Nano-texturization provides sensitive routes for selection of preferred phonon modes. Biomimetic gallium arsenide (GaAs) nano-tips, with a pencil-like structure, prepared by an electron cyclotron resonance plasma etching of planar GaAs wafer demonstrates tunable strength of the surface optic (SO), and long wavelength transverse optic and longitudinal optic phonon modes. These modes can be tuned as a function of the length (L) of the nano-tips enabling phonon engineering. Invalidation of symmetry rules due to nano-texturization results in the excitation of a SO mode that can also be tuned, in strength and position, with L. Red shift of this mode with a change in the dielectric constant of the medium (air to aniline) confirms the SO nature. The theoretically estimated length scales indicate that the diameter modulated apexes of the nano-tips, whose length (L’) increases consistently with L, could be responsible in transferring the required momentum to the SO phonons.
© 2011 OSA
Fundamental phonon characteristics in polar and non-polar low dimensional systems have been extensively studied to extract rich information about its structure, optoelectronics, and device properties. Even a minimal perturbation to the structure is reflected in the phonon spectra. The analysis, of course, is difficult to the extent that any deviation of the phonon spectra in the low dimensions, vis-à-vis the bulk, requires a thorough theoretical model to explain its origin and behavior. Take for example the unexpected asymmetry of the one- phonon Raman bands in nano-particles [1–3] that was observed in conjunction with a downshift, in wavenumbers, of the optical phonons. A phenomenological model was developed by Richter et al.  attributing the phenomenon to phonon confinement in low dimensional systems. In polar semiconductors, such as GaP and GaAs, dipoles may appear at the boundary of the two dielectrics, say GaP and air, under the action of an external electric field. Oscillations of these dipoles, commonly called surface optic (SO) modes , alter the phonon spectra between the optical phonon modes (transverse and longitudinal) at long wavelengths, that is q ( = 2π/λ = 0), where q is the wave vector and λ is the wavelength. This mode is sensitive to the dielectric constant of the surrounding medium (air, liquid). A range of polar semiconductors such as GaP [5–8], GaN , ZnS , InP , and GaAs [8,11] have shown this special feature with typical intensities that are sometimes too small for a reasonable deconvolution required for a line shape analysis or to study any splitting  or degeneracy in it. Such intricate but important observations have become critical in the study of low dimensional systems and also central to phonon engineering.
Semiconductor nanostructures are systems offering freedom for phonon engineering via their size and shapes [5,9,11]. Quantum confinement effects, to alter the electronic or phonon states, are expected when the dimensions of these nanostructures are below their respective exciton Bohr radius (RB). In this respect, polar GaAs is special for the fact that its RB (~14 nm) is large and size effects can easily be observed compared to smaller RB materials such as Si or GaP . However, there may exist another characteristic length, l (λ>l>RB), over which specific material properties, such as optical reflection, can change if λ of the electromagnetic radiation bears a correlation with or far exceeds it . A correlated λ and l results in light localization , whereas λ>>l condition could excite the SO mode  in porous polar semiconductors. In this work we demonstrate both the bulk and surface phonon engineering in a high aspect ratio (length: base diameter ratio) biomimetic GaAs nanotip (GaAsNT) structures prepared through nano-texturization of planar GaAs wafers.
2. Experimental details
The GaAsNTs (Figs. 1 and 2 ) were fabricated from undoped bulk (100) wafers, using the single step self masked dry etching technique described elsewhere [16,17]. These nano-tips mimic the corneal structures of moth-eyes, used for anti-reflection purposes, and are interesting biomimetic photonic nano-structures . The biomimetic functionality of the GaAsNTs can be confirmed from their extremely low reflectance value, below 0.2% over the visible spectrum (data not shown), compared to the planar wafers. Hence, these nanotip structures could be beneficial for solar cell designs that require anti-reflection properties. In short, the GaAs wafers were randomly decorated with hard SiC particles originating from a silane (SiH4) and methane (CH4) electron cyclotron resonance (ECR) plasma. The coating density of these 2-10 nm size SiC nano-particles  increases with increasing reaction time and/or increasing substrate temperature . For example at 700 C, virtually no tip structures on Si could be formed due to a thick mask of SiC on it . Subsequent to the SiC formation, the wafer is physico-chemically etched through this hard-mask by a combination of hydrogen and argon plasma of similar excitation. The length (L) of the nano-tips can be changed by controlling the etching time; their density can be controlled by the SiC coverage of the substrate which is a direct function of the growth temperature . The fabrication process is, in principle, similar to the formation of cylindrical structure of III-V semiconductors and InGaN quantum dots by using diblock copolymer lithography [19,20]. In our experiments the length of the GaAsNTs were controlled by the reaction time keeping gas flow ratios and other plasma parameters the same. The gas flow ratio used was CH4: SiH4:Ar: H2 = 3: 0.2: 5: 8 sccm. The reaction (etching) time used was 18, 12, 6, and 1 hr for GaAsNTs with lengths of 3.1, 2, 0.7, and 0.05 μm, respectively. The SiC nanoparticle coverage during the initial stages (<1 hr) of the reaction was very small due to a low substrate temperature . The substrate temperature increases to ~250 C at longer plasma exposures promoting the SiC growth . For a long duration ECR plasma reaction, agglomeration of SiC nano-particles could be obtained, dynamically, on the tips as shown for the GaAsNT case. This means that the tip formation start with the etching of the GaAs wafer through the very low density SiC nanoparticle mask, but with longer processing time the SiC kept depositing on the growing tips and at full surface coverage inhibit the growth of GaAsNTs. This is why GaAsNTs longer than ~3 μm was never obtained even for a 24 hr reaction.
The structure and morphology of the GaAsNTs were studied by high resolution (HR) scanning electron microscope (SEM) and transmission electron microscope (TEM). A field emission SEM (JEOL JSM 6700F), for the former, and a Tecnai G2 F20 machine, for the latter, was used. The Raman scattering measurements were done using a micro Raman spectrometer (Jobin Yvon, LabRAM HR800). A laser excitation of 633 nm and beam diameter of 2 microns was used in the backscattering mode to collect the spectra at room temperature, in air or aniline medium. To minimize the heating effect from the laser, its power was reduced below 1 mW by a neutral density filter. No significant peak broadening, shift or decrease in intensity was observed during the data acquisition, indicating that thermal heating effect can be ruled out.
3. Results and discussion
The GaAsNTs (Fig. 1) were studied thoroughly using HRSEM, and HRTEM. The SEM images demonstrate that the GaAsNTs (Fig. 1(a)) are ‘pencil-like’ structures, touching at the base, having base diameters (D = 2r) of 100-200 nm, density of ~109-1010 /cm2, and tunable L up to ~3 μm. The TEM images of a single, long GaAsNT (Figs. 1(b) and 1(c)) demonstrate a core c-GaAs with significant random disorder, destroying the crystalline continuity, as a result of the strong etching in the ECR plasma. The apex regions of the long GaAsNTs were wholly covered in a thin sheath of SiC based nanocomposite (Figs. 1(d) and 1(e)). The SiC sheath was absent for the shorter (L<~50 nm) GaAsNTs, prepared for only 1 hr, as observed from the TEM studies (Fig. 2). The short GaAsNTs exhibits clean single crystalline nature, with sharp physical edges, and no obvious crystalline or morphological disorders (Figs. 2(a) and 2(b)). Although the long GaAsNT is like a nanowire (fixed D), the apex is diameter modulated (Fig. 1(a)) giving it a tapered structure. The length of this apex (L’) also increases with increasing etching time or L. L’ values are 15 (Fig. 2(a)) and 300 nm (Figs. 1(a) and 1(b)) for GaAsNTs with L ~50 and 3100 nm, respectively. This is important for the observation of the SO Raman modes as shown later.
Raman spectroscopy carried out on the commercial GaAs wafer expectedly showed a strong longitudinal optic (LO) and a weak transverse optic (TO) phonon centered at 293 and 269 cm−1, respectively (Fig. 3(a) ). The TO phonon should be forbidden in a backscattering geometry, but expresses itself due to lattice distortion and / or elastic scattering due to ionized dopants. The strong integrated intensity (I) ratio of the LO and the TO modes, ILO/ITO, in the wafer indicated a good backscattering geometry.
As the wafer was physico-chemically etched in the ECR plasma, a systematic roughening started, leading to the formation of the nano-tips. Raman spectroscopy of GaAsNTs demonstrated a decay of the ILO and a simultaneous increase of the ITO as L increased (Figs. 3(b)–3(d)). A concomitant softening and asymmetric broadening on the low energy side of both the LO and TO modes were observed (Figs. 3(b)–3(d)). The amount of this softening is ~3 and 5 cm−1, respectively, for the LO and TO modes in the longest GaAsNTs measured (Fig. 3(d)). The asymmetry on the lower energy shoulder of the LO phonon broadens, as L is increased, and develops into a distinctly observable peak in the frequency gap between the optical phonon modes (Fig. 3(d)). This entirely new feature in the spectrum, not observed in perfect crystals due to momentum conservation restrictions, arises here due to the breakdown of polarization selection rule in the etched GaAs. Such modes were predicted  and observed previously [21,22] and attributed to low dimensionality of the system . This feature bears the characteristics, a dielectric  and shape  dependence, of the SO mode observed in polar semiconductors . This was verified by performing the Raman scattering measurements of GaAsNTs in air (Fig. 3(e)) and aniline (Fig. 3(f)) medium. The softening of the mode between the LO and the TO by ~4 cm−1 in aniline (Fig. 3(f)), compared to that in air, confirmed its SO nature. However, estimating from effective medium theory we assumed that the presence of the SiC embedded nanocomposite sheath may not alter the effective εm significantly .
The information content in (Figs. 3(a)–3(d)) is graphically analyzed in Fig. 4 . In addition to ILO/ITO, the ratio (ISO/[ITO + ILO]) was also found to be extremely sensitive to L (Fig. 4(a)). While the decay of the former was more drastic and significant, the latter increased steadily with L. The breakdown of the selection rules for a true backscattering geometry and hence an intense TO mode could have been due to multiple scattering of light within the nanotip array or due to photon confinement and lattice disorder . We will confirm later that it is the latter which contributes more to a large ITO.
Figure 4(a) indicates the control of L over phonon engineering in GaAs. The additional SO phonon has dispersion correlated to its cause, namely, the surface nano-texturization characterized by L. The dispersion can be simply derived by assuming the GaAsNTs as nano-wires guided by a similar aspect ratio, keeping in mind that the shape of the nanostructure does affect the SO mode. This assumption is reasonable since the GaAsNTs had a wire like structure only except at the apex which is diameter modulated. Such an approximation can only marginally lower the effective radius (r) of the NT structure when averaged over the entire length of it without disturbing the dispersion. In a cylindrical geometry the dispersion of the SO mode is governed by the equationEq. (3). Figure 4(b) shows the theoretical dispersion of the SO mode in GaAsNTs according to Eq. (1). The TO and LO modes in bulk GaAs, assumed dispersion-less, are shown by the thick horizontal lines as the two limits of the SO dispersion curve. The LO and TO modes in the GaAsNTs softens within the frequency range, shown by the grey boxes in Fig. 4(b). A LO phonon softening of 3 cm−1 in the longest GaAsNTs may amount to a local temperature increase of ~200 K, assuming a bulk temperature coefficient of 1.3 x 10−2 cm−1/ K . However the local temperature increase estimated from the intensity ratio of the Stokes to anti-Stokes line in the Raman spectrum was within 100 K and such temperature effects are minimal and can be safely ignored. This indicates an effect of phonon confinement which is possible since the apex diameters of the GaAsNTs, which are 5-10 nm in size, is well within the RB (~15 nm) for GaAs.
The maximum dispersion in the curve (Fig. 4(b)) is denoted by the linear region enhanced by the dashed line. The experimentally observed positions of the SO modes in the GaAsNTs with L = 3.1, 2.0 and 0.7 μm falls on this dashed line and corresponds to the theoretical SO dispersion for nano-wires with x = 0.2, 0.8 and 0.9, respectively. This supports our previous approximation and the use of the dispersion relation given by Eq. (1). To arrive at the corresponding phonon wave-vectors (q), we assume that i) the GaAsNTs are basically wire like with tapered apexes (Figs. 1(a) and 5(a) ), and ii) to excite the SO mode, the crystallite size must be an order of magnitude smaller than λexc, which in this case is 633 nm . Electron microscopy supported dimension information from the apexes yielded average maximum crystallite sizes (d = 2r) of 20, 30 and 80 nm, for the GaAsNTs (Fig. 5(a)) of L = 3.1, 2.0 and 0.7 µm, respectively. Respective q-values (q = x/r) of 2 x 107 m−1, 5 x 107, and ~2 x 107 m−1 could be arrived at. These q, in turn, yields another length scale l ( = 2π/q) which could be responsible for the SO modes in the Raman spectrum. This length scale (l) is roughly of the order of 300 nm for the GaAsNTs and much higher than that obtained for GaP nano-wires (l = 40 nm) . They attributed the small length scale to the nearly periodic diameter modulation in the GaP nano-wires  as seen by TEM. The weak SO modes observed in the cylindrical or wire geometry of GaAs were attributed to low dimensions only and the authors didn’t look for a feature that could transfer the required momentum [21,22]. The body of the GaAsNTs, with fixed diameters (Fig. 5(a)), cannot impart any momentum transfer required for the SO mode. Intuitively, the SO mode, for the GaAsNTs, seems to be originating due to the tapered apexes. The large length scales obtained in our studies can be partly because we have a conical geometry (Fig. 5(b)), unlike nano-wires with fixed diameters, and only the apex and not the entire length (L, (Fig. 5(a)) is responsible for the SO mode. Since, to excite the SO mode, the crystallite size must be an order of magnitude smaller than λexc, the physical meaning of the length scale might indicate the length of the apex with base diameters (d = 2r) smaller than ~80 nm (Fig. 5(a)). The length of this SO active apex (L’, (Fig. 5(a)) for the 3.1, and 2.0 µm long GaAsNTs were approximately 300, and 200 nm, respectively, which corresponds, approximately, to the length scales calculated before. However, the volume fraction of the GaAsNTs that excite the SO, in the limit λexc >> l, is obviously higher for the longer GaAsNTs and hence a stronger SO. In other words, as the tips get longer the SO active apex length L’ increases, with line 2 approaching line 6 (Fig. 5(a)), increasing the strength of the SO mode.
In conclusion, we have demonstrated phonon engineering in gallium arsenide nano-tips. The strength of the transverse and longitudinal optic modes could be tuned with the total length (L) of the nano-tips. The forbidden surface optic mode could be triggered and tuned in strength and position with the extent of surface nano-texturization. Theoretical estimates indicate a length scale of 200-300 nm to be responsible for the SO mode. This length scale can be correlated to the length (L’) of the diameter modulated apex, of the GaAsNTs, that may transfer the required SO phonon momentum. L’ was found to increase consistently with L. The observation of the surface optic phonon comes in conjunction with simultaneous phonon softening in both the long wavelength optical phonons.
The authors acknowledge research funding from the National Science Council (grant # 98-2112-M-010-005-MY3), Academia Sinica, Taiwan, and the US AFOSR-AOARD.
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