS) structures fabricated by reactive ion etching (RIE). Fabrication of self-organized, nanostructured silicon surfaces by RIE for photonic applications has gained much interest over the last years because the process exhibits some advantages over other wet etching or laser based methods. For example, RIE is equally applicable to multicrystalline silicon [21] or even crystalline silicon thin films [22] and offers the possibility of integration into in-line production facilities [23]. Furthermore, RIE fabricated silicon nanostructures are free from metal contaminations and exhibit low crystal damage [24, 25]. Nevertheless, currently there is no work available that considers their ultrafast carrier dynamics. Therefore, we would like to contribute a comprehensive study consisting of a detailed analysis of their optical properties, the carrier trapping and their influence on the resulting THz emission behaviour. In the following, we will concentrate on two different BS structures fabricated by RIE that have already been discussed in the past for other photonic applications like solar cells [26]. Our work is divided into three parts. In the first part we describe the main morphological and optical properties of the fabricated structures whereat special attention is paid to the altered absorption behaviour under the excitation conditions used for the THz emission experiments. In the second part we discuss the influence of trapping processes on the ultrafast carrier dynamics by applying optical-pump THz-probe experiments (OPTP). In the last part we discuss the influence of structure geometry on THz emission behaviour in comparison to previous works on semiconductor nanowires.

2. Sample preparation and experiment

2.1. Preparation of black silicon (BS) surfaces

The nanostructures were fabricated by a reactive ion etching process in a SF₆-O₂ plasma using a SI-500C plasma reactor from Sentech Instruments. The reactor has a planar inductively coupled plasma (ICP) source and is additionally equipped with an RF source which is used to adjust the substrate bias voltage. This combination allows the adjustment of the ion energy independently from the plasma density, which is determined by the ICP power. The nanostructures are formed due to chemical etching of the silicon surface with fluorine radicals under the formation of volatile SiF₄ and the highly directional removal of the passivation layer that is formed by a chemical reaction of ionized etch products and oxygen radicals [27–29]. The structure geometry can be adapted by changing the process pressure, bias, etching time, gas flow ratios or the substrate temperature [29]. The samples used throughout this study were prepared on double-side polished 4 inch, p-type silicon wafers having a thickness of 525 µm, 〈100〉 orientation and a resistivity of ϱ = 5 − 10 ˙cm. Two different structure geometries (Type A and B see Fig. 1) were prepared. Those structure types have been chosen due to their recent application in other optoelectronic devices. The ICP power and etching time were fixed to P_ICP = 750 W and t = 10 min. For the preparation of structure type A the process pressure was p = 4 Pa and the power of the HF-Bias source was P_HF = 6 W. Structure type B was prepared at a pressure of p = 2 Pa and at a HF-Bias power of P_HF = 2 W. The process pressure has a high impact on the structure formation since it controls the energy and directionality of the impinging ions. In case of increased process pressure the highly anisotropic physical etching mechanism is reduced and the etch profiles show a more isotropic appearance with positive sidewalls [29].

 

Fig. 1 Top view and cross-sectional SEM images of structure type A and B.

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The morphological properties of the BS structures were investigated with a scanning electron microscope by taking both top view and cross-sectional images. From the top view images the correlation length L_c of the random features was determined by finding the first minimum of the radial autocorrelation function. We found L_c = 160 nm for structure A and L_c = 200 nm for structure B. The correlation length determined in this fashion corresponds roughly to the mean etch pore diameter. From the cross-sectional images the peak to valley height H_pv was measured. The height of structure A was about H_pv = 690 nm and the height of structure B was about H_pv = 1740 nm. Optical spectra of the nanostructured surfaces were taken under near normal incidence (AOI(R) = 8°, AOI(T) = 0°) with a PerkinElmer Lambda 950 spectrometer equipped with an integrating sphere (see section 3.1).

2.2. Numerical calculation of the BS absorption profile

For a better understanding of the altered absorption behaviour, the light propagation and absorption in the BS structures was simulated under excitation conditions which were comparable to the conditions of the THz emission experiments. An illumination wavelength of λ = 800 nm was used. This wavelength is close to the scaled correlation length L_c·n_Si indicating that the BS features are too large to be treated as an effective medium but too small to be considered in the geometrical optical limit. Both large scattering angles and large structure depth furthermore require a rigorous and fully vectorial treatment of Maxwell’s equations. Therefore the light propagation was simulated with the finite-difference time-domain (FDTD) method using the open source software MEEP [30]. For the numerical simulation synthetic models of the BS geometry were created by detecting the etched pores in the top view SEM images by a grey level threshold. At the position of the pores material was removed from a voxel representation of the structure. Two different sets of pores were assumed: Smaller shallow pores and deeper larger pores. For the shallow and for deep pores different side wall angles were assumed. The pore depths and the sidewall angles of the pore regions were chosen to produce consistent results with the measured peak-to-valley height and correlation lengths. The lateral extent of the simulated model BS structures was 5 × 5 µm² and the voxel size was 10 nm. The spatial resolution of the FDTD simulations was chosen accordingly. Along the lateral dimensions (x and y) periodic boundary conditions were assumed while along the propagation direction (z) the computational domain was bounded by perfectly matched layers. Behind the BS structures a propagation through additional 10 µm of bulk silicon was simulated. Reflections from the rear side of the wafer were not taken into account. A p-polarized (i.e. electric field parallel to the plane of incidence) cw plane wave source incident at an angle of θ = 45° was used and the simulations were run until steady state was reached. From the steady state fields the average absorption rate was calculated by integrating the z-derivative of the z-component of the Poynting vector over the lateral coordinates and normalizing it to the incident power P_in:

Additionally the enhancement of the absorption rate was calculated as the relative increase compared to a planar wafer:

2.3. Optical-pump THz-probe studies (OPTP)

Since trapping of carriers on a ps timescale is known to have a large impact on the emission of THz radiation we performed an OPTP study on the nanostructured silicon samples to monitor the ultrafast charge carrier dynamics. The reflection OPTP setup used within the experiments is depicted in Fig. 2(a). The measurements were accomplished using an amplified laser system working at a repetition rate of f = 150 kHz. The amplifier (Reg A, Coherent Inc.) yields a pulse energy of E = 7 µJ and a typical pulse width of τ = 70 − 80 fs (FWHM). It is seeded by the λ₀ = 800 nm pulses of a Ti:sapphire oscillator with a repetition rate of f = 80 MHz (Mira, Coherent Inc.). The beam was split into three parts. Two parts of the beam were used to generate and sample the THz pulses. Generation and detection of THz radiation was achieved by optical rectification and electro-optical sampling in [110] oriented ZnTe crystals using the λ₀ = 800 nm laser pulses [31]. A pair of parabolic mirrors collimate and focus the THz pulses vertically on the sample with a FWHM spot size of about 1.2 mm [32]. The third part of the laser beam was used to excite the sample optically. The optical pump pulse excites photocarriers within the sample that alter the transmission and reflection behaviour of the THz radiation. The optical excitation beam is guided through a pinhole within the parabolic mirror onto the sample. Throughout the experiments the THz radiation reflected from the sample was measured using a beam splitter as shown in Fig. 2(a). For the optical excitation of the sample wavelengths of λ₀ = 800 nm or λ₀ = 400 nm were used. An excitation wavelength of λ₀ = 400 nm was used to excite most of the carriers within the silicon needles whereas the λ₀ = 800 nm excitation allows to account for the bulk as well. The size of the excitation spot was 3x4 mm (FWHM) and the average excitation power was 30 mW. The excitation with λ₀ = 400 nm was accomplished via second harmonic generation in a 300 µm thick BaB₂O₄ crystal. The laser beams for THz generation and optical excitation are both optically chopped and the setup is equipped with two delay lines as shown in Fig. 2(a). Within the experiments the second delay line was set to a fixed delay between the THz and sampling pulse and only the first delay line was shifted. This way the THz beam probes the sample at different times after it was optically excited. The measured pump induced change in the reflected THz field ΔE/E is proportional to the pump induced conductivity Δσ [32]:

 

Fig. 2 THz time domain spectrometers for a) the OPTP study, after [32] and b) the measurement of the emitted THz emission. The abbreviations denominate the following elements: TD: delay line, OC: optical chopper, BD: beam splitter, M: mirror and BBO: crystal for second harmonic generation of the pump pulse.

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A signal change can therefore be attributed either to a varying carrier concentration ΔN, a varying electron µ_e or hole mobility µ_h. The setup is placed in a box that is purged by N₂. The measurements were taken at room temperature.

2.4. Study of THz emission

The THz emission of the nanostructured samples was investigated with a THz time domain spectrometer, using a Ti:Sapphire oscillator (Coherent Mira, λ₀ = 800 nm, τ = 170 fs, f = 78 MHz, P_avg = 900 mW) as an excitation source. Contrary to the OPTP experiments, in this experiment the BS sample itself serves as a source of THz radiation. The laser beam is split in two parts where the first part of the beam was used to excite the BS samples with λ₀ = 800 nm. The samples were orientated under an incidence angle of θ = 45° using p-polarized light and the emitted THz radiation was detected in quasireflection geometry. This configuration is necessary since the acceleration of carriers is expected to happen mainly perpendicular to the surface creating a dipole emitting mostly parallel to the surface [33]. The incoming beam was adjusted to a size of 2 mm² and an average excitation power of P_avg = 450 mW was used. The outcoming THz radiation was collimated and refocussed on a photoconducting detector by a pair of parabolic mirrors. The detector is a photoconducting large-area microlens detector with an active area of 1 mm² based on low-temperature grown GaAs (LT-GaAs) [34]. The detector was excited at λ₀ = 800 nm as well. For measuring a time resolved signal the excitation pulse was temporally delayed with respect to the pulse gating the detector. Additionally the pump beam is optically chopped to provide a modulation that allows using a lock-in amplification for signal detection. All measurements were performed at room temperature under ambient atmosphere.

3. Results and discussion

3.1. Optical properties

The hemispherical reflectance spectra obtained from the two different structure types are displayed in Fig. 3. An unstructured reference is shown for comparison. As can be seen in Fig. 3(a) the reflectance is strongly reduced throughout the whole visible spectral range for both structure types. The residual reflectance is less than 3% and the two structure types differ only very little throughout the visible (VIS) and near infrared (NIR). For instance at λ = 800 nm there is only a negligible difference of 0.3%. The slightly higher reflectance values of structure type A below λ = 500 nm are typical for BS structures having a rather small structure depth and positive sidewall angles [29, 35].

 

Fig. 3 Hemispherical reflectance a) and absorptance b) spectra of the nanostructured silicon wafers.

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The absorption spectra in Fig. 3(b) reveal a significant difference in optical behaviour of BS compared to silicon nanowires. While the RIE structures show an absorption of approximately 98% at λ = 800 nm the silicon nanowires as prepared by Jung et al. showed a strong depth dependence of the absorption with values below 80% for wires of comparable length to our RIE structures [9]. Additionally the absorption spectra show that BS structures cause not only a strong anti-reflection effect but also a significant absorption enhancement in the NIR. This enhancement is mainly due to scattering and light trapping by total internal reflection at the polished rear side of the wafer and not by resonant effects in the silicon needles as has been shown earlier by numerical investigations [36]. This unique combination of anti-reflective and light-trapping properties is the main reason for the efforts made to integrate BS surfaces in photovoltaic applications.

Anyhow optical measurements do not provide depth resolved information of the absorption. For this reason the altered absorption behaviour of the nanostructures was investigated with FDTD simulations under comparable excitation conditions as the ones used throughout the THz emission experiments (λ = 800 nm, angle of incidence θ = 45°, p-polarization). In Fig. 4(a) the depth dependence of the absorption rate is depicted for structure type A and B together with the results obtained for a planar surface and a planar surface without reflection losses (i.e. a perfect antireflection coating (ARC)). The plot shows that close to the surface the average absorption rate within the black silicon structures (blue and red curve) is lower than in the planar reference. However, normalizing the absorption rate to the silicon volume fraction reveals an enhancement of the local generation in the silicon needles (light blue and magenta curve) due to a concentration of light in the high refractive index regions. Below a depth of about 300 nm the total absorption rates within the BS samples eventually exceed the value of the planar reference and remain elevated also in the homogeneous bulk region below the needles due to the oblique propagation of the scattered light. However, the plot of the absorption enhancement shown in Fig. 4(b) reveals that the maximum absorption enhancement reaches only moderate levels of about 50% that do not cause a fundamental change of the absorption profiles. The total fraction of light absorbed within the BS needles is still much smaller than the fraction of light absorbed in the bulk below. An estimation of the volume averaged filling factor from focused ion beam cross-sections yielded no significant difference between both samples (within the accuracy of this method it was determined to be 35–40%). Despite similar volume averaged values, the depth dependent fill factors and consequently the absorption rates corrected by the silicon volume fraction depend on the geometry of the silicon needles as can be seen in Fig. 4(a). Therefore, in case of structure type A only 3.5% of the incident light is absorbed within the structured domain. In case of type B this fraction is increased to 15.7%. Comparing the resulting enhancement factor of approximately 4.5 with the increase in structure depth (≈2.5) demonstrates that the geometry of the nanostructures has a significant impact on the absorption enhancement within the silicon nanostructures as well.

 

Fig. 4 Absorption properties of structure type A and B simulated with the FDTD method: a) Depth dependent absorption rates of structure type A and B. The light blue and magenta lines indicate the absorption rates corrected by the silicon volume fraction, whereas the red and blue lines are averaged over the whole volume therefore including the air between the silicon needles. The depth dependent silicon volume fraction is plotted in light grey. The position d = 0 refers to the tip of the highest needle. For comparison the plots contain the theoretical absorption rate for a planar silicon surface (black curve) and a surface with a perfect antireflection coating (ARC) (black, dashed curve). b) Depth resolved absorption enhancement of the structured samples and a planar reference with and without a perfect ARC.

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3.2. Optical-pump THz-probe studies (OPTP)

The results of the OPTP experiments with excitation wavelengths of 800 nm and 400 nm are shown in Fig. 5(a) and Fig. 5(b), respectively. The 800 nm excitation corresponds to the THz emission studies which were done under comparable conditions. The 400 nm excitation is more surface sensitive and was used to study the surface nanostructuring. At an excitation wavelength of 800 nm the transient at negative times in Fig. 5(a) shows a persistent induced conductivity of 20% for the unstructured reference sample and no signal for the nanostructured sample. Negative times correspond to excitation by the previous excitation pulse with a delay of 6.7 µs. In case of the reference sample this signal is due to the bulk carrier lifetime in silicon which reaches values from several ten to hundreds of µs [37]. The surface structuring lowers the carrier lifetime due to an increased surface recombination [25] and therefore after 6.7 µs the carriers already have recombined. The increased surface recombination is known to have a negative impact on the electronic properties of BS based devices, e.g. in photovoltaic applications. This counteracts the beneficial effect of the enhanced absorption. This is especially important in case of rather thick wafer-based technologies [26, 38]. Therefore, great efforts have been made to properly passivate the nanostructured surfaces [2, 25].

 

Fig. 5 Dynamics of the pump-induced absolute change ΔE/E in reflection for structure type A and B in comparison to a planar reference sample. The change was temporally scanned at the maximum amplitude of the THz waveform; a) Excitation with 800 nm, b) Excitation with 400 nm. Each of the the data sets is normalized to its maximum value.

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At τ = 0 ps both samples show a comparable instantaneous signal increase due to the ≈ 100 fs pump pulse. For both samples there is no signal decay observable over the 1.2 ns time window of the experiment as expected when reduction of the conductivity due to carrier trapping is taking place [19, 20, 39]. Therefore, the nanostructured silicon surface has no significant effect on the fast charge carrier dynamics under 800 nm excitation. This is in line with the fact that most charge carriers are excited within the bulk.

Contrary to the excitation with 800 nm the non-zero signal for negative times vanishes for all samples when an excitation wavelength of 400 nm is used (see Fig. 5(b)). This can be attributed to the excitation close to the surface. Since the penetration depth in case of the unstructured reference is only about 100 nm, carrier lifetime is expected to be dominated by surface recombination.

All of the samples show an instantaneous signal contribution at τ = 0 that is lower for increasing structure depth. We attribute this behaviour to an effective medium effect of the nanostructured surface which consists of silicon and air. The conductivity measured by OPTP in an inhomogeneous medium like the nanostructures is lower than in the pure high mobility Si bulk [40]. With increasing depth of the nanostructures a larger fraction of carriers is generated in the low effective mobility nanostructures and the overall induced conductivity is reduced compared to the planar silicon sample where all carriers are generated in the high mobility bulk. After excitation the nanostructured surfaces show a slow increase of the induced conductivity for τ > 0 where structure type A and B reach constant signal values at about 300 ps and 900 ps, respectively. We attribute this increase to the diffusion of charge carriers from the low effective mobility nanostructures into the high mobility Si bulk which has been reported for nanostructured Si before [18]. If we consider an electron mobility of 1400 cm²/Vs we obtain an estimation of the diffusion time of 135 ps in case of structure type A (L ≈ 0.7 µm) and 798 ps for type B (L ≈ 1.7 µm) which is in reasonable agreement with the observed time ranges in our experiments. The planar reference sample also exhibits a small increase within the first 100 ps which can be attributed to cooling of charge carriers with high excess energy into more mobile band edge states [41]. For τ > 1 ns both BS signals converge to a constant value. Similar to the excitation with 800 nm there is no signal decay observable within the measured time window.

Many authors observed an ultrafast carrier trapping in semiconductor nanostructures where the instantaneous increase in photoconductivity is followed by a decay with time constants ranging from several ps to hundreds of ps depending on the structure size and fabrication procedure used [19, 20, 42, 43]. Several authors reported an increase of the respective time constants under increasing excitation density due to a saturation of trap states [19, 43]. To verify that a saturation of trap states is not responsible for the signal behaviour observed in Fig. 5(b) we also performed intensity dependent measurements but could not observe a decay of our transient signal for lower excitation densities either.

TEM studies on BS surfaces fabricated by an RIE process revealed that the single crystallinity of the silicon samples is preserved after structuring [35, 44] leading to the conclusion that the process introduces mainly point defects [24, 35]. Point defects can, for example, be introduced by low fluence energy bombardment. Pump-probe experiments on ion induced damage in semiconductors revealed a strong decrease of carrier trapping times with increasing damage accumulation and therefore an increased number of trap states [45, 46]. Accordingly we suspect that the concentration of defects introduced in the subsurface region due to the RIE process is not high enough to dominate the ultrafast charge carrier dynamics. This is also supported by results of Tang et al. who found a trap-limited carrier lifetime of 0.7 ns in nanowires fabricated by metal-assisted chemical etching which was attributed to the high crystallinity and surface quality of the wires compared to other fabrication methods, where trapping times in the order of ps had been observed [42]. Our conclusion is also supported by the fact that we did observe the characteristic exponential signal decay under comparable excitation conditions in plasma-etched silicon, where crystal damage is only concentrated to the first nanometers of the substrate as well, but where the ion energies and fluences used are significantly higher as compared to the RIE process [47]. Therefore, we currently have no indication that trapping processes on an ultrafast timescale influence THz emission from our nanostructures fabricated by RIE.

Since the RIE process is transferable to crystalline silicon thin films [5] it is a suitable candidate for an integration of nanostructures in thin film devices. Silicon thin films are usually created by crystallization of deposited amorphous layers and suffer from high defect densities that cause recombination on a ns-timescale [48]. Therefore, in case of an integration of nanostructures in those devices the RIE process might be preferable compared to other methods since it is not expected to introduce a high number of additional trapping centers.

3.3. Study of THz emission

The time resolved THz emission of the two structure types is presented in Fig. 6(a) in comparison to the emission of an unstructured sample. All THz signals possess the same polarity and a bipolar pulse shape. The structuring of the silicon surfaces leads to an enhancement of the emitted THz radiation. In case of the shallow structure A the increase is rather low. The deeper structure B exhibits a much stronger enhancement and a strongly asymmetric pulse shape with a dominating negative part. Comparing the THz signals presented in Fig. 6(a) the signal amplitude of the unstructured reference sample is 18% and the amplitude of structure type A is only 24% of the amplitude of structure type B. This results in an enhancement factor of 4.2. Averaging over 3 different measurements taken at three different locations of the samples with structure type A and B yielded the same result. Beside this strong enhancement of the THz amplitude structure type B also shows a slight broadening of its pulse features. This can also be seen from the spectra of the THz radiation emitted by the nanostructured samples (Fig. 6(c) and Fig. 6(d)). The asymmetrical pulse shape remained unchanged when the excitation power on structure type B was varied (Fig. 6(b)). We found the same linear dependency of the field amplitude on excitation power as was earlier observed by Hoyer et al. [8]. This linear dependency (respectively a quadratic dependency of the emitted THz power) has been also observed for InAs where the Photo-Dember-effect has been reported to be the main contribution of THz emission with an additional nonlinear contribution under moderate excitation conditions [49, 50]. Nevertheless, we found no strong influence of THz emission on the polarization angle of the incidence laser beam which is in agreement with the results obtained by Hoyer et al. who could not observe a significant influence of THz emission on the polarization angle under similar excitation conditions as used within this work either [8]. Therefore, we currently exclude a dominant contribution from nonlinear effects [51, 52].

 

Fig. 6 Study of THz emission from nanostructured silicon surfaces; a) Time domain THz signals of planar and nanostructured silicon. To demonstrate the signal enhancement due to nanostructuring the signals were normalized to the highest signal amplitude; b) Normalized Peak-to-Peak amplitude of sample B for increasing excitation power; c) Resulting frequency spectra on logarithmic and d) linear scale (normalized to the highest spectr. amplitude).

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The ultrashort laser pulse excites carriers via interband absorption thus leading to a transient current that is driven by the intrinsic surface field of the semiconductor and the diffusion of the carriers after photoexcitation (photo-Dember effect) [53–55]. Based on the existing works on THz emission from semiconductor nanostructures [8–10, 51] we currently consider the following three effects as a possible cause of the enhanced THz emission from the BS structures fabricated by RIE:

In the following we will discuss the individual effects in detail.

A fast decay of the photoinduced current due to ultrafast trapping processes is a well known method to create THz emitters and detectors based on photoconductive switches [56, 57]. Trapping processes happening on a timescale of several picoseconds can strongly enhance THz emission as has been revealed from theoretical considerations based on the Drude-model [58]. Trapping is furthermore expected to play an increasing role when the surface to volume ratio is enhanced as in case of increasing structure height. Nevertheless, our OPTP studies revealed no clear impact of carrier trapping on a timescale small enough to influence THz emission. Therefore, we currently neglect the influence of carrier trapping processes on the emission enhancement of structure type B.

Beside the carrier trapping especially the strength of the built-in field at the interface of the semiconductor and its native oxide determines the emission behaviour. THz emission dominated by the screening of the surface field has been mainly reported for wide bandgap materials like GaAs or InP [54, 59, 60]. On the other hand small bandgap semiconductors with high electron mobilities like InAs or InSb have been mainly reported to emit THz radiation due to the photo-Dember effect under an excitation with 800 nm [54, 61]. Silicon as indirect semiconductor with its wide bandgap and rather low electron mobilites is therefore expected to be dominated by the ultrafast screening of the surface depletion field as well. The analysis of the interface state distribution at the Si/SiO₂-interface of planar silicon has revealed that the U-shape density distribution leads to a Fermi-Level pinning position near the middle of the bandgap, resulting in an opposite band bending at the interface [62]. Therefore, an opposite polarity of the THz signals from p- and n-type silicon would be expected. However, we observed the flipping in amplitude between n- and p-type planar silicon at an excitation wavelength of 800 nm only for a doping concentration above 10¹⁶ cm⁻³ [63]. For lower doping concentrations the THz-polarity on both p- and n-type wafers was the same as observed in Fig. 6(a). This behaviour contradicts the surface field mechanism to be the dominant cause of THz emission. The same THz polarity irrespective of the doping type has been also reported earlier in case of the Black Silicon surfaces [64]. Especially in case of the nanostructured surfaces the number of carriers created within the needles and therefore near to the surface is increased with increasing structure depth as shown by the optical simulations. Therefore, we currently suspect the THz emission of the RIE structures to stem mainly from the surge current, dominated by the Dember effect. Nevertheless, a change of the built-in field at the interface due to the RIE process can currently not be excluded. Lee et al. observed a strong depth dependent increase of THz emission from germanium nanowires synthesized by the VLS method that was partly addressed to an increase of the built-in field at the nanowire surface [10]. Since this behaviour was found to be a direct consequence of the nanowires being covered with gold particles due to the VLS synthesis such an interaction is not expected to play a role for nanostructures fabricated via reactive ion etching. Anyway, the influence of the process gases used during the RIE process on the surface condition of silicon is rather unknown. It has been shown that chemical treatments strongly influence the interface state distribution and thereby the position of the Fermi level at the surface [65]. A polarity as observed in Fig. 6(a) could be the result of a negative interface charge leading to an accumulation of carriers. Those charges could be the consequence of metal contaminations or an altered bonding structure at the interface. Therefore, further studies will have to concentrate on the impact of the reactive gases used on the chemical surface constitution of silicon and its relation to the THz emission behaviour of the silicon needles.

We therefore will concentrate our current discussion on the question how the BS surfaces alter the outcoupling of the THz radiation. Within the surge current model the emitted THz radiation is described as the time derivative of the induced photocurrent resulting in a bipolar pulse shape where the first peak amplitude is mainly associated with the rising part of the photocurrent due to the generation and acceleration of the photoinduced carriers [58, 66]. Considering the volume averaged absorption rates we would expect a comparable emission enhancement for both structure types. However, the strong enhancement in THz amplitude of structure type B is rather comparable to the enhancement factor in the amount of photons generated directly within the Black Silicon needles as discussed in section 3.1. This leads to the presumption that not the overall absorption enhancement is responsible for the emission enhancement but that the generation of THz emission in our RIE structured samples is mainly related to the transport of photocarriers created directly within the silicon needles. The lateral distances of the silicon needles are in the order of 200 nm and therefore much smaller than the wavelength of the emitted THz radiation (0.5 THz ≈ 600 µm). Thus the Black Silicon surface can be considered as an effective medium with a refractive index smaller than that of planar silicon. Since the dipole created by optical excitation is mainly orientated perpendicular to the surface the THz radiation is mainly emitted parallel to the semiconductor surface. Due to the high refractive index of the planar semiconductor only a small portion of the generated radiation can be effectively coupled to free space [51].

To provide a better understanding on how the nanostructured surface influences the emission process we simulated the power emitted through the front side of a stratified medium consisting of 400 µm silicon and an homogeneous, effective medium with n_eff < n_Si of variable thickness on top. The respective geometry is shown in Fig. 7(a). The THz polarization P(ν,x′,y′) is located in the middle of an effective medium of thickness 2d_eff and is orientated perpendicular to the interface. The amplitude of the THz polarization is considered to be proportional to the local fluence of the laser beam and a local linear phase Δϕ_ν(x′) is added to each frequency component due to the local pulse delay because of the oblique incidence. The dipole source is then incorporated into a scattering-matrix formalism for the calculation of the field components emitted through the interface as described by Whittaker et al. [67].

 

Fig. 7 Illustration of the emission enhancement of a dipole located in the middle of an effective medium with refractive index n_eff <n_Si; a) Geometry used for the calculation of the dipole radiation; b) Ratio of the power P_front(n_eff)/P_front(n_Si) emitted through the front side of a medium with n_eff to the planar surface with n_Si.

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The enhancement of emission through the front side of the stratified medium is shown in Fig. 7(b) for different refractive indices of the effective medium. The enhancement is exemplarily shown for a frequency of 0.5 THz. The thickness of 2 µm was chosen according to the depth of structure type B. As can be seen in Fig. 7(b) the enhancement is the strongest when the dipole is completely located in air n_eff = 1. In contrast, the ratio P_front(n_eff)/P_front(n_Si) drops down to 1 when the refractive index approaches the value of planar silicon. At an effective index of 2 the emission is still about ten times higher compared to a surface with a refractive index of pure silicon. The behaviour shown in Fig. 7(b) is nearly independent of frequencies up to 5 THz for the considered layer thicknesses of 2 µm. For a larger layer thickness in the range of several tens of microns interference effects start to occur. The results of Fig. 7(b) demonstrate that a dipole located in an effective medium with reduced refractive index strongly enhances the power emitted into free space compared to a planar surface as has been demonstrated earlier for InAs nanowires [51]. Therefore, it is expected that the emitted radiation increases as the amount of carriers created within the effective medium increases as we indeed did observe in our THz emission experiments. Although our calculation explains the geometry and depth dependence of the THz signals it does not give a satisfying explanation for the asymmetric pulse shape observed in case of structure type B. This indicates that additional geometrical factors determine the THz emission process that cannot be attributed to the altered optical properties alone.

In general our results indicate that for THz emission from nanostructured semiconductor surfaces the absorption within the nanostructures can be optimized by the structure geometry, where the needle-like structure geometry is preferable over the pyramidal ones. Therefore, in case of the RIE process a low pressure regime should be chosen for the preparation of nanostructures. The structure height can further be enhanced by increasing the etching time which is also expected to reduce the fill factor of the BS layer since a longer etching time is known to increase the pore diameter as well [29]. Both effects are expected to further enhance THz emission. This argumentation has to be proven by further studies. The maximum achievable structure height using the RIE process as described in section 2.1 is restricted to ≈ 10 µm. For achieving larger aspect ratios and structure depths cryogen RIE etching or additional masking techniques have to be applied.

4. Conclusion

Silicon nanostructures gained great attention for optoelectronic applications over the last years and it has been shown recently that those structures emit THz radiation as well. Within this work we performed a study on THz emission from nanostructured surfaces fabricated by reactive ion etching. We fabricated two different structure types that have been recently discussed for other optoelectronic applications and investigated the influence of structure geometry on the optical absorption behaviour, carrier trapping processes and THz emission. For this purpose we included for the first time detailed numerical simulations of the optical generation profile within the silicon nanostructures under the excitation conditions of the THz emission experiments performed. From our studies we found that the overall absorption enhancement at λ = 800 nm is not considerably different between both structure types. The structure height and geometry mainly alters the amount of carriers absorbed directly within the silicon needles. Trapping processes on a ps-timescale as found for other fabrication processes could not be revealed to play a major role in our structures as determined by OPTP experiments. Furthermore, we found that the amplitude of the THz emission strongly depends on the structure geometry and depth of the silicon nanostructures. While shallow, pyramidal nanostructures with a depth of about 0.7 µm showed almost the same performance as the planar reference sample, needle-like structures with an increased structure depth of 1.7 µm led to a 4-fold enhancement of the emitted THz peak amplitude. We attribute this enhancement mainly to the increased amount of carriers directly generated within the silicon needles, where an efficient outcoupling of the generated THz radiation takes place. We currently suspect the photo-Dember effect to be the main source of THz radiation. However, influences of an altered built-in field at the semiconductor surface and geometrical effects on the carrier transport that are not related to the altered absorption behaviour cannot be excluded completely. Further studies are necessary to gain a better understanding of the exact transport properties within the silicon needles.