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The optical characteristics of silicon nanowires grown on Si layers on glass have been modeled using the FDTD (Finite Difference Time Domain) technique and compared with experimental results. The wires were grown by the VLS (vapour-liquid-solid) method using Sn catalyst layers and exhibit a conical shape. The resulting measured and modeled absorption, reflectance and transmittance spectra have been investigated as a function of the thickness of the underlying Si layer and the initial catalyst layer, the latter having a strong influence on wire density. High levels of absorption (>90% in the visible wavelength range) and good agreement between the modeling and experiment have been observed when the nanowires have a relatively high density of ~4 wires/µm2. The experimental and modeled results diverge for samples with a lower density of wire growth. The results are discussed along with some implications for solar cell fabrication.
©2012 Optical Society of America
1. Introduction
There has been a growing interest in the study of silicon nanowires (SiNW) for a variety of applications including photovoltaics [1–4]. A number of solar cell structures have been suggested and demonstrated from radial [5,6] and axial [7] p-n junctions to nanowire/polymer hybrid designs [8,9]. Both top-down and bottom-up methods of wire formation have been developed. The former include reactive ion etching [10,11], laser processing [12] and electroless chemical etching [13–15]. The most common bottom-up method is based on the vapor-liquid-solid (VLS) effect [16] using a catalyst metal to seed the wire growth. The metal seed particles act as preferential sites for silicon deposition absorbing silicon from a feed stock gas. This results in the super saturation of the particle with the excess silicon expelled at the liquid solid interface, thereby giving rise to wire growth.
Gold has traditionally been used as the catalyst metal for SiNW growth. The Au/Si binary phase system [17] is of the simple eutectic type and features a eutectic point at 363°C at which the composition of the liquid alloy is 18.6 at.% Si. The relatively high Si solubility and surface tension of the Au-Si alloy make Au very favorable for wire growth [18]. However, Au is a well-known minority lifetime killer in Si, leading to poor solar cell performance [19]. Alternative and more benign catalyst metals such as Sn have also been studied. Sn is isoelectronic with Si and hence a neutral impurity. The phase diagram of the Sn/Si binary system also shows a single dominant eutectic point but located at much lower Si concentrations (<1 at.% Si). The eutectic temperature is also lower at 232 °C [20] which is potentially favorable for lower temperature SiNW growth. It has been suggested by Nebol’sin et.al [21]. that Sn as a catalyst metal is too unstable for SiNW growth due to its low surface tension in the liquid state. However, several reports on SiNW growth using Sn have recently been published [20,22–24].
As optical properties of nanowires arrays control solar cell performance, many groups have carried out studies in an attempt to characterize and understand these properties. Such work has demonstrated a reduction in both diffuse and specular reflection [25] and suggested principles for designing arrays to suppress reflective losses [26]. The modeling of SiNW arrays has investigated the effects of wire diameter, length and filling ratio [27] along with core-shell nanowires [28], nanodome structure [29] and disordered vertical wires [30]. Sn catalyzed SiNWs have exhibited good anti-reflective properties in line with those grown from Au of similar sizes [21,31]. While high levels of broadband optical absorption have been observed in SiNWs grown from Au [32–34] similar behavior has not been reported for Sn catalyzed wires on glass [24]. It has also been suggested that a combination of thin Si film and SiNWs could have superior absorption properties when compared to SiNWs alone [35]. Therefore we present results on the optical properties of SiNWs grown on Si thin films on glass. Finite Difference Time Domain(FTDT) modeling of the optical properties has been carried out and compared with the experimental data. SiNWs have been grown using three different initial thicknesses (3, 6 and 12nm) of the catalyst metal Sn. The wires were grown using electron cyclotron resonance chemical vapor deposition (ECRCVD) with the catalyst films providing self-organized particles for wire growth via the VLS effect. Varying the initial Sn catalyst layer thickness gave SiNWs of different morphologies and densities. These were analyzed to provide data for the FDTD modeling. The underlying thickness of the Si layer was varied from 13 nm to 0.8µm in both the experimental and modeling regimes. Modeling of wires grown from a 3nm Sn catalyst layer without an under lying Si layer was also undertaken for comparison.
2. Experimental
2.1 Catalyst formation and SiNW growth
Corning glass substrates were ultrasonicated in acetone followed by a deionized (DI) water rinse and nitrogen blow dry. This was followed by an etch for 20 minutes in 3:1 H2SO4: H2O2 ‘piranha’ solution, DI rinse and N2 blow dry. Films of Si varying in thickness were sputtered using a JLS 500 sputter system the parameters of which are shown in Table 1 .
Table 1. Thin Film Si Sputter Parameters
The resulting Si films were then subjected to a further acetone clean in an ultrasonic bath, DI rinse, N2 blow dry and 20 minute ‘piranha’ etch, DI rinse, N2 blow dry. The samples were then dipped in a <2% HF solution for 30s. After loading into a KJL PVD75 e-beam deposition system layers of Sn varying between ~3-12nm in thickness were deposited from 99.999% pure pellets. Film thickness was calculated with a crystal thickness monitor.
Samples were loaded into an ECRCVD system and brought up to the deposition temperature under 10 mT of hydrogen, forming self-organized catalyst seed particles. Upon reaching deposition temperature the growth of conically shaped wires took place with the parameters shown in Table 2 .
Table 2. ECR Processes Parameters
2.2 Modeling parameters
The computational electromagnetic modeling was carried out using the FDTD code MEEP [36]. In our calculations we consider the scattered field and the absorption. The forward and backward scattering coefficients were calculated by considering the power flow through computational surfaces above the Si nanowires and below the substrate. The normalized absorption was then found by subtracting the total scattering from one, where the total scattering is the sum of the forward and backward scattering [37]. A number of simulations were executed to find appropriate distances of the computational surfaces from the top of the nanowires and the air/Si bottom interface. In all the calculations presented here the computational surfaces were at least 1 μm from the top of the nanowires and bottom surfaces of the silicon substrate.
The top and bottom boundaries of the computational domain were terminated using perfectly matched layers (PML’s) which prevent any non-physical reflections. The other four FDTD edges of the computational domain were periodic boundaries which created the infinite two-dimensional array of particles. The incident electric field upon the nanowire array was polarized in the y direction, as defined by Fig. 1 , and was normally incident. In our calculations the cone-shaped Si nanowires were in periodic arrays on the upper surface of a silicon substrate layer. The wire direction was assumed to be vertical for ease of modeling. The dispersive dielectric function of silicon ε(ω) was represented using a Lorentz model given by Eq. (1) [38]:
where ε∞ is the instantaneous dielectric function, p is the plasma frequency, f j is the oscillator strength, oj is the resonant frequency and Γj is the damping frequency for each oscillator.
Fig. 1 Diagram showing the polarization of incident electric field and the position of the computational surfaces in relation to the Si substrate and nanowire.
In our calculations ∞ = 3.803, the plasma frequency p = 6.77 eV, the oscillators’ strength f = [0.22, 1, 2.01, 0.252], the damping frequency of each oscillation in eV = [0.141, 0.483, 61.34, 0.383] and the resonant frequency, o, of each oscillator in eV = [3.439, 3.697, 4.313, 5.317].
2.3 Sample analysis and characterization
Initial sample analysis was carried out using a Hitachi S-4300 scanning electron microscope (SEM). SEM micrographs with a x9K magnification and working distance of 9mm were analyzed using the Image J analysis program to calculate wire density. Images were set at a proportionally equal threshold value to allow comparison. Micrographs angled at 30° and x20K magnification were used to determine diameter and length. The measured wire parameters were then subsequently used for modeling. Transmission electron microscopy was carried out on a JEOL 2100F FEG TEM operating at 200 kV. The Si NWs were mechanically removed from the glass substrates and deposited onto a holey carbon grid for TEM examination. Optical analysis was carried out using a Cary 500 UV-VIS-NIR spectrophotometer featuring an integrating sphere. Measurements were taken for transmission and reflection, with absorption plotted as 1-T-R.
3. Results
3.1 Wire growth
A simplified sample fabrication process and structure is shown in Fig. 2(a) . The initial Sn catalyst layers were 3, 6 and 12nm thick. A SEM image of wire growth on a 0.8µm thick Si layer using a 3nm thick catalyst layer is shown in Fig. 2(b). The wires are tapered and terminate at a diameter of ~10-20 nm with no obvious residual catalyst particles observed under the growth conditions used. This was typical of the wire growth observed in this work. The direction of wire growth is distributed over a range of angles with a substantial degree of vertical growth.
Fig. 2 (a) Simplified sample fabrication process (b) Growth on a 3nm thick Sn layer, scale bar 2µm. (c) Bright field TEM micrograph, scale bar 50nm. (d) Phase contrast TEM micrograph, scale bar 5nm
Figure 2(c) is a typical bright field TEM image of growth from the 3nm thick catalyst layer showing a narrow central core surrounded by a shell. The phase contrast TEM image of Fig. 2(d) confirms that the core is single crystalline as evidenced by continuous lattice fringes running along the length of the nanowire. However, it is defective and heavily twinned. The shell consists of nanocrystalline columnar grains which appear to grow from the core. The surfaces of the nanowire are rough due to the contours of the individual grains. Wires grown using different thickness catalyst layers had a similar morphology but the wire density, length and base diameter varied. This variation is shown in Table 3 for growth on a 0.8µm thick Si layer on glass. Wire density was determined using the Image J analysis program. The thinnest catalyst layer gives the densest growth, with length and base diameter increasing with catalyst thickness whilst density decreases by a factor of ~4.
Table 3. SiNW Parameters for Growth on 0.8µm Thick Si Layers on Glass
3.2 Optical properties of grown SiNWs
The measured and modeled absorption, transmission and reflection of SiNWs grown from the different initial thickness Sn catalyst layers of Table 3 are shown in Fig. 3(a) , 3(b) and 3(c), respectively.
Fig. 3 Comparison of experimental and modeled optical spectra of SiNWs grown from varying Sn catalyst layer thicknesses on glass coated with 0.8 µm of Si (a) absorption (b) transmission (c) reflection.
The wires were grown on a 0.8 µm thick Si layer on glass. Also shown for comparison in Fig. 3(a) is the absorption spectrum of the Si layer on glass without the nanowires, illustrating the enhancement in light absorption due to the wires. A number of observations can be made.
All the wire samples show similar levels of absorption (to within ~10%) across the wavelength range considered. However, the SiNWs from the thinnest catalyst layer (corresponding to the highest wire density from Table 3) give the highest absorption at visible wavelengths whereas the wires from the thickest catalyst layer give the highest absorption beyond ~800-900 nm. Reasonable agreement between the modeled and experimental data is obtained only for the highest wire density sample at wavelengths below ~800-900 nm. At longer wavelengths, the modeled results show oscillations. Averaging through the oscillations, the model underestimates the absorption and overestimates the reflection.
For the 6 nm and 12 nm thick catalyst layer samples the modeled results significantly underestimate the absorption with, again, a pronounced oscillatory behavior at longer wavelengths. The underestimation of absorption is reflected in an overestimation of reflection for these samples. Interestingly, the transmittance results for all three sample types show a reasonable agreement with experiment for wavelengths below ~900nm but then begin to diverge with the divergence increasing with increasing catalyst thickness.
With the initial layer of Sn remaining constant at 6nm SiNWs were grown on three different thicknesses of Si on the glass substrate. The maximum absorption was above 80% for all three Si layers as can be seen in Fig. 4 . At long wavelengths the samples grown on the thicker Si layer exhibited higher absorption than those on the thinner Si layers.
Fig. 4 Comparison of absorption spectra from SiNWs grown from 6nm Sn on Si layer of 0.013, 0.12 and 0.8µm thickness.
Comparing SiNW growth from a 3nm initial Sn layer on 0.12µm and 0.013µm of Si on glass we see from Fig. 5(a) that there is an overall drop in absorption for the thinner Si layer. Up to ~550nm the spectra exhibit similar trends but with the absorption reduced by ~10% for the thinner layer. At longer wavelengths the divergence in the absorption spectra increases. The SiNW grown from an initial 3nm Sn catalyst layer on 0.013µm Si on glass were modeled using the density, diameter and length data from Table 3. The results are shown in Fig. 5(b). The modeled over estimates the absorption in the visible region but under estimates at longer wavelengths in the infra-red. Comparing the results of the modeled wires on the 0.013µm Si layer and those modeled without an underlying Si layer it can be seen that even a Si layer of this thickness increases the absorption in the visible by ~10%. There is little contribution above ~700 nm.
Fig. 5 (a) Comparison of SiNW grown from 3nm Sn on Si layers of 0.013 and 0.12µm thickness (b) Comparison of modeled SiNW from 3nm Sn on Si layers of 0.013µm with measured and modeled with no Si layer.
4. Discussion
Given the low solubility of Sn in Si we do not expect a high density of Sn from the catalyst particles to remain in the SiNW. No Sn clusters were observed in the TEM micrographs or from high resolution SEM images. However preliminary EDX analysis on an individual wire detected the presence of low levels of Sn (~0.3 wt.%) on the wire with a slightly higher proportion at the tip (~0.4 wt.%). A number of factors could be considered to account for the lack of catalyst particles on the wire tips. These include evaporation of the catalyst during growth or wetting of the particle to the surface of the SiNW. It has been suggested that a very thin sidewall-spreading layer of Sn helps to stabilize the catalyst drop during growth [39]. This could account for the low level observed by EDX along the length of the wire, with the site of the catalyst particle leading to the slightly higher concentration at the wire tip. It has also been suggested that Sn can be etched by hydrogen in the plasma [23]. Further work is required to ascertain the mechanism by which the particle disappears.
A number of possible reasons exist for the oscillations observed in the modeled optical data. They could be due to numerical errors such as time domain truncation in the FDTD simulations. Another reason could be the PML’s becoming increasingly thin compared to the wavelength, resulting in reflections from the upper and lower boundaries of the workspace.
It can be seen that our modeling results are at variance with experiment except for the thinnest catalyst layer, highest density wire growth. Other than for this case, the model underestimates the absorption and overestimates the reflection as shown in Fig. 3. There are several possible reasons for this related to the structure and morphology of the wire samples.
The FDTD calculations assume a perfect periodic array structure with smooth, vertical wires of uniform shape and size for a given catalyst layer thickness. In reality self-organized catalyst formation leads to disordered wire arrays along with varying angles and inter-wire surface deposition. The wires have a core-shell structure with nanocrystalline surfaces as shown by the TEM analysis. For the highest density samples, which exhibit the greatest degree of vertical growth, we believe the absorption due to the wires dominates, giving reasonable agreement with the model. The lower wire density samples have a larger fraction of inter-wire areas which have a rough surface morphology formed by Si deposition, together with a greater degree of angled wire growth. In the model the increased absorption can only be due to reduced reflection and the higher volume of Si, due to the wires. The model does not take into account any diffuse scattering or disorder in the wire arrays. We would suggest that the greater differences between the calculations and measurements for the lower wire density samples (6nm, 12nm initial Sn catalyst layers) may be due to an increase in diffuse scattering from the areas of inter-wire deposition of Si which has occurred during SiNW growth and possibly the increased disorder of the wire array.
For a constant initial Sn catalyst layer thickness and varying Si film thickness as in Fig. 4 and 5, the SiNW parameters are expected to be similar. Hence the observed changes in absorption can most likely be largely ascribed to the varying Si thin film layer thickness. We suggest the high absorption at short wavelengths can be attributed to SiNW dominated absorption whereas the drop in long wavelength absorption is dominated by the reduction in the underlying Si layer thickness. The modeled data in Fig. 5(b) indicates the likely absorption behavior of the nanowires on their own and on the 0.013 µm Si layer, suggesting Si layers of this thickness have littler effects on absorption beyond ~700nm.
Finally, the data presented in Fig. 3 to 5 suggests that absorption can be tuned by varying the initial layer thickness of Sn along with the underlying Si layer thickness. This suggests that solar cells fabricated from SiNWs grown from these catalyst layers on Si would require carefully tuned Si layers to optimize absorption at the longer wavelengths.
Further modeling work is being undertaken in an attempt to quantify the effects of randomly angled wires along with wire and inter-wire surface roughness.
5. Conclusions
Data has been presented comparing the measured and modeled optical characteristics of SiNW grown from 3, 6 and 12nm thick Sn catalyst layers on sputtered Si thin films of varying thicknesses on glass. The modeled results show a good correlation with the measured data for wires grown from the 3nm Sn layer which have relatively high wire densities of ~4 wires/µm2 and where the wires dominate the absorption. The model diverges for wires grown from the 6 and 12nm thick catalyst layers where the wire density is a factor of ~4 lower and is accompanied by a larger fraction of inter-wire deposition areas. We suggest these could, together with the rough wire surfaces, lead to increased diffuse scattering and hence higher absorption compared to the model predictions.
We suggest that solar cells fabricated from SiNWs of the length, diameter and density observed in this work would require a carefully tuned under lying thin Si layer to maximize absorption in the longer wavelength regions beyond the visible. Without this underlying layer the modeling work shows a rapid fall in the absorption at wavelengths above ~700nm.
Acknowledgments
J. Ball and H. S. Reehal thank the EPSRC and PV21 SUPERGEN consortium for support of this work. A Centeno and N Alford acknowledge the partial funding of this work by EPSRC and the King Abdullah University of Science and Technology (KAUST).
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