1. Introduction

Distributed Bragg reflectors (DBRs) have been widely used in specific or broadband wavelength applications for optoelectronic devices including vertical-cavity surface-emitting lasers, light-emitting diodes, and solar cells [1,2]. Conventional DBRs are composed of repeated pairs of low- and high-refractive index (low-n/high-n) materials with optical quarter-wavelength (λ/4) film thicknesses and their performance (i.e., reflectivity and stop bandwidth) is determined by the number of pairs as well as the refractive index contrast between low-n and high-n materials [3]. Hence, larger refractive index contrast and higher number of pairs can lead to a higher reflectivity and a wider stop bandwidth. Additionally, the wavelength region with a high reflectivity can be controlled by adjusting the λ/4 thicknesses of alternating two films [4]. However, these conventional DBRs made of two different materials have fundamental limitations such as material selection, thermal expansion mismatch, and high fabrication cost due to the use of expensive growth equipments. To avoid these disadvantages, it is necessary to develop highly-reflective DBRs with good thermal stability and mechanical durability in an effective way including cost-effective and simple processes. Over the past years, the same material-based DBRs (i.e., silicon (Si) [5], indium tin oxide [6], and germanium [7]) produced by the oblique angle deposition (OAD) technique have been demonstrated for optical and optoelectronic applications. In the OAD method, at higher incident vapor flux angles, the nanoporous films with more inclined columnar structures, which exhibit a lower n value compared to the dense films in the same materials, can be formed due to the further enhanced self-shadowing effect and limited mobility of incoming atoms [8,9].

Meanwhile, titanium dioxide (TiO₂) is one of dielectric materials used in various optical coatings such as DBRs, antireflection coatings, and passivation layers in optical and optoelectronic devices due to its high transparency, non-toxicity, good chemical stability, mechanical durability/hardness, and excellent insulation property [10]. However, there is very little or no work on the tunable DBRs consisting of the alternating nanoporous/dense TiO₂ films as low-n/high-n pairs by the OAD method for visible wavelength applications. Indeed, TiO₂ is almost no absorption in the visible wavelength region. Thus, it is very meaningful to study reflection properties of the TiO₂-based DBRs prepared by the OAD. In this work, we fabricated the DBRs with different pairs consisting of alternating nanoporous/dense TiO₂ films on Si substrates by the electron-beam (e-beam) evaporation via the OAD method and investigated their optical reflection characteristics at different center wavelengths, together with a theoretical analysis using the rigorous coupled-wave analysis (RCWA) method. For the TiO₂ DBR with 5 pairs, the wafer-scale uniformity on a 3 inch Si wafer and the angle dependent reflectance property of incident light were also explored.

2. Experimental details

Figure 1 shows the (a) schematic diagram for the fabrication of DBRs consisting of nanoporous/dense (low-n/high-n) TiO₂ film pairs by the OAD method via e-beam evaporation at two incident vapor flux angles (θ_α) of 0 and 80° and (b) cross-sectional scanning electron microscopy (SEM) images of the fabricated TiO₂ DBRs with 1, 3, and 5 pairs. To fabricate TiO₂ DBRs, single-side polished (100) Si wafers were used. To obtain two TiO₂ films with a high refractive index contrast, the deposition process was performed at θ_α = 0° for high-n and θ_α = 80° for low-n without substrate rotation by using an e-beam evaporation system at room temperature. The deposition rate was kept at 0.15 nm/s using a quartz crystal thickness monitor and the TiO₂ source with 99.95% purity was used. The TiO₂ DBRs with different pairs of 1-5 were prepared on Si substrates. Here, one pair of DBRs is made up of the hierarchical structure consisting of dense high-n film at θ_α = 0° on the top of the nanoporous low-n film at θ_α = 80°. The λ/4 thicknesses of the TiO₂ films at θ_α = 0 and 80° were estimated to be ~66 and 94 nm, respectively, by n_high = 2.053 at θ_α = 0° and n_low = 1.438 at θ_α = 80° for a center wavelength (λ_c) of 540 nm. As shown in the SEM images of Fig. 1(b), the TiO₂ DBRs with 1, 3, and 5 pairs were well fabricated on Si substrates. For two deposited TiO₂ films, the λ/4 thicknesses were ~66 ± 4 and 94 ± 8 nm at θ_α = 0 and 80°, respectively. The deposited profiles of the fabricated samples were observed by the field-emission SEM (LEO SUPRA 55, Carl Zeiss). The optical reflectance was measured by using a UV-vis-NIR spectrophotometer (Cary 5000, Varian) at normal incidence. Spectroscopic ellipsometry (V-VASE, J. A. Woollam Co.Inc.) was used to determine the refractive index (n) and extinction coefficient (k) of two TiO₂ films and to measure the angle-dependent reflectance at incident angles of 20-70° in p-, s-, and non-polarized lights. The relative reflectance mapping was characterized by using a rapid photoluminescence and reflectance mapping system (RPM 2000, Accent).

 

Fig. 1 (a) Schematic diagram for the fabrication of DBRs consisting of nanoporous/dense (low-n/high-n) TiO₂ film pairs by the OAD method via e-beam evaporation at two incident vapor flux angles (θ_α) of 0 and 80° and (b) cross-sectional SEM images of the fabricated TiO₂ DBRs with 1, 3, and 5 pairs.

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The theoretical analysis on the optical properties of the fabricated TiO₂ DBRs was carried out by the RCWA method using a commercial software (DiffractMOD 3.1, Rsoft Design Group). In simulations, it was assumed that the incident light enters from air into the DBR structure at incident angles of 0-80° and the nanoporous TiO₂ film with inclined columns, which was deposited by the OAD at θ_α = 80°, is a homogeneous medium with an effective refractive index at each wavelength. The optical parameters (i.e., n and k) of the Si used in these calculations were referred from the SOPRA N&K Database [11].

3. Results and discussion

Figure 2 shows the (a) measured and (b) calculated reflectance spectra of the nanoporous/dense TiO₂ DBRs with different pairs and (c) the calculated electric-field (E-field) intensity distributions of the TiO₂ DBRs with 1, 3, and 5 pairs for λ_c = 540 nm at normal incidence. The n and k values of TiO₂ films deposited at θ_α = 0 and 80° are shown in the inset of Fig. 2(a). In the OAD process with larger incident vapor flux angles, the nanoporous films with slanted columnar structures, which have a lower n value compared to that of the dense films in the same materials, are formed because of strong atomic self shadowing under conditions of the limited mobility of the deposited atoms [8,9]. As shown in the inset of Fig. 2(a), therefore, the n and k values of the TiO₂ film deposited at θ_α = 80° are lower than those of TiO₂ film at θ_α = 0° due to the increase of porosity within the film. The porosity within the film can be calculated by a well-known Bruggeman effective medium approximation [12]. The porosity of the TiO₂ film deposited at θ_α = 80° was estimated to be approximately 55% from the parameters, i.e., n_low = 1.438 and n_high = 2.053 at λ = 540 nm. In this calculation, the normally deposited dense TiO₂ film at θ_α = 0° has a zero porosity. As can be seen in Fig. 2(a), the maximum values in reflectance spectra were gradually increased with increasing the number of pairs from 1 to 5. Particularly, the TiO₂ DBR with only 5 pairs exhibited high reflectance (R) values of > 90% over a wavelength range (∆λ) of 505-600 nm and the maximum R values of ~95.1% at wavelengths around λ_c = 540 nm, leading to the large normalized stop bandwidth (∆λ/λ_c) of ~17.8% for R values of > 90%. As shown in Fig. 2(b), the theoretically calculated reflectance spectra agree well with the measured data with increasing the number of pairs in TiO₂ DBRs. For the TiO₂ DBRs with pairs larger than 5, the maximum R values are slightly further increased and almost saturated at wavelengths around λ_c = 540 nm, exhibiting the maximum R values of ~98.2% for the TiO₂ DBR with 8 pairs. For the calculated E-field intensity distributions at λ_c = 540 nm in Fig. 2(c), as the number of pairs increases from 1 to 5, the E-field intensity in the Si substrate also becomes lower due to the higher reflectivity of TiO₂ DBRs with higher number of pairs as can be seen in Fig. 2(b).

 

Fig. 2 (a) Measured and (b) calculated reflectance spectra of the nanoporous/dense TiO₂ DBRs with different pairs and (c) calculated E-field intensity distributions of the TiO₂ DBRs with 1, 3, and 5 pairs for λ_c = 540 nm at normal incidence. The n and k values of TiO₂ films deposited at θ_α = 0 and 80° and scale-modified simulation model of the TiO₂ DBR with 5 pairs used in this simulation are shown in the insets of (a) and (b), respectively.

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To demonstrate the high process tolerance and the large-scalable capability, the nanoporous/dense TiO₂ DBRs were also fabricated on the Si wafer with a size of 3 inch. Figure 3 shows the (a) measured reflectance spectra of the patterned TiO₂ DBR with 5 pairs at λ_c = 540 nm on the 3 inch-sized Si wafer for different points, (b) relative reflectance mapping image of the corresponding sample, and (c) influence of thickness deviation of nanoporous TiO₂ film at the λ/4 thickness of 94 nm on the reflectance of TiO₂ DBR with 5 pairs at λ_c = 540 nm. The photographic image of the patterned TiO₂ DBR with 5 pairs on the 3 inch Si wafer at λ_c= 540 nm is shown in the inset of Fig. 3(a). To realize the selectively patterned TiO₂ DBR with 5 pairs, simple transparent plastic adhesive tapes and metal shadow masks were employed. As shown in Fig. 3(a), for all the points from 1 to 5 on the surface of sample, there exists a slight discrepancy between reflectance spectra at some wavelengths. This is mainly attributed to the thickness error in nanoporous TiO₂ films deposited at the high θ_α = 80° due to the difference of deposition distances between the source and different positions on large-scale wafer in the OAD process without substrate rotation, indicating the thickness error of approximately ± 8 nm between the near and far points on the 3 inch wafer from the source for the nanoporous TiO₂ film at θ_α = 80°. However, for all the points, the R values at λ_c = 540 nm were almost ~95% and the large ∆λ/λ_c values of ~15.7-17.8% were obtained while keeping high R values of > 90%. This is because the deposition of the nanoporous TiO₂ film was performed with varying the θ_α value of 80° (i.e., θ_α = 80° and −80°), as shown in Fig. 1(b), which can suppress the variations of the reflectivity and stop bandwidth of DBRs due to the thickness mismatch compared to the optical λ/4 thickness caused by the deposition speed difference between the near and far wafer positions. Besides, the uniformity of reflectivity on large area can be confirmed by the relative reflectance mapping image in Fig. 3(b). The TiO₂ DBR with 5 pairs exhibited the high R value of ~95% whereas the R value on the surface of Si wafer was ~32%. From this image, thus, it is found to show a uniform relative reflectivity over the whole surface of 3 inch Si wafer for λ_c = 540 nm. In the RCWA calculations of Fig. 3(c), it can be also noted that the reflectivity of the TiO₂ DBR is definitely dependent on the film thickness, but it does not have a serious effect at target wavelengths though there is a slight variation of film thickness [5]. Over all, these results show that the highly-tolerant and highly- reflective DBRs with a relative uniformity as well as any features can be realized on large-sized substrates by the OAD using various pattering techniques.

 

Fig. 3 (a) Measured reflectance spectra of the patterned TiO₂ DBR with 5 pairs at λ_c = 540 nm on the 3 inch-sized Si wafer for different points, (b) relative reflectance mapping image of the corresponding sample, and (c) influence of thickness deviation of nanoporous TiO₂ film at the λ/4 thickness of 94 nm on the reflectance of TiO₂ DBR with 5 pairs at λ_c = 540 nm. Photographic image of the patterned TiO₂ DBR with 5 pairs on the 3 inch Si wafer at λ_c= 540 nm is shown in the inset of (a).

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The reflectivity of DBRs also depends strongly on the incident angle (θ_inc) of light. For the fabricated TiO₂ DBRs with 5 pairs, angle-dependent reflectance characteristics were studied for different polarized lights. Figure 4 shows the (a) measured reflectance spectra at θ_inc = 20-70° and (b) contour plots of variations of the calculated reflectance spectra at θ_inc = 0-80° for the TiO₂ DBR with 5 pairs at λ_c = 540 nm in (i) p-, (ii) s-, and (iii) non-polarized lights. For both the p- and s-polarized lights, the high R bands are shifted toward shorter wavelengths with increasing the θ_inc. However, the maximum R values and bandwidth for the p-polarized light are considerably decreased while those are slightly increased for the s-polarized light. For the non-polarized light, therefore, as the θ_inc value becomes larger, the high R band is moved to the shorter wavelength region and its values and bandwidth also decreased, indicating the maximum R values of ~94.5% at λ = 540 nm and θ_inc = 20° and ~82.1% at λ = 490 nm and θ_inc = 70°. This may be due to the variation of film thickness for inclined incident lights [13]. Nevertheless, at λ_c = 540 nm, the R values of > 70.4% were kept in a broad θ_inc range of 20-70°. For theoretical optical analysis of incident light angle-dependent reflectance of the TiO₂ DBR with 5 pairs, the simulation results show a similar trend to the measured data in wide ranges of wavelengths and incident angles for all the (i) p-, (ii) s-, and (iii) non-polarized lights, as shown in Fig. 4(b).

 

Fig. 4 (a) Measured reflectance spectra at θ_inc = 20-70° and (b) contour plots of variations of the calculated reflectance spectra at θ_inc = 0-80° for the TiO₂ DBR with 5 pairs at λ_c = 540 nm in (i) p-, (ii) s-, and (iii) non-polarized lights.

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The high R band of TiO₂ DBRs can be controlled by varying the λ_c/4 thicknesses of alternating two TiO₂ nanoporous/dense (low-n/high-n) film stacks [4]. Figure 5 shows the (a) measured reflectance spectra of the fabricated TiO₂ DBRs with 5 pairs for λ_c = 450, 540, and 680 nm, (b) contour plot of variations of the calculated reflectance spectra of TiO₂ DBR with 5 pairs as functions of λ_c and wavelength, and (c) photographic image of the corresponding samples at λ_c = 450, 540, and 680 nm. For both λ_c = 450 and 680 nm, the λ_c/4 thicknesses of TiO₂ films at θ_α = 0/80° were estimated to be ~53 nm/75 nm and ~84 nm/120 nm by n = 2.134/1.494 and n = 2.03/1.421 at θ_α = 0/80°, respectively. As shown in Fig. 5(a), for each TiO₂ DBR with 5 pairs, the high R bands of > 90% were shifted toward the longer wavelength region and its bandwidth became slightly broader with increasing the λ_c value of TiO₂ DBRs, exhibiting the increased ∆λ values (i.e., R> 90%) from 76 nm for λ_c = 450 nm to 102 nm for λ_c = 680 nm. In RCWA simulations, the thicknesses of two nanoporous/dense TiO₂ films were set to be λ_c/4 thicknesses for each λ_c. As shown in Fig. 5(b), it can be observed that there is also a similar tendency with the experimentally measured data, indicating that the high R region of > 90% is shifted toward the longer-wavelength range and its bandwidth becomes wider when the λ_c value increases. This phenomenon can be verified from the photographic image in Fig. 5(c). For the TiO₂ DBRs with 5 pairs at λ_c = 450, 540, and 680 nm, each blue-, green-, red-like reflected color is matched with the corresponding wavelength region with maximum R values in Fig. 5(a).

 

Fig. 5 (a) Measured reflectance spectra of the fabricated TiO₂ DBRs with 5 pairs for λ_c = 450, 540, and 680 nm, (b) contour plot of variations of calculated reflectance spectra of the TiO₂ DBR with 5 pairs as functions of λ_c and wavelength, and (c) photographic image of the corresponding samples at λ_c = 450, 540, and 680 nm.

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4. Conclusion

The same material-based DBRs consisting of alternating nanoporous/dense TiO₂ film stacks were fabricated by the OAD method via the e-beam evaporation. To obtain the TiO₂ films with a high refractive contrast, two dense and nanoporous films were alternatingly deposited at different θ_α values of 0 and 80° for high-n and low-n, respectively. By controlling the λ_c/4 thickness for each film, the tunable broadband TiO₂ DBRs with high R values of > 90% for 5 pairs were realized for λ_c = 450, 540, and 680 nm, respectively. The ∆λ/λ_c of ~17.8% at λ_c = 540 nm was obtained while maintaining high R values of > 90% at normal incidence and R values of > 70.4% in a wide θ_inc range of 20-70° for non-polarized light. Also, for λ_c = 540 nm, the TiO₂ DBR with 5 pairs was well-uniformly formed on 3 inch Si wafer. The theoretically calculated reflectance results by the RCWA method showed similar tendencies with the experimentally measured data in wide ranges of wavelengths and incident light angles. These same material-based highly-tolerant TiO₂ DBRs made of the alternating nanoporous/dense pairs can provide wide-angle and broadband highly-reflective characteristics for visible wavelength applications.