IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 23 (2012) 325301 (6pp)
doi:10.1088/0957-4484/23/32/325301
Nanostructured porous silicon films for terahertz optics Michael Riley1 , Albert Redo-Sanchez2 , Panagiotis Karampourniotis2 , Joel Plawsky1 and Toh-Ming Lu2 1 2
Chemical Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180, USA Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
E-mail:
[email protected]
Received 10 May 2012, in final form 14 May 2012 Published 17 July 2012 Online at stacks.iop.org/Nano/23/325301 Abstract A simple technique is reported to create 31 and 45 µm thick, graded-index Si films in the form of nanospirals on a Si substrate using a dynamic, oblique angle deposition technique. We show that the success in producing such a thick, nanostructured film without delamination from the Si substrate is primarily due to the nano-porous nature of the film which effectively eliminates the stress generated during growth. Effective refractive indices of 1.9 and 2.1 were extracted from the terahertz time-domain reflectivity data, which correspond to 57% and 51% porosity for the 31 and 45 µm thick films, respectively. The gradient of porosity through the film was modeled to describe quantitatively the terahertz reflectance data in the 0.2–2.0 THz regime. (Some figures may appear in colour only in the online journal)
1. Introduction Recently there has been considerable interest in the fabrication of nanostructured films using physical vapor deposition to control the electrical, optical, and magnetic properties of the films. An effective way to achieve this is to deposit the film with the incident flux making an angle with respect to the surface normal and this is called oblique angle deposition (OAD), or inclined substrate deposition [1–7]. Oblique angle deposition can be achieved either by thermal means or by sputtering. In this technique, films are deposited with the incident flux aligned at an angle with respect to the substrate surface normal. At deposition conditions where there is limited surface diffusion, islands of different heights are nucleated on the surface. Initially taller islands would obstruct or shadow the flow of incident flux to other areas near the islands that have a lower height. This causes the morphology to deviate from the smooth and regular surface that results from depositions performed at normal incidence. An illustration of the shadowing effect caused by oblique angle deposition is shown in figure 1. The degree of the shadowing effect can be controlled by adjusting the deposition rate, incidence angle, and substrate rotation speed. It has been shown that 3D nanostructures with very large aspect ratio and controllable porosity, shape and symmetry 0957-4484/12/325301+06$33.00
Figure 1. During deposition, vapor particles arrive and nucleate growth sites that eventually lead to voids due to shadowing. The angle of the incident flux with respect of the substrate surface normal determines the degree of porosity of the film.
can be deposited using this technique with appropriate substrate rotation schemes. A particular area of interest is the use of oblique angle deposition to create films suitable for optical device applications such as filters, polarizers, anti-reflection coatings, and photonic crystals [7–16]. Examples of materials tested include Si, SiO2 , TiO2 , MgF2 , MgO2 , and indium–tin-oxide (ITO). For optical applications in the visible and near visible range, these films are typically several microns thick. For 1
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around 5 × 10−7 Torr. The substrate mount was also equipped with liquid nitrogen cooling lines which help during long depositions to maintain the sample to below 100 ◦ C and to reduce thermal stress-induced delamination which may be exacerbated by large temperature gradients. The substrates were low-resistivity Si(100) (45◦ ), and it is believed that the porosity alleviates the stress by offering void space in the film to expand into. The 31 µm film was grown starting with a tilt angle of α = 70◦ to avoid delamination completely. The 45 µm AR coating was made starting at a 45◦ tilt, increasing the tilt angle in 5 or 6◦ increments for each layer to 86◦ , fast enough to avoid delamination. Porosity changes in the film are not obvious from figure 3 until the tilt angle exceeds 80◦ , whereupon individual spirals become distinct from one another. The 31 µm sample begins at a higher tilt angle (α = 70◦ ) and maintains a spiral structure throughout the film, as opposed to the higher density of the 45 µm sample that only appears spiral shaped after the third layer, possibly due to sticking of the motor during rotation. The effect of this on the porosity of the first couple of film layers should not be severe.
f
εo − ε εs −ε + (1 − f ) = 0, εo + 2ε εs + 2ε
(2)
where f = volume fraction of the empty space or porosity, ε = the effective dielectric constant (n2 ), and εo and εs are the dielectric constants of air and silicon, respectively. Solving for f , the porosities were found to be ∼57% and ∼51% for the 31 µm and 45 µm samples, respectively. The time-domain data were converted to frequencydomain spectra by Fourier transform. The window for the conversion included only the first peak up to the beginning of the second, which effectively isolated only the reflection from the front side interface for analysis. The reflectance spectra for the 31 µm and 45 µm samples are shown as dotted curves in figures 4(a) and (b), respectively. The reference line at 30% represents an uncoated silicon sample. The coating reduces the reflectance across the measured range, reaching 0.7% at 1.6 THz for the 31 µm coating and 1% at 1.05 THz for the 45 µm coating. As expected, over the range measured, the thicker coating performs better at lower frequency. 3
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Figure 3. SEM cross-sectional and top-down (inset at the bottom right with scales equal to the cross-sectional view) images of the (a) 31 µm thick and (b) 45 µm thick films.
follows [27]: R=
u + v cos 2θ , w + v cos 2θ
(3)
where u = r12 + r22 , v = 2r1 r2 , w = 1 + r12 r22 , and θ = 2πnd λ . n−no ns −n Here r1 = n+no and r2 = ns +n are the Fresnel coefficients at each interface calculated from the indices of air (no = 1), the coating (n = 1.9 and 2.1), and the substrate (ns = 3.42) at normal incidence. Calculation for the single layer 31 µm thick coating with an effective index of 1.9 yields a minimum reflectance below 0.1% at 1.3 THz, while the single layer 45 µm thick coating with an effective index of 2.1 gives a minimum reflectance below 0.1% at 0.9 THz. As we can see from figure 5, these single layer models do not predict quantitatively the experimentally determined reflectance of the samples, including the positions of the minima. The discrepancy may come from the over simplified model which assumes an effective and uniform refractive index throughout each of the films. In reality, the coatings are graded in that the index and porosity change from the film–Si interface to the air. This gradient acts to reduce the index contrast at each interface, thereby reducing the reflection. A multilayer film based on the layered structure shown in table 1 was next modeled in an attempt to describe the reflectance data more quantitatively and determine the likely gradient across the film. A 1D optical modeling of a multilayer coating is commonly carried out using a transfer matrix algorithm [28, 29]. The forward and reverse reflectance and h −iktransmittance i are elements of a propagation matrix Pj = e 0 e0ik for each layer j, starting with air (j = 0) and ending with the silicon substrate (j = N), with a phase shift, k = 2πλ n , that changes based on the index of each layer. The effect of each interface between h layers is given i by the transmission matrix Mj−1 =
µ
µ
Figure 4. Time-domain reflectance for the 31 and 45 µm thick samples, as well as the uncoated silicon references. The smaller first peak of the coated samples demonstrates the anti-reflection effect. The ‘no sample’ reflection is from the sample holder which is an aluminum reflector.
3.2. Modeling of the reflectance spectra We first model the reflectance spectra assuming a single layer of film with effective indices of refraction of 1.9 and 2.1 for the 31 µm and 45 µm samples, respectively. These are shown as the solid black curves in figure 5. The frequency at which the minimum occurs is a result of the thickness of the film, which can be found as
1 2nj+1
4
nj+1 + nj nj+1 − nj nj+1 − nj nj+1 + nj
. The overall transmission matrix is the
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Figure 5. Frequency-domain THz spectra for (a) the 31 µm sample and (b) the 45 µm sample. The dotted curves are measured reflectance data. The black solid curves represent the single layer model with effective refraction indices of 1.9 and 2.1 for the 31 µm and 45 µm films, respectively. The solid colored curves are the result of a multilayer model fit using a linearly graded index as a function of the distance from the substrate. The dashed curves represent the modeled spectra resulting from a film that uses an index gradient calculated from equation (1) proposed by Tait et al [20].
product of this stack of layers and interfaces in the form of " # N Y A B M = P0 Mj−1 Pj = , (4) CD j=2
µ µ
µ µ
where A, B, C, and D are scattering matrix elements that lead to the calculations of the reflectance and transmittance using 2n0 2 0 +Bn0 nN −C−DnN 2 R = [ An An0 +Bn0 nN +C+DnN ] and T = [ An0 +Bn0 nN +C+DnN ] . These calculations were facilitated for flexibility and fitting capabilities by using the software package c from W Theiss [30]. SCOUT 3.3. Determination of the index gradient across the films
µ
Figure 6. The index profile through the two films was modeled as a linear gradient, which generated the solid curves in figure 4 that closely match the data. For comparison, the index gradient based on Tait et al’s model calculated from equation (1) is also displayed.
A simple two-parameter linear equation representing the graded index as a function of the distance from the substrate c to fit the reflectance data shown in was used in SCOUT figure 5 for the 31 µm sample (a) and the 45 µm sample (b). The solid colored curves shown in figures 5(a) and (b) are the results of the multilayer model fit. The linear graded index for the two samples as a function of the distance from the substrate used for the fit is shown in figure 6. As seen from figure 5, this linear graded index describes the reflectance data quite well. Also shown in figure 6 is the index gradient across the film using the tilt angles and film thicknesses from table 1, calculated from Tait et al’s model (equation (1)) and Bruggeman’s EMA (equation (2)). This gradient was then c for a converted into a reflectance spectrum using SCOUT comparison with the measured data, which are represented as the dashed curves in figure 5. It is apparent that the small difference in slope and curvature in the gradient of the Tait et al model changes the reflectance spectra significantly. This point emphasizes the importance of understanding the effect of the deposition parameters on layer porosity. Once this is established, more sophisticated index gradients such as the quintic profile can be achieved to gain better broadband and omnidirectional capabilities [12, 31].
3.4. Comparison with other technologies Previous anti-reflection films for long wavelength and THz applications include solid single layers [18, 32, 33] and structures etched into silicon [29, 34–37]. The etching process creates patterned void space in the silicon which allows the index to be altered in the film. In the case of etching, however, the pores are usually large, but the net effect is a refractive index that can be very accurately set to any value below that of the bulk material. Consecutive patterning and etching steps are required to generate multiple layers and thereby control the porosity in a direction normal to the surface. Pillars [37], pyramids [29], and inverted gratings [35] have been made with feature aspect ratios calculated to minimize reflection. An array of pyramids, etched into silicon, was made by Han et al [29] to create a continuous graded-index film with anti-reflection behavior [29]. The three layer inverted gratings made by Chen et al [35] exhibited very good broadband 5
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performance (below 5% reflectance) in a range from 3 to 5 THz. These layers encounter diffraction problems for short wavelengths, however, as the large holes and dense parts begin to scatter the light [37]. Our oblique angle deposition technique can provide an alternative, perhaps simpler, way to produce such anti-reflection coatings. The coatings described here can be made in 8 h, and the substrate motion control can be automated to produce the desired layer structure. While the feasibility of the technique has been demonstrated, optimization is required to fine tune the process.
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4. Conclusions The fabrication of 31 and 45 µm thick silicon nanospiral films on a silicon substrate using active tilt oblique angle deposition was realized without delamination. The THz time-domain data provided estimations of the effective film indices, n = 1.9 (57% porous) for the 31 µm sample and n = 2.1 (51% porous) for the 45 µm sample. The reflectance spectra from 0.2 to 2 THz were obtained for the coated sides of the films, showing strong anti-reflection reaching below 0.7% at 1.6 THz for the 31 µm coating and 1.0% at 1.05 THz for the 45 µm coating. A model assuming a linear index gradient was used to calculate the reflectance spectra and was seen to describe quite well the experimentally measured data. The tilt angle to porosity prediction of Tait et al’s model is shown to underestimate the film’s density at low angles. With appropriate design and optimization, the oblique angle deposition technique has the potential to fabricate efficient broadband anti-reflection coatings for THz devices.
Acknowledgments This material is based upon work supported by the National Science Foundation IGERT under Grant No. 0333314. This work was also partially supported by the Engineering Research Centers Program of the National Science Foundation under NSF Cooperative Agreement No. EEC-0812056 and in part by New York State under NYSTAR contract C090145. We thank Drs S Y Lin and X-C Zhang for valuable discussions.
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