1. Introduction

Semiconductor nanowires exhibit unique optoelectronic properties that can be optimized for use in light emitting diodes [1], solar cells [2, 3] and photodetectors [4, 5]. To engineer optimal extrinsic figures of merit in such devices, it is essential to quantitatively characterize their intrinsic photonic, electronic and structural characteristics. Raman spectroscopy provides a nondestructive means to probe each of these characteristics at the single nanowire level, having been applied to investigations of optical resonances [6], carrier concentration [7–10], structural defects [11], and phonon confinement [12]. Despite great recent progress in nanowire characterization, Raman spectroscopy of single nanowires presents certain challenges. The signal to noise ratio in small volume nanostructures can be increased by increasing the excitation power, but this leads to broadening and shifting of Raman peaks due to heating, and this in turn complicates and limits line shape analysis [13–15]. In extreme cases, phase transitions [16] and even melting can occur. Here we show that a simple dielectric film can be used to both concentrate light in the nanowire and reduce laser-induced heating, improving the signal to noise ratio in single nanowire Raman spectra without affecting the line shape. While surface plasmons generated from metallic nanostructures can also be exploited to increase the Raman intensity, design and fabrication of a structure that additionally addresses thermal management is not straightforward. Resonant Raman scattering is another approach to enhance signal to noise, but enhanced absorption will increase heating, and different excitation sources are needed for different materials, whereas our approach is quite general. The preparation of a dielectric film involves a one-step deposition process, offering a practical and cheap alternative to both resonant scattering and metallic nanostructures. We note, however, that a dielectric coating will perturb the surface modes in materials that lack inversion symmetry.

2. Method

Ge nanowires of 50 ± 5 nm diameters were drop cast from an isopropyl alcohol solution onto a Si substrate coated with 200 nm of Si₃N₄. SiO₂ windows of different thicknesses (58, 125, 227 nm) were fabricated on top of selected regions of single Ge nanowires using electron beam lithography, thermal evaporation, and lift-off. Spatial maps of Raman spectra were obtained using a 532 nm excitation laser in a scanning confocal microscope (WITec Alpha300 R) with a 50 µm collection aperture defined by the optical fiber core.

3. Results and discussion

In a wavelength range for which Ge is strongly absorbing, a coaxial dielectric shell or a dielectric layer blanketing the nanowire can act as an anti-reflection coating and concentrate light in the nanowire. We first compare 2D finite difference time domain (FDTD) models of the core-shell geometry and layer-on-substrate geometry using a plane wave excitation to establish the quantitative magnitude of the effect and the differences between geometries. Either structure can be fabricated, but the blanket coating is perhaps more straightforward to achieve by deposition methods including sputtering, evaporation, or atomic layer deposition. The absorption cross section, Q_abs, of a 50 nm diameter Ge nanowire coaxially surrounded by a SiO₂ shell is simulated in Fig. 1(a) and (b) as a function of wavelength and shell thickness for both TM and TE polarizations. Below λ ~600 nm, where Ge interband transitions lead to strong absorption [17], the TM Q_abs map shows bands of enhanced absorption at thicknesses ~(2m + 1) λ/4n, where m is an integer, and n is the refractive index. This is the familiar criterion for antireflection by thin film interference. Simulations of Q_abs(TM, TE) for a blanket coated nanowire are shown for comparison in Fig. 1(c) and (d) respectively. As expected, the blanket coating can also maximize absorption by minimizing reflection.

 

Fig. 1 Simulated absorption cross-sections Q_abs of a core-shell nanowire (a),(b) and a blanket coated nanowire (c),(d) as function of dielectric thickness and excitation wavelength for a 50 nm core-diameter Ge nanowire. (e),(f) Comparison of Q_abs at λ = 532 nm between core-shell and coated nanowires as a function of thickness. TM is at left and TE at right throughout.

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Deviations from the core-shell geometry, specifically the presence of the Si₃N₄ substrate and the extension of dielectric film in the lateral direction, introduce a small shift in the thickness dependence of the absorption cross section and also dampen the peak absorption cross-sections. A more quantitative understanding can be gained by comparing the thickness dependent absorption in the two structures at a fixed excitation wavelength of 532 nm (Fig. 1(e) and (f)). The core-shell model overestimates the anti-reflection effect of the blanket coating. The interference effect arising from the uniform shell thickness in the core-shell model becomes less effective in the blanket coating because the lateral extension of the SiO₂ film breaks the interference criterion at the sides of the nanowire. Despite the quantitative differences, the qualitative similarities in the absorption cross sections between core-shell and coated nanowire geometries for both TM and TE polarizations suggest that the core-shell geometry can provide a reasonable estimate of the absorption characteristics of blanket coated nanowire geometries. One can therefore use an analytical model of core-shell absorption to build physical intuition and target appropriate diameter and shell thicknesses for experiments and quantitative simulations. Below we focus on the TM polarization as it is more strongly absorbed for small-diameter nanowires and more commonly used for characterization.

To identify the practical ranges of diameters and thicknesses that lead to absorption enhancements in Ge nanowires, we analytically calculated the enhancement in the TM absorption cross-section of a core-shell nanowire relative to a bare nanowire as a function of shell thickness and core diameter, both scaled by the wavelengths in the respective material (Fig. 2 ). We choose excitation wavelengths of 532, 633 and 785 nm corresponding to commonly available lasers. An antireflection effect is present for all excitation wavelengths, as seen in the two strong bands of enhanced absorption across a broad range of diameters, at shell thicknesses corresponding to the 0^th and 1^st order antireflection condition. At λ = 532 nm, strong absorption from the interband transitions dominates across a continuous range of diameters (Fig. 2(a)). All light is strongly absorbed with little dependence on nanowire diameter above λ/2n. At 633 nm, the imaginary dielectric function decreases rapidly, corresponding to a decrease in absorption (Fig. 2(b)). Light is no longer strongly absorbed and is able to leak intothe surrounding dielectric. However, the leaky light can form standing waves at specific diameters in the form of leaky mode resonances [18]. The periodic enhancements in absorption with the scaled diameter demonstrate the emergence of these leaky mode resonances. The modulation of absorption by these modes is most pronounced at 785 nm, which is the most weakly absorbed of the three excitation wavelengths in Ge (Fig. 2(c)). To demonstrate experimentally the magnitude of absorption enhancement one can achieve with this approach, we consider below Raman spectroscopy studies with 532 nm excitation, for which the antireflection condition is not strongly modulated by the leaky mode resonances. The potential for substantial enhancements in Raman scattering arises from the fact that the Raman signal is proportional to |E|⁴; the absorption is proportional to |E|² at the excitation frequency and the enhancement in emission is proportional to |E|² at the scattered frequency.

 

Fig. 2 TM absorption enhancement in a core-shell nanowire relative to a bare nanowire as a function of effective shell thickness and effective core diameter, scaled by wavelength. Excitation wavelengths are 532 nm (a), 633 nm (b), and 785 nm (c), corresponding to common commercially available lasers.

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A representative Ge nanowire (diameter 48 ± 2 nm) with a coating of thermally evaporated SiO₂ (thickness 124 ± 2 nm of SiO₂) is shown in the atomic force microscope topographic image of Fig. 3(a) . This thickness of SiO₂ establishes the 0^th order antireflection coating condition. The corresponding spatial map of the 1^st order Ge Raman resonance clearly demonstrates a signal enhancement in the region with the dielectric coating (Fig. 3(b)), with the intensity of Raman scattering from the coated region twice as large as that of the bare nanowire at equal powers and acquisition times (Fig. 3(c)). Qualitatively, the enhancement arises from the concentration of light in the nanowire, as shown by FDTD simulations of |E|⁴ with (Fig. 3(d)) and without (Fig. 3(e)) a dielectric coating. Because the Raman signal is proportional to |E|⁴, the quantitative enhancement is described by the ratio of the volume integrated |E|⁴ between the coated and bare regions [6, 7, 19]. Figure 3(f) shows that the experimental Raman enhancement factors for different thicknesses are well described by the calculations for both TM and TE excitation.

 

Fig. 3 (a) AFM image of a 50 nm-diameter Ge nanowire coated with 120 nm of SiO₂ in the middle of the nanowire. (b) Spatial map of the 1st order Ge Raman mode, excited with TM polarized light. (c) Raman spectra sampled from a coated (solid red line) and bare region (dotted blue line). (d),(e) Spatial cross-section of TM-polarized |E|⁴ in a bare nanowire (d) and in a coated nanowire (e). (f) Simulated (solid line) and experimental (red circle) Raman enhancements relative to bare nanowire as a function of thickness.

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Significantly, the two-fold increase in Raman signal in the coated nanowire region is accompanied by a reduction in laser-induced nanowire heating, which produces a red-shift and broadening of the spectrum, due to improved thermal sinking. The ability to maximize signal to noise while minimizing heating is important to accurate line shape analysis in investigations of, for example, defect structure [11] and carrier concentration [7–10]. The two-fold Raman enhancement in this structure is maintained for the range of powers investigated (Fig. 4(a) ) [20]. To quantify the benefit of the dielectric overcoating on heating mitigation, the temperature of the bare and coated nanowire as a function of intensity was determined by converting the Raman frequency shifts to temperature using well-established models [21]. We note that the 50 nm-diameter nanowire is well above the size threshold for which phonon confinement effects become significant [12], so there is no confinement-induced broadening. At Raman intensities equivalent to those generated from the coated nanowire, the bare nanowire experiences a significantly larger increase in temperature, as shown in Fig. 4(b). Therefore, the coating can improve the signal to noise ratio and also reduce perturbations in the line shape from heating, enabling more accurate Raman analyses.

 

Fig. 4 Power dependence of Raman intensity and nanowire heating for a 50 nm Ge nanowire coated with 120 nm of SiO₂. (a) Raman peak intensity for coated and bare nanowire observed as a function of excitation power. (b) Raman shift and corresponding temperatures in the nanowire observed as a function of Raman intensity.

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4. Conclusion

We have demonstrated a two-fold increase in the Raman signal of single Ge nanowires in the strongly absorbing regime through deposition of a blanket SiO₂ antireflection coating. Good agreement is found with FDTD calculations of the field enhancement. At longer wavelengths with energies below the interband transitions, the absorption is modulated by leaky mode resonances. We have also shown that laser-induced heating is reduced for coated nanowires compared to bare nanowires generating the same Raman intensity. This provides an important advantage compared to resonant Raman spectroscopy or plasmonic enhancement strategies in that the perturbation of the line shape is mitigated. While the SiO₂ coating showed a modest enhancement factor of 2, dielectrics such as Si₃N₄ and Al₂O₃ can generate higher enhancement factors due to their higher refractive indices. In support of this direction, thin semiconducting shells have been shown to enhance the Raman signal by orders of magnitude [7], and could be combined with the blanket dielectric coating approach described here. We conclude that anti-reflection coating is a straightforward way to both improve the signal to noise ratio and mitigate laser-induced heating, thereby facilitating Raman analysis in small-volume nanostructures.