The growth of CuSi composite nanorod arrays by oblique angle co-deposition, and their structural, electrical and optical properties

Figure 1 shows top view (in the left column) and cross-sectional view (in the right column) SEM images of the CuSi samples fabricated by OAD or OACD. The SEM images reveal that all the samples consist of arrays of aligned and tilted nanorod structures with different dimensions, densities/separations and tilting angles. The inset in each top-view image shows a two-dimensional power spectrum obtained from the same sample surface. These power spectra are basically composed of four elongated spots. Along and perpendicular to the vapor incident direction the spots have separations of 2k_∥ and 2k_⊥ by which the average separations between nanorods can be determined according to Δ_∥ = 1/k_∥ and Δ_⊥ = 1/k_⊥ in these two different directions, respectively. The obtained results are summarized in table 2. The Cu atomic concentration in each composite sample measured by EDX, C_Cu, is also listed in table 2. The measured C_Cu values are close to the nominal ${C}_{\mathrm{Cu}}^{\mathrm{N}}$ values estimated from the deposition rate ratios with no more than 10% deviation. To quantitatively analyze how the morphology of the OAD Si nanorod array evolves with the addition of Cu through co-evaporation, we measured the average nanorod width w from the top-view images and the nanorod thickness δ, height h and tilting angle β from the cross-view images. All these structural parameters are illustrated in figure 1(a). To clarify the morphology evolution with the Cu amount in the nanorods, all the structural parameters, w, δ, h, β, Δ_∥ and Δ_⊥ as functions of the Cu atomic concentration are plotted in figure 2.

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By combining figures 1 and 2 and table 2, one can capture the detailed morphology evolutions. When a small amount of Cu (≤15 at.%) is co-deposited with Si, the obtained nanorods with widths of w_Cu0 = 400 ± 200 nm, w_Cu5 = 500 ± 200 nm and w_Cu15 = 500 ± 300 nm have similar widths statistically, considering their significant uncertainty; however, further increasing the amount of Cu causes the nanorod width to decrease gradually from w_Cu25 = 400 ± 200 nm until the narrowest width of w_Cu100 = 80 ± 40 nm. The incorporation of Cu decreases the nanorod thickness δ from δ_Cu0 = 90 nm to δ_Cu5 ≈ 70 nm initially, but the δ is not sensitive to C_Cu amount and remains almost constant at 70 nm, which is thicker than that of the pure Cu nanorods with δ_Cu100 ≈ 40 nm. Both the w and δ curves with the nanorod width w being larger than the thickness δ indicate that the OAD nanorods fan out visibly along the direction perpendicular to the incident vapor direction during growth, due to the lack of atomic shadowing in this direction [24, 25]. This makes the gap between nanorods in this fan-out direction smaller than that in the perpendicular direction, which is consistent with the results obtained from the power spectra, i.e., the separations in the direction perpendicular to the vapor flux Δ_⊥ are always smaller than those in the direction parallel to the vapor flux Δ_∥, as shown in figure 2(b). From figure 2(b), it can also be seen that the addition of a small amount of Cu,  ≤ 25 at.%, causes a slight increase in both the separations Δ_∥ and Δ_⊥; however, both Δ_∥ and Δ_⊥ decrease gradually with further increasing Cu concentration. The cross-sectional view images show that nanorod height h decreases gradually from pure Si to pure Cu nanorods with increasing Cu amount in the CuSi composites; however, the tilting angle β of the nanorods with respect to the substrate normal decreases from β_Cu0 ≈ β_Cu5 ≈ 51° to β_Cu15 ≈ β_Cu25 ≈ 50°, and then increases gradually with increasing Cu amount from β_Cu50 ≈ 52° to β_Cu75 ≈ 60° until β_Cu100 ≈ 76°.

With the incident flux angles for both Cu and Si fixed at α = 88°, the tangent rule, tanβ_t = 1/2tanα [26], predicts β_t ≈ 86°, while the cosine rule, β_c = α − arcsin[(1 − cosα)/2] [27], gives β_c ≈ 59°. Clearly, such a change of the tilting angle β with the Cu and Si composition obtained in the present experiment demonstrates that the 'universal' model, the tangent rule or the cosine rule, is not suitable to describe the tilting angle of composite nanorods formed by OACD. By considering the stacking of the two atoms during deposition, the self-shadowing effect and other atomistic effects on the surface, we have proposed a semi-empirical statistic model. The details have been described elsewhere [28]. Based on the proposed model, the tilting angle of the CuSi composite nanorods can be expressed as

$$\begin{eqnarray} &&\beta =-1 0.4 5{C}_{\mathrm{Cu}}^{3}+5 6.5{C}_{\mathrm{ Cu}}^{2}-2 1.0 5{C}_{\mathrm{ Cu}}+5 1. \end{eqnarray} \tag{ 1 }$$

The solid β–C_Cu curve in figure 2(a) shows the result from the above equation with the symbols corresponding to the experimental data. This equation clearly fits the experimental results very well. Equation (1) demonstrates that the tilting angle of composite nanorods during OACD does depend on the nanorod composition. It is also a function of the deposition angle, deposition temperature, etc [28].

For nanorod height h, one can assume

$$\begin{eqnarray} &&\begin{array}{@{}c@{}} \displaystyle {h}_{\mathrm{Cu}}\propto {d}_{\mathrm{Cu}}^{\mathrm{QCM}}={A}_{\mathrm{Cu}}^{h}{d}_{\mathrm{Cu}}^{\mathrm{QCM}}\tqs \mathrm{and}\\ \displaystyle {h}_{\mathrm{Si}}\propto {d}_{\mathrm{Si}}^{\mathrm{QCM}}={B}_{\mathrm{Si}}^{h}{d}_{\mathrm{Si}}^{\mathrm{QCM}}, \end{array} \end{eqnarray} \tag{ 2 }$$

where A_Cu and B_Si are proportional coefficients for Cu and Si [29]. In the experiment, since ${d}_{\mathrm{Cu}}^{\mathrm{QCM}}+{d}_{\mathrm{Si}}^{\mathrm{QCM}}=2.5~\mu \mathrm{m}$ is fixed, the nanorod height h can be expressed as

$$\begin{eqnarray} h&=&{h}_{\mathrm{Cu}}+{h}_{\mathrm{Si}}={A}_{\mathrm{Cu}}^{h}{d}_{\mathrm{ Cu}}^{\mathrm{QCM}}+{B}_{\mathrm{ Si}}^{h}{d}_{\mathrm{ Si}}^{\mathrm{QCM}}\nonumber\\ &=&{A}_{\mathrm{ Cu}}^{h}{d}_{\mathrm{ Cu}}^{\mathrm{QCM}}+{B}_{\mathrm{ Si}}^{h}(2.5-{d}_{\mathrm{ Cu}}^{\mathrm{QCM}}). \end{eqnarray} \tag{ 3 }$$

According to ${d}_{\mathrm{Cu}}^{\mathrm{QCM}}/{d}_{\mathrm{Si}}^{\mathrm{QCM}}={C}_{\mathrm{Cu}}/(1-{C}_{\mathrm{Cu}})$* (ρ_SiM_Cu/ρ_CuM_Si) and ${d}_{\mathrm{Cu}}^{\mathrm{QCM}}+{d}_{\mathrm{Si}}^{\mathrm{QCM}}=2.5~\mu \mathrm{m}$, one can obtain

$$\begin{eqnarray} &&{d}_{\mathrm{Cu}}^{\mathrm{QCM}}=1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}}). \end{eqnarray} \tag{ 4 }$$

By combining equations (3) and (4), one can derive the relationship between h and C_Cu,

$$\begin{eqnarray} h&=&{A}_{\mathrm{Cu}}^{h}[1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]\nonumber\\ &&+~{B}_{\mathrm{Si}}^{h}[2.5-1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]. \end{eqnarray} \tag{ 5 }$$

In addition, both the nanorod width w and the nanorod thickness δ should depend on the surface diffusion and fan-out effect [25, 30], and we can assume

$$\begin{eqnarray} &&\begin{array}{@{}c@{}} \displaystyle {w}_{\mathrm{Cu}}\propto ({h}_{\mathrm{Cu}})^{P\mathrm{Cu}}\propto ({d}_{\mathrm{Cu}}^{\mathrm{QCM}})^{P\mathrm{Cu}}={A}_{\mathrm{Cu}}^{w}({d}_{\mathrm{Cu}}^{\mathrm{QCM}})^{P\mathrm{Cu}}, \\ \displaystyle {w}_{\mathrm{Si }}\propto ({h}_{\mathrm{Si }})^{P\mathrm{Si }}\propto ({d}_{\mathrm{Si }}^{\mathrm{QCM }})^{P\mathrm{Si }}={B}_{\mathrm{Si }}^{w}({d}_{\mathrm{Si }}^{\mathrm{QCM }})^{P\mathrm{Si }}, \end{array} \end{eqnarray} \tag{ 6 }$$

where P_Cu and P_Si are the fan-out exponents for Cu and Si, respectively. Then,

$$\begin{eqnarray*} w&=&{w}_{\mathrm{Cu}}+{w}_{\mathrm{Si}}={A}_{\mathrm{Cu}}^{w}({d}_{\mathrm{ Cu}}^{\mathrm{QCM}})^{P\mathrm{Cu}}+{B}_{\mathrm{ Si}}^{w}({d}_{\mathrm{ Si}}^{\mathrm{QCM}})^{P\mathrm{Si}}\nonumber\\ &=&{A}_{\mathrm{ Cu}}^{w}({d}_{\mathrm{ Cu}}^{\mathrm{QCM}})^{P\mathrm{Cu}}{+}_{}{B}_{\mathrm{ Si}}^{w}(2.5-{d}_{\mathrm{ Cu}}^{\mathrm{QCM}})^{P\mathrm{Si}}. \end{eqnarray*}$$

Based on the work by Karabacak et al [31], P_Cu ≈ 0.3 and P_Si ≈ 0.32, one has

$$\begin{eqnarray} w&=&{A}_{\mathrm{Cu}}^{w}({d}_{\mathrm{ Cu}}^{\mathrm{QCM}})^{0.3}+{B}_{\mathrm{ Si}}^{w}(2.5-{d}_{\mathrm{ Cu}}^{\mathrm{QCM}})^{0.3 2}\nonumber\\ &=&{A}_{\mathrm{ Cu}}^{w}[1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]^{0.3}\nonumber\\ &&+~{B}_{\mathrm{ Si}}^{w}[2.5-1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]^{0.3 2}. \end{eqnarray} \tag{ 7 }$$

Similarly, one can obtain the relationship between δ and C_Cu,

$$\begin{eqnarray} \delta &=&{A}_{\mathrm{Cu}}^{\delta }[1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]^{0.3}\nonumber\\ &&+~{B}_{\mathrm{ Si}}^{\delta }[2.5-1.5 3{C}_{\mathrm{ Cu}}/(1 0 0-0.3 9{C}_{\mathrm{Cu}})]^{0.3 2}. \end{eqnarray} \tag{ 8 }$$

Using the relationships of h–C_Cu (equation (5)), w–C_Cu (equation (7)), and δ–C_Cu (equation (8)) to fit the corresponding experimental data in figure 2(a), as shown by the solid curves, the fitting parameters A_Cu and B_Si are obtained and summarized in table 3. For all three relationships, the obtained A_Cu value is always smaller than that of B_Si, which implies that, for the same concentration of Cu and Si, the Cu will make a smaller contribution than the Si to the nanorod height h and fan-out effect (smaller w and δ) during co-deposition.

Figure 3 shows the crystal structure evolution of CuSi nanorods with the addition of Cu. When grown at room temperature by electron beam evaporation, the resultant Cu nanostructure is a face-centered-cubic (fcc) polycrystalline phase, as shown by XRD in figure 3(a), where the diffraction peaks can be indexed to Cu (111) at 2θ ≈ 43.44°, Cu(200) at 2θ ≈ 50.56° and Cu(220) at 2θ ≈ 74.26°; however, the deposited Si nanostructure is amorphous due to the absence of Si crystalline peaks in its XRD pattern (figure 3(b)). The incorporation of 5 at.% Cu does not make any difference to the XRD pattern (figure 3(c)) compared to that of pure Si (figure 3(b)). When 15 at.% Cu is added, an extremely weak and wide peak centered at 2θ ≈ 44.8° is detected in figure 3(d). In addition, another peak at 2θ ≈ 36.4° starts to appear at C_Cu = 25 at.% (figure 3(e)). These two XRD peaks become stronger and stronger on increasing the Cu amount to 50 at.% (figure 3(f)) and 75 at.% (figure 3(g)), while they both disappear in the pure Cu sample (figure 3(a)). This implies that, during co-deposition, another phase other than Cu and Si could form, which is orthorhombic Cu₃Si. The peak at 2θ ≈ 44.8 could come from the Cu₃Si(300) diffraction, possibly overlapped with the Cu₃Si(012) diffraction since their standard diffraction peaks are very close, Cu₃Si(012) at 2θ = 44.57° and Cu₃Si(300) at 2θ = 44.99°, and the peak at 2θ ≈ 36.4° can be well indexed to Cu₃Si(201). As seen from the XRD pattern in figure 3(g), a small amount of polycrystalline Cu can also be detected besides the polycrystalline Cu₃Si phase in Cu75. All the diffraction peaks in the CuSi composite samples are very wide and weak, indicating that their degrees of crystallinity are low. By applying the Scherrer formula [32] to those well-separated peaks such as Cu(220) and Cu₃Si(201) in Cu75, the average crystal sizes are estimated to be D_Cu ≈ 6 nm and D_Cu3Si ≈ 10 nm in diameter; using the strongest Cu (111) peak in Cu100, the Cu crystal size in pure Cu nanorods is D_Cu ≈ 17 nm. For all the other CuSi samples, the size of polycrystals could be less than 1 nm. Note that it is hard to exclude the following two possibilities: (1) amorphous Cu₃Si could form in Cu5; (2) the unreacted Cu could remain in the form of amorphous phase in the co-deposited composite nanorod samples. As a result, the crystal structure of the nanorods evolves from the amorphous Si in Cu0, to the mixture of amorphous Si, Cu and Cu₃Si in Cu5, to the mixture of polycrystalline Cu₃Si as well as amorphous Si and Cu in Cu15, Cu25 and Cu50, to the polycrystalline Cu₃Si of D_Cu3Si ≈ 10 nm and Cu of D_Cu ≈ 6 nm embedding in the amorphous Si matrix in Cu75, and then to the polycrystalline Cu of D_Cu ≈ 17 nm in Cu100.

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Since both the CuSi nanorod and film samples for each composition were fabricated in the same deposition, they have similar composition and crystal structure. To simplify the electrical transport characterization on the CuSi nanorod arrays, in the experiment, we measured the sheet resistances R_□ of the corresponding CuSi films at room temperature and thus estimated their inherent resistivity ρ values according to the relationship ρ =R_□×t, where t is the film thickness. This is based on the consideration that the individual Si-based nanorods could have comparable composition-dependent electrical properties to those of the corresponding films. Figure 4 shows the obtained ρ–C_Cu relationship for the CuSi composite films, as indicated by circle symbols. The amorphous Si film has a resistivity ρ_Cu0  ≈ 4.9 × 10⁴ Ω cm , which is of the same order as that of the bulk Si, ρ_{bulk  Si}  = 6.4 × 10⁴ Ω cm  [33]. When only 5 at.% Cu is co-evaporated with Si, the conductance of the formed composite Cu5 is significantly increased by two orders of magnitude, with a lower resistivity of ρ_Cu5 ≈ 2.9 × 10² Ω cm. With further increasing the Cu amount, the conductance is improved gradually from ρ_Cu15 ≈ 1.8 Ω cm, to ρ_Cu25 ≈ 1.4 × 10⁻¹ Ω cm, to ρ_Cu50 ≈ 3.6 × 10⁻³ Ω cm and to ρ_Cu75 ≈ 1.1× 10⁻⁴ Ω cm; these values represent four, five, seven and eight orders of magnitude increase in conductance, respectively, compared to the pure Si film. Such electrical conductance enhancement in Si is due to the incorporation of conductive metal Cu with ρ_bulk Cu = 1.68 × 10⁻⁶ Ω cm [34] and/or Cu₃Si with ρ_bulk Cu3Si = 5.5 × 10⁻⁵ Ω cm [35], as confirmed by XRD in figure 3.

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For the CuSi composite films consisting of conductive metal Cu and/or Cu₃Si clusters/nanoparticles embedded in amorphous Si matrix, two classic effective medium theory models, the Maxwell-Garnett model [36] and the Bruggeman model [37], have been used to describe their conductivities. Regarding such a dispersed system where spherical shaped metal nanoparticles with a small volume fraction of f_i are uniformly dispersed in a dielectric matrix and the interaction among these metal nanoparticles can be neglected, one can obtain the effective conductivity σ_e of the composite system by the Maxwell-Garnett formula [36]

$$\begin{eqnarray} &&\frac{{\sigma }_{\mathrm{e}}-{\sigma }_{\mathrm{m}}}{{\sigma }_{\mathrm{e}}+2{\sigma }_{\mathrm{m}}}={f}_{\mathrm{i}}\frac{{\sigma }_{\mathrm{i}}-{\sigma }_{\mathrm{m}}}{{\sigma }_{\mathrm{i}}+2{\sigma }_{\mathrm{m}}}. \end{eqnarray} \tag{ 9 }$$

Here, σ_m and σ_i are the conductivities of the host matrix (Si) and the incorporated metal nanoparticles (Cu and/or Cu₃Si), respectively. With increase of the metal volume fraction f_i, strong interaction among the metal nanoparticles appears, and thus the effective conductivity can be well described by the Bruggeman formula [37]

$$\begin{eqnarray} &&(1-{f}_{\mathrm{i}})\frac{{\sigma }_{\mathrm{m}}-{\sigma }_{\mathrm{e}}}{{\sigma }_{\mathrm{m}}+2{\sigma }_{\mathrm{e}}}+{f}_{\mathrm{i}}\frac{{\sigma }_{\mathrm{i}}-{\sigma }_{\mathrm{e}}}{{\sigma }_{\mathrm{i}}+2{\sigma }_{\mathrm{e}}}=0. \end{eqnarray} \tag{ 10 }$$

For the CuSi composite films with different C_Cu, for simplicity, we assume that only Cu₃Si nanoparticles are dispersed in the amorphous Si matrix, considering that Cu₃Si is the dominant metal phase compared to Cu even in Cu75, as revealed by XRD in figure 3. Thus, σ_i = 1/ρ_bulk Cu3Si = 1.82 × 10⁴ S cm⁻¹ and σ_m = 1/ρ_Cu0 = 2.04 × 10⁻⁵ S cm⁻¹. The metal volume fraction f_i values for different CuSi samples are estimated according to ${f}_{\mathrm{i}}={f}_{{\mathrm{Cu}}_{3}\mathrm{Si}}\approx {f}_{\mathrm{Cu}}={d}_{\mathrm{Cu}}^{\mathrm{QCM}}/2.5\times 1 0 0\%$ vol%, assuming that all the co-deposited Cu exists in the form of Cu₃Si, and the data are summarized in table 2. Based on equations (9) and (10), the calculated results are also plotted in figure 4, as shown by the square symbols for the Maxwell-Garnett model and the triangle symbols for the Bruggeman model, respectively. Clearly, it can be seen that at high C_Cu such as Cu50 and Cu75, the Bruggeman theory predicts the experimental results quite well; however, at low C_Cu ranging from Cu5 to Cu25, there are big differences between the calculated resistivity values and the experimental results. This implies that these two models fail to describe the electrical properties of the present CuSi film system in such a small metal fraction region. Such failure could indicate that the CuSi composite film system containing Cu of 5–25 at.% or 3.2–16.8 vol% is close to its percolation threshold [38]. In other words, electrical change of the CuSi films from insulator/semiconductor to conductor with the increase of Cu could occur in this range.

Silicon is the most common semiconductor material with a narrow band gap of ${E}_{\mathrm{g}}^{\mathrm{Si}}=1.1 1$ eV (or wavelength λ = 1117 nm). The band gap characteristic of Si determines that it is opaque at visible wavelengths but partially transparent in the near-infrared (NIR) range [39], which is caused by its strong visible interband absorption and relatively weak NIR free carrier absorption [40]. In addition, the optical properties of Si are subject to modification by doping/embedding other compositions, such as Cu clusters or nanoparticles, as well as the amount of the dopant. Moreover, the structures of materials determine their properties. An anisotropic nanostructure could induce anisotropic physical properties [19]. For the CuSi composite nanoarrays with different Cu concentrations obtained by OACD, polarized optical transmission spectra were measured in the range of 300–2000 nm using linear polarized incident light normal to the substrate surface. When the incident electric field E is in the nanorod tilting plane, i.e., φ = 0°, the polarization is defined as p-polarization. We define s-polarization as the E direction where φ = 90°, as illustrated in figure 1(g).

Figures 5(a) and (b) show the transmission spectra in two polarization directions, p-polarization (φ = 0°) and s-polarization (φ = 90°), for each CuSi nanorod sample, respectively. Since Si has different absorption mechanisms in different wavelength ranges, we will discuss the optical properties of the CuSi nanorods correspondingly. In the NIR free carrier absorption region with photon energy $E\lt {E}_{\mathrm{g}}^{\mathrm{Si}}$ (λ > 1117 nm), the addition of metal Cu and/or Cu₃Si will increase the free carrier concentration, which will cause an increase in the optical absorbance of the Si matrix. As a result, the Si nanorod array (Cu0) has the highest NIR optical transmission to both p- (figure 5(a)) and s- (figure 5(b)) polarized light, and the transmission also decreases with the addition of Cu. However, the interband absorption of Si in the photon energy range of $E\gt {E}_{\mathrm{g}}^{\mathrm{Si}}$ (λ < 1117 nm) is a complex process and strongly depends on the defects produced in the Si nanorods. Therefore, there is not a monotonic Cu concentration-dependent optical transmission relationship in this region, as shown in figures 5(a) and (b).

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In order to gain further insight into the effect of adding Cu on the optical properties of Si nanorods, we choose two typical wavelengths, one is visible at λ = 500 nm which is above ${E}_{\mathrm{g}}^{\mathrm{Si}}$ and the other is NIR at λ = 1500 nm which is below ${E}_{\mathrm{g}}^{\mathrm{Si}}$, to investigate the optical behaviors of the CuSi samples. Figure 5(c) plots the p- and s-polarized optical transmission T at λ = 500 nm, ${T}_{5 0 0}^{\mathrm{p}}$ and ${T}_{5 0 0}^{\mathrm{s}}$, and at λ = 1500 nm, ${T}_{1 5 0 0}^{\mathrm{p}}$ and ${T}_{1 5 0 0}^{\mathrm{s}}$, as functions of the Cu concentration C_Cu. Clearly, the ${T}_{5 0 0}^{\mathrm{p}}$ and ${T}_{5 0 0}^{\mathrm{s}}$ are small, 0% < T₅₀₀ < 20%, for all the CuSi samples, and they only depend weakly on C_Cu. Although the T₅₀₀ tends to decrease with increasing C_Cu, some exceptions exist. For example, the ${T}_{5 0 0}^{\mathrm{s}}$ of Cu5 is higher than that of Cu0, which could be related to the defect effect as mentioned above. While the T₁₅₀₀ depends strongly on C_Cu, for pure Si or Cu0, T₁₅₀₀ ≈ 100%, with increasing C_Cu, the T₁₅₀₀ decreases significantly and monotonically until T₁₅₀₀ ≈ 0% of Cu75. In addition, one can see that the s-polarized transmission is always stronger than the p-polarized transmission, ${T}_{5 0 0}^{\mathrm{s}}\gt {T}_{5 0 0}^{\mathrm{p}}$ and ${T}_{1 5 0 0}^{\mathrm{s}}\gt {T}_{1 5 0 0}^{\mathrm{p}}$ in figure 5(c). In other words, the absorbance in the s-direction is always smaller than that in the p-direction, which is due to the size and alignment of the nanorods resulting in the nanorod width projected in the s-direction being smaller than the nanorod length projected in the p-direction [19, 41].

To demonstrate the polarization and Cu concentration dependence of the optical properties of the anisotropic CuSi nanorod arrays, angular-dependent polarized optical transmissions at λ = 500 nm (T₅₀₀) and λ = 1500 nm (T₁₅₀₀) were recorded by rotating the polarizers every 15° from the p-polarization direction for all the CuSi samples with different C_Cu, as plotted in polar plots in figures 5(d) and (e), respectively. For all the obtained curves except the T₁₅₀₀ of Cu0, the angular-dependent transmission curves have two-fold symmetry, indicating optical anisotropy. The maximum and minimum transmission values occur approximately in the directions of s-polarization and p-polarization, respectively, while for the T₁₅₀₀ of Cu0, the obtained angular-dependent transmission curve looks like a circle, indicating an optical isotropy behavior. In addition, at λ = 500 nm, the total trend is that the transmission intensity decreases with the incorporation of more and more Cu, but the Cu0 is much less transparent than the Cu5 in the polarized angular range other than near the p-polarization direction (figure 5(d)), while at λ = 1500 nm, the transmission decreases gradually with increasing C_Cu (figure 5(e)).

To correlate quantitatively the Cu concentrations and optical anisotropic properties of CuSi composite nanorods in different wavelength regions, we fitted all the transmission T–φ curves at λ = 500 and 1500 nm with the equation T_λ(φ) = T_λ + ΔT_λsin²(φ − Δφ). Here Δφ denotes the angular deviation of the symmetry axes from φ = 90°, ${T}_{\lambda }^{\mathrm{p}}={T}_{\lambda }$ is the p-polarized transmission, and ${T}_{\lambda }^{\mathrm{s}}={T}_{\lambda }+\Delta {T}_{\lambda }$ is the s-polarized transmission. The obtained optical parameters are summarized in table 4. Basically, |Δφ| < 10°, and the small angle deviation could be caused by experiment alignment error in marking the growth direction of the nanorods and/or the polarization directions of the polarizers. To characterize the discrepancy in the degree of anisotropy, we use a parameter called the eccentricity e, which is defined as $e=\sqrt{1-({T}_{\lambda }^{\mathrm{p }}/{T}_{\lambda }^{\mathrm{s }})^{2}}$. Here e = 0 means optical isotropy. The larger the e value, the higher the anisotropy. According to the e values listed in table 4 and the plot of e–C_Cu in figure 5(f), one can see that the CuSi nanorods exhibit different optical anisotropic behaviors in different wavelength regions. Specifically, at λ = 500 nm, the e values in all the CuSi samples are very high, e ≈ 1, indicating their remarkable anisotropic responses to visible light, while at λ = 1500 nm, the e increases exponentially from e ≈ 0 of Cu0, to e ≈ 0.37 of Cu5, to e ≈ 0.70 of Cu15, to e ≈ 0.87 of Cu25 and to e ≈ 1 of Cu50 and Cu75, indicating the significant effect of adding Cu on the anisotropic response to NIR light.

Table 4.  The optical parameters obtained by fitting the angular dependent T_λ (λ = 500 and 1500 nm) plots for different CuSi nanorod arrays.

Sample	λ (nm)	Tλ(φ) = Tλ + ΔTλsin2(φ − Δφ)			${T}_{\lambda }^{\mathrm{p }}={T}_{\lambda }$ (nm)	${T}_{\lambda }^{\mathrm{s }}={T}_{\lambda }+\Delta {T}_{\lambda }$ (nm)	e
		Tλ (nm)	ΔTλ(nm)	Δφ (deg)
Cu0	500	4.60 ± 0.02	8.60 ± 0.04	5.0 ± 0.1	4.60	13.2	0.9397
	1500	97.9 ± 0.2	− 0.2 ± 0.4	6 ± 3	97.9	97.7	∼0
Cu5	500	2.98 ± 0.03	14.81 ± 0.05	6.3 ± 0.1	2.98	17.79	0.9859
	1500	84.5 ± 0.2	6.6 ± 0.3	4 ± 1	84.5	91.1	0.3737
Cu15	500	0.79 ± 0.01	6.81 ± 0.02	5.6 ± 0.1	0.79	7.60	0.9946
	1500	52.8 ± 0.2	21.7 ± 0.3	4.7 ± 0.4	52.8	74.5	0.7055
Cu25	500	0.39 ± 0.01	4.56 ± 0.02	6.5 ± 0.1	0.39	4.95	0.9969
	1500	30.1 ± 0.2	31.1 ± 0.3	7.7 ± 0.3	30.1	61.2	0.8707
Cu50	500	1.62 ± 0.02	4.31 ± 0.04	0.8 ± 0.3	1.62	5.93	0.9620
	1500	4.4 ± 0.2	31.2 ± 0.3	5.0 ± 0.3	4.4	35.6	0.9923
Cu75	500	0.062 ± 0.002	0.128 ± 0.003	− 0.4 ± 0.7	0.062	0.19	0.9453
	1500	0.12 ± 0.04	4.97 ± 0.07	8.1 ± 0.4	0.12	5.09	0.9997