The terahertz (THz) radiation from transient dipoles, formed by distinct diffusion coefficients between oppositely charged carriers as often observed in low band gap semiconductors, propagates with an anisotropic amplitude distribution perpendicular to the dipole axis along the diffusive motion. By directionally adjusting the electronic diffusion, we conceptualize groove-patterned THz emitters based on (100) InAs thin films and demonstrate the unidirectional radiation. Line-of-sight emission along the surface-normal direction is greatly enhanced in a distributed asymmetric trapezoid with its period similar to the electronic diffusion length of InAs. This directional enhancement is in clear contrast to the constant emission amplitude along the lateral direction, regardless of pattern scale, which manifests the role of groove patterns as microscale reflectors in laterally corrugating the carrier density. In contrast to the rather limited nonlinearity in (100) plane, the azimuthal angle dependence of the THz field amplitude in corrugated samples shows a combined effect of diffusive transport and second-order nonlinearity, whose compositional contributions varies in different structures.
© 2013 Optical Society of America
As an important practical source of pulsed electromagnetic radiation at terahertz (THz) frequencies, the photo-excitation of semiconductor surfaces by femtosecond (fs) laser pulses has been widely used over the past two decades. A vast array of compound semiconductors has been examined with regard to their material parameters, including InAs, InSb, GaAs, and InP . The THz radiation emitted from these materials has been attributed to either transient dipole current generation caused by the potential gradient in depletion regions or the large diffusion velocity difference between electrons and holes (referred to as the photo-Dember effect) while the nonlinearity contribution is sometimes ignored in single crystalline materials, as in the case of semiconductors grown along the  axis (in the case of zinc-blende semiconductors ) or c-axis (in the case of wurzite semiconductors ) at low excitation fluence regime. In the case of GaAs, THz radiation has been found to originate from surge currents by the surface electric field [4, 5], whereas the radiation from InAs is mainly governed either by the photo-Dember effect in a thick scale (similar to that of the diffusion length) [2, 6] or by carrier drift motion in the smaller thickness region (similar to the thickness of the surface-space charge layer (SCL)) . Although the photo-Dember effect in bulk (100) InAs  is further enhanced with increased electron mobility accompanied by higher excess energy of photo-carriers, the second-order nonlinear effect becomes crucial in other crystal faces such as (110) and (111) plane . Sometimes, the polycrystalline nature of inhomogeneous semiconductors shows the nonlinear emission from grain boundaries .
Further technological advances in the field of THz technology have been made in the form of efficient radiation sources with higher output powers and/or tunability , and with better spatial resolution that is sometimes beyond the diffraction limit . Recently, THz waves with increased amplitude and bandwidth have been reported in periodically metal-patterned In0.53Ga0.47As and GaAs by breaking lateral symmetry in their diffusion currents [12, 13]. At the same time, the transfer of THz waves over long distances was demonstrated using either a laser-plasma filament , or an optical fiber coupled with tilted InAs tips retaining superior spatial resolution .
Despite the moderate efficiency of semiconductor-based THz transmitters, significant obstacles persist for realizing more accessible industrial applications, including bio-medical imaging , nondestructive evaluation , and wireless communications , particularly with regard to low emission power, beam path interference, and difficulty in directional control. For example, in conventional THz time-domain spectroscopy (THz-TDS) systems with fs laser illumination, InAs sources are tilted with an angle of 45° to the incident beam; the generated THz waves inevitably diverge in free space. We also note that the directionally controlled diffusion currents in InAs, with a maximized photo-Dember field, could offer efficient THz emitters, resulting in THz rays primarily aligned along the line-of-sight path favorable for imaging and data transmission through free space. In this work, we have implemented micro-scale groove patterns in InAs-based structures, with the aim of producing enhanced directional emission of THz waves, as measured in various detection geometries.
2. Experimental setup
We performed THz-TDS measurements under excitation with a pulsed Ti:sapphire laser at 300 K (pulse duration ∼ 150 fs, centered at 800 nm). The incident angle θ of the IR beam (defined from the InAs surfaces in this work for a convenience’s sake) was either 45° in the conventional reflective geometry or 90° in the transmissive geometry. The generated THz waves were collected using a pair of gold-coated 4-in. parabolic mirrors and guided via a silicon (Si) lens coupled with a photo-conductive antenna (PCA). In both cases, the acceptance angles of the THz waves are about 14° (cf. insets of Fig. 2) from the propagation axis. When θ =90°, for comparison purposes, the pair of PCA and Si lens was placed ∼ 1 mm away from the sample, along the surface in the lateral detection geometry without the parabolic mirrors [cf. inset of Fig. 3(a)]. The acceptance angle of the THz waves in lateral detection geometry was 31° from the surface in Fig. 3. The pump beam orthogonally polarized relative to the groove axis supplies an excitation fluence of about 0.9 μJ/cm2 on an 800 μm beam diameter.
The groove patterns were fabricated on 1 μm-thick InAs epilayers which were grown on 500 μm-thick GaAs substrates and p-type doped with density of 1.5 × 1019 cm−3. A 2.5 μm-thick GaSb layer was inserted to compensate for the lattice mismatch between InAs and GaAs. Considering the spot size, which was two orders of magnitude larger than the diffusion length (∼ 1 μm), the photo-Dember currents feature prominently along the  growth direction of the InAs epilayers, as sketched in Fig. 1(a). The InAs epilayers used here were processed to have the groove patterns potentially acting either as reflectors with a gap of 0.9 μm and a groove depth of ∼ 300 nm (in samples with ridge width W=0.5, 1.2 μm) or as parabolic apertures with a gap of 1 μm, a groove depth of ∼ 190 nm and ridge width W of 2.5 μm. The fabrication procedures are described elsewhere in more detail . The grooves in Fig. 1(b) were implemented to produce enhanced lateral diffusion by the generation of abrupt photo-carrier gradients at the air-(010) interfaces, concomitantly followed by the enhanced THz radiation along the surface-normal direction, as depicted by a large green cone along the  direction; this was due to the radially emitted THz waves from the dipoles with a power distribution proportional to sin2α, where α is the radiated THz direction from the dipole axis . The grating grid (with W=0.5, 1.2 μm, or 2.5 μm) was clearly developed as demonstrated in the scanning electron microscopy (SEM) images of Fig. 1(c). The ridge width W was designed to have a similar scale to the diffusion length (∼ 1 μm) of the electrons measured along the  direction which showed slightly increasing behavior with growth thickness in previous works [7, 19]. Considering the absorption depth of InAs layer at 800 nm excitation (∼ 150 nm ), the influence from GaAs substrate was safely ignored .
3. Results and discussions
The THz-TDS measurements, similar to those conducted previously in InAs epilayers without the groove structures, were performed as shown in Fig. 2(a), in both the reflective geometry and in the transmissive geometry. The experimental setups used for the two geometries are depicted in the insets. The THz emission along the surface-normal direction (solid line) in Fig. 2(a) was relatively suppressed, which can be attributed to the combined effects of longitudinal diffusion and the reduced radiation out-coupling efficiency caused by the refractive index mismatch at the interfaces . The slight and slow oscillations in Fig. 2(a) are related to the Fabry-Perot effect, for which the period of 12.5 ps is well-matched with the round-trip time in the GaAs substrate.
The lateral photo-carrier density modulation for surface-normal incidence could remove a major hindrance that affected the transmission emission suppression. When the asymmetric trapezoidal patterns were periodically configured for activating lateral diffusion current modulation, the THz wave amplitude increased with evident pattern scale (W) dependence, as demonstrated in Fig. 2 (b). The signals from these patterned structures (non-solid lines) were maximized by rotating samples around the (100) axis and compared to those from a bare sample without patterns (solid line); this comparison revealed a role of laterally modulated dipole ensemble density in the enhanced emission amplitude along the line-of-sight direction. The strongest amplitude was observed in a sample with W of 1.2 μm, which was similar to the reported value of the maximum diffusion length of 1.3 μm , but still larger than the vertical diffusion length measured in our sample . It could possibly be more associated with the optimized lateral diffusion than other values of W. The reduced performance of the structure with W of 2.5 μm could be more influenced from the symmetric nature of the groove structure, rather than from the actual value of the groove period. On the other hand, the out-coupling efficiency in the corrugated samples was not improved to that in the bare epilayer, as inferred from the persistently observed Fabry-Perot oscillations in samples either with or without patterns. The ratios of the peak amplitudes to the Fabry-Perot peaks were estimated and turned out almost the same among the samples shown in Fig. 2(b). These results are somewhat intuitive, because the wavelength of the THz waves is much larger than the groove scale and we would not expect enhanced scattering at the interfaces of the patterned samples along the surface-normal direction. In Fig. 2(c), the Fourier-transformed spectra were taken from Fig. 2(b). In the corrugated samples, the lower frequency side (≤ 0.25 THz) was found to be more greatly enhanced when compared with the bare sample, which is not clearly understood at this moment. However, there is a possible examinable point to show the difference: The surface normal emission in patterned samples could also be affected by the diffusion along the  direction [cf. Fig. 1(b)] with a higher electron effective mass , thus leading to reduced carrier mobility in the Einstein diffusion equation of μ = eτm/m*, where m* is the effective mass and τm is the scattering time. The polar radiation patterns from the high density ensemble of dipoles diffusing along the  direction could encompass the emissions along the surface-normal direction . The scattering in the IR range at the air-InAs interface in patterned samples could restrict further emission amplitude enhancements, leading to further complexities in guiding the THz waves along the line-of-sight direction.
Lateral emission measurements, under the same IR pumping conditions as those described for Fig. 2(b), were taken on the corrugated samples and on the bare epilayer without patterns. The corresponding results are shown in Fig. 3(a) for the time-domain transients and in Fig. 3(b) for the Fourier-transformed spectra. The geometrical schematic for the lateral detection setup is depicted in the inset of Fig. 3(a), where the focal spot position of the IR pump beam was displaced by approximately 2 mm and the Si lens coupled with the PCA was 1 mm away from the sample edge, respectively. The typical time-domain traces in the lateral detection geometry did not show any distinct features among the samples. The similar line-shapes among different structures in Fig. 3(a), expanded over the longer timescale, imply that the lateral emission is rather influenced by the propagation effect through the GaAs substrates; this propagation is also manifested in the narrower spectrum shown in Fig. 3(b) and observed in waveguide structures with attenuation and dispersion . Also, a similar emission amplitude in the lateral detection geometry among samples implies that the diffusion along the growth direction is still efficient, irrespective of the pattern fabrication. The amplitude enhancement ratio in Fig. 3(c) was derived from the THz signal intensities, either in the transmissive geometry or in the lateral detection geometry, and normalized relative to those taken from the bare sample. In the transmissive detection, the amplitude enhancement ratio from the sample with W of 1.2 μm was seven times that of the bare sample, whereas the ratio from a sample with periodic apertures (W=2.5 μm) was not significantly different from the bare sample. In contrast, in the lateral detection, almost no amplitude enhancement was observed, indicating that the patterns affected the diffusion in a limited manner along the lateral direction. The scale and the structural dependence of these amplitude enhancements could lead to opportunities for both amplitude and directional controllability. The optimally adjusted doping concentrations [2, 24] and improved groove shapes for the effective role of the micro-scale mirrors could further enhance these emissions along the line-of-sight.
The second-order nonlinear effects from the bulk (100) InAs is not allowed at surface-normal incidence , which was also confirmed from suppressed THz signal as a function of crystallographic rotation in our sample (not shown here). Nevertheless, a contribution from nonlinear effects, possibly due to additional electric field components from lateral electron density modulation other than the vertical surface depletion field in SCL and different crystal symmetries among exposed crystal planes in patterned structures, could be examined in comparison to the contribution from photo-Dember effects. We also note that the χ2 process conventionally leads to a well-defined periodicity in axial measurements such as four-fold symmetry in (100) and six-fold symmetry in (111) InAs  as long as we can ignore the surface electric field induced nonlinear response in SCL. In this regard, we traced the peak amplitude in transient THz signals as a function of azimuthal angle ϕ in reflective and transmissive geometries, as shown in Fig. 4.
The corrugated samples were rotated around the  crystal axis and the azimuthal angle ϕ was set to zero when the p-polarized incident IR beam was perpendicular to the groove orientation. The PCA was also adjusted to be sensitive to p-polarized THz emission; thus, lateral photo-Dember currents along the perpendicular direction to the groove axis would result in cosϕ dependence as the groove patterns were rotated by ϕ. Nevertheless, in reflective detection geometry, THz amplitudes in patterned samples showed almost the same behavior as the bare InAs layer in Fig. 4(a) in a way that the signals vary as cos2ϕ. The four-fold symmetry of the oscillation (∼ 12% of signal) in Fig. 4(a) without cosϕ dependency indicates that the THz waves along the reflective direction is not influenced by groove patterns as manifested in lateral detection geometry [cf. Fig. 3(a)]. The similar non-oscillatory offset amplitude (∼ 88% of signal) among samples with or without patterns further implies that the vertical photo-Dember currents contribute to the THz wave generation in a similar way in corrugated samples [2, 6].
In the transmission geometry, on the other hand, the corrugated samples showed distinct and complicated ϕ dependence among samples in Fig. 4(b)–4(d), in clear contrast to the suppressed signal in the bare sample regardless of the ϕ variation (not shown here). At this point, we note that the form of angular dependence from nonlinear processes emerges, either from bulk dipoles or from dipoles under surface electric field for the two exposed surfaces of (110) and (100) faces in corrugated structures. The expected dependence of the nonlinear response from different crystal surfaces was previously itemized in the paper by Reid et al.. Adding the relevant angular dependence from nonlinear responses with the functional form for photo-Dember component (cosϕ), we fit the radiated THz field amplitudes asEq. (1), the least-square curve-fitting (solid line) in Fig. 4(b)–4(d) identified the parameterized coefficients of (red-colored) P and nonlinear response-related (blue-colored) ( ), as shown in the insets. There were clearly distinct sets of behavior: In the trapezoidally patterned sample with W of 1.2 μm, the photo-Dember component was the strongest as manifested previously by the largest signal amplitude in Fig. 2(b). As we decreased the W into 0.5 μm (which is smaller than the diffusion length) the photo-Dember components were reduced even with a relatively large bulk dipole nonlinear response both in (100) and (110) crystal faces. From the parabolic aperture structure with W=2.5 μm, the nonlinear response was almost suppressed with the remnant photo-Dember component probably as (110) crystal face only limitedly exposed in this structure, and, thus, with a diminished nonlinear response therein. ϕ-independent component S1, originated from the surface-field induced nonlinear response, also followed the general trend of total signal amplitude, which possibly implies that the surface region under the influence of photo-Dember effects also simultaneously undergo the nonlinear response via the current-induced local symmetry break-down.
In conclusion, we have developed a new method of implementing groove patterns to activate the lateral photo-Dember currents together with various non-linear responses, eventually to increase the THz wave emission restrictedly along the line-of-sight transmissive direction. The amplitude of the associated THz waves along the surface-normal direction was alternated, depending on the period and shape of the groove patterns. The mirror-like patterns that were separated by the ridge width of 1.2 μm were found to be the most efficient among our samples, whereas periodic aperture patterns with the ridge width of 2.5 μm did not assist with the directionality compared to the bare bulk sample. The lateral emission signals, in contrast, did not show many differences among the samples, indicating the longitudinal diffusion was persistent with or without the groove patterns. By comparing the azimuthal angular dependence of the THz wave amplitude from the patterned samples, we concluded that the primary mechanism of THz emission is the directional diffusion via the groove patterns and the contributions of the photocarrier-related emission between nonlinear responses could be controlled by the patterns. These results show that, under excitation with IR laser pulses, the optimization and controllability of the lateral carrier diffusion in InAs could be useful for alignment-free THz applications in imaging and communications. The groove emission patterns in a massive scale could possibly be optimized using low-cost methodologies such as echelon gratings  and pattern imprinting .
The authors would like to thank J. Ahn at KAIST for helpful discussions. This work was supported by the Bio-Imaging Research Center at GIST and by the Basic Science Research Program through the National Research Foundation of Korea ( NRF-2012-042232). The work at KIST was supported by the KIST Institutional Program including Dream Project, MEST 2012K001280 and the Korea-Sweden Research Cooperation Program.
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